Control Approach for Legged Robots with Fast Gaits

A constructive control approach is proposed for legged robots with fast dynamic gaits. These systems interact intermittently with the environment. Our approach is based on Controlled Limit Cycles (CLC) and stabilizes periodic system trajectories. The designed control law generates (on-line) the desired trajectories and control input.     

An adaptive locomotion controller for a hexapod robot: CPG,kinematics and force feedback

Insects can perform versatile locomotion behaviors such as multiple gaits, adapting to different terrains, fast escaping, etc. However, most of the existing bio-inspired legged robots do not possess such walking ability, especially when they walk on irregular terrains. To tackle this challenge, a central pattern generator （CPG）-based locomotion control methodology is proposed, integrated with a contact force feedback function. In this approach, multiple gaits are produced by the CFG module. After passing through a post-processing circuit and a delay-line, the control signal is fed into six trajectory generators to generate predefined feet trajectories for the six legs. Then, force feedback is employed to adjust these trajectories so as to adapt the robot to rough terrains. Finally the regulated trajectories are sent to inverse kinematics modules such that the position control instructions are generated to control the actuators. In both simulations and real robot experiments, we consistently show that the robot can perform sophisticated walking patterns. What is more, the robot can use the force feedback mechanism to deal with the irregularity in rough terrain. With this mechanism, the stability and adaptability of the robot are enhanced. In conclusion, the CPG-base control is an effective approach for legged robots and the force feedback approach is able to improve walking ability of the robots, especially when they walk on irregular terrains.     

六足步行机横向行走最佳步态及其运动特性初探

本文分别以纵向稳定裕量和一般稳定裕量为准则,通过对六足步行机横向行走几何模型的分析和计算机优化计算,得出六足步行机横向运动时的最佳步态为广义三角步态.此外,文中对广义三角步态的运动特性(包括静态稳定性、爬坡能力、越沟能力等)进行了初步研究,阐明了这些运动特性与步行机若干几何参数间的内在联系,为六足步行机的总体尺寸设计提供了理论依据。     

Genetic Programming-Based Automatic Gait Generation in Joint Space for a Quadruped Robot

This paper introduces a new approach to developing a fast gait for a quadruped robot using genetic programming (GP). Planning gaits for legged robots is a challenging task that requires optimizing parameters in a highly irregular and multi-dimensional space. Several recent approaches have focused on using genetic algorithms (GAs) to generate gaits automatically and have shown significant improvement over previous gait optimization results. Most current GA-based approaches optimize only a small, pre-selected set of parameters, but it is difficult to decide which parameters should be included in the optimization to get the best results. Moreover, the number of pre-selected parameters is at least 10, so it can be relatively difficult to optimize them, given their high degree of interdependence. To overcome these problems of the typical GA-based approach, we have proposed a seemingly more efficient approach that optimizes joint trajectories instead of locus-related parameters in Cartesian space, using GP. Our GP-based method has obtained much-improved results over the GA-based approaches tested in experiments on the Sony AIBO ERS-7 in the Webots environment. The elite archive mechanism is introduced to combat the premature convergence problems in GP and has shown better results than a traditional multi-population approach.     

Synchronization of a class of cyclic discrete-event systems describing legged locomotion

It has been shown that max-plus linear systems are well suited for applications in synchronization and scheduling, such as the generation of train timetables, manufacturing, or traffic. In this paper we show that the same is true for multi-legged locomotion. In this framework, the max-plus eigenvalue of the system matrix represents the total cycle time, whereas the max-plus eigenvector dictates the steady-state behavior. Uniqueness of the eigenstructure also indicates uniqueness of the resulting behavior. For the particular case of legged locomotion, the movement of each leg is abstracted to two-state circuits: swing and stance (leg in flight and on the ground, respectively). The generation of a gait (a manner of walking) for a multi-legged robot is then achieved by synchronizing the multiple discrete-event cycles via the max-plus framework. By construction, different gaits and gait parameters can be safely interleaved by using different system matrices. In this paper we address both the transient and steady-state behavior for a class of gaits by presenting closed-form expressions for the max-plus eigenvalue and max-plus eigenvector of the system matrix and the coupling time. The significance of this result is in showing guaranteed stable gaits and gait switching, and also a systematic methodology for synthesizing controllers that allow for legged robots to change rhythms fast.     

Continuous free-crab gaits for hexapod robots on a natural terrain with forbidden zones: An application to humanitarian demining

Autonomous robots are leaving the laboratories to master new outdoor applications, and walking robots in particular have already shown their potential advantages in these environments, especially on a natural terrain. Gait generation is the key to success in the negotiation of natural terrain with legged robots; however, most of the algorithms devised for hexapods have been tested under laboratory conditions. This paper presents the development of crab and turning gaits for hexapod robots on a natural terrain characterized by containing uneven ground and forbidden zones. The gaits we have developed rely on two empirical rules that derive three control modules that have been tested both under simulation and by experiment. The geometrical model of the SILO-6 walking robot has been used for simulation purposes, while the real SILO-6 walking robot has been used in the experiments. This robot was built as a mobile platform for a sensory system to detect and locate antipersonnel landmines in humanitarian demining missions.     

Online Optimization of Swimming and Crawling in an Amphibious Snake Robot

An important problem in the control of locomotion of robots with multiple degrees of freedom (e.g., biomimetic robots) is to adapt the locomotor patterns to the properties of the environment. This article addresses this problem for the locomotion of an amphibious snake robot, and aims at identifying fast swimming and crawling gaits for a variety of environments. Our approach uses a locomotion controller based on the biological concept of central pattern generators (CPGs) together with a gradient-free optimization method, Powell's method. A key aspect of our approach is that the gaits are optimized online, i.e., while moving, rather than as an off-line optimization process. We present various experiments with the real robot and in simulation: swimming, crawling on horizontal ground, and crawling on slopes. For each of these different situations, the optimized gaits are compared with the results of systematic explorations of the parameter space. The main outcomes of the experiments are: 1) optimal gaits are significantly different from one medium to the other; 2) the optimums are usually peaked, i.e., speed rapidly becomes suboptimal when the parameters are moved away from the optimal values; 3) our approach finds optimal gaits in much fewer iterations than the systematic search; and 4) the CPG has no problem dealing with the abrupt parameter changes during the optimization process. The relevance for robotic locomotion control is discussed.     

Gait optimization of step climbing for a hexapod robot

RHex-style hexapod robot is a type of legged robot which can perform multiple moving gaits according to different applications, due to its simple structure and strong mobility. However, traversing high obstacles has always been a big challenge for legged robots. In this paper, gait optimization of a hexapod robot is proposed for climbing steps at different heights, which even enables the robot to climb the step 3.9 times of the leg length. First, a previous step-climbing gait is optimized by adjusting body inclination when placing front legs on top of the step, which enables RHex with different sizes to perform the rising stage of the gait. Second, to improve the climbing heights, a novel quasi-static climbing gait is proposed by using the reversed claw-shape legs to reach the higher step. The nondeformable legs are used to raise the center of mass (COM) of the body by lifting the front and rear legs alternately so that the front legs can reach the top of the step, then the front and middle legs are lifted alternately to maneuver COM up onto the step. The simulations and dynamic analysis of climbing steps are utilized to verify the feasibility of the improved gait. Finally, the step-climbing experiments at different heights are performed with the optimized gaits to compare with the existing gaits. The results of simulations and experiments show the superiority of the proposed gaits due to climbing higher steps.     

Kinematic Constraints on Fault-Tolerant Gaits for a Locked Joint Failure

Fault-tolerant gaits in legged locomotion are defined as gaits with which legged robots can continue their walking after a failure event has occurred to a leg of the robot. For planning an efficient fault-tolerant gait, kinematic constraints and remaining mobility of the failed leg should be closely examined with each other. This paper addresses the problem of kinematic constraints on fault-tolerant gaits. The considered failure is a locked joint failure which prevents a joint of a leg from moving and makes it locked in a known place. It is shown that for the existence of the conventional fault-tolerant gait for forward walking on even terrain, the configuration of the failed leg must be within a range of kinematic constraints. Then, for coping with failure situations where the existence condition is not satisfied, the conventional fault-tolerant gait is adopted by including the adjustment of the foot trajectory of the failed leg. The foot trajectory adjustment procedure is analytically derived to show that it can help the fault-tolerant gait avoid dead-lock resulting from the kinematic constraint. To demonstrate its effectiveness, the proposed method is applied to the fault-tolerant gait generation for a quadruped robot walking with the wave-crab gait before a locked joint failure.     

Kinematic and dynamic analysis of a hexapod walking-running-bounding gaits robot and control actions

Kinematic and dynamic analysis, and control actions of a hexapod robot were realized for walking, running and bounding gaits in this study. If biological inspiration can be used to build robots that deal robustly with complex environments, it should be possible to demonstrate that legged biorobots can function in natural environments. Firstly, we tried to report on theoretic work with a six legged robot designed to emulate spider behavior like walking, running and bounding. We demonstrated theoretically that it can successfully walk, run and bound like a spider over natural terrain. Secondly, limitations in its capability were evaluated, and many biologically based important improvements were obtained for future experimental work. Thirdly, the hexapod robot with bounding gait was controlled by proportional-derivative control algorithm and was carried out by using spring loaded inverted pendulum model. Consequently, the developed kinematic and dynamic methods, and control action method makes both the system control easy and the system performance is improved by decreasing the run time for each loop.     

Autonomous evolution of dynamic gaits with two quadruped robots

A challenging task that must be accomplished for every legged robot is creating the walking and running behaviors needed for it to move. In this paper we describe our system for autonomously evolving dynamic gaits on two of Sony's quadruped robots. Our evolutionary algorithm runs on board the robot and uses the robot's sensors to compute the quality of a gait without assistance from the experimenter. First, we show the evolution of a pace and trot gait on the OPEN-R prototype robot. With the fastest gait, the robot moves at over 10 m/min, which is more than forty body-lengths/min. While these first gaits are somewhat sensitive to the robot and environment in which they are evolved, we then show the evolution of robust dynamic gaits, one of which is used on the ERS-110, the first consumer version of AIBO.     

Symmetry position/force hybrid control for cooperative object transportation using multiple humanoid robots

A symmetry position/force hybrid control framework for cooperative object transportation tasks with multiple humanoid robots is proposed in this paper. In a leader-follower type cooperation, follower robots plan their biped gaits based on the forces generated at their hands after a leader robot moves. Therefore, if the leader robot moves fast (rapidly pulls or pushes the carried object), some of the follower humanoid robots may lose their balance and fall down. The symmetry type cooperation discussed in this paper solves this problem because it enables all humanoid robots to move synchronously. The proposed framework is verified by dynamic simulations.     

Crab walking of quadruped robots with a locked joint failure

Fault tolerance is an important aspect in the development of control systems for multi-legged robots since a failure in a leg may lead to a severe loss of static stability of a gait. In this paper, an algorithm for tolerating a locked joint failure is described in gait planning for a quadruped robot with crab walking. A locked joint failure is one for which a joint cannot move and is locked in place. If a failed joint is locked, the workspace of the resulting leg is constrained, but legged robots have fault tolerance capability to continue walking maintaining static stability. A strategy for fault-tolerant gaits is described and, especially, a periodic gait is presented for crab walking of a quadruped. The leg sequence and the formula of the stride length are analytically driven based on gait study and robot kinematics. The adjustment procedure from a normal gait to the proposed fault-tolerant crab gait is shown to demonstrate the applicability of the proposed scheme.     

腿式机器人的研究综述

分析了国内外腿式机器人的研究现状,讨论了腿式机器人在机械结构、稳定性和控制算法方面的现有研究方法,给出了腿式机器人研究存在的问题,展望了腿式机器人的发展方向．     

Study of a distributed control architecture for a quadruped robot

Looking at legged robots, it is sometimes very important to take into account some of the practical aspects (when focusing on theoretical ones) in order to implement control-command levels.In this way, we have treated the problem of the realization of dynamic or quasi-dynamic gaits with a quadruped robot using a new approach from which we have derived an efficient control/command scheme. This is based on a simple consideration which lies in the fact that the Dynamic Model (DM) can be decomposed into two main parts. From our point of view, we consider a part devoted to the command of the legs which could be called a Leg Inverse Dynamic Model (LIDM). We consider a second part dealing with the global characteristics of the platform. At this level, one can control the system. It will be called the LPIM (Leg to Platform Interaction Model).This goal is reached assuming a dichotomy in a distributed architecture and by the way we present it. Further justification of our method will be given in several stages throughout the paper. We paid great attention to time-saving considerations with respect to communication protocols and data exchange at the same level and between the three levels we derived from our basic investigations.     

Generating high-speed dynamic running gaits in a quadruped robot using an evolutionary search

Over the past several decades, there has been a considerable interest in investigating high-speed dynamic gaits for legged robots. While much research has been published, both in the biomechanics and engineering fields regarding the analysis of these gaits, no single study has adequately characterized the dynamics of high-speed running as can be achieved in a realistic, yet simple, robotic system. The goal of this paper is to find the most energy-efficient, natural, and unconstrained gallop that can be achieved using a simulated quadrupedal robot with articulated legs, asymmetric mass distribution, and compliant legs. For comparison purposes, we also implement the bound and canter. The model used here is planar, although we will show that it captures much of the predominant dynamic characteristics observed in animals. While it is not our goal to prove anything about biological locomotion, the dynamic similarities between the gaits we produce and those found in animals does indicate a similar underlying dynamic mechanism. Thus, we will show that achieving natural, efficient high-speed locomotion is possible even with a fairly simple robotic system. To generate the high-speed gaits, we use an efficient evolutionary algorithm called set-based stochastic optimization. This algorithm finds open-loop control parameters to generate periodic trajectories for the body. Several alternative methods are tested to generate periodic trajectories for the legs. The combined solutions found by the evolutionary search and the periodic-leg methods, over a range of speeds up to 10.0 m/s, reveal "biological" characteristics that are emergent properties of the underlying gaits.     

Gait transition for a quadrupedal robot by replacing the gait matrix of a central pattern generator model

The pattern-generator-based approach for legged robot control is inspired by biological neural mechanisms of locomotion, in which a special challenge is gait transition. In this paper we build a holosymmetric central pattern generator model and propose parameter-setting principles for a gait matrix capable of producing typical quadrupedal gaits, and based on them present an approach of directly replacing the gait matrix for gait transition, with a focus on three problems emerging during transition: breakpoint, phase-lock and oscillation-stop. Breakpoints are smoothed by remaining the current outputs during transition, similar to a zero-order holder. Breaking the phase-lock is accomplished by adding a perturbation to the state matrix at the transiting point. An oscillation-stop of less than one period can be ignored. With such treatments, it is proved that gait transitions between any two gaits on a quadrupedal robot can be achieved at arbitrary phase locations in a walk cycle, theoretically and experimentally in part.     

A lattice-type reconfigurable robotic system for achieving gaits of chain-type robots

Traditional lattice-type reconfigurable robots can only achieve the flow-style locomotion with low efficiency. Since gaits of chain-type robots are proved to be efficient and practical, this paper presents a novel lattice distortion approach for lattice-type reconfigurable robots to achieve locomotion gaits of chain-type robots. Using this approach, the robotic system can be actuated by local lattice distortion to move as an ensemble. In this paper, a rule that makes the lattice distortion equivalent to joint rotation is presented firstly. Then, a kind of module structure is designed according to requirements of the lattice distortion. Finally, a motion planning for achieving locomotion is developed, which works well in physics-based simulations of completing a serpentine locomotion gait of a snake-like robot and a tripod gait of a hexapod robot.     

一种多足步行机器人行走状态分析模型

结合步行机器人行走的动力学特性,通过对机器人的加速度传感器信息进行离散傅立叶变换,建立了行走相关特征值的概率模型.通过使用马氏距离作为判定标准,对步行机器人的行走稳定性给出定量描述.四足步行机器人平台上的实验结果表明,该模型能够实时反映机器人的行走特性,帮助机器人在行走状态受环境影响发生改变时,根据行走特征及时调整运动,保证其稳定性.