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.     

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.     

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.     

Generation of a continuous free gait for quadruped robot over rough terrains

Generating a robust gait is one of the most important factors to improve the adaptability of quadruped robots on rough terrains. This paper presents a new continuous free gait generation method for quadruped robots capable of walking on the rough terrain characterized by the uneven ground and forbidden areas. When walking with the proposed gait, the robot can effectively maintain its stability by using the Center of Gravity (COG) trajectory planning method. After analyzing the point cloud of rough terrain, the forbidden areas of the terrain can be obtained. Based on this analysis, an optimal foothold search strategy is presented to help quadruped robot to determine the optimum foothold for the swing foot automatically. In addition, the foot sequence determining method is proposed to improve the performance of robot. With the free gait proposed in this paper, quadruped robot can walk through the rough terrains automatically and successfully. The correctness and effectiveness of the proposed method is verified via simulations.     

Energy-optimal gait analysis of quadruped robots

It is important for walking robots such as quadruped robots to have an efficient gait. Since animals and insects are the basic models for most walking robots, their walking patterns are good examples. In this study, the walking energy consumption of a quadruped robot is analyzed and compared with natural animal gaits. Genetic algorithms have been applied to obtain the energy-optimal gait when the quadruped robot is walking with a set velocity. In this method, an individual in a population represents the walking pattern of the quadruped robot. The gait (individual) which consumes the least energy is considered to be the best gait (individual) in this study. The energy-optimal gait is analyzed at several walking velocities, since the amount of walking energy consumption changes if the walking velocity of the robot is changed. The results of this study can be used to decide what type of gait should be generated for a quadruped robot as its walking velocity changes. This work was presented, in part, at the Sixth International Symposium on Artificial Life and Robotics, Tokyo, Japan, January 15–17, 2001.     

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.     

Prior notice method of robotic arm motion for suppressing a threat to a human

The ability to develop a gait with one or more legs missing is an important issue for multi-legged robots used in demining applications. Accordingly, this paper presents a three-legged gait under the assumption that one leg of a quadruped walking robot is missing. After outlining a posture classification scheme for three-legged walking, the kick-and-swing gait is proposed as a basic and reasonable gait for three-legged walking and analyzed using a simple dynamic model. Minimum energy gait planning and an active shock-absorbing method are also investigated. The validity of the proposed gait is shown based on experiments using the quadruped walking robot TITAN VIII.     

智能决策改进的四足机器人ZMP爬行步态算法

提出了一种基于反馈控制和贪婪决策的四足机器人爬行步态规划算法。该算法利用机载惯性传感器IMU（Inertial Measurement Unit）来实时计算零力矩点和姿态角,以稳态裕度为指标在支撑平面内实时规划期望零力矩点（Zero Moment Point,ZMP）轨迹,结合非线性反馈控制器实现对机体ZMP点的连续平滑调节,保证机器人在按给定速度矢量进行连续爬行的同时具有抵抗一定外力扰动的能力。步态规划采用动态步态周期,基于机器人结构约束和贪婪决策实现跨腿的自动触发,提高了步态自适应性。最终通过样机行走实验验证了所提算法应用于微型四足机器人中的可行性,机器人实现了在平坦地面上稳定地全向行走和旋转,所提算法同时兼顾了自适应性和稳定裕度。     

融合元学习和PPO算法的四足机器人运动技能学习方法

具备学习能力是高等动物智能的典型表现特征, 为探明四足动物运动技能学习机理, 本文对四足机器人步 态学习任务进行研究, 复现了四足动物的节律步态学习过程. 近年来, 近端策略优化(PPO)算法作为深度强化学习 的典型代表, 普遍被用于四足机器人步态学习任务, 实验效果较好且仅需较少的超参数. 然而, 在多维输入输出场 景下, 其容易收敛到局部最优点, 表现为四足机器人学习到步态节律信号杂乱且重心震荡严重. 为解决上述问题, 在元学习启发下, 基于元学习具有刻画学习过程高维抽象表征优势, 本文提出了一种融合元学习和PPO思想的元近 端策略优化(MPPO)算法, 该算法可以让四足机器人进化学习到更优步态. 在PyBullet仿真平台上的仿真实验结果表 明, 本文提出的算法可以使四足机器人学会行走运动技能, 且与柔性行动者评价器(SAC)和PPO算法的对比实验显 示, 本文提出的MPPO算法具有步态节律信号更规律、行走速度更快等优势.     

Implementation of omnidirectional crawl for a quadruped robot

As a reptile animal crawls in a cluttered environment, so a quadruped robot should be able to crawl on an irregular ground profile with its static stability by adopting the straightgoing and standstill-turning free gaits. The generalized and explicit formulations for the automatic generation of straight-going gaits and various standstill-turning gaits are presented in this paper. The maximized stride for the straight-going gait and the maximum turning angle for the turning gait of a quadruped robot named TITAN-VIII in a gait cycle are discussed by considering the robot's mechanism constraints and the irregularities of the ground profile. The control algorithm, including control of the joint positions of the robot, is described to implement the desired walking path of the quadruped robot. The effectiveness of the proposed method is demonstrated through experimental result.     

基于重心动力学及虚拟模型的负载型四足步行平台对角步态控制方法

为提高负载型四足步行平台对角步态行走的稳定性,减小较大的腿部质量及偏心质量对稳定行走的影响,提出融合重心动力学及虚拟模型的控制方法．应用虚拟模型控制方法对机身及摆动腿加速度进行求解．结合平台重心动力学模型得到其所受合外力,而后应用二次规划将平台合外力分配到支撑腿足端．接着运用逆向动力学和关节空间PD控制得到步行平台关节力矩．通过Adams和Simulink对负载型四足步行平台对角步态行走进行仿真,并将该方法与虚拟模型控制算法进行对比．结果表明重心动力学及虚拟模型控制方法能够使平台姿态角稳定在目标值附近,在平台受到侧向冲击情况下横滚角、俯仰角分别减小约42%、21.8%,在机身偏心全向行走过程中减小50%、89%．证明了所提控制方法能够有效应对较大的腿部质量及偏心质量的影响,提高负载型四足步行平台对角步态行走的稳定性和鲁棒性．     

Application of parallel mechanism in varistructured quadruped/biped human-carrying walking chair robot

For the existing problems of walking chair robot such as simple function,lower bearing capacity and not walking in complex environment,a novel varistructured quadruped / biped human-carrying walking chair robot is proposed.The proposed robot could be used as biped and quadruped walking chair robots.Considering the conversion of the walking chair robot from the quadruped to the biped or vice versa,6-UPS and 2-UPS+UP(U,P and S are universal joint,the prismatic pair,and sphere joint,respectively) parallel mechanisms are selected as the leg mechanism of the biped walking robot and quadruped walking robot,respectively.Combining the screw theory and theory of mechanism,the degrees of freedom of the leg mechanism and the body mechanism in diferent motion states are computed so as to meet the requirements of mechanism design.The motion characteristics of the 2-UPS+UP parallel mechanism which is the key part of the walking chair robot are analyzed.Then,the workspace of the moving platform is drawn and the efect of the structural parameters on the workspace volume is studied.Finally,it is found that the volume of the workspace of the moving platform is bigger when the side length ratio and the vertex angle ratio of the fxed platform and the moving platform which are isosceles triangles are close to 1.This study provides a theoretical foundation for the prototype development.     

How to optimize the slope walking motion by the quadruped walking robot

Reduction of the energy consumption is one of the most important problems to utilize quadruped walking robots for various works on rugged terrain. The authors have studied basic strategy to achieve high energy efficiency when the quadruped walking robot do the motion essentially requires positive power by the analysis of body rising motion. This paper discusses the energy efficiency of the slope walking motion by the quadruped walking robot. First, we investigate the walking posture in consideration of ideal actuator characteristics where the robot consumes few negative powers at each joint which causes the main energy loss of the walking robot. Then, we investigate optimal walking posture in consideration of DC motor characteristics by the full search of three gait parameters which define the crawl gait. Furthermore, we derive the optimal walking motion by the optimization of three gait parameters which are kept constant during one cycle gait and instantaneous parameters such as body velocity and supporting forces changed at each moment simultaneously.     

Dynamic characteristics and stability criterion of rotary galloping gait with an articulated passive spine joint

Based on the simplified planar quadruped model with a passive spine joint, this paper focuses on studying the effect of the spine joint on the dynamic performance and the stability of the rotary galloping gait. The stable, periodic, and symmetric rotary galloping gait is achieved by the particle swarm optimization method without any parameter symmetry for leg motion and without any limitation for spine motion. By analyzing the symmetric pattern of the rotary galloping gait, the stability criterion is derived: the closer to zero is the pitching angle at peak time of the center of mass, the better is the stability of the galloping gait. Then, we study the effect of rear leg touchdown angle and spine stiffness on the stability. Moreover, the unstable rotary galloping gait can be stabilized by adjusting one or more of the touchdown angle, spine stiffness, and leg stiffness. Furthermore, the effect of the spine stiffness on the key kinematic and kinetic properties is also studied for different initial values and mechanical parameters. The presented stability criterion and the achieved dynamic performance analysis results will be instructive for the design and control of the quadruped robot.     

The Design and Control of a Prototype Quadruped Microrover

We describe the design, construction and control of a quadruped robot which walks on uneven terrain. A control system which produces a statically stable gait has been implemented; results showing a straight and turning gait are presented. The control of quadruped robots poses interesting challenges due to a small stability margin (when compared to hexapods for example). For this reason most implemented systems for outdoor walking on uneven terrain have been hexapods. The system described here has the added virtue of using very few inexpensive sensors and actuators. One of the aims of this work is to build a reduced complexity (low power, low mass and direct drive) walking robot for statically stable walking. The other aim is to compare the performance of this robot with a wheeled robot roughly the same size and weight. In this paper we report on progress towards the first of these two goals using a traverse across an obstacle field as an example.     

Neural network approach to acquiring free-gait motion of quadruped robots in obstacle avoidance

In obstacle avoidance by a legged mobile robot, it is not necessary to avoid all of the obstacles by turning only, because it can climb or stride over some of them, depending on the obstacle configuration and the state of the robot, unlike a wheel-type or a crawler-type robot. It is thought that mobility efficiency to a destination is improved by crawling over or striding over obstacles. Moreover, if robots have many legs, like 4-legged or 6-legged types, then the robot's movement range is affected by the order of the swing leg. In this article a neural network (NN) is used to determine the action of a quadruped robot in an obstacle-avoiding situation by using information about the destination, the obstacle configuration, and the robot's self-state. To acquire a free gait in static walking, the order of the swing leg is realized using an alternative NN whose inputs are the amount of movement and the robot's self-state. The design parameters of the former NN are adjusted by a genetic algorithm (GA) off-line. This work was presented in part at the 9th International Symposium on Artificial Life and Robotics, Oita, Japan, January 28–30, 2004     

基于体感的仿人机器人步态学习与控制

针对现有理想化步态动力学模型规划方法复杂、人为指定参数过多、计算量大的问题,提出一种基于体感数据学习人体步态的仿人机器人步态生成方法。首先,用体感设备收集人体骨骼信息,基于最小二乘拟合方法建立人体关节局部坐标系;其次,搭建人体与机器人映射的运动学模型,根据两者间主要关节映射关系,生成机器人关节转角轨迹,实现机器人对人类行走姿态的学习;然后,基于零力矩点(ZMP)稳定性原则,对机器人脚踝关节转角采用梯度下降算法进行优化控制;最后,在步态稳定性分析上,提出使用安全系数来评价机器人行走稳定程度的方法。实验结果表明,步行过程中安全系数保持在0~0.85,期望为0.4825,ZMP接近于稳定区域中心,机器人实现了仿人姿态的稳定行走,证明了该方法的有效性。     

Gait planning for quadruped robot based on dynamic stability: landing accordance ratio

In this article, the method for increasing dynamic stability of quadruped robot is proposed. Previous researches on dynamic walking of quadruped robots have used only walking pattern called central pattern generator (CPG). In this research, different from walking generation with only CPG, a instinctive stability measure called landing accordance ratio, is proposed and used for increasing dynamic stability. In addition, dynamic balance control and control to adjust walking trajectory for increasing dynamic stability measure is also proposed. Proposed methods are verified with dynamic simulation and a large number of experiments with quadruped robot platform.     

Neural networks IC controlled multi-legged walking MEMS robot with independent leg mechanism

In this paper, we will compare the walking behavior of quadruped and hexapod walking MEMS robots. These robots are fabricated by connecting same modules, which are composed of a couple of independent leg mechanisms. Independent leg mechanisms can actuate the single leg by a single artificial muscle wire. The neural networks IC that mimics real living organisms controls the mechanical systems. The length and weight of the quadruped MEMS robot were 7.2 mm and 95.8 mg, respectively. The quadruped robot showed the walking speed of 24.6 mm/min. The robot tended to lose its balance and the weight balance is quite important for the moving quadruped. On the other hand, the length and weight of the hexapod MEMS robot were 9.0 mm and 162 mg, respectively. The hexapod robot showed stable walking. The speed was 27.0 mm/min.