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.     

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.     

Bionic Quadruped Robot Dynamic Gait Control Strategy Based on Twenty Degrees of Freedom

Quadruped robot dynamic gaits have much more advantages than static gaits on speed and efficiency, however high speed and efficiency calls for more complex mechanical structure and complicated control algorithm. It becomes even more challenging when the robot has more degrees of freedom. As a result, most of the present researches focused on simple robot, while the researches on dynamic gaits for complex robot with more degrees of freedom are relatively limited. The paper is focusing on the dynamic gaits control for complex robot with twenty degrees of freedom for the first time. Firstly, we build a relatively complete 3D model for quadruped robot based on spring loaded inverted pendulum (SLIP) model, analyze the inverse kinematics of the model, plan the trajectory of the swing foot and analyze the hydraulic drive. Secondly, we promote the control algorithm of one-legged to the quadruped robot based on the virtual leg and plan the state variables of pace gait and bound gait. Lastly, we realize the above two kinds of dynamic gaits in ADAMS-MATLAB joint simulation platform which testify the validity of above method.      

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.     

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.     

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.     

Steady Crawl Gait Generation Algorithm for Quadruped Robots

The capability of stable walking on irregular terrain is the primary advantage of legged robots over wheeled mobile robots. However, the traditional foothold selection-based gait generation algorithms are not suitable at some points for blind robots which cannot obtain the exact terrain information. A velocity-based gait generation algorithm with real-time adaptation rules which are necessary for steady walking is suggested. Particularly, we have developed a steady crawl gait with duty factor β = 0.75. The main feature of the suggested algorithm is that it is not based on foothold selection and it can be used for the walking of blind robots on more realistic irregular terrain. The adaptation rules are the translational velocity modification to satisfy the steady gait requirement and the swing period modification to avoid the kinematic limitation. The suggested gait generation algorithm has been implemented in a simple quadruped robot that has a total of eight actuated joints on the legs. Using PD controllers for each actuated joint for the trajectory following and the adaptation algorithm of gait parameters, the steady periodic crawl gait on irregular terrain has been demonstrated.     

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.     

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.     

基于改进蚁群算法的四足机器人步态规划

四足机器人关节众多、运动方式复杂,步态规划是四足机器人运动控制的基础。传统的算法多基于仿生原理,缺乏广泛适应性。 在建立运动学方程的基础上,提出了一种基于改进蚁群算法的步态规划算法。该算法利用了四足机器人4条腿运动的线性无关性,将步态规划问题转换为在四维空间里求取最长路径问题。仿真结果表明,该算法得出了满足约束条件的所有步态,最后通过机器人样机检验,验证了该算法求取结果的有效性和合理性。     

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.     

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.     

一种多模型融合的仿猎豹四足机器人复杂运动控制方法

针对具有2自由度主动脊柱关节的仿猎豹四足机器人,基于任务分解思想和生物神经系统机理,提出多模型融合的控制方法。该方法以弹簧负载倒立摆模型实现单腿跳跃控制,通过中枢模式发生器（CPG）实现4条腿之间以及脊柱―腿之间的协调控制,利用虚拟模型控制实现机器人与环境交互,采用基于CPG输出的有限状态机来融合3个控制模型,构建仿猎豹四足机器人的多模型分层运动控制器。参考猎豹脊柱运动特征,设计了机器人脊柱关节运动模式,给出脊柱与腿的协调控制策略。最后,在Webots仿真环境中搭建了仿猎豹四足机器人虚拟样机,实现了不同步态下的脊柱―腿的协调控制、在崎岖地形上稳定奔跑,以及平滑的对角―疾驰―对角步态转换,仿真结果验证了所提出的多模型融合的四足机器人运动控制方法的有效性。     

Effects of turning gait parameters on energy consumption and stability of a six-legged walking robot

Minimization of energy consumption plays a key role in the locomotion of a multi-legged robot used for various purposes. Turning gaits are the most general and important factors for omni-directional walking of a six-legged robot. This paper presents an analysis on energy consumption of a six-legged robot during its turning motion over a flat terrain. An energy consumption model is developed for statically stable wave gaits in order to minimize dissipating energy for optimal feet forces distributions. The effects of gait parameters, namely angular velocity, angular stroke and duty factors are studied on energy consumption, as the six-legged robot walks along a circular path of constant radius with wave gait. The variations of average power consumption and energy consumption per unit weight per unit traveled length with the angular velocity and angular stroke are compared for the turning gaits of a robot with four different duty factors. Computer simulations show that wave gait with a low duty factor is more energy-efficient compared to that with a high duty factor at the highest possible angular velocity. A stability analysis based on normalized energy stability margin is performed for turning motion of the robot with four duty factors for different angular strokes.     

Temporal gait control of a quadruped robot

The design and control of a four-legged robot for operation on vertical surfaces is described. The requirement that the robot trajectory be continually modifiable on-line in response to external sensor data is addressed with the development of a temporal gait control strategy. The ensuing gait automatically converges to various classical gaits for straight-line, turning and spinning maneuvres, and naturally accommodates transitions between these. Simulation results are presented to demonstrate the performance of this control strategy.     

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.     

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.     

Optimal Trajectories for a Quadruped Robot with Trot,Amble and Curvet Gaits for Two Energetic Criteria

In this paper, optimal cyclic reference trajectories aredesigned for three gaits of a quadruped robot, the curvet, theamble, and the trot, taking into account the actuatorscharacteristics. The gaits are composed of stance phases andinstantaneous double supports. The principle of virtual leg isused to obtain simpler dynamic model describing the motion ofthe quadruped. The impact phases are modeled by passive impactequations. For the curvet the step is composed of twodifferent half steps. For the amble and trot gaits twofollowing half steps are symmetrical.The optimization problem is solved with an algebraicoptimization technique. The actuated joint evolution is chosenas a polynomial function of time. The coefficients of thepolynomial functions are optimization parameters. Thequadruped studied has non-actuated ankles. The kineticmomentum theorem permits to define the evolution of this non-actuated variable in function of the actuated variables. Twoenergetic criteria are defined: a torque cost and an energetic cost. The first is represented by the integral of the torquenorm and the second by the absolute value integral of theexternal forces work. The two criteria are calculated for adisplacement of one meter. During the optimization process,the constraints on the ground reactions, on the validity ofimpact, on the torques, on the joints velocities and on themotion velocity of the robot prototype are taken into account.Simulation results are presented for the three gaits. Allmotions are realistic. Curvet is the less efficient gait withrespect to the criteria studied. For slow motion, trot is themore efficient gait. But amble permits the fastest motion withthe same actuators.     

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.