A fault tolerant gait for a hexapod robot over uneven terrain

The fault tolerant gait of legged robots in static walking is a gait which maintains its stability against a fault event preventing a leg from having the support state. In this paper, a fault tolerant quadruped gait is proposed for a hexapod traversing uneven terrain with forbidden regions, which do not offer viable footholds but can be stepped over. By comparing performance of straight-line motion and crab walking over even terrain, it is shown that the proposed gait has better mobility and terrain adaptability than previously developed gaits. Based on the proposed gait, we present a method for the generation of the fault tolerant locomotion of a hexapod over uneven terrain with forbidden regions. The proposed method minimizes the number of legs on the ground during walking, and foot adjustment algorithm is used for avoiding steps on forbidden regions. The effectiveness of the proposed strategy over uneven terrain is demonstrated with a computer simulation.     

Fault-tolerant locomotion of the hexapod robot

In this paper, we propose a scheme for fault detection and tolerance of the hexapod robot locomotion on even terrain. The fault stability margin is defined to represent potential stability which a gait can have in case a sudden fault event occurs to one leg. Based on this, the fault-tolerant quadruped periodic gaits of the hexapod walking over perfectly even terrain are derived. It is demonstrated that the derived quadruped gait is the optimal one the hexapod can have maintaining fault stability margin nonnegative and a geometric condition should be satisfied for the optimal locomotion. By this scheme, when one leg is in failure, the hexapod robot has the modified tripod gait to continue the optimal locomotion.     

Fault-Tolerant Gait Planning for a Hexapod Robot Walking over Rough Terrain

Multi-legged robots need fault-tolerant gaits if one of attached legs suffers from a failure and cannot have normal operation. Moreover, when the robots with a failed leg are walking over rough terrain, fault-tolerance should be combined with adaptive gait planning for successful locomotion. In this paper, a strategy of fault-tolerant gaits is proposed which enables a hexapod robot with a locked joint failure to traverse two-dimensional rough terrain. This strategy applies a Follow-The-Leader (FTL) gait in post-failure walking, having the advantages of both fault-tolerance and terrain adaptability. The proposed FTL gait can produce the maximum stride length for a given foot position of a failed leg and better ditch-crossing ability than the previous fault-tolerant gaits. The applicability of the proposed FTL gait is verified using computer graphics simulations.     

六边形对称分布六腿机器人的典型步态及其运动性能分析

为了便于在不同地理条件下合理地选择较优的步态,实现稳定高效的智能行走,本文针对一种六边形 对称分布的六腿机器人研究其不同步态的优劣．主要从行走能力、稳定性和能耗3 个角度对六边形对称结构的六腿 机器人在同样占空比下的3 种静态稳定周期步态进行了比较研究,此外还简要分析了其越障能力和穿越窄道的能 力．研究分析结果表明3 种步态（横向昆虫式摆动步态、哺乳动物式踢腿步态和混合步态）在不同条件下各有优劣： 横向昆虫式摆动步态在能耗和越障能力方面较其他两种步态有优势;而混合步态在稳定性上最具优势,其它能力处 于中间;哺乳动物式踢腿步态则可穿越窄道,步长上较昆虫摆动步态略好．本文的研究工作为六边形对称结构的六 腿机器人在未知复杂地貌环境下的智能行走提供了重要参考．     

Planar legged walking of a passive-spine hexapod robot

This paper proposes a new legged walking method for a novel passive-spine hexapod robot. This robot consists of several body segments connected by passive body joints. Each of the body segments carries two 1-DoF (degree of freedom) actuated legs. The robot is capable of achieving planar legged walking by rapidly abducting and adducting its legs. To model the mobility of a robot based on this simple design, the candidate configurations from all possible configurations are first selected in a mobility analysis of the robot based on the screw theory. All the feasible sequences of these candidate configurations are then searched to form planar locomotion gaits. Next, locomotive performance of the gaits is analyzed. Finally, the proposed locomotion design and gait planning methods are verified through simulations and experiments.     

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.     

圆周对称分布六腿机器人三种典型行走步态步长及稳定性分析

针对现有圆周对称分布六腿步行机器人步长研究中存在的缺点和不足,提出了并联机构支链工作空间相交法,将由机器人本体、支撑腿和地面组成的并联机构分割成不同的分支,利用各分支工作空间求交,从而确定机器人在某一本体高度上的步长和稳定裕度.该方法可在已知机器人立足点和本体高度的情况下求得机器人的最大可行步长和稳定裕度,也可以求得机器人在某一本体高度上的极限可行步长和在这种情况下的立足点的位置,还可以根据已知步长和机器人本体高度来确定最大稳定裕度和最大稳定裕度下的立足点的位置.这种方法为圆周对称分布六腿机器人采用不同步态行走过程中立足点、本体高度和步长的选取提供重要参考.     

A comparison of three insect-inspired locomotion controllers

This paper compares three insect inspired controllers which were implemented on an autonomous hexapod robot. There is a growing interest in using insect locomotion schemes to control walking robots. Researchers' interest in insect-based controllers ranges from understanding the biological basis of locomotion control in insects to building real-time walking machines which require relatively little computational power. Several models for insect locomotion exist, and robotics researchers tend to adopt one approach and experiment with it.

In contrast, this paper offers a comparison of three insect inspired controllers — all of which were implemented and tested on the same autonomous hexapod robot. Some of the controllers used reflex-based mechanisms whereas others used pattern-based mechanisms. Reflexive controllers exploit sensory stimulus and response reactions to produce leg motion and gait coordination. In contrast, pattern-based controllers depend more upon pre-programmed patterns of behavior which may be influenced by external events. Typically, these pre-programmed patterns of behavior are implemented using central pattern generators (CPGs).

In this work, we compare gait coordination performance of three controllers on flat terrain. We extend the comparison to include leg loading considerations, disabled leg compensation, and externally applied leg perturbations. We discuss the differences between controllers with respect to inconsistent leg retraction velocities, leg design issues, sensing requirements, and computational issues. The robot performed quite differently under varying experimental conditions depending upon which controller was used. We found that controller performance was the most sensitive to robot design parameters. For our case, we had the most success with pattern-based mechanisms given the leg design of our robot and its limitations in controlling the retraction velocity of its legs. The pattern-based mechanisms allowed the robot to remain stable over a variety of gaits while the robot was subjected to loading the legs, disabling a leg, and physically disturbing the legs. The reflexive mechanisms were less successful at maintaining stability when the robot's legs were increasingly disrupted.     

The ASURA I harvestman-like hexapod walking robot: compact body and long leg design

This paper reports the design of a new hexapod walking robot, ASURA I, inspired by the physical features of a harvestman’s behavior. ASURA I has a special mobile form with one compact body and much longer legs than conventional hexapod walking robots. This form enhances the walking performance of the robot on rocky or uneven terrain. Here, we present the design and analysis of the leg mechanism, body structure design, gait planning, and prototype development. The long legs (relative to the body) are managed by special parallel link mechanisms, which powerfully and effectively drive the leg joints. The leg mechanism is analyzed by its kinematics, singularity, and static characteristics. The leg length and weight of ASURA I is 1.3 m and 27 kg, respectively. The alternating tripod and wave gaits of ASURA I are successfully demonstrated in a series of walking experiments.     

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.     

Evolving gaits for hexapod robots using cyclic genetic algorithms

A major facet of multi-legged robot control is locomotion. Each leg must move in such a manner that it efficiently produces thrust and provides maximum support. The motion of all the legs must be coordinated so that they are working together to provide constant stability while propelling the robot forward. In this paper, we discuss the use of a cyclic genetic algorithm (CGA) to evolve control programs that produce gaits for actual hexapod robots. Tests done in simulation and verified on the actual robot show that the CGA successfully produces gaits for both fully capable and disabled robots.     

A gait study for a one-leg-disabled hexapod robot

—As a remarkably strong point of a hexapod walking robot, it is considered that even if one of the six legs is disabled, static walking may be maintained by the remaining five legs. However, to maintain the static stability at maximum, a gait study for five-legged walking is a necessary factor. Hence, this paper describes a method of gait study for such a situation. Since it is very difficult to find a suitable gait by use of an analytical method without any model, such as a model based on insects' walking, we employed a programming method with the help of recent powerful computers. Some devices are applied to reduce the number of computations. As a result, we have obtained two kinds of gaits which can maintain the gait stability margin at a high level for a duty factor in the range of 0.6β < 1.     

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.     

An approach to analyzing biped locomotion dynamics and designing robot locomotion controls

An approach to analyzing biped locomotion problems is presented. This approach applies the principles of Lagrangian dynamics to derive the equations of motion of locomotion gaits, state-variable techniques to analyze locomotion dynamics, and multivariable feedback to design locomotion controls. A robot model which has no knee joints or feet and is constrained to motion in the sagittal plane is chosen as a sufficiently simple model of a biped to illustrate the approach. A goal of the analysis is the design of a locomotion control for the robot which produces a walking gait having a velocity and stride length similar to those of a human walking gait. The principle feature of the approach is a much deeper understanding of the dynamics of biped locomotion than previous approaches have provided.     

六足机器人不规则地形下的运动规划算法研究

以六足类昆虫典型代表——蚂蚁爬越障碍柱和障碍柱堆的两种运动过程及其特点为分析对象,总结了蚂蚁在应对不规则地形时的运动策略,建立了更为合理的六足机器人的运动学数学模型;并仿照蚂蚁在应对不规则地形时的运动策略,提出在进行仿生六足机器人运动规划时,可将地形划分为浅度不平地形和深度不平地形两种情况,进而针对两种地形情况提出了六足机器人在不规则地形条件下的运动规划算法。最后通过样机试验验证所提算法的有效性。     

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.     

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.     

Accurate tracking of legged robots on natural terrain

Statically stable walking locomotion research has focused mainly on robot design and gait generation. However, there is a need to expand robots’ capabilities so that walking machines can accomplish the kinds of real tasks for which they are eminently suited. Many such tasks demand trajectory tracking, but researchers have traditionally ignored this subject. This article focuses on the tracking of predefined trajectories with hexapod robots walking on natural terrain with forbidden zones. The method presented herein, which relies on gait algorithms defined elsewhere, describes certain localization strategies and control techniques that have been employed to follow trajectories accurately and have been implemented in a real walking hexapod. Several experimental examples are included to assess the proposed algorithms.     

Translational Crawl and Path Tracking of a Quadruped Robot

Translational crawl and path tracking are presented for a quadruped robot, named TITAN‐VIII, to walk on rough ground. The generalized and explicit formulation is derived to generate the translational crawl gait in an arbitrary direction automatically, to control the joint positions, and to estimate the robot localization in a walking environment. Compared to conventional gaits, the proposed gait is characterized by a natural and continuous transition between any successive gait cycles, by a maximized stride of the robot in each gait cycle, and by different foot trajectories corresponding to the uneven terrain. Especially, the proposed approach enables the quadruped robot to track a reference path in a complex walking environment, based on dead‐reckoning localization for the robot. The effectiveness of the proposed method is demonstrated through the experimental results. © 2002 Wiley Periodicals, Inc.     

Reflex-oscillations in evolved single leg neurocontrollers for walking machines

As a prerequisite for developing neural control for walking machines that are able to autonomously navigate through rough terrain, artificial structure evolution is used to generate various single leg controllers. The structure and dynamical properties of the evolved (recurrent) neural networks are then analysed to identify elementary mechanisms of sensor-driven walking behaviour. Based on the biological understanding that legged locomotion implies a highly decentralised and modular control, neuromodules for single, morphological distinct legs of a hexapod walking machine were developed by using a physical simulation. Each of the legs has three degrees of freedom (DOF). The presented results demonstrate how extremely small reflex-oscillators, which inherently rely on the sensorimotor loop and e.g. hysteresis effects, generate effective locomotion. Varying the fitness function by randomly changing the environmental conditions during evolution, neural control mechanisms are identified which allow for robust and adaptive locomotion. Relations to biological findings are discussed.