State identification for a class of uncertain switched systems by differential neural networks

This paper presents a non-parametric identification scheme for a class of uncertain switched nonlinear systems based on continuous-time neural networks. This scheme is based on a continuous neural network identifier. This adaptive identifier guaranteed the convergence of the identification errors to a small vicinity of the origin. The convergence of the identification error was determined by the Lyapunov theory supported by a practical stability variation for switched systems. The same stability analysis generated the learning laws that adjust the identifier structure. The upper bound of the convergence region was characterized in terms of uncertainties and noises affecting the switched system. A second finite-time convergence learning law was also developed to describe an alternative way of forcing the identification error's stability. The study presented in this paper described a formal technique for analysing the application of adaptive identifiers based on continuous neural networks for uncertain switched systems. The identifier was tested for two basic problems: a simple mechanical system and a switched representation of the human gait model. In both cases, accurate results for the identification problem were achieved.

Substability and Substabilization: Control of Subfully Actuated Systems

The region of attraction of the Lyapunov asymptotic stability at the origin is defined to be a ball centered at the origin, which is clearly simply connected and also bounded in the local case. In this article, the concept of substability is proposed, which allows "gaps" and "holes" in the region of attraction of the Lyapunov exponential stability, and also allows the origin to be a boundary point of the region of attraction. The concept is meaningful and useful in many practical applications, but is particularly made so with the control of single- and multi-order subfully actuated systems. Specifically, the singular set of a sub-FAS is first defined, and a substabilizing controller is then designed such that the closed-loop system is a constant linear one with an arbitrarily assignable eigen-polynomial, but with its initial values restricted within a so-called region of exponential attraction (ROEA). Consequently, the substabilizing controller drives all the state trajectories starting from the ROEA exponentially to the origin. The introduced concept of substabilization is of great importance because, on the one side, it is often practically useful since the designed ROEA is often large enough for certain applications, while on the other side, Lyapunov asymptotically stabilizing controllers can be further easily established based on substabilization. Several examples are given to demonstrate the proposed theories.

Bipedal walking and push recovery with a stepping strategy based on time-projection control

In this paper, we present a simple control framework for online push recovery on biped robots with dynamic stepping properties. Owing to relatively heavy legs in our humanoid robot COMAN, we use a linear model called 3LP, which is composed of three pendulums to take swing and torso dynamics into account. Based on 3LP equations, we formulate discrete linear quadratic regulator (LQR) controllers and use a particular time-projection method to adjust footstep locations during the motion continuously. This process, which is based on pelvis and swing foot tracking errors, naturally considers swing dynamics and leads to leg-retraction properties. Suggested adjustments are added to the Cartesian 3LP gaits and converted into joint-space trajectories through inverse kinematics. Fixed and adaptive foot lift strategies are also used to ensure enough ground clearance in perturbed walking conditions. The proposed control architecture is robust, yet uses very simple state estimation and basic position tracking. We rely on series elastic actuators to absorb impacts while introducing simple laws to compensate for spring compressions. Extensive experiments on COMAN (real) and Atlas (simulated) robots demonstrate the functionality of different control blocks and prove the effectiveness of time-projection in extreme push recovery scenarios. We also show self-produced and emergent walking gaits when the robot is subject to continuous dragging forces. These gaits feature dynamic walking robustness with minimal reliance on the ankles and avoiding any active zero moment point (ZMP) control. The proposed architecture is therefore generic, computationally very fast and yet with no critical parameter to tune.

Design of active disturbance rejection controller for compass-like biped walking

This article proposes an active disturbance rejection controller design scheme to stabilize the unstable limit cycle of a compass-like biped robot. The idea of transverse coordinate transformation is applied to form the control system based on angular momentum. With the linearization approximation, the limit cycle stabilization problem is simplified into the stabilization of an linear time-invariant system, which is known as transverse coordinate control. In order to solve the problem of poor adaptability caused by linearization approximation, we design an active disturbance rejection controller in the form of a serial system. With the active disturbance rejection controller, the system error can be estimated by extended state observer and compensated by nonlinear state error feedback, and the unstable limit cycle can be stabilized. The numerical simulations show that the control law enhances the performance of transverse coordinate control.

Dynamically and Biologically Inspired Legged Locomotion: A Review

[abstFig src='/00290003/01.jpg' width='300' text='Passive dynamic walking: RW03 and Jenkka III' ] Legged locomotion, such as walking, running, turning, and jumping depends strongly on the dynamics and the biological characteristics of the body involved. Gait patterns and energy efficiency, for instance, are known to be greatly affected, not only by travel speed and ground contact conditions but also by body structure such as joint stiffness and coordination, and foot sole shape. To understand legged locomotion principles, we must elucidate how the body’s dynamic and biological characteristics affect locomotion. Efforts should also be made to incorporate these characteristics inventively in order to improve locomotion performance with regard to robustness, adaptability, and efficiency, which realize more refined legged locomotion. For this special issue, we invited our readers to submit papers with approaches to achieving legged locomotion based on dynamic and biological characteristics and studies investigating the effects of these characteristics. In this paper, we review studies on dynamically and biologically inspired legged locomotion.

Asymmetric Swing-Leg Motions for Speed-Up of Biped Walking

[abstFig src='/00290003/04.jpg' width='120' text='Stick diagram of limit cycle walking with asymmetric swing-leg motion' ] This study presents a novel swing-leg control strategy for speed-up of biped robot walking. The trajectory of tip of the swing-leg is asymmetric at the center line of the torso in the sagittal plane for this process. A methodology is proposed that enables robots to achieve the synchronized asymmetric swing-leg motions with the stance-leg angle to accelerate their walking speed. The effectiveness of the proposed method was simulated using numerical methods.

3LP: A linear 3D-walking model including torso and swing dynamics

In this paper, we present a new mechanical model for biped locomotion, composed of three linear pendulums (one per leg and one for the whole upper body) to describe stance, swing and torso dynamics. In addition to a double support phase, this model has different actuation possibilities in the swing hip and stance ankle which produce a broad range of walking gaits. Without the need for numerical time-integration, closed form solutions help to find periodic gaits which could simply scale in certain dimensions to modulate the motion online. Thanks to linearity properties, the proposed model can potentially provide a computationally fast platform for model predictive controllers to predict the future and consider meaningful inequality constraints to ensure feasibility of the motion. Such a property comes from describing dynamics with joint torques directly and therefore, reflecting hardware limitations more precisely, even in the very abstract template space. The proposed model produces human-like torque and ground reaction force profiles, and thus, compared to point-mass models, it is more promising for the generation of dynamic walking trajectories. Despite being linear and lacking many features of human walking like center of mass excursion, knee flexion and ground clearance, we show that the proposed model can explain one of the main optimality trends in human walking, i.e. the nonlinear speed-frequency relationship. In this paper, we mainly focus on describing the model and its capabilities, comparing it with human data and calculating optimal human gait variables. Setting up control problems and advanced biomechanical analysis remains for future works.

A Switching Control Strategy for Energy Efficient Walking on Uneven Surfaces

This paper studies the problem of achieving an energy efficient walking on an uneven surface for a compass-like biped robot with flat feet. To this end, reference walking gaits, which consist of two phases including the static foot phase and the foot rotation phase, are designed on several typical slopes via minimizing the dimensionless specific mechanical cost of transport. Moreover, for other slopes, a simple transformation method is proposed to generate interim reference walking gaits from the reference ones on those typical slopes. Then an input–output feedback linearization approach is considered to design a tracking control law in the static foot phase and a time-scaling approach is adopted to construct a tracking control law in the foot rotation phase as the dynamics in this phase is underactuated. By switching the control law at different phases and switching the reference walking gaits on different slopes, a compass-like robot can achieve energy efficient walking on uneven surfaces. The validity of our method is illustrated by numerical simulations.

Feedback control for compass-like biped robot with underactuated ankles using transverse coordinate transformation

This paper deals with the walking control problem of a compass-like biped robot with underactuated ankles in the framework of hybrid control systems. The compass-like biped robot is equipped with a constraint mechanism to lock the hip angle when the swing leg retracts. First, based on the Poincare return map, a limit cycle gait is obtained, and the stability of the gait is also checked. Then, a method based on transverse coordinate transformation is introduced to transform the problem of tracking a desired limit cycle into the stabilization problem of a linear time-invariant impulsive system. A feedback control design for stabilizing the walking gait is then presented. Finally, comparisons to several existing approaches for the similar model are provided to demonstrate the advantages of our proposed approach.

Gait generation via unified learning optimal control of Hamiltonian systems

This paper proposes a repetitive control type optimal gait generation framework by executing learning control and parameter tuning. We propose a learning optimal control method of Hamiltonian systems unifying iterative learning control (ILC) and iterative feedback tuning (IFT). It allows one to simultaneously obtain an optimal feedforward input and tuning parameter for a plant system, which minimizes a given cost function. In the proposed method, a virtual constraint by a potential energy prevents a biped robot from falling. The strength of the constraint is automatically mitigated by the IFT part of the proposed method, according to the progress of trajectory learning by the ILC part.

GAIT GENERATION AND OPTIMIZATION USING THE ESTIMATION OF DISTRIBUTION ALGORITHM FOR TEENSIZE HUMANOID SOCCER ROBOT RESr-1

This paper gives an overview of locomotion planning and control of a TeenSize humanoid soccer robot, Robo-Erectus Senior (RESr-1), which has been developed as an experimental platform for human–robot interaction and cooperative research in general and robotics soccer games in particular. The locomotion planning and control, along with an introduction of hierarchical control architecture, vision-based behavior and its application in the Humanoid TeenSize soccer challenge, are elaborated. The Estimation of Distribution Algorithm (EDA) is used in locomotion generation and optimization to achieves dynamically stable walk and a powerful kick. By setting different objective functions, smooth walking and powerful kicking can be generated quickly. RESr-1 made its debut at RoboCup 2007, and got fourth place in the Humanoid TeenSize penalty kick competition. In addition, some experimental results on RESr-1's walking, tracking and kicking are presented.

A BIPED WITH A MOVING TORSO

The moving torso plays an important role in the dynamics of bipeds like human beings, the exploitation of which is the essential focus of this paper. A design is presented where the torso is actuated to make the biped walk with the required step-length while allowing the legs to move passively. A periodic response excitation is achieved and the motion of the torso is optimized with respect to the external energy input. A working model of the biped is designed and built in which only the torso is actuated and the legs are passive. This laboratory model is used to test and validate the analytical solutions.

A novel dynamic walker with heel, ankle, and toe rocker motions

This paper proposes a novel dynamic walker capable of walking with heel, ankle, and toe rocker motions. The heel and toe rocker motions are obtained by using inelastic stoppers between leg and foot, which limit the range of rotation of the foot about the ankle joint. A generalized set of equations of motion and associated transition equations applicable for multiple foot segments is derived. Passive dynamic walking is studied with equal heel and toe strike angles for the case of symmetric foot walking. It is shown that by including the ankle joint, low-speed walking is made possible. The energy efficiency of the proposed walker is studied theoretically and through numerical simulations. Finally, three different underactuated modes of active walking that do not require toe and heel actuation are presented. In order to implement these modes of walking, the proposed walker can be constructed with little modification from an existing flat-foot walker that uses ankle rocker motion alone. Results show that substantial benefits can be obtained in efficiency and stability compared to point/flat-foot walker of the same leg length and mass distribution.

Stable dynamic walking over uneven terrain

We propose a constructive control design for stabilization of non-periodic trajectories of underactuated robots. An important example of such a system is an underactuated “dynamic walking” biped robot traversing rough or uneven terrain. The stabilization problem is inherently challenging due to the nonlinearity, open-loop instability, hybrid (impact) dynamics, and target motions which are not known in advance. The proposed technique is to compute a transverse linearization about the desired motion: a linear impulsive system which locally represents “transversal” dynamics about a target trajectory. This system is then exponentially stabilized using a modified receding-horizon control design, providing exponential orbital stability of the target trajectory of the original nonlinear system. The proposed method is experimentally verified using a compass-gait walker: a two-degree-of-freedom biped with hip actuation but pointed stilt-like feet. The technique is, however, very general and can be applied to a wide variety of hybrid nonlinear systems.

Efficient walking with optimization for a planar biped walker with a torso by hip actuators and springs

This paper focuses on the use of passive dynamics to achieve efficient walking with simple mechanisms. A torso is added to a biped walker; and hip actuators, instead of ankle actuators, are used. A numerical approach is used to find the optimal control trajectories. A comparison between the cost functions of simple feedback control and optimal control is presented. Next, springs are added to the biped walking model at the hip joints to demonstrate the advantage of hip springs in terms of energy cost and ground conditions. The comparison between the torque costs with and without hip springs indicates that hip springs reduce the torque cost, particularly at a high walking speed.

Energy-efficient gait generation for biped robot based on the passive inverted pendulum model

From the viewpoint of the system's mechanical energy, the passive inverted pendulum model (PIPM) is proposed for the generation of more energy-efficient biped gait pattern. The generated walking pattern, based on the PIPM, enables the fully actuated biped robots to closely mimic the behavior of stable passive walking, so that it can have good energy-efficiency, which is the inherent advantage of the passive system. Furthermore, the pattern generation method is extended to any desired terrain as well. As for SHR-1, the first-generation biped robot of Shanghai Jiao Tong University, gait synthesis is clarified in detail. Finally, the walking experiments are carried out on SHR-1, and the effectiveness of the proposed pattern generation method is confirmed.

Outdoor Environments Walking by Biped Passive Dynamic Walker with Constraint Mechanism

This paper verified the stability of passive dynamic bipedal walking indoors and outdoors using a foot shape enhancing walking stability and implementing control constraint. Outdoor walking is difficult for walkers due to the unpredictable aspects of loose slopes, bumpy surfaces, and uneven friction on roads.

Stabilizing Passive Dynamic Walk Under Wide Range of Environments by Constraint Mechanism Fitted to Sole of Foot

This paper proposes a foot shape design to enhance the stability of passive dynamic walk by constraining fall down phenomenon in both sagittal and lateral planes. We focus on excessive side-to-side and forward leg swinging that causes a passive dynamic biped walker to fall over. Geometrical analysis showed that stability under a wide range of slope inclinations is achievable by limiting the swinging leg spatially to within a certain angle. Such a limit, or constraint, on swinging effectively prevents falling down on the lateral plane, while stable walking is maintained on the sagittal plane by constraining forward movement using a sharp edge at the head of a foot. We propose a foot prototype realizing these two constraints using a three-dimensional (3D) sole design and show that the proposed constraint is more effective for walking than an arctic foot shape. In verification experiments, the constraint stabilized the passive dynamic walker in a wide range of outdoor environments.

Origami Folding by a Robotic Hand

Dexterous manipulation by a robotic hand is a difficult problem involving (1) how to design a robot that gives the capability to achieve the task and (2) how to control the designed robot to actually conduct the task. In this paper, we take a task-oriented approach called “task capture” to construct a dexterous robot hand system. Before designing the robot, we analyze how a human being conducts the task, focusing on how the target object is manipulated rather than trying to imitate human finger movement. Based on the captured task, we design a robot that manipulates an object in the same way as a human being may do, with a mechanism as simple as possible, rather than concerning human appearance. As a target task, we choose origami paper folding. We first analyze the difficulty of origami manipulation and design a robotic mechanism that folds an origami form, the Tadpole, based on the proposed approach. The proof of how well the “task capture” approach works is demonstrated by a simple robot we developed, which folds a Tadpole consecutively.

Reinforcement learning for a biped robot based on a CPG-actor-critic method

Animals' rhythmic movements, such as locomotion, are considered to be controlled by neural circuits called central pattern generators (CPGs), which generate oscillatory signals. Motivated by this biological mechanism, studies have been conducted on the rhythmic movements controlled by CPG. As an autonomous learning framework for a CPG controller, we propose in this article a reinforcement learning method we call the "CPG-actor-critic" method. This method introduces a new architecture to the actor, and its training is roughly based on a stochastic policy gradient algorithm presented recently. We apply this method to an automatic acquisition problem of control for a biped robot. Computer simulations show that training of the CPG can be successfully performed by our method, thus allowing the biped robot to not only walk stably but also adapt to environmental changes.