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.     

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.     

Optimal fault tolerant gait sequence of the hexapod robot withoverlapping reachable areas and crab walking

This paper extends the authors' previous results on fault tolerant locomotion of the hexapod robot on even terrain by relaxing nonoverlap of redefined reachable cells of legs and considering crab walking. It is shown that in fault tolerant locomotion two adjacent legs of the hexapod robot can have overlapping redefined reachable cells with each other and consequently the stride length of the gaits is increased. Also, the optimal fault tolerant periodic gaits for hexapod robots to have the maximum stride length in one cycle in crab walking on even terrain are derived with distinct reachable cells. The derived sequence for crab walking has different orders of leg swing according to the relative values of the crab angle and some design parameters of the robot     

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.     

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.     

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.     

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.     

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．     

Motion planning of walking robots using ordinal optimization

A general approach for coordinating the legs of a multi-legged statically stable walking machine on an uneven terrain. The method of ordinal optimization is used to find a good motion plan for low travel time that specifies the footholds and the gait of the walking machine. Numerical simulations illustrate the approach and demonstrate that we can find a good motion plan for uneven terrain with high complexity in a reasonably short time     

Optimal impedance control based on body inertia for a hydraulically driven hexapod robot walking on uneven and extremely soft terrain

This paper presents the implementation of impedance control for a hydraulically driven hexapod robot named COMET‐IV, which can walk on uneven and extremely soft terrain. To achieve the dynamic behavior of the hexapod robot, changes in center of mass and body attitude must be taken into consideration during the walking periods. Indirect force control via impedance control is used to address these issues. Two different impedance control schemes are developed and implemented: single‐leg impedance control and center of mass‐‐based impedance control. In the case of single‐leg impedance control, we derive the necessary impedance and adjust parameters (mass, damping, and stiffness) according to the robot legs' configuration. For center of mass–based impedance control, we use the sum of the forces of the support legs as a control input (represented by the body's current center of mass) for the derived impedance control and adjust parameters based on the robot body's configuration. The virtual forces from the robot body's moment of inertia are adapted to achieve optimal control via a linear quadratic regulator method for the proposed indirect attitude control. In addition, a compliant switching mechanism is designed to ensure that the implementation of the controller is applicable to the tripod sequences of force‐based walking modules. Evaluation and verification tests were conducted in the laboratory and the actual field with uneven terrain and extremely soft surfaces. © 2011 Wiley Periodicals, Inc.     

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.     

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.     

双足机器人预观控制的ZMP补偿步行模式研究

针对双足机器人的稳定行走,提出了一种预观控制的零力距点（ZMP）补偿步行模式在线生成方法。利用实际ZMP与目标ZMP之间的未来误差信息,基于预观控制计算机器人行走过程中质心的补偿量,事先调整质心轨迹来改变步态。最终使实际ZMP更好地跟踪目标值。12自由度的双足机器人动力学仿真验证了所提出方法的有效性,而且机器人能在一定程度不平整地面上实现稳定行走。     

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.     

An aperiodic straight motion planning method for a quadruped walking robot

In even terrain, wave gait is the periodic gait having the optimal stability. In this paper, we focus on aperiodic forward straight motion having the lifting sequence of wave gait in order for quadruped to adapt to terrain and to have good moving capability. We investigated the condition of support pattern from which such gait motion can be generated. It is proved that from any support pattern satisfying the condition, it is always possible to transform the given support pattern to the support pattern of wave gait. An aperiodic gait planning method that adapt to terrain and maximize moving capability is proposed. A simulation result shows that the proposed method works well in rough terrain having forbidden areas.     

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.     

仿生六足步行机器人步态轨迹的研究与仿真

针对仿生六足步行机器人关节较多,其步态轨迹规划和关节控制量计算都较为复杂的现状,采用Solidworks软件与MSC.ADAMS软件相结合的方式对六足仿生步行机器人的样机模型进行了运动学仿真与分析.通过仿真,验证了所设计的三角步态的适用性和所选择的三次样条曲线作为机器人足端点轨迹曲线方案的可行性.详细阐述了六足仿生步行机器人轨迹仿真的原理、方法及过程,找到了一种在ADAMS环境下求解机器人逆解的方法,简化了理论计算,提高了设计效率.     

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.     

基于deep Q-network双足机器人非平整地面行走稳定性控制方法

针对双足机器人在非平整地面行走时容易失去运动稳定性的问题,提出一种基于一种基于价值的深度强化学习算法DQN（Deep Q-Network）的步态控制方法。首先通过机器人步态规划得到针对平整地面环境的离线步态,然后将双足机器人视为一个智能体,建立机器人环境空间、状态空间、动作空间及奖惩机制,该过程与传统控制方法相比无需复杂的动力学建模过程,最后经过多回合训练使双足机器人学会在不平整地面进行姿态调整,保证行走稳定性。在V-Rep仿真环境中进行了算法验证,双足机器人在非平整地面行走过程中,通过DQN步态调整学习算法,姿态角度波动范围在3°以内,结果表明双足机器人行走稳定性得到明显改善,实现了机器人的姿态调整行为学习,证明了该方法的有效性。     

Terrain evaluation and its application to path planning for walking machines

Motion planning of walking machines normally contains two aspects: gait planning and body trajectory planning. When generating an optimal body trajectory on natural terrain, the leg movement must be taken into account. Due to the large searching space resulting from the combination of leg movement and terrain conditions, it is quite time consuming to produce an optimal result of body trajectory planning. In this paper, an effective method of body trajectory planning is introduced by virtue of a terrain evaluation that links the terrain conditions with machine mobility. Based on the evaluation, a potential field is constructed for graph searching. Best first planning (BFP) is adopted to search the optimal path. The path generated with the proposed method could offer the best opportunity to place the machine feet moving with a certain gait over a rough terrain. The assumptions and shortages associated with the present work are also discussed.