Morphological properties of mass-spring networks for optimal locomotion learning

Robots have proven very useful in automating industrial processes. Their rigid components and powerful actuators, however, render them unsafe or unfit to work in normal human environments such as schools or hospitals. Robots made of compliant, softer materials may offer a valid alternative. Yet, the dynamics of these compliant robots are much more complicated compared to normal rigid robots of which all components can be accurately controlled. It is often claimed that, by using the concept of morphological computation, the dynamical complexity can become a strength. On the one hand, the use of flexible materials can lead to higher power efficiency and more fluent and robust motions. On the other hand, using embodiment in a closed-loop controller, part of the control task itself can be outsourced to the body dynamics. This can significantly simplify the additional resources required for locomotion control. To this goal, a first step consists in an exploration of the trade-offs between morphology, efficiency of locomotion, and the ability of a mechanical body to serve as a computational resource. In this work, we use a detailed dynamical model of a Mass–Spring–Damper (MSD) network to study these trade-offs. We first investigate the influence of the network size and compliance on locomotion quality and energy efficiency by optimizing an external open-loop controller using evolutionary algorithms. We find that larger networks can lead to more stable gaits and that the system’s optimal compliance to maximize the traveled distance is directly linked to the desired frequency of locomotion. In the last set of experiments, the suitability of MSD bodies for being used in a closed loop is also investigated. Since maximally efficient actuator signals are clearly related to the natural body dynamics, in a sense, the body is tailored for the task of contributing to its own control. Using the same simulation platform, we therefore study how the network states can be successfully used to create a feedback signal and how its accuracy is linked to the body size

Synchronization Control for Discrete-Time-Delayed Dynamical Networks with Switching Topology under Actuator Saturations

10.13039/501100001809-National Natural Science Foundation of China (Grant Number: 61773156, 61873148, 61673141 and 61933007); 10.13039/501100018551-Program for Science and Technology Innovation Talents in the Universities of Henan Province of China (Grant Number: 19HASTIT028); 10.13039/501100010029-Research Fund for the Taishan Scholar Project of Shandong Province of China; 10.13039/501100000288-Royal Society of the U.K.; 10.13039/100005156-Alexander von Humboldt Foundation of Germany

Sampled-Data Control for Singular Neutral System

This study is concerned with the ∞ control problem for singular neutral system based on sampled-data. By input delay approach and a composite state-derivative control law, the singular system is turned into a singular neutral system with time-varying delay. Less conservative result is derived for the resultant system by incorporating the delay decomposition technique, Wirtinger-based integral inequality, and an augmented Lyapunov-Krasovskii functional. Sufficient conditions are derived to guarantee that the resulting system is regular, impulse-free, and asymptotically stable with prescribed ∞ performance. Then, the ∞ sampled-data controller is designed by means of linear matrix inequalities. Finally, two simulation results have shown that the proposed method is effective

H

This study is concerned with the H∞ control problem for singular neutral system based on sampled-data. By input delay approach and a composite state-derivative control law, the singular system is turned into a singular neutral system with time-varying delay. Less conservative result is derived for the resultant system by incorporating the delay decomposition technique, Wirtinger-based integral inequality, and an augmented Lyapunov-Krasovskii functional. Sufficient conditions are derived to guarantee that the resulting system is regular, impulse-free, and asymptotically stable with prescribed H∞ performance. Then, the H∞ sampled-data controller is designed by means of linear matrix inequalities. Finally, two simulation results have shown that the proposed method is effective

Sincronização de sistemas lur’e com controle amostrado

Este trabalho apresenta soluções para o problema de sincronização de sistemas Lur’e mestre-escravo através de uma lei de controle. Inicialmente, o caso de sistemas em tempo discreto é formulado com um controle saturante. Em seguida, no caso de sistemas em tempo contínuo, considera-se um controle a partir de dados amostrados (sampled-data control). A sincronização é abordada como um problema de estabilização do erro entre os estados dos sistemas mestre e escravo, e o controle projetado através de um problema de otimização. No caso de sistemas em tempo discreto, a partir de uma função de Lyapunov quadrática e condições de setor, desigualdades matriciais lineares (LMI) são obtidas com o objetivo de garantir que a diferença entre os estados mestre e escravo convirja assintoticamente para zero na ocorrência da saturação do sinal de controle. Condições de estabilidade seguindo uma modelagem por funções zona-morta também são obtidas, no caso particular onde a não linearidade Lur’e é descrita por uma função linear por partes. Um problema de otimização para o projeto do controlador é proposto com o objetivo de maximizar um conjunto de erros iniciais admissíveis, para os quais a sincronização é garantida. Na abordagem via controle amostrado são considerados uma função de Lyapunov do tipo Lur’e e um funcional looped para a obtenção de condições LMI que garantam a sincronização de sistemas mestre-escravo sempre que o intervalo entre duas amostras respeitar um determinado limite. Um problema de otimização que visa maximizar o intervalo admissível entre duas amostras consecutivas é apresentado. Os resultados das metodologias propostas são avaliados através de exemplos numéricos.This work presents solutions to the synchronization problem of master-slave Lur’e systems via a control law. Initially, the discrete-time systems case is formulated under a saturating control. Then, in the continuous-time systems case, a sampled-data control is considered. Synchronization is addressed as a problem of stabilization of the error between the states of the master and slave systems and the control is designed via an optimization problem. In the discrete-time systems case, from a quadratic Lyapunov function and sector conditions, linear matrix inequalities (LMI) are derived with the objective of ensuring that the difference between the master and slave states converges asymptotically to zero under the saturation of the control signal. Stability conditions based on a dead zone function modeling are also obtained, in the particular case where the Lur’e nonlinearity is described by a piecewise-linear function. An optimization problem for the controller design is proposed in order to maximize a set of admissible initial errors for which the synchronization is guaranteed. In the sampled-data control approach, a Lur’e-type Lyapunov function and a loopedfunctional are considered to derive LMI conditions that guarantee the synchronization of master-slave systems whenever the interval between two samples respects some bounds. An optimization problem that aims to maximize the allowable interval between two consecutive samples is presented. The results of the proposed methodologies are evaluated with numerical examples

Robust efficiency and actuator saturation explain healthy heart rate control and variability

The correlation of healthy states with heart rate variability (HRV) using time series analyses is well documented. Whereas these studies note the accepted proximal role of autonomic nervous system balance in HRV patterns, the responsible deeper physiological, clinically relevant mechanisms have not been fully explained. Using mathematical tools from control theory, we combine mechanistic models of basic physiology with experimental exercise data from healthy human subjects to explain causal relationships among states of stress vs. health, HR control, and HRV, and more importantly, the physiologic requirements and constraints underlying these relationships. Nonlinear dynamics play an important explanatory role––most fundamentally in the actuator saturations arising from unavoidable tradeoffs in robust homeostasis and metabolic efficiency. These results are grounded in domain-specific mechanisms, tradeoffs, and constraints, but they also illustrate important, universal properties of complex systems. We show that the study of complex biological phenomena like HRV requires a framework which facilitates inclusion of diverse domain specifics (e.g., due to physiology, evolution, and measurement technology) in addition to general theories of efficiency, robustness, feedback, dynamics, and supporting mathematical tools

Guidance Law and Neural Control for Hypersonic Missile to Track Targets

Hypersonic technology plays an important role in prompt global strike. Because the flight dynamics of a hypersonic vehicle is nonlinear, uncertain, and highly coupled, the controller design is challenging, especially to design its guidance and control law during the attack of a maneuvering target. In this paper, the sliding mode control (SMC) method is used to develop the guidance law from which the desired flight path angle is derived. With the desired information as control command, the adaptive neural control in discrete time is investigated ingeniously for the longitudinal dynamics of the hypersonic missile. The proposed guidance and control laws are validated by simulation of a hypersonic missile against a maneuvering target. It is demonstrated that the scheme has good robustness and high accuracy to attack a maneuvering target in the presence of external disturbance and missile model uncertainty

Comparative evaluation of approaches in T.4.1-4.3 and working definition of adaptive module

The goal of this deliverable is two-fold: (1) to present and compare different approaches towards learning and encoding movements us- ing dynamical systems that have been developed by the AMARSi partners (in the past during the first 6 months of the project), and (2) to analyze their suitability to be used as adaptive modules, i.e. as building blocks for the complete architecture that will be devel- oped in the project. The document presents a total of eight approaches, in two groups: modules for discrete movements (i.e. with a clear goal where the movement stops) and for rhythmic movements (i.e. which exhibit periodicity). The basic formulation of each approach is presented together with some illustrative simulation results. Key character- istics such as the type of dynamical behavior, learning algorithm, generalization properties, stability analysis are then discussed for each approach. We then make a comparative analysis of the different approaches by comparing these characteristics and discussing their suitability for the AMARSi project