Pseudo-passive dynamic walkers designed by coupled evolution of the controller and morphology

In this paper we investigated the morphology and controller of biped robots. We viewed them as design components that together can induce dynamically stable bipedal locomotion. We conducted coupled evolution of the morphology and controller of a biped robot, consisting of nine links and eight joints, actuated by oscillators without sensor feedback in three-dimensional simulation. As a result, both pseudo-passive dynamic walkers and active-control walkers emerged, but the pseudo-passive dynamic walkers showed more dynamic stability than the active-control walkers. This is because compliant components in morphology function as noise filters and passive oscillators. Analysis on this latter class of walkers revealed that this was achieved by two novel functions: self-stabilization and self-regulation. Because these functions were handled by the passive dynamics induced in the robot morphology, due to its compliance, we concluded that a computational trade-off between the controller and morphology occurs in these devices. Finally, we have concluded that appropriate compliance is a key to achieving dynamical stability during locomotion.     

仿生机器人运动步态控制:强化学习方法综述

仿生机器人是一类典型的多关节非线性欠驱动系统，其步态控制是一个非常具有挑战性的问题。对于该问题，传统的控制和规划方法需要针对具体的运动任务进行专门设计，需要耗费大量时间和精力，而且所设计出来的控制器往往没有通用性。基于数据驱动的强化学习方法能对不同的任务进行自主学习，且对不同的机器人和运动任务具有良好的通用性。因此，近年来这种基于强化学习的方法在仿生机器人运动步态控制方面获得了不少应用。针对这方面的研究，本文从问题形式化、策略表示方法和策略学习方法3个方面对现有的研究情况进行了分析和总结，总结了强化学习应用于仿生机器人步态控制中尚待解决的问题，并指出了后续的发展方向。     

Recurrent Motion Refiner for Locomotion Stitching

Stitching different character motions is one of the most commonly used techniques as it allows the user to make new animations that fit one's purpose from pieces of motion. However, current motion stitching methods often produce unnatural motion with foot sliding artefacts, depending on the performance of the interpolation. In this paper, we propose a novel motion stitching technique based on a recurrent motion refiner (RMR) that connects discontinuous locomotions into a single natural locomotion. Our model receives different locomotions as input, in which the root of the last pose of the previous motion and that of the first pose of the next motion are aligned. During runtime, the model slides through the sequence, editing frames window by window to output a smoothly connected animation. Our model consists of a two-layer recurrent network that comes between a simple encoder and decoder. To train this network, we created a sufficient number of paired data with a newly designed data generation. This process employs a K-nearest neighbour search that explores a predefined motion database to create the corresponding input to the ground truth. Once trained, the suggested model can connect various lengths of locomotion sequences into a single natural locomotion.     

Swing-Leg Retraction for Limit Cycle Walkers Improves Disturbance Rejection

Limit cycle walkers are bipeds that exhibit a stable cyclic gait without requiring local controllability at all times during gait. A well-known example of limit cycle walking is McGeer's ldquopassive dynamic walking,rdquo but the concept expands to actuated bipeds as involved in this study. One of the stabilizing effects in limit cycle walkers is the dissipation of energy that occurs when the swing foot hits the ground. We hypothesize that this effect can be enhanced with a negative relation between the step length and step time. This relation is implemented through an open-loop strategy called swing-leg retraction; a predefined time trajectory for the swing leg makes the swing leg move backwards just prior to foot impact. In this paper, we study the effect of swing-leg retraction through three bipeds; a simple point mass simulation model, a realistic simulation model, and a physical prototype. Their stability is analyzed using Floquet multipliers, followed by an evaluation of how well disturbances are handled using the Gait Sensitivity Norm. We find that mild swing-leg retraction is optimal for the disturbance rejection of a limit cycle walker, as it results in a system response that is close to critically damped, rejecting the disturbance in the fewest steps. Slower retraction results in an overdamped response, characterized by a positive dominant Floquet multiplier. Likewise, faster retraction results in an underdamped response, characterized by a negative Floquet multiplier.     

Self-reconfigurable M-TRAN structures and walker generation

The M-TRAN is a modular robot capable of both three-dimensional self-reconfiguration and whole body locomotion. Introducing regularity in allowed structures reduced difficulties of its reconfiguration problems. Several locomotion patterns in various structures were designed systematically using a CPG controller model and GA optimization. Then they were verified by experimentation. Results showed a feasible scenario of operation with multiple M-TRAN modules, which is presented herein, including metamorphosis of a regular structure, generation of walkers from the structure, walker locomotion, and reassembling of walkers to the structure.     

Generation of bipedal walking through interactions among the robot dynamics,the oscillator dynamics,and the environment: Stability characteristics of a five-link planar biped robot

We previously developed a locomotion control system for a biped robot using nonlinear oscillators and verified the performance of this system in order to establish adaptive walking through the interactions among the robot dynamics, the oscillator dynamics, and the environment. In order to clarify these mechanisms, we investigate the stability characteristics of walking using a five-link planar biped robot with a torso and knee joints that has an internal oscillator with a stable limit cycle to generate the joint motions. Herein we conduct numerical simulations and a stability analysis, where we analytically obtain approximate periodic solutions and examine local stability using a Poincaré map. These analyses reveal (1) stability characteristics due to locomotion speed, torso, and knee motion, (2) stability improvement due to the modulation of oscillator states based on phase resetting using foot-contact information, and (3) the optimal parameter in the oscillator dynamics for adequately exploiting the interactions among the robot dynamics, the oscillator dynamics, and the environment in order to increase walking stability. The results of the present study demonstrate the advantage and usefulness of locomotion control using oscillators through mutual interactions.     

On the design and synthesis of limit cycles using switching linear systems

This article deals with the design and synthesis of limit cycles for a class of switched linear systems. This work is motivated by an application in the context of electrical networks, but the methodologies can be applied in other engineering fields as well. Several methods for the design and synthesis of limit cycles are presented. Based on a monodromy matrix associated with a periodically switched system, a design method and two feedback strategies are developed. The first strategy is based on linear feedback design using pole placement. The second strategy is based on the observation that certain state-dependent switching strategies can be implemented by means of a simple nonlinear output feedback controller. Advantages of this latter strategy are not only the ease with which the switching strategy can be implemented, but also the fact that classical techniques may also be used to ascertain the stability of the resulting limit cycle. Our next contribution is the development of a novel frequency domain-based approach to limit cycle design. This approach is based on the observation that the existence of certain limit cycles can be deduced from an infinity of circle criteria generated by a family of periodic systems. By making use of recent results, this observation can be used to develop a one-parameter spectral search to deduce the approximate frequencies of feasible limit cycles. Having selected a frequency of oscillation, one may then make use of the aforementioned nonlinear elements to realise a switching strategy that generates a stable limit cycle with given frequency and amplitude. Examples are given to illustrate the effectiveness of the approaches presented.     

胸鳍推进型机器鱼的CPG 控制及实现

结合仿生游动机理,针对胸鳍推进型机器鱼提出了一种基于中枢模式发生器（CPG）的运动控制方法． 该模型采用一类振荡频率和幅值可以独立控制的非线性微分方程作为其神经元振荡器模型,通过最近相邻耦合的方 式,对n 个这样的神经元振荡器进行耦合,构建了仿生机器鱼的CPG 网络模型．证明了此模型单个神经元振荡器的 极限环的存在性、唯一性及稳定性．在此基础上,通过对胸鳍推进的运动学分析,导出机器人直游、倒游、胸鳍—尾 鳍协调运动等多种模式的运动控制方法．仿真及实验结果验证了此中枢模式发生器模型的可行性与所提控制方法的 有效性．     

Global stability analysis of fuzzy path tracking using frequency response

This paper studies the stability of fuzzy path tracking of autonomous vehicles. This problem lies in the generation of the steering commands for a vehicle to follow a given path autonomously. In this control loop, both the plant and the fuzzy controller are nonlinear. Due to this nonlinearity, complex behavioral phenomena can occur, giving rise to the loss of global stability. The extension of conventional frequency response methods for the stability analysis of the nonlinear fuzzy path-tracking control loop is proposed. Simulation experiments show the validity of the proposed method in three different cases: stable origin and unstable limit cycle, delay-induced Hopf bifurcation, and delay-induced unstable limit cycle.     

AmphiBot I: an amphibious snake-like robot

This article presents a project that aims at constructing a biologically inspired amphibious snake-like robot. The robot is designed to be capable of anguilliform swimming like sea-snakes and lampreys in water and lateral undulatory locomotion like a snake on ground. Both the structure and the controller of the robot are inspired by elongate vertebrates. In particular, the locomotion of the robot is controlled by a central pattern generator (a system of coupled oscillators) that produces travelling waves of oscillations as limit cycle behavior. We present the design considerations behind the robot and its controller. Experiments are carried out to identify the types of travelling waves that optimize speed during lateral undulatory locomotion on ground. In particular, the optimal frequency, amplitude and wavelength are thus identified when the robot is crawling on a particular surface.     

快速刀具伺服系统自抗扰控制的研究与实践

快速刀具伺服系统(fast tool servo, FTS)是实现非圆截面和非轴对称表面零件加工的关键部件. 加工过程中,FTS应克服时变切削力负载和自身参数的非线性, 驱动刀具完成高频高精度跟踪运动. 为了解决FTS的快速精密跟踪控制问题, 根据刀具运动参考轨迹已知的特点, 应用自抗扰控制原理和前馈控制策略, 针对基于剪应力和正应力电磁驱动的两种直线执行机构, 分别设计了采用线性和非线性扩张状态观测器的自抗扰控制器, 并利用传递函数和描述函数方法, 分析了线性控制器的跟踪精度和动态刚度特性, 探讨了非线性控制系统的极限环问题. 两种基于自抗扰控制的快速刀具伺服系统已应用于发动机椭圆截面活塞的精密车削和二维正弦微结构表面的超精密车削,满足了加工需求. 研究与应用结果表明: 自抗扰控制思想独特、算法易于工程实现, 具有很好的工程应用价值.     

Modeling and analysis of passive viscoelastic-legged rimless wheel that generates measurable period of double-limb support

Limit cycle walking including passive-dynamic walkers is generally modeled as a nonlinear hybrid dynamical system with state jumps. The inelastic collision model is usually derived on the assumption that the rear leg leaves the ground immediately after landing of the fore leg. This model is, however, inappropriate in the case of compliant-legged walkers. This paper then reconsiders the traditional collision model and discusses the conditions for transition to double-limb support (DLS) motion, which is not instantaneous through investigations of passive dynamic walking of a viscoelastic-legged rimless wheel. First, we experimentally confirm that measurable period of DLS motion emerges after landing of the fore leg, and develop the corresponding mathematical model. Second, we numerically analyze the fundamental properties of the generated passive-dynamic gaits. Furthermore, we discuss the conditions for transition to DLS motion and specify the computational procedures.     

Intelligent robots as artificial living creatures

This article introduces a multi locomotion robot, MLR III, which has multiple locomotion types, i.e., not only brachiating but also walking. Conventionally we have studied dexterous locomotion robots and their controller design. One is a simplified two-link robot, Brachiator II. This is an example of an underactuated system in which a robot mechanism has more degrees of freedom than actuators. The desired motions are encoded as the output of a target dynamical system inspired by the pendulum-link motion of an apes brachiation. The other is a monkey-type robot, Brachiator III. Brachiator III achieves a dexterous motion using redundant degrees of freedom. The motion is generated in an empirical learning process on an intelligent structure, on which the learning algorithm coordinates some primitive motions to generate the desired motion. MLR III is an extended locomotion robot that has multiple types of locomotions: brachiation, bipedal walking, and quadrupedal walking, similar to a monkey or gorilla. This article introduces the mechanism and controller design for brachiating motion.This work was presented, in part, at the 8th International Symposium on Artificial Life and Robitics, Oita, Japan, January 24–26, 2003     

Analysis of stability in quadratic mean of the limit cycles of nonlinear stochastic systems

Consideration was given to the exponential stability in quadratic mean of the stochastically perturbed limit cycles of the nonlinear systems. An approach was developed using the spectral theory of positive operators for the stability analysis. Within the framework of this approach, a positive operator of stochastic stability is assigned to the limit cycle. The spectral radius of this operator characterizes stability of the limit cycle. An iterative numerical method was proposed for calculation of the spectral radius of the stochastic stability operator, and a theorem about its convergence was proved. The constructive potentialities of the results obtained were demonstrated by the example of bifurcational analysis of the stochastic Ressler system at transition to chaos by multiple duplication of the limit cycle period.     

The frequency-domain analysis of discrete variable structure control and chattering-free criteria

Conventionally, the discrete variable structure control always suffers from the chattering phenomenon. Therefore, in this paper, we shall show that, for the discrete variable structure control, there always exist a limit cycle if the traditional nonlinearity of the sign function is used. This limit cycle behaviour is just the chattering phenomenon in the variable structure control theory. In particular, the frequency of this limit cycle is identical to the Nyquist frequency in the sampling theorem. In addition, a theorem related to the chattering-free design for the multiple-input multiple-output variable structure control is proposed. If the nonlinear function is memoryless and belongs to the sector [0,2), the chattering phenomenon can be eliminated. If the width of the boundary layer is enough, the reaching condition as well as chattering-free design can be attained; otherwise, it will result in the chattering phenomenon.     

Limit cycle computation for describing function approximable nonlinear systems with box‐constrained parametric uncertainties

We propose an algorithm to compute the limit cycle set of uncertain non‐rational nonlinear systems with nonlinear parametric dependencies. The proposed algorithm computes the limit cycles for a wide class of uncertain nonlinear systems, where the transfer function of the linear element and describing function of the nonlinear element need to be only continuous with respect to the parameters and continuously differentiable with respect to the amplitude and frequency of periodic input signal. The proposed algorithm guarantees that the limit cycles are reliably computed to a prescribed accuracy, and that none of the actual limit cycle point is missed out irrespective of the tightness of the prescribed accuracy. Moreover, for a prescribed accuracy, the proposed algorithm computes all the limit cycles in a finite number of iterations, and an upper bound for this number is also computable. The algorithm is demonstrated on a challenging non‐rational example with nonlinear parametric dependencies. Copyright © 2005 John Wiley & Sons, Ltd.     

Maximal entanglement from quantum random walks

The conditions under which entanglement becomes maximal are sought in the general one-dimensional quantum random walk with two walkers. Moreover, a one-dimensional shift operator for the two walkers is introduced and its performance in generating entanglement is analyzed as a function of several free parameters, some of them coming from the shift operator itself and some others from the coin operator. To simplify the investigation an averaged entanglement is defined.     

The role of connection in the nonlinear behavior of locomotion systems with symmetry

Using a geometric framework, the role of connection in nonlinear behavior of locomotion systems with symmetry is investigated in this paper. It is shown that the covariant derivative of connection plays a fundamental role in describing the nonlinear behavior of locomotion systems with Lie group symmetries. In particular, by placing prescribed closed paths properly in the shape space, it is argued that the system will exhibit nonlinear behaviors such as limit cycles and bifurcation in the fiber. The idea is used to investigate nonlinear behavior of a three link fish-like articulated body in perfect fluid. Numerical results are presented showing limit cycles and other coherent gaits resulting from various locations of shape circle.     

Fitting nonlinear low-order models for combustion instability control

Tools for fitting low-complexity nonlinear models based on experimental data are examined through the example problem of finding a reduced-order model suitable for control of a combustion instability operating in a limit cycle. This proceeds in four parts; physical modeling, linear system identification, nonlinear analysis, and validation test design. It is shown how the nonlinear tools of describing functions, bifurcation methods and manifold analysis assist in developing a simple nonlinear model capable of describing the data and consistent with physical understanding. The system being modeled is a lean gas turbine combustor which exhibits a sustained mid-range (100–1000 Hz) limit cycle instability. The closed-loop experimental data does not contain a sufficiently rich spectrum for confident modeling in the first linear system identification phase. Despite the paucity of information quality, a grey-box nonlinear model is created and parametrized which provides an explanation both of the limit-cycle fundamental oscillation and of a high frequency nonharmonic signal also present. The model structure is explored and various operating conditions simulated to understand the model better.

The validation and/or refinement of this model is then considered. The model validation problem is important because of the poor information content of the periodic limit cycle data. The challenge is to provide a practically feasible, small excitation to the loop to improve identifiability and to provide qualitative tests of model performance. We examine this problem by considering the nonlinear dynamics of the model class and feasible excitation mechanisms.     

Computational strategies for reliability-based structural optimization of aeroelastic limit cycle oscillations

Gradient-based optimization, via the adjoint method, is needed to realistically enable the reliability-based design of a nonlinear unsteady aeroelastic system with many random and/or deterministic design variables. The adjoint derivatives of a time-marched system entail a cumbersome reverse-time integration, and so a time-periodic spectral element scheme is used here to efficiently capture the gradients of the limit cycle oscillations. Further reductions in the computational cost of the monolithic-time adjoint vector are obtained with proper orthogonal decomposition, which projects the large system onto a reduced basis. Design reliability is computed with the first order reliability method, which provides an estimate of the failure probability without resorting to sampling-based approaches (infeasible for large systems). Analytical gradients are needed to obtain the most probable point (in the random variable space), as well as the reliability design derivatives. These computational strategies are utilized to locate the optimal thickness distribution of a cantilevered wing operating beyond its flutter point in supersonic flow (via piston theory). Specifically, the wing mass is minimized under both deterministic and non-deterministic limit cycle oscillation amplitude constraints, with both structural and flow uncertainties considered in the latter.