The objective of this paper is to amplify the output voltage magnitude from a piezoelectric vibration energy harvester under nonstationary and broadband vibration conditions. Improving the transferred energy, which is converted from mechanical energy to electrical energy through a piezoelectric transducer, achieved a high output voltage and effective harvesting. A threshold-based switching strategy is used to improve the total transferred energy with consideration of the signs and amplitudes of the electromechanical conditions of the harvester. A time-invariant threshold cannot accomplish effective harvesting under nonstationary vibration conditions because the assessment criterion for desirable control changes in accordance with the disturbance scale. To solve this problem, we developed a switching strategy for the active harvester, namely, adaptive switching considering vibration suppression-threshold strategy. The strategy adopts a tuning algorithm for the time-varying threshold and implements appropriate intermittent switching without pre-tuning by means of the fuzzy control theory. We evaluated the proposed strategy under three realistic vibration conditions: a frequency sweep, a change in the number of dominant frequencies, and wideband frequency vibration. Experimental comparisons were conducted with existing strategies, which consider only the signs of the harvester electromechanical conditions. The results confirm that the presented strategy achieves a greater output voltage than the existing strategies under all nonstationary vibration conditions. The average amplification rate of output voltage for the proposed strategy is 203% compared with the output voltage by noncontrolled harvesting. Vibration energy harvesting technology has attracted considerable research attention because of its role as a power supply for electronic devices. This technology provides various smart applications depending on the vibration scale and harvester size, for example, power supply to electric vehicles with magnetic spring suspensions from rough road driving , or actiTo fulfill the aforementioned requirement, control-engineering-based switching strategies were proposed with a self-powered digital controller ,35,36. YThreshold-based strategies that employ a threshold for considering the amplitude of the harvester state values have been proposed. The previously proposed threshold-based strategies are categorized as mechanical strategies and electrical strategies. A harvester adopting mechanical-threshold-based strategy has two mechanical switch elements mounted on the top and bottom of the harvester cantilever beam. The distance between the mechanical switches and the stational position of the cantilever beam acts as the threshold. Switching actions are performed only when these mechanical switches are pushed by the vibrating cantilever, and they allow effective harvesting because the large magnitude of the displacement is always satisfied. Liu et al. , Liu et If the disturbance working on the harvester is predictable and stationary, the threshold can be adjusted to an appropriate magnitude during the harvester design phase. The nature-based disturbance is not predictable and changes its scale over time. The mechanical vibration excited on the harvester by the disturbance becomes nonstationary during the harvesting process ,46,47. BThis study modifies the threshold using a control engineering approach. Simple feedback control with a specific reference cannot be used with the threshold tuning method because the disturbance measurement, which is necessary for the reference derivation, is computationally expensive. A tuning algorithm needs to tune an appropriate threshold from the limited information without a reference. Fuzzy control theory accomplishes appropriate control under a scenario with impossible mathematical discussions . Fuzzy cIn previous research, we developed a threshold-based ASCVS (ASCVS-t) strategy that enhances output voltage using fuzzy control theory . The invCs. The second configuration is the charge inversion circuit composed of a switch device S and an inductor L. LR is the parasite resistance in the inductor L. The harvester circuit has three circuit equations based on the conditions of the two semiconductor elements, a switch element, and a rectifier, thereby dominating the circuit connection. The switch element changes its status in accordance with the control signals determined by the switching strategy. The rectifier used in this paper is passive and conducts both input and output circuits only when the amplitude of the input AC voltage is larger than that of the output DC voltage.A harvester comprises three elements: a transducer, and mechanical and electrical components. The mechanical component of the harvester is modeled as a two-degree-of-freedom (2-DOF) structure with a single piezoelectric transducer inserted between the first mass and the base . The 2-Dx, Qp, and Qs denote the mass displacement, the electric charge stored in the piezoelectric transducer, and that stored in the smoothing capacitor, respectively. The governing equations of electric charges depend on the circuit connections .As the piezoelectric voltage is increased by the piezoelectric charge, the piezoelectric transducer with a large piezoelectric voltage caused by switching actions can supply more energy compared to standard harvesting (STDH). Inequality (6) presents two suggestions for determining the switching moment to increase the amount of the piezoelectric charge:When the mechanical vibration in the harvester has only one dominant frequency, implementing switching actions at the peaks of the mechanical displacement satisfies the aforementioned two suggestions. Moreover, these moments provide the largest increment of the piezoelectric charge at one switching action because the peak corresponds to the maximal magnitude of the mechanical vibration. The SSHI strategy advocated at the beginning of the active harvester development includes peak switching as an appropriate moment of switching actions.Disturbances in real-world environments lead to complex vibrations that have two or more dominant frequencies and nonstationary waveforms on the harvester. The original SSHI strategy cannot handle such complex vibrations because all peaks of the mechanical displacement do not always satisfy inequality (6). The switching strategy must be able to determine the magnitude of the relationship between both electromechanical variables to effectively operate the harvester following inequality (6) in a real-world environment.T1, Ts, and k denote the higher resonance period of the two vibrating masses, sampling period, and discrete time, respectively. The RMS values are used with the previous state values to indirectly detect the trend of changes in the present condition of the harvester. When a short resonant period is used for RMS calculation, a small change in the harvester conditions is strongly reflected in the calculation result. Small changes in the harvester are undesirable to tune the time-varying threshold because it induces control chatter; therefore, the longer resonance period is adopted. In this research, the piezoelectric voltage-based threshold is adopted as a criterion for switching execution. Hence, the threshold isVth denotes the threshold and β represents the threshold coefficient. Switching actions execute only when the piezoelectric voltage amplitude is higher than the threshold.The time-invariant threshold is available only when the disturbance vibrating the harvester in the operating environment is predictable and stationary. The time-varying threshold and its tuning mechanism achieve effective harvesting under unpredictable and nonstationary disturbance conditions during the harvesting process. The simplest adaptive time-varying threshold uses the root-mean-square (RMS) value of the piezoelectric voltage or mechanical displacement. Even though the level of disturbance changes during the harvesting process, the RMS values can follow the change in those magnitudes. The equation for RMS calculation is defined asThe magnitude of the threshold coefficient determines the dominant harvesting actions. The harvesting actions are roughly separated into three control types: STDH, SSHI, and SCVS. The STDH control type, which occurs by the exceedingly large threshold coefficient magnitude, does not perform switching actions in the harvesting process. This type relinquishes the opportunities of the increment of the piezoelectric charge by switching actions and should be avoided by decreasing the threshold magnitude.The SSHI control type, which occurs because of the exceedingly small threshold coefficient magnitude, performs switching actions, including both desirable and undesirable actions. This type leads to the attenuation of the piezoelectric charge because of the undesirable switching actions and should be avoided by increasing the threshold magnitude.The SCVS control type, which occurs because of the adequate threshold coefficient magnitude, accomplishes appropriate intermittent switching actions for effective harvesting. The present threshold design is aimed at this type.The key technology of the tuning algorithm for the time-varying coefficient threshold is based on the detection of the present control type of the harvester. The control type does not relate to the magnitude of the electromechanical variables of the harvester under unknown vibration conditions. Monitoring changes in the magnitude of both electromechanical variables during the harvesting process provides rough inferences of the present control type of the harvester indirectly. However, the calculation of the concrete manipulated value of the threshold coefficient from the vague inference is unrealistic under general mathematical discussions. The fuzzy control theory in a threshold tuning algorithm was used to detect the present control type of the active harvester that has nonstationary vibrations. In addition, it was employed to calculate the concrete manipulated value of the threshold from a vague inference to maintain the SCVS control type. A detailed explanation of the threshold coefficient tuning algorithm was provided in our previous publication . The sumbp, was calculated from the least-squares estimation. The voltage was measured through the voltage follower to prevent the influence of the outflowing piezoelectric charge. The capacitance in the transducer, which is Cp, was measured by the impedance analyzer. Because the deformation of the piezoelectric transducer during impedance analysis was minute, the measured capacitance was dealt with as the constant-strain capacitance. The inductor in the charge inversion circuit was selected to satisfy the frequency requirement under switching actions. The values of the piezoelectric and electric parameters denoted by bp, Cp, Cs, L, LR, and Rload, were 4.5 × 105 V/m, 4.3 × 10−7 F, 4.7 × 10−5 F, 2.0 × 10−2 H, 2.0 × 101 Ω, and 2.2 × 106 Ω, respectively.The piezoelectric coefficient was estimated from the slope of the line between the piezoelectric voltage and the first mass displacement in the phase plane. The slope, which is The active fuzzy harvester with the ASCVS-t strategy was experimentally assessed under three disturbance conditions. The first disturbance condition provides a frequency sweep experiment from the first modal frequency to the second one. The mechanical displacement response from this disturbance condition is shown in β [0] = 1.3 for all excitation conditions. For comparing the performance of the ASCVS-t strategy, the ASCVS strategy [The active harvester started switching actions 12 s after the start of the measurement. The initial value of the threshold coefficient of the ASCVS-t strategy was set to strategy  and the strategy  were adoThe output voltage results shown in  implemenThe time histories of the output voltages acquired in the experiment of the changing number of dominant frequencies are shown in The time histories of the output voltages acquired in the random excitation experiment are shown in The ASCVS-t strategy achieved a two times higher output voltage than the output voltage under the STDH control at 80 s in When controlling for random dynamics c, strateRobustness discussed in this research refers to the ability to maintain a high output voltage without any off-line works such as the manual interference adjusting parameters and gains in the control strategy despite the harvester being subjected to various disturbances. The harsh environment against the control strategies includes the unknown disturbance exposures to the harvester. Deriving an analytical solution of the harvesting performance guarantees that a control strategy will improve the performance. In cases wherein it is difficult to perform disturbance modeling in advance, derivation of an analytical solution of the harvesting performance is equally difficult. In particular, active harvesters with charge inversion circuits pose added difficulty in the derivation of analytical solutions than that of the passive harvesters; this is due to the nonlinear electromechanical coupling dynamics in active harvesters. To demonstrate the robustness of the control strategy, operations of the harvester with the proposed control strategy under various disturbance environments are necessary. The three experiments in The output voltage obtained from the experimental apparatus can accommodate the power required to operate the controller. Details of the power consumption of the self-powered controller have been reported in our previous publications. The self-powered controller was operated within a power consumption range of 1.10–13.7 mW ,36. The The stored energy in the battery is greater than the required energy of the self-powered controller; consequently, the controller can accomplish self-powered operation only when the battery stored sufficient energy. The purpose of this paper is not to discuss the self-powered operation but the operational performance of the ASCVS-t strategy under several disturbance conditions. The implementation will be presented in the next paper that we are preparing.The effectiveness of the vibration energy harvesters equipped with nonlinear mechanical components has been discussed ,56,57,58In this paper, the ASCVS-t switching strategy demonstrated a high output voltage from an active harvester with the charge inversion circuit. It was assessed under nonstationary and random vibration conditions as realistic vibrations. The ASCVS-t strategy could select the switching actions that amplify the output voltage with the threshold as the assessment criterion for the piezoelectric voltage. Because the threshold used in the ASCVS-t strategy was time varying considering the harvester conditions, the ASCVS-t strategy can maintain an efficient switching action even if the disturbance is nonstationary and random during the harvesting process. The thresholds adjust the intervals between switching actions to reflect changes in the piezoelectric voltage and mechanical displacement caused by the switching action itself, thereby forcing a nonstationary disturbance. Owing to the fuzzy control theory adopted as the tuning algorithm for the threshold coefficients, the changes in both electromechanical variables can be treated ambiguously. The ambiguous criterion realizes robust tuning even under unknown disturbance conditions.The experiments confirmed that the ASCVS-t strategy maintains a high output voltage when the harvester was exposed to nonstationary disturbances. The comparison of the magnitude of the output voltages with two previous switching strategies under each excitation experiment confirmed that the ASCVS-t strategy properly implemented efficient harvesting because of the selection of the desirable switching actions with the tuned time-varying threshold.The proposed control strategy can increase both output voltage and energy. Therefore, the proposed strategy is suitable for an operational scenario that alternately implements harvesting and consumption. As an application area, the proposed control strategy can be used to power a tire-pressure monitoring system. The implementation of the proposed strategy needs sensors measuring the voltage and vibration, and a controller equipped with high computational power. The self-powering of these devices is a technical issue of the implementation. Our self-sensing technique and the self-powered digital controller for a harvester can solve the above technical issue.In this paper, the ASCVS-t strategy was implemented in a powered active harvester controlled by a PC with an external power source. The implementation of the ASCVS-t strategy in a self-powered active harvester is the next research goal.


The Abecedarian Approach is an early intervention and contains a broad-spectrum adult/child curriculum. The Approach has been studied in three longitudinal randomized controlled trials in the USA, starting in 1972 and continuing today. Recent research studies in multiple countries have examined the Abecedarian Approach during the first three years of life. The collective findings from these studies lead to the conclusion that human development is malleable, especially in the years before school entry, and that high-quality early intervention exerts positive, early, and long-lasting influences on human development, including social development and mental health. A broad-spectrum program such as the Abecedarian Approach attempts to influence multiple strands of development in a holistic way. “Broad-spectrum curricula exist because professionals who facilitate development recognize that each child is more than a collection of skills and attitudes. The ‘more’ can be seen in the pattern by which the skills fit together and reinforce each other. The broad-spectrum curriculum is congruent with the goal of developing an individual who is internally integrated and whose skills are generalized across many situations of life. Because of its emphasis on life situations, a young child’s broad-spectrum curriculum, when being implemented, looks like play. This type of curriculum comprehensively spans large blocks of time and is incorporated into all or most of the things the child does during the day”  (p. 2).The Abecedarian Approach is distinctive in its design and research and in its persistent and pervasive focus on adult-child interaction. It is the only educational program that begins at the child’s birth, continues until the child enters school, is supported by over 40 years of high-quality scientific research , and hasThe Abecedarian Approach has been implemented in multiple countries. The Approach has been adapted and used as a birth to age three or birth to age five program in Australia, Canada, China, Denmark, France, India, Jordan, Mexico, Mongolia, Pakistan, Singapore, and Zambia ,9,10,11.Abecedarian studies that were conducted after the first study, were not traditional replications in that they did not simply repeat the original study at another time or place. Each study tried to produce new knowledge by varying some aspect such as the method of program delivery, setting, length of treatment, or program staffing. These are components that have been varied across the Abecedarian research studies.Samples: children from low-resource families, children born prematurely and at low birth weight, children with cerebral palsy, children from various countries, Indigenous children, children in an orphanage.Method of program delivery: center-based group care, family child care homes, play groups, home visiting.Length of intervention: birth to 36 months of age, birth to school entry.In the early 1970s, the original Abecedarian researchers asked the question: Could a positive early childhood experience really help historically low-achieving children develop in a pattern similar to the general population of children and have greater success in school? To begin the process of answering this question, the Abecedarian Approach was created to serve as the core of the “educational treatment” in the Abecedarian Project, a rigorous longitudinal research study. The investigators hypothesized that providing theory-based, active, contingent experiences to children across the very early years of development could significantly improve their academic achievement and social adjustment once they reached school. Full day child care was chosen as the platform for delivering these experiences in the first study because it allowed the researchers the opportunity to verify that the educational program was being delivered faithfully and in sufficient amounts.The theoretical underpinnings of the Abecedarian Approach were derived from three classic sources. Vygotsky’s  concept A key Abecedarian feature is that its educational program begins at birth  and suppThe adult-child curriculum of the Abecedarian Approach is a strong set of teaching and learning strategies implemented through intentional adult-child interactions that are explicitly described and illustrated in the Abecedarian program resources, activities, learning strategies, and training.In creating this Approach for the Abecedarian Project in the early 1970s, we strove to capture the emerging scientific knowledge about how infants and young children grow and develop and to translate this technical information into playful activities and educational interactions. We attempted to create activities that could be understood and used by parents and by all adults working with and caring for young children. The Approach incorporated many features of a stimulating home environment as well as some features of a high-quality child care center.Language Priority—making each part of the child’s day an opportunity for talking, listening, responding, and taking turns. Young babies’ glances and gestures are accepted as important parts of a two-way conversation.Conversational Reading—reading books interactively, emphasizing the child’s active role. The adult provides graded or hierarchical prompts to gradually elicit more developmentally advanced responses from the child. The word “conversational” emphasizes the back-and-forth, reciprocal nature of this type of reading.Interaction Games—playing interactively through adult-child games tailored to the child’s interests and developmental level. The games appear easy on the surface but challenge the adult to find just the right level and variation for the individual child. While the action of the game is simple, the significance to the child’s development can be profound.Enriched Caregiving—incorporating educational content and social-emotional connection into the child’s daily care routines such as feeding/eating, changing diapers/toileting, bathing/washing hands, getting dressed/undressed. Adults enhance the basic level of care they provide by emphasizing its social-emotional aspect as well as incorporating explicit educational content such as shapes, sizes, colors, numbers, and processes.These are the four elements of the Abecedarian Approach briefly described:Each element is one way of looking at adult-child interactions. In the Abecedarian Approach, interactions occur intentionally, individually, and frequently. If the adults are educators, they have written plans. If they are parents, the “plans” may be more informal. This allows the adults to engage in the activities intentionally and focusing on individual children. Most of the interactions are performed one-on-one  allowing the adult to tailor content and responses to the child’s individual needs. Each of the elements of the Abecedarian Approach is incorporated into the child’s day multiple times, the repetition providing many opportunities for practice.Since the Abecedarian Approach focuses on multiple strands of child development, one way to think about the Approach is to consider how the parts of the Abecedarian adult-child curriculum are intended to relate to the observed or hypothesized Abecedarian effects or outputs. The map presents a rudimentary topographical view of the intersection between the Abecedarian Approach (the program inputs) and the Abecedarian child effects (the program outputs). The darker areas are hypothesized to be areas of strong influence, the lighter areas to be areas of moderate influence, and the unshaded areas to represent non-hypothesized or minimal influence.Some child care providers who read about the Abecedarian Approach notice that some of the ideas in the four elements of the Approach seem familiar and are similar to some of their current practices. Their response is, “This is not special, I already do it” . It is tThe research reported below does not imply that students from families of low economic and low educational backgrounds who do not participate in a program such as the Abecedarian Approach tend to have immutable developmental profiles that are not amenable to change by the school after age five. The research demonstrates that, on average, children from low-resource backgrounds who have experienced an early Abecedarian program enter school with a developmental and educational advantage compared to children from similar backgrounds who have not experienced the program and that the advantage accrues to their benefit throughout their school years and into middle adulthood.Since the Abecedarian Approach has been studied for a number of decades, there have been hundreds of peer-reviewed journal articles and book chapters published on the research findings of this program. Multiple Abecedarian studies show that intervening broadly for children from low resource families yields a variety of early and long-lasting positive outcomes . Often, Because the first Abecedarian study, called the Abecedarian Project, was delivered through group child care, the researchers wanted to know if there was a positive or negative effect from the child care experience itself. At one year of age the infants and their mothers were observed in the Ainsworth Strange Situation paradigm . This obIn the first Abecedarian study video data were collected on how 20-month-old infants from low resource families use intentional communication in a free-play setting. Children who received the Abecedarian program were compared to randomly assigned children who received other programs or stayed at home. They were also compared to a group of normally developing middle-class infants. The frequency of communicative initiations and the proportion of spontaneous communicative initiations—classified as “showing” and “requesting”—were used for the comparison. Receiving the Abecedarian Approach through child care significantly enhanced both the frequency and the developmental level of the communicative initiations of infants from low-resource families .A 2019 impact study sought to determine if the classic Abecedarian Approach, in the current time and in an on-going service setting, could improve the early developmental progress of historically underachieving Canadian children, including those of First Nations (FN) status. A treatment group received the Abecedarian Approach in a child care center supplemented by home visiting, and a control group received child care at other centers or care at home. Children were assessed on the language scale of a standardized instrument, the Brigance Screen  at enrolAn academic locus-of-control measure , collectA randomized clinical trial in eight states, the Infant Health and Development Program (IHDP), examined the Abecedarian Approach intervention with children born preterm and at low birth weight. The parents completed the Achenbach Problem Behavior Checklist  in each Cortisol is a hormone that has been used to study human responses to stress. During and following an Abecedarian intervention in the first three years of life in a Romanian Orphanage, researchers gathered saliva cortisol samples from treatment, control, and general population comparison children. Saliva samples were collected at 8 AM, noon, and 7 PM on two consecutive days at age two and again at age three. Saliva samples were also collected before, during, and after a stressful event. The cortisol levels indicated that children who had experienced the Abecedarian Approach were better at handling the general stress of the day and specific stressful events than were the control group. In addition, for the untreated group there were some negative correlations between cortisol levels and cognitive development ,30.Subjects in the Abecedarian low birthweight study (IHDP) received a follow-up assessment at 18 years of age using questions from the Youth Risk Behavior Surveillance System . Items fYoung adults who were in the treatment and control groups of the Abecedarian Project completed the Brief Symptoms Inventory  at age 2Abecedarian young adults showed a significant treatment-related reduction in reports of recently using marijuana. Use of other drugs and alcohol were not different between the groups. There was a trend in the Abecedarian follow-up data for fewer individuals who had early childhood intervention to report being regular smokers in young adulthood compared with controls. Additionally, for participants who received the Abecedarian treatment, the odds of reporting a healthier, more active lifestyle in young adulthood were 3.92 times greater compared to participants from the control groups .A long-term follow-up study summarizing data gathered at ages 21, 30, 34 looked at the crime-reducing impacts of the Abecedarian early childhood program. Proportionately, more women than men who participated in the early childhood Abecedarian program had less criminal activity than the control group. This gender difference occurred because the home environments were worse for the girls, with corresponding greater scope for improvement by the program. For both genders, treatment effects were larger for the least advantaged children, as measured by their mother’s education at the beginning of the early childhood intervention. The dollar value of the social cost of criminal activity averted was higher for men because they committed more costly violent crimes .The percentage of the Abecedarian treated and control groups at age 30 who worked full time for at least 2/3 of the preceding 24 months showed that the odds of being employed for those in the Abecedarian treated group were more than twice the odds for those in the control group. Similarly, the group with Abecedarian early childhood treatment had slightly higher job prestige scores than the control group but the difference did not reach statistical significance. Approximately a quarter of each group had married by age 30, but the odds of being the head of one’s own household were almost twice as high for the treated group. Administrative data on use of government welfare funds showed that, within an 89-month time window, individuals in the control group were 6 times more likely to receive benefits at least 10% of the time .The Abecedarian investigators recruited all study participants for an adult physical examination whose findings could be compared as a function of early childhood treatment. At the time of the medical study, participant age ranged from 32 to 39 years and were an average of 35.4 years. Findings for the study indicated that males who had received Abecedarian treatment had significantly lower blood pressure than did males in the control group. None of the males in the treatment group exhibited the complex of conditions called metabolic syndrome  known to be predictive of heart disease, whereas 25% of the males in the preschool control condition did so. Females did not show the same treatment effects as males, but females who had been in the early childhood Abecedarian treatment group were less likely to be affected by abdominal obesity and were less likely to fall in the pre-hypertension category than were the control females .Education Week [When the Abecedarian treatment and control alumni were in their early 40s, they and a sample of general population young adults played the “ultimatum game.” In this game they were asked to accept or reject offers that divided an amount of money between themselves and another (unseen) player. Social decision making was measured—especially in terms of how the subjects would choose to divide resources. The Abecedarian treatment alumni opted for greater fairness and equity in the division of resources than did the control group or a general population sample . Educatiion Week  summarizThe year-by-year levels of participation of individual children and families showed a clear association between participation levels and cognitive progress at ages two and three . For eacKnowing that the level of family and child participation in the low birthweight study made an impact, the original researchers looked further into program process variables. They especially used the data related to the learning activities that comprise the four elements of the Abecedarian Approach. They analyzed these curriculum-related records to see if for individual children a basic measure of curriculum such as a count of Abecedarian learning activities per child-care day and per home visit could predict child cognitive outcome. First, the researchers statistically equalized the effects of initial status variables  and the effects of family and child participation. After all those effects were accounted for, the analysis showed that the rate of delivery of Abecedarian learning activities still added significantly to the prediction of child 36-month Stanford Binet IQ . So, notAnother group of researchers continued to look into this topic. They created an Active Experience Index comprised of the level of interest parents showed regarding the Abecedarian learning activities during home visits plus the degree of mastery of the learning activities that children achieved in the child care center. After controlling for child and family initial status variables, they showed that Active Experience improved the prediction of child 36-month IQ to even a greater degree than did the simple rate of curriculum delivery . This anearly factors bear on later achievement in school and life? Following a mediation of effects strategy, an analysis of several early interventions showed that a predictive model comprised of cognitive advantage, plus social adjustment, plus motivational advantage accounted for 100% of the preschool effect on years of education at age 21 for children who had received the Abecedarian Approach in the first five years of life. This three-part cognitive/social/motivational model makes intuitive sense and relates closely to the other observations in this article. The fact that these three predictors explain, respectively, only 77.94% and 38.15% of the preschool effect on education at age 21 for the Perry Preschool project and the Chicago Child-Parent Centers [What  Centers  (p. 432)The Abecedarian Approach, like many interventions, has a logic map that assumes that the educational program first is incorporated into an adult’s behavior and reaches the target child as the adult and child interact. In many studies the child’s behaviors are measured but not the adult’s. However, one randomized Abecedarian study in the USA measured the behavior of child care providers who were trained in the Abecedarian Approach and implemented it in family child care homes. The training of caregivers had statistically significant impacts on caregiver behaviors. That is, compared with the control group, the Abecedarian trained caregivers had substantially higher frequencies of rich oral language interactions, interactions to support children’s understanding of vocabulary or concepts, and responsiveness to the children . None ofIn a Canadian qualitative study of caregivers and parents, the main themes that emerged were strengthened relationships between parents and program staff, as well as between parents themselves; increased awareness among parents about early development and of their role in supporting child development; and opportunities for parents’ personal growth . The finMultiple Abecedarian studies ,45 have If an academically at-risk child has daily had individualized games, reading sessions, and information-filled caregiving/language interactions from responsive adults during three to five years of educational child care and/or home life, then the experience of school  is likely to be easy to comprehend and respond to. Successfully playing a game with a caregiving adult will map onto the new experience of doing a lesson with a teacher. From his or her early experience, the child expects to receive adult input, to pay attention, to respond, and to succeed. This is the social, attitudinal, and learning dispositions advantage the child brings to school. Moreover, the child enters school developmentally on track  and does not have to play catch-up. This is the cognitive advantage that enables the child to benefit from each succeeding experience as it presents itself.


Evidence indicates that long-term memory formation creates long-lasting changes in neuronal morphology within a specific neuronal network that forms the memory trace. Dendritic spines, which include most of the excitatory synapses in excitatory neurons, are formed or eliminated by learning. These changes may be long-lasting and correlate with memory strength. Moreover, learning-induced changes in the morphology of existing spines can also contribute to the formation of the neuronal network that underlies memory. Altering spines morphology after memory consolidation can erase memory. These observations strongly suggest that learning-induced spines modifications can constitute the changes in synaptic connectivity within the neuronal network that form memory and that stabilization of this network maintains long-term memory. The formation and elimination of spines and other finer morphological changes in spines are mediated by the actin cytoskeleton. The actin cytoskeleton forms networks within the spine that support its structure. Therefore, it is believed that the actin cytoskeleton mediates spine morphogenesis induced by learning. Any long-lasting changes in the spine morphology induced by learning require the preservation of the spine actin cytoskeleton network to support and stabilize the spine new structure. However, the actin cytoskeleton is highly dynamic, and the turnover of actin and its regulatory proteins that determine and support the actin cytoskeleton network structure is relatively fast. Molecular models, suggested here, describe ways to overcome the dynamic nature of the actin cytoskeleton and the fast protein turnover and to support an enduring actin cytoskeleton network within the spines, spines stability and long-term memory. These models are based on long-lasting changes in actin regulatory proteins concentrations within the spine or the formation of a long-lasting scaffold and the ability for its recurring rebuilding within the spine. The persistence of the actin cytoskeleton network within the spine is suggested to support long-lasting spine structure and the maintenance of long-term memory. Memory can last for years. The prevailing hypothesis is that memory is encoded by a neuronal circuit, and therefore, this circuit needs to be preserved to maintain the memory. This circuit includes, in many instances, excitatory and inhibitory synapses in excitatory neurons. Most of the synaptic excitatory transmission, but also some of the inhibitory synaptic transmission, occurs in dendritic spines that are small extensions of the dendrite. It was found that the morphological structure of the spine can affect the transmission of the synaptic signal into the neuron and can determine its activity. Moreover, the number of dendritic spines and their location in the neuron contribute to the way the inputs that arrive at the neuron activate it. Thus, dendritic spines can sculpt and determine the function of the neuronal circuit that encodes memory. It also implies that if the neuronal circuit that encodes a lasting memory is preserved, then the overall influence of the dendritic spines on the activity of the neurons, and hence their morphology and distribution within the circuit, needs to be maintained. Indeed, studies have shown that dendritic spines formed after learning can be preserved for a very long time, exhibiting a strong correlation between the number of the maintained new spines and the strength of memory. Long-lasting elimination of spines can also play a role in shaping the neuronal circuit that forms the memory trace. These observations suggest that long-term memory maintenance is subserved by long-lasting dendritic spines. Dendritic spines morphology is mediated by the actin cytoskeleton structure. However, the actin cytoskeleton is very dynamic, and the lifetime of proteins that regulate and preserve the actin cytoskeleton structure is relatively short. How, therefore, is the structure of dendritic spines preserved by the actin cytoskeleton to maintain long-term memory? This review discusses this topic and suggests models that can resolve the issue. Dendritic spines are protrusions extending from the neuronal dendrites. Most of the excitatory transmission in excitatory neurons is located in spines ,2. Some 2+ that enters the spine heads through NMDARs. Larger spines have necks that permit a greater efflux of Ca2+ into the dendritic shaft, whereas smaller spines display a larger increase in [Ca2+]i within the spine compartment because of a smaller Ca2+ flux through the neck  into LA, to interfere with VASP binding to profilin, impaired long-term, but not short-term, fear memory formation [The translocation of actin regulatory proteins into spines has also been induced by learning. Fear conditioning leads to the movement of profilin into dendritic spines in the lateral amygdala (LA). These profilin-containing spines undergo enlargements in their postsynaptic densities (PSDs) . Profiliormation .The preservation of the composition of actin regulatory proteins in spines requires the persistent trafficking of specific proteins but not others into specific “memory spines”. Proteins can be translocated into spines using Myosin motor proteins that use actin filaments . For exaThe prevailing hypothesis is that the persistence of long-term memory requires a stable underlying neuronal network. Dendritic spines contain most of the excitatory synapses in excitatory neurons, and their morphology affects synaptic transmission. Therefore, it is suggested that stable dendritic spines morphology may underlie the maintenance of the neuronal network and long-term memory. The morphology of dendritic spines is supported by the actin cytoskeleton. However, the actin cytoskeleton is dynamic, and the turnover of proteins that control this actin cytoskeleton network is relatively fast. To overcome this and to keep the actin cytoskeleton structure within the spines in a relatively stable form, for the maintenance of the general structure of the spine, two models have been suggested: (1) The concentrations of the actin cytoskeleton regulatory proteins within the spine’s nano-domains should be kept consistent. This could be done by funneling specific proteins or mRNAs into the spine by routes created by learning. (2) A structure has been formed during learning and is maintained the same by replacing the actin-binding proteins and actin, which builds the structure and are destined to degradation, with new proteins.Although there is evidence that supports the first model, i.e., insertion of specific proteins into activated spines to control their morphology and the formation of routes of transportation of proteins and mRNAs into the spines, future studies will need to investigate this model. These studies can inspect: (1) the concentrations of proteins in a spine’s nano-domain after activation over time, (2) how altering these concentrations affects a spine’s nano-domain and the spine structure and (3) how the trafficking routes arrive at these nano-domains to deliver the proteins and how these routes remain stable over time. The second model, namely, the formation, by learning, of an actin cytoskeleton network and the constant replacement of proteins to keep the network stable for memory maintenance, should also be studied.


In spite of the unprecedented resolution provided by non-contact atomic force microscopy (AFM) with CO-functionalized and advances in the interpretation of the observed contrast, the unambiguous identification of molecular systems solely based on AFM images, without any prior information, remains an open problem. This work presents a first step towards the automatic classification of AFM experimental images by a deep learning model trained essentially with a theoretically generated dataset. We analyze the limitations of two standard models for pattern recognition when applied to AFM image classification and develop a model with the optimal depth to provide accurate results and to retain the ability to generalize. We show that a variational autoencoder (VAE) provides a very efficient way to incorporate, from very few experimental images, characteristic features into the training set that assure a high accuracy in the classification of both theoretical and experimental images. Atomic force microscopy (AFM)  in combitruction ,5 or poitruction . The lattruction . These htruction . The NCAtruction ,11,12,13truction .The main contrast mechanism for AFM with inert tips is Pauli repulsion . This reArtificial intelligence (AI) techniques, also known as machine learning (ML), have demonstrated an extraordinary ability to differentiate patterns and perform predictions with high accuracy in many different fields ,25,26,27The main challenge in AI is to determine the complexity of the model (the number of layers and the filters included in each layer) needed to strike the right balance between the specialization needed for an accurate prediction ,37,38 anTogether with the technical problems described above, the possible application of deep learning to the problem of molecular identification based on AFM images has to face two main challenges that are intrinsic to the technique: how to achieve chemical identification within the molecule at the single atom level, and how to deal with markedly non-planar, 3D structures. The last problem has been recently assessed by a combination of AFM experiments and image simulations with machine learning in order to determine partial 3D structures of small molecules . The strThe goal of this work is to fill this gap with the development of a strategy to combine high-resolution AFM imaging and machine learning in order to achieve molecular identification. We focus on a set of quasi-planar molecules that spans relevant structural and compositional moieties in organic chemistry. We describe how, from each of these molecules, we build the necessary training dataset of 2D theoretical images, striking the right balance to incorporate enough variation and to prevent overfitting.Firstly, we show the limited performance of two well-established deep learning models for image recognition ,46 in thPubChem web [The SPMTH-60 dataset mostly contains a collection of theoretical constant-height AFM images built from a selection of 60 essentially flat organic molecules see  whose stChem web . These mAFM experiments are conducted on adsorbed molecules, whose structure and electronic properties may be affected by the interaction with the substrate. These changes, together with different experimental conditions, lead to a significant variability in the recorded AFM images, as shown in PubChem web-supported database of chemical compounds [Most SPMTH-60 dataset simulations are calculated with a simplified version of the full-density-based model (FDBM) ,23 impleompounds . More deAs discussed below, machine learning models trained exclusively with theoretical images completely failed in the classification of experimental images. We have augmented our training data set with 540 images generated with a VAE from three experimental images for acridine, carbazole, and dibenzothiophene taken from Reference  see Fig. An addiz-axis is perpendicular to the molecular plane, and AFM experiments are conducted on adsorbed molecules, whose structure and electronic properties may be affected by the interaction with the substrate. In order to take into account these effects, SPMTH-60 includes a set of images for each molecule generated with different molecular orientations, that mimic the possible effect of the adsorption.In particular, we have applied 48 rotations arising from the combination of the following Euler angles: To ensure that SPMTH-60 reflects all the image variants of each molecule, we have considered a variety of operational AFM settings for each of the rotated configurations described above. As a result, a group of AFM images is provided for each of the molecules. Namely, we have simulated each structure with 4 different values of the elastic constant describing the tilting of the CO molecule  following the implementation provided in the VASP code ,55. An ePubChem web [The bare molecules were subjected to single-point calculations (electronic self-consistency) using the geometries provided in the Chem web . In few The idea of providing a machine with the ability to classify images is one of the main challenges in machine learning and has fostered a significant amount of work in recent years. Deep learning techniques, in particular convolutional neural networks (CNN) architectures, have played a key role in this effort and several models based on this paradigm have achieved remarkable results. We have applied two of these models, MobileNetV2  and VGG1MobileNetV2  is an exIn order to avoid overfitting, we have employed different common procedures: we have halved the number of filters in each layer, applied a strong image data augmentation to the training set  backwards. The error propagation method calculates the gradients of the loss function computing the chain rule for derivatives to determine the contribution of each neuron in the previous layer to the error and to modify its parameters accordingly. Considering that the depth of a deep learning model like VGG16 is 16 layers , while AFM data, and correspondingly SPMTH-60, is composed by grayscale (single channel) images. Secondly, standard datasets contain hundreds of classes while the SPMTH-60 dataset is composed by only 60 different classes. Finally, AFM images share rather similar features, i.e., the basic features in the AFM image of a benzene are not substantially different from the ones for anthracene, and this also applies when comparing pyridine and pyrimidine. In the task of discriminating between these images is not so important that different filters are activated but that the same filters are activated in different areas of the image See .paths—different ways provided by the model in order to link the input and output layers of the model—(ii) the presence of dropout layers, and (iii) the regularization in convolutional layers  to some key layers of the model See . The purThe training of the model includes, as for the standard models, an image data augmentation , and is The prediction of the ML-AFM model with the theoretical test set is as accurate as the one obtained with the standard models (0.99 accuracy). However, when considering the performance with the set of experimental images described at the end of The limitations of our ML-AFM model in the classification of experimental AFM images discussed above have prompted us to explore different ways to improve our training set. It is clear that experimental images have some characteristic features that are not captured by simulations. Differences between experimental and theoretical AFM images for a given molecule could be due to the approximations made in the simulation of AFM images, or to the fact that molecules relax and deform due to the interaction with the substrate, while we are considering ideal, gas-phase structures in the simulations. In order to cope with the first issue, 36 AFM images calculated using more sophisticated simulation methods ,23 have variational autoencoder that adds a probabilistic contribution to the code space turning it into a latent space (a code space with probabilistic distributions).In what follows, we discuss how to augment our training data set including images with features similar to those found in the experiment generated with a variational autoencoder (VAE) ,49 in orAutoencoders have been used for different purposes such as image denoising , image ss vector b, we genThe VAE has to be trained with theoretical images. Our results show that, in order to endow the VAE with the ability to reflect the characteristic features of the experimental AFM images, it is necessary to ensure that the training images reflect details that are absent from the the simulations of the isolated molecules. Simulated images for the relaxed structures obtained with DFT for these molecules upon adsorption on Au(111) slab have been used to replace the images obtained from the isolated structures. In addition, we have applied an augmentation using the image data generator (IDG) see a.We have applied the encoder to three experimental AFM images, one for each of the molecules acridine, carbazole, and dibenzothiophene , we have built a total dataset of almost half a million images, that we split into training, validation, and test sets with 314.460, 120.960, 48.420 images, respectively.Standard models for image classification with different complexity like MobileNetV2 and VGG16, trained and tested with the SPMTH-60 dataset, do not perform particularly well. With the use of a combination of different strategies during training, including the reduction in a number of filters and the application of a strong image data augmentation, they can achieved a high accuracy in the classification of theoretical images, but failed dramatically when confronted with experimental AFM images. Our analysis of the activation of some filters in different blocks of the VGG16 architecture indicates that the model has run into overfitting: it has too many parameters and some of their filters in the deeper layers have specialized excessively during the training while others in the first ones remain completely random.Standard models do not work with SPMTH-60 dataset as they are not suited to the grayscale information and to the small set of common features that dominate AFM molecular contrast. A properly designed model, like our ML-AFM, with the optimal depth and incorporating different paths for the data, provides the necessary flexibility to avoid overfitting and to achieve the training necessary to produce a successful classification. When posed with experimental images, ML-AFM performs rather well, but does not achieve the accuracy demonstrated with theoretical images. However, we have shown that it is possible to design a VAE to generate, from very few experimental images, a small set of AFM images to incorporate characteristic features of the experiments into our training dataset. The ML-AFM model, trained with this set composed mainly by theoretical images and enlarged with very few experiment-like images  is able to succeed with almost equal accuracy in the classification of both theoretical and experimental images.Looking back at the theoretical and experimental AFM images shown in From this perspective, this work represents a promising step but we need to be aware of the problems ahead. Our classification has been restricted to 60 different molecular structures. If the model is confronted with an image that does not belong to any of the classes in the dataset used in the training, the output of the model will be still one of those 60 classes, and, thus, wrong. New strategies, probably based in the identification of the number and location within the molecule of atoms belonging to different chemical species, are needed to generalize the classification to cover the richness and complexity of organic chemistry.


Most of the locomotion and contact planners for multi-limbed robots rely on a reduction of the search space to improve the performance of their algorithm. Posture generation plays a fundamental role in these types of planners providing a collision-free, statically stable whole-body posture, projected onto the planned contacts. However, posture generation becomes particularly tedious for complex robots moving in cluttered environments, in which feasibility can be hard to accomplish. In this work, we take advantage of the kinematic structure of a multi-limbed robot to present a posture generator based on hierarchical inverse kinematics and contact force optimization, called the null-space posture generator (NSPG), able to efficiently satisfy the aforementioned requisites in short times. A new configuration of the robot is produced through conservatively altering a given nominal posture exploiting the null-space of the contact manifold, satisfying geometrical and kinetostatics constraints. This is achieved through an adaptive random velocity vector generator that lets the robot explore its workspace. To prove the validity and generality of the proposed method, simulations in multiple scenarios are reported employing different robots: a wheeled-legged quadruped and a biped. Specifically, it is shown that the NSPG is particularly suited in complex cluttered scenarios, in which linear collision avoidance and stability constraints may be inefficient due to the high computational cost. In particular, we show an improvement of performances being our method able to generate twice feasible configurations in the same period. A comparison with previous methods has been carried out collecting the obtained results which highlight the benefits of the NSPG. Finally, experiments with the CENTAURO platform, developed at Istituto Italiano di Tecnologia, are carried out showing the applicability of the proposed method to a real corridor scenario. To overcome this issue, previous works adopt simplifying assumptions to reduce the state space dimension or use a discrete control space  completeness or global optimality and it is non-trivial to generate optimal collision-free trajectories within time frames acceptable for online planning, especially in complex environments.Achieving autonomous whole-body motion behaviors for humanoid and legged robots still represents a challenging research topic. The capability to take autonomous decisions while walking or manipulating objects is fundamental for complex platforms working in real and uncertain environments, without the need for human supervision and intervention footstep/multi-contact plannersA further possibility is to use null-space posture generator (NSPG), able to generate collision-free and statically balanced configurations for arbitrarily complex floating-base robots. In particular, the NSPG exploits the null-space of the robot, which is used to locally correct its posture around a nominal configuration, generated starting from the history of previously computed feasible postures. In our method, the previous configuration becomes also the seed configuration of the HIK solver, guaranteeing minimal differences between adjacent postures. If a chain of the robot is in contact with the environment or in self-collision, instead of generating a new whole posture, only the involved kinematic chain is moved to avoid the collision, in the neighborhood of the nominal configuration. Hence, we take advantage of the kinematic structure of multi-limbed robots to restore feasibility. Differently, when the generated posture is statically unstable, only the root link is moved to restore feasibility.Addressing these concerns, in this work, we propose a novel posture generator algorithm based on the hierarchical inverse kinematics (HIK), called the The method, compared with previous works, contributes with a smart selection of the seed and nominal configurations for the HIK solver, seeking for a new feasible one inside a small workspace around the nominal configuration whose volume is defined by the parameters of the algorithm. Specifically, it exploits the robot workspace in random directions, moving in the neighborhood of the nominal configuration. This allows the posture generator to look for a feasible configuration instead of discarding the state as soon as the first computed configuration is unfeasible, improving the performance of the planner and the algorithm itself. Last, the number of parameters to be tuned is kept minimum and is not dependent neither on the environment nor on the robot (discussed in detail in This paper introduces the literature on previous related approaches and novel contributions to posture generation applied to contacts and whole-body motion planning in The generation of feasible whole-body configurations for a legged robot coupled with footsteps or multi-contact planners has been widely investigated in the past years. The previous work is based on pre-computed paired forward–inverse dynamic reachability maps (DRM/iDRM) to sample in the reachable workspace those configurations that could accomplish a loco-manipulation task while guaranteeing stability and collision safeness on flat In Other approaches explore fixed-size In A different approach was used in Recently, in The NSPG aims to generate collision-free whole-body configurations realizing both kinematic and statics constraints that will be detailed in configurationn joint positions and the pose of the floating base w.r.t. the inertial frame. We denote as • A stancek contacts where each kth contact • A compliant with a stance σ if it realizes all the contact poses specified by σ, i.e., σ and a compliant configuration state s:• A configuration The contact planner defines the pose of the active contacts for the legged robot moving from a start to a goal stance. The basic elements used are as follows:For each state The configuration space velocities associated with the configurations In addition, with proper validity functions, we assume to sample stances with poses of the contacts in the workspace of the robots and not inside any obstacle.The Cartesian velocity differential inverse kinematics, permits to compute the configuration velocities least-square problem in the formλ being a gain which ensures exponential convergence of the Cartesian error The inverse problem of constraints as well The problem in hard priorities between tasks can be enforced in the QP-based IK by means of a cascade of QPs Furthermore, Contact Taskσ. For example, the surface contact task is defined as• • with • with Postural Task• • As done in the Cartesian case (5), it is possible to define the desired configuration velocity with a term that tracks a reference robot configuration Joint Limits Constraint• • with We define the following tasks and constraints:math of tasks, follows the work done in We organize these tasks and constraints in the following stack To grant quasi-static stability for a given robot configuration The resulting QP in the variables The first term in ith local frame ith contact, x and y are half the size of the surface contactith contact frame This reduced description assumes fixed contact placements with associated linearized friction models and unilaterality of the contact force It is worth noticing that modeling a surface contact using forces and moments, together with the constraints The residual of the first term in the cost function In a contact planner application case, a feasible sequence of adjacent postures is required to be connectable in order to build a configuration path that moves the robot safely from a start configuration  of qi−1 . This asFurthermore, in the assumption that near stances differ by exactly one active contact, the generated configuration Our approach is based on a complete reshape of the robot configuration, obtained by adjusting the pose of kinematic chains in a collision, or moving the root link to recover the static stability, in the null-space of the Cartesian (contact) tasks. Specifically, each detected unfeasibility will generate random velocity components aiming to recover feasibility. This section follows a pipeline going through each component of the algorithm: first, the nominal configuration and the random velocity vector seed configurationFirst, the candidate configuration In the following, the procedure to generate the random velocity vector In this phase, we take advantage of the kinematic structure of a multi-limbed robot to avoid collisions while keeping low differences between adjacent configurations. Indeed, the motion of a kinematic chain is independent concerning the others, assuming that its end-effector is not constrained onto a contact pose. In this way, we can freely move only the chain(s) involved in unfeasibility, preventing avoidable motions that could lead to other collisions.C. The kinematic chain is defined as the set of links and joints moving from the tip link  to the base link. For each of the joints belonging to those chains, a random bounded velocity vector is generated as written in line 16. The random velocity vector comes from a uniform random distribution bounded between the joint velocity limits. In detail, when It is worth mentioning that collisions/self-collisions can be avoided as well as integrating specific cost functions or constraints in the HIK With this methodology, the NSPG moves only the joints involved in unfeasibility preventing avoidable motions of the rest of the body.A second scenario occurs when In this case, linear velocities of the root link are generated from a uniform random distribution bounded between two arbitrarily big numbers , and the HIK is solved generating a new robot configuration While running, the algorithm will generate configurations with arbitrarily small differences which depends on its parameters and velocity vector Collision and stability checks strictly depend on the current candidate configuration of the robot that changes at each iteration of the algorithm. Thus, the velocity vector Specifically, at each iteration, the colliding chains are updated, and two new sub-sets are defined:At each iteration, this method looks for a feasible configuration inside a maximum allowable workspace around the nominal configuration. The maximum volume of the robot workspace is defined by the parameters The proposed NSPG algorithm has been tested in two scenarios with increasing difficulty, applied on two different types of legged hyper-redundant robots: the hybrid wheeled-legged quadrupedal robot CENTAURO and the biped robot COMAN+. CENTAURO is a robot with 39 DoFs split between a quadrupedal lower body and a bimanual humanoid upper body, while COMAN+ is a biped humanoid robot with 28 DoFs.The first considered scenario consists of multiple tiles, placed at different heights and orientations, where the robot has to step on or place its limbs, while the second one is a narrow corridor on a flat terrain. Additionally, an experiment of this last scenario has been carried out on CENTAURO.qpOASESOSQPFlexible Collision Library (FCL) Our NSPG implementation is based on the OpenSoT All videos showing the presented simulations and real experiments are included in the material accompanying this paperThe NSPG has been tested in the scenario where an external planner returns a series of feasible stances only. In this case, the contact state can be written ashoming configuration Specifically, the humanoid robot has to climb a stair of three steps on a sequence of 18 stances. The first two steps are flat, while the last two are rotated 0.25 rad along the x-axis see . The staIn this scenario, we want to stress the capability of the NSPG to find collision-free and stable configurations while stepping on non-co-planar stances, using a whole-body approach.We analyze the NSPG performance on 10 runs using the same sequence of stances. The results are collected in The NSPG has been also tested in a particularly tricky scenario for a sample-based planner algorithm: a narrow corridor . In partWhen planning with COMAN+ instead, locomotion is achieved by continuously switching between the two feet, i.e., the walking pattern. In particular, a sequence of single and double stances is computed by the planner and connectivity is guaranteed generating single-stance statically stable configurations. Indeed, the next double-stance configuration can be reached if and only if it is single-stance stable, avoiding the robot to go through an unstable region while walking see . This isIn this scenario, the NSPG is used inside a planner routine, implemented using OMPL m being the total NSPG calls. Additionally, the NSPG performance is evaluated considering also its rate of success and the average number of iterations the NSPG takes to find a feasible solution computed asThree parameter setups were tried in this scenario to test how the performance of the NSPG changes. This was evaluated collecting data about the average time employed to find a feasible posture:An additional statistic has been added considering the causes of failure. Indeed, the NSPG can fail due to collision check and static stability check failure. The necessity to always check both the stability and collision safeness is required by the NSPG to update the velocity vector Differently, when generating configurations with COMAN+, the stability check fails twice the collision check since we are looking for a single-stance stable configuration while moving through a narrow environment. Notice that the sum of the two percentages goes over 100% since the NSPG can fail due to a contemporary fail of the stability and collision checks.The results are collected in The NSPG has been designed to generate whole-body configurations for multi-limbed robots in a particularly complex environment. For instance, (multi-)contact planners generally require a precise representation of an extensive environment, usually obtained through point clouds. As already mentioned, in these scenarios, the use of HIK solvers, coupled with specific constraints for obstacle avoidance, can be computationally heavy since they are based on the computation of the distances between each link of the robot and each obstacle in the environment . Based on these distances, several methods have been proposed to move the robot away from the singularity. On the contrary, the NSPG does not need any particular strategy to avoid collisions, and the only requirement is the computation of the distances mentioned above. The results in To motivate this, an additional simulation with COMAN+ has been run in an environment similar to the one described in As expected, when using the linear constraint for collision avoidance in a complex environment detected through a dense point cloud, the time to solve the HIK dramatically increases by three orders of magnitude. The average time for the collision check is dropped to zero, but this improvement is not enough to justify such an increase in computational cost for the HIK and this is reflected in the overall performances of the NSPG. The percentage of success drops to 43.7% since the average time to find a feasible configuration goes over 2 s with a timeout of 1 s. In addition, the average number of iterations for each call of the NSPG decreases to 15 reducing its capability to explore the workspace.This work presents a novel algorithm, named the null-space posture generator (NSPG), able to efficiently generate stable and (self-)collision-free whole-body postures for a generic, multi-limbed, floating-base robot, given a sequence of stances. The NSPG has been developed to speed up the whole-body motion planning of complex robotic systems when passing through particularly challenging environments keeping the tuning procedure as light as possible. Indeed, benefits from computation and efficiency points of view have been demonstrated when applying this algorithm in a particularly complex environment compared to previous methods that use the constraint in the HIK to generate statically stable and collision-free configurations. Furthermore, it can also be used independently as a posture generator, given the active contacts as shown in Multiple experiments on two profoundly different robotic platforms, COMAN+ and CENTAURO, demonstrated that the NSPG is capable of quickly generating stable and collision-free configurations for a legged robot in contact with the environment, exploiting null-space motions. In particular, CENTAURO represents a challenging platform for planning considering the high number of DoFs. Real experiments were also carried out on CENTAURO using a Lidar sensor to perceive the environment, demonstrating the applicability of the proposed approach to a real scenario.Our implementation of the NSPG can generate approximately 1,000 configurations per second, guaranteeing a good exploration despite using a light random approach able to adapt while exploiting the robot’s workspace depending on the unfeasibility occurrence.The proposed method, even if based on a random approach, presents a good level of reliability which is observed in the result obtained in the two considered scenarios. Additionally, it does not require a big effort to tune its parameters, which does not depend on the robotic platform in use, as it has been seen by the general applicability of the algorithm to two profoundly different robotic platforms.Comparing our results to the recent work proposed in Future work will involve the use of the NSPG in a multi-contact planner scenario similar to the one used to generate stances in


Accurate 3D passive tracking of an underwater uncooperative target is of great significance to make use of the sea resources as well as to ensure the safety of our maritime areas. In this paper, a 3D passive underwater uncooperative target tracking problem for a time-varying non-Gaussian environment is studied. Aiming to overcome the low observability drawback inherent in the passive target tracking problem, a distributed passive underwater buoys observing system is considered and the optimal topology of the distributed measurement system is designed based on the nonlinear system observability analysis theory and the Cramer–Rao lower bound (CRLB) analysis method. Then, considering the unknown underwater environment will lead to time-varying non-Gaussian disturbances for both the target’s dynamics and the measurements, the robust optimal nonlinear estimator, namely the adaptive particle filter (APF), is proposed. Based on the Bayesian posterior probability and Monte Carlo techniques, the proposed algorithm utilizes the real-time optimal estimation technique to calculate the complex noise online and tackle the underwater uncooperative target tracking problem. Finally, the proposed algorithm is tested by simulated data and comprehensive comparisons along with detailed discussions that are made to demonstrate the effectiveness of the proposed APF. The marine resources have significant influences on human’s living and social developments. Furthermore, the ocean plays an important role for national security and the underwater target tracking is one of the most significant research areas of marine science and underwater acoustic engineering nowadays. Therefore, to exploit the ocean resources and defend the national territory, the technology of accurately and reliably tracking an uncooperative underwater target is of vital importance.There are two categories of underwater target tracking techniques, namely the active underwater target tracking and the passive underwater target tracking. The former always utilizes high-power active sonar equipment to transmit active detection signals to track the target in real time ,2. This For the aspect of the passive sonar tracking system, two kinds of measurements are commonly utilized to track an uncooperative underwater target. The first one is the angle-based measurements. By collecting the passive signals from an underwater target, various kinds of DOA algorithms can be utilized to output both the azimuth angle and the elevation angle of the target ,7. Then,In order to build a robust and accurate underwater passive tracking system, the observability along with the accuracy analysis should be firstly studied comprehensively. Since the passive tracking system only utilizes the radiations from the interested underwater target to accomplish the tracking process and the frequency-based measurements are not available when the target moves at a slow speed far from the tracking system, only the angle information can be obtained and utilized. Therefore, the passive tracking process sometimes is called the bearing-only tracking in a 2D scenario and angle-only tracking in a 3D scenario. The observability analyses are comprehensively studied by several researchers ,10,11, aFirstly, the observability of a tracking system is not “constant”. For the nonlinear system of underwater target tracking, even a full observable tracking system has different levels of observability for different configurations of the distributed underwater buoys that participate in the current tracking process. According to ref. , the obsIn addition, for a distributed system containing several underwater buoys, it is understandable that more measurements being utilized at the same tracking time can provide more accurate tracking results. However, since the underwater acoustic communicating resources are very limited, more underwater buoys will cost more underwater acoustic communicating resources which, as a result, will make the information fusion procedure much longer and decrease the tracking accuracy at its expense. Hence, the goal is to utilize an appropriate number of buoys to satisfy the accuracy requirements and save underwater acoustic communicating resources in the meantime. Therefore, the method of balancing the tracking accuracy and the system observability is crucial for the passive distributed underwater buoys system and has great researching significance. Although some researchers have developed the sensor scheduling and control principle for the distributed radar systems ,17,18, tBesides the considerations of the measurements, the target tracking algorithms also play an indispensable role in the tracking procedure. Since the underwater uncooperative target always stays in a certain moving mode for a long time and seldom makes maneuvering, the kinematics of the target can be modeled as the constant velocity (CV) model like many researchers supposed in ref. . Hence, By utilizing the CRLB and FIM analysis method along with the nonlinear observability analysis techniques, a real-time optimal topology design method of the distributed passive underwater buoys is proposed to balance the estimation robustness and accuracy dynamically.An online noise estimator is proposed based on the Sage-Husa estimating technique to estimate the 1st order and 2nd order momentum of the time-varying noise dynamically.An intelligent tracking algorithm for a time-varying non-Gaussian environment is proposed, namely the adaptive particle filter (APF). The proposed algorithm guarantees the convergence of underwater target tracking accuracy.Considering all the above-mentioned challenges and in order to track the underwater uncooperative target in a 3D real-time scenario under the time-varying non-Gaussian environment by distributed passive submerged buoys, this paper firstly proposed a real-time optimal topology-forming method of the distributed measurement system that balances the tracking robustness and accuracy. Then, a robust algorithm that combined the advantages of both the Bayesian posterior estimation techniques and the online noise estimation techniques is designed. The contributions can be summarized as follows:The rest of this paper is organized as follows. In In this section, the kinematics model of the underwater target and the measurement model of the distributed buoys system are proposed. Assuming the underwater uncooperative target performs a constant velocity (CV) mode, the underwater uncooperative target usually remains at the same speed to save energy. In addition, the measurements of the distributed underwater buoys are the passive angle-only information which can be divided into the azimuth angle information and the elevation angle information. The following section gives the details of the above-mentioned models, respectively.The main motive of the 3D tracking problem considered in this work is to estimate the position and velocity of an underwater uncooperative target with CV motion mode using noise-corrupted angle-only measurements from the passive distributed underwater buoys system. Consider  to ref. , the kinIt should be noted that, unlike many researches supposing te noise ,20,21,22The measurement model of the i-th buoy at tracking time k.Assuming the tracking procedure is performing in the free 3D space ) and the system state (From Equations (4)–(6) and the time-updated state The maximum likelihood estimation-based underwater target tracking problem can be represented as maximizing the likelihood function Considering Hence, the FIM of the system formed by Equations (1) and (5) can be represented as:According to ref. , the minAdditionally, the CRLB can be represented by the inverse of the FIM, namely:Consequently, by minimizing the value computed by the above Equation (13), two out of three buoys of the distributed measuring system can be selected and the optimal topology based on estimating accuracy can be determined, namely:m is the discrete tracking step during the overall tracking procedure, Observability analysis of a nonlinear tracking system is the foundation of making reliable tracking results. From Equations (1) and (4), it can be found that the system to be analyzed is highly nonlinear. According to ref. , the GraAccording to the linear observability theory, the states can be estimated from the measurements at any biased initial guesses when a linear system is fully observable. Hence, in order to make the tracking procedure reliable and robust, it is essential to guarantee that the tracking system is fully observable especially when the target to be tracked is uncooperative, which means that the tracking process must have the ability of convergence at any random initial guesses. However, unlike the linear system, the theory of determining whether an arbitrarily nonlinear system is fully observable is still an open question. From Equation (15), it can be found that the OG matrix is time-varying which leads to the observability of a nonlinear system having local characteristics.According to the observability analysis criterion proposed in ref. , a nonlik.Since the conditional number can reflect whether a matrix is “healthy”, the index of observable degree is introduced to reveal whether an OG matrix is better under a certain topology of the distributed buoys. The observable degree is represented as follows:From the matrix analysis theory, the OG matrix is more robust to the disturbances when the value of According to the above analysis, if the tracking system is locally weak observable at tracking time k, the optimal topology design criterion based on robust tracking aspect can be represented as:In order to track the underwater uncooperative target as accurate as possible and consume the least acoustic communicating resources, an unity objective function considering both the tracking accuracy and the communication usage is designed as the following:Hence, by defining the adjust parameter From Equations (1) and (4), it can be found that the 3D passive tracking process is a high nonlinear problem with uncertain noise. Unlike many researches which regard the noise as the Gaussian white noise, we model the process noise and the measurement noise as the time-varying non-Gaussian noise since this assumption is closer to the reality. Hence, many of the existing nonlinear estimating algorithms cannot be directly adopted. To make the time-varying noise estimated online, several adaptive techniques have been developed ,28. HoweThe Sage-Husa online noise estimator is firstly introduced by ref.  for lineFrom Equation (21) to Equation (26), it can be found that the classic nonlinear Sage-Husa online noise estimator must utilize all the smooth values of the state within a certain tracking period, which leads to the total process hard to compute. According to ref. , the recFor time-varying noise, the latest measurement should be given more attention than the historical data. Therefore, the fading factor It can be found in Equation (36) that, when the index Since the passive underwater target tracking system is highly nonlinear and the disturbances are time-varying and non-Gaussian, the classic nonlinear estimators cannot be utilized. Here, we introduce the APF to make reliable estimations under the time-varying non-Gaussian environment.1.InitializationThe designed APF united the modified Sage-Husa online noise-estimating technique and the PF tracking technique to track an uncooperative underwater target by a certain topology of the distributed buoys system. Depending on the nonlinear tracking system represented by Equations (1) and (5), the APF can be divided into the following steps:2.Time updateAt tracking time 3.Measurement noise online estimationAccording to Equations (1) and (32), the time updated by every state particle under the time-varying non-Gaussian environment can be represented as:According to Equations (33) and (35), the measurement noise at time 4.Weight calculationFrom Equations (38)–(41), the time-varying non-Gaussian measurement noise According to the theory of PF, the weight of every particle can be represented as:According to ref. , q(xki∣xFrom Equation (43), the weight of every particle can be computed by 5.Measurement UpdateFrom Equations (43) and (44), the weight of 6.ResamplingAccording to Equations (37) and (45), the measurement updated state based on Monte Carlo theory can be computed as:In order to avoid the particle degradation phenomenon and make the whole tracking process robust, the resampling method is adopted to generate new particles based on the weights calculated by Equation (45). The principle of the resampling method is to duplicate the more likely particles and cut off the less likely ones, which will lead to some same particles in the new particle system . Before 7.Process noise online estimationIf 8.Time propagationThe 1-st order momentum of the time-varying non-Gaussian noise at the current tracking time can be updated online by the modified Sage-Husa online noise estimator as:The tracking time will be propagated to Three-dimensional passive underwater target tracking algorithm for the time-varying non-Gaussian environment by distributed underwater buoysAlgorithm 1: 3D passive underwater target tracking algorithm for the time-varying non-Gaussian environment by distributed underwater buoys1. Optimal topology determination1 Use every two out of three measurements from the buoys to form the observable measurements sets as 2 Calculate the accuracy index 3 Calculate the robust index 4 Use the results from step 1 and 2 to calculate the overall index 5 With the preset index 2. Tracking the underwater uncooperative target by APF under the time-varying non-Gaussian environment1 Based on the determined sets of measurements at tracking time 2 Particles are time-updated by Equation (37);3 Online noise estimation by Equation (39);4 New weights are calculated by Equation (45);5 Resampling procedure are checked and performed by Equation (47) and resampling method introduced by ref. [6 Estimate the current process noise by Equation (48);7 Time propagation to run the whole algorithm at tracking time  by ref. ;6 EstimaConsidering both the optimal topology design criterion by In this section, comprehensive simulations are made to verify the proposed 3D underwater uncooperative target passive tracking algorithm. In addition, by setting the reference coordination, the coordinates of every buoy of the distributed system and the target are represented in the reference coordination. The detailed configuration of the distributed buoys is set out in In the simulations, the underwater target is supposed to perform in the CV motion mode with the actual initial state as It is also assumed that all the underwater buoys have the same stochastic process of the time-varying non-Gaussian measurement noise and can be modeled as:All the simulations in this paper are performed using MATLAB R2019b on the computer with the Microsoft Windows 10 system and the computer is configured with Intel(R) Core (TM) i7-9700k CPU @3.2 GHz. The simulation results are the average of 50 Monte Carlo experiments with the particle number of 2000 for every simulation. According to ref. , the totIn this subsection, the optimal topology design algorithm proposed by In the subsection, the APF algorithm proposed by From the simulation results, the estimating accuracies are enhanced by 92.4% and 83.4% by the proposed APF for The computational complexity of the APF, AEKF, and traditional PF are shown in The 3D passive tracking of the underwater uncooperative target using distributed underwater buoys for a time-varying non-Gaussian environment is studied in this paper. Firstly, for the sake of accurate tracking and minimum underwater acoustic resource utilization, the optimal topology of the distributed underwater buoys system is designed based on both accuracy theory and observability analysis. Then, based on the determined optimal topology of the distributed underwater buoys at current tracking time, an APF is proposed to tackle the nonlinear underwater target tracking problem with time-varying non-Gaussian noise. From the simulation results, the following conclusions can be drawn. Firstly, the optimal topology design method introduced by this paper can select proper sets of buoys dynamically and can provide the best estimations among all the possible configurations of the distributed buoys. Secondly, by adopting the online noise estimation technique, the APF has significantly higher accuracies compared to the AEKF and the traditional PF with very little extra computational load. It is believed that the APF proposed by this paper has great potential in real-time 3D underwater target passive tracking missions.