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.     

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.     

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.     

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.     

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.     

Path planning for a quadruped robot: an artificial field approach

In this paper, we consider the problem of planning a feasible path for a quadruped walking robot in an environment of obstacles. In conventional path-planning problems, the main focus is merely collision avoidance with obstacles since a wheeled robot is involved. However, in the case of a legged robot, both collision avoidance and crossing over obstacles must be taken into account in the process of path planning. Furthermore, the constraints of the gait should be considered to guarantee the feasibility of a planned path. To resolve this complicated problem in a systematic way, a new concept of an artificial thermal field is proposed. Specifically, with the assumption that a robot walks with a periodic crab gait, a robot and obstacles in a three-dimensional (3D) space are projected on a 2D plane. Next, the 2D obstacles are transformed into the configuration space of a quadruped robot. A feasible path is finally sought in an artificial thermal field which is constructed numerically on the discretized configuration space. To verify the efficacy of the proposed approach, three notable simulation results are provided.     

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.     

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.     

Generation and Analyses of the Reinforced Wave Gait for a Mammal-Like Quadruped Robot

The statically stable gait control of a mammal-like quadruped robot that provides an adequate or stable manner of traversing over irregular terrain was addressed. The reinforced wave gait which integrates new parameters of the lateral offset and displacements of the center of gravity (COG) based on the profiles of standard wave gait was investigated. The continuous and discontinuous motion trajectory of a robot’s COG in the periodic reinforced wave gait could be realized. The longitudinal and lateral stability margins of a reinforced wave gait were formulated for the gait generation and control of a quadruped robot. Moreover, the effects of the lateral offset on the stability, velocity and the energy efficiency were studied in details. The reinforced wave gait with lateral sway motion adequately improved the stability, and two particular gait patterns that involve the lateral sway motion for a maximal velocity and maximum achievable stability were described. With consideration of a quadruped robot with asymmetric carrying loads on its body, a scheme that relates to the gait parameters of the displacement of a robot’s COG to avoid losing stability was proposed. The simulation and experimental results about the effects of lateral offset added in the reinforced wave gait on the minimum power consumption during a quadruped robot walking on a flat terrain indicated that the reinforced wave gait with a larger lateral offset would generate a better wave gait with a higher velocity and energy efficiency.     

An aperiodic Z type spinning gait planning method for a quadruped walking robot

Spinning gaits are used for altering the direction of body in a narrow space. Previous studies reveal thatz type leg-lifting sequence is suitable for spinning motion. In this paper, we focus on anz type aperiodic spinning gait for a quadruped walking robot. We proposed a condition of support pattern suitable for the aperiodicz type spinning motion. Based on the condition, we proposed an aperiodicz type spinning gait planning method. It is shown that spinning capability can be independent of required stability margin. A simulation shows that good spinning capability and good terrain adaptability are obtained.     

Development of a quadruped walking robot AiDIN-III using biologically inspired kinematic analysis

This paper presents a bio-inspired mechanism design for a quadruped walking robot. The approach is derived from the observation on the behaviors of quadruped locomotion, skeletal structure, and the study on the stability of walking based on morphological analysis. In the first, we define the design parameters such as the dimensions of the body and limbs, the center of mass position, and locomotion mechanisms based on surveys on the literatures from biologists. Then, by using the parameters, we propose an useful framework for determining the design parameters of a quadruped walking robot. For implementations, we manufacture a dog-type self-contained quadruped walking robot, named AiDIN-III (Artificial Digitigrade for Natural Environment version III) and the effectiveness of the proposed idea is validated via experimental works.     

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.     

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.     

Omnidirectional static walking of a quadruped robot

In this paper, we propose a successive gait-transition method for a quadruped robot to realize omnidirectional static walking. The gait transition is successively performed among the crawl gaits and the rotation gaits, while the feet hold in common positions before and after gait transition. The gait-transition time is reduced by carefully designing the foot positions of the crawl gait and the rotation gait, while limiting the feet in rectangular reachable motion ranges. Computer simulations and experiments were executed to show the validity and the limitation of the proposed gait-transition method.     

Feasibility Study on Stability of Gait Patterns with Changeable Body Stiffness Using Pneumatic Actuators in a Quadruped Robot

An oscillator-type gait controller for a quadruped robot with antagonistic pairs of pneumatic actuators is proposed. By using the controller, a feasibility study on the stability of gait patterns with changeable body stiffness is reported. The periodic motions of the legs are generated and controlled by an oscillator network with state resetting. This type of controller has robustness in its gaits against variation in walking conditions or changes of environment. However, it sometimes loses robustness under conditions of actuation delay, decrease of actuator accuracy, etc. We investigated whether an oscillator-type controller with phase resetting is also effective under such conditions. The stability of locomotion also strongly depends on the mechanical properties of the body mechanism, especially the joint stiffness. In this report, the muscle tone of the robot on the pitching motion at the trunk is changeable by using the changeable elasticity of the pneumatic actuators. The stability of quadruped locomotion in walk and trot patterns with changeable body stiffness was evaluated with numerical simulations and hardware experiments.     

Feedforward and Feedback Dynamic Trot Gait Control for Quadruped Walking Vehicle

To realize dynamically stable walking for a quadruped walking robot, the combination of the trajectory planning of the body and leg position (feedforward control) and the adaptive control using sensory information (feedback control) is indispensable. In this paper, we propose a new body trajectory, the 3D sway compensation trajectory, for a stable trot gait; we show that this trajectory has a lower energy consumption than the conventional sway trajectory that we have proposed. Then, for the adaptive attitude control method during the 2-leg supporting phase, we consider four methods, that is, a) rotation of body along the diagonal line between supporting feet, b) translation of body along the perpendicular line between supporting feet, c) vertical swing motion of recovering legs, and d) horizontal swing motion of recovering legs; we then describe how we verify the stabilization efficiency of each method through computer simulation, stabilization experimentation, and experimenting in walking on rough terrain using the quadruped walking robot, TITAN-VIII.     

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.     

The standard circular gait of a quadruped walking vehicle

A quadruped walking vehicle has the potential capability of being developed into a vehicle of high mobility and adaptability to terrain by making use of its high degree of motion freedom. The authors have investigated the gait control problems of a walking vehicle, i.e. the straightforward or crab walk of the vehicle on rough terrains. This paper introduces a more generalized gait, namely, a circular gait around an arbitrarily located turn center, and discusses a standard circular gait. The standard circular gait is the one which maximizes the speed of walking and the rotational angle in a circular walk, and this consideration forms the basis of the discussion on advanced gait control problems. This paper formalizes the problems and analyses them by using mathematical optimization methods such as non-linear programming. Computations are carried out on a TITAN III, the quadruped walking vehicle model constructed by the authors. Several characteristics of the optimum gait and the final gait selection chart are derived. The validity of these conditions was verified by a circular walking experiment using the TITAN III.     

Mechanical Design of a Trunk with Redundant and Viscoelastic Joints for Rhythmic Quadruped Locomotion

Passive mechanisms, such as free joints and viscoelastic components, enable natural oscillation of the robot body, which allows rhythmic locomotion with low energy and computational costs. In particular, joint viscoelasticity can be a powerful candidate for changing natural oscillation and so influence the operation performance of locomotion. The present study considers the passive mechanism of a trunk, and investigates the contributions of a trunk mechanism with redundant joints and tunable viscoelasticity to quadruped locomotion. A physical quadruped robot with a trunk mechanism is developed, and the walking performance of this robot for various gait patterns and joint viscoelasticities is investigated. A simulation model is also constructed based on the physical robot, and the contribution of the viscoelasticity to trunk oscillation and the appropriate joint viscoelasticity and number of trunk joints are discussed. Experimental results obtained using the physical robot indicate that the proposed trunk mechanism contributes to successful locomotion as compared to a robot with a rigid trunk and that the velocity is influenced by not only the gait pattern, but also the joint viscoelasticity (i.e., there are appropriate couplings of the joint viscoelasticity and gait pattern). The simulation results indicate that the trunk mechanism requires joint viscoelasticity in order to achieve oscillation and that a greater number of joints having a smaller joint viscoelasticity enables higher velocity. These results suggest that, in addition to the leg mechanism and the controller design, the design of the trunk mechanism is also important.