Path tracking with quadruped walking machines using discontinuous gaits

Discontinuous gaits for walking machines offer great advantages over wave gaits, and they seem more adequate for following a path over irregular terrain. This paper, focused on quadruped walking robots, addresses the problem of following an arbitrary path using both discontinuous crab and turning gaits. First, the paper presents the algorithms to generate these gaits as local motions and highlights their advantages in comparison with continuous gaits. This comparison considers stability, velocity, power consumption and terrain adaptability. The algorithms for tracking an arbitrary trajectory using these gaits are then introduced, and some simulations and experimental results are reported.     

Stability analysis of wave-crab gaits of a quadruped

Crab walking is as important as forward walking as applied to walking machine control. Crab walking is especially important to a quadruped since a quadruped has a similar leg geometric layout in both longitudinal and lateral directions. In the studies of forward walking gaits, the wave gait was found to be the optimally stable. In this article, the wave gait is applied to the crab walking of a quadruped and it is modified into four types of wave-crab gaits according to the range of crab angle. The stability formulae of these wave-crab gaits are then derived analytically based on the following three stability measurements: stability margin (S_m), body-longitudinal (or lateral) stability margin (S_bl or S_bt) and crab longitudinal stability margin (S_cl). S_m is the true stability index under quasi-static walking condition. However, the equations are more complicated. S_bl (or S_bt) is simpler and can be used as a good approximation of S_m. S_cl was commonly adopted as the stability index in the previous gait studies. Nevertheless, S_cl is found to be misleading for a large portion of crab angle range. The analytical results derived in this paper are useful to the geometric design and to the real-time control of a quadruped.     

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.     

Path planning and gait of walking machine in an obstacle-strewn environment

The locomotion of a quadrupedal walking machine in an obstacle-strewn environment is studied. The path planning of the walking machine body includes the following two features: first, the path is generated based on the Bezier curve so that its shape can be easily adjusted to avoid obstacles; second, the velocity and acceleration are assigned independently from the path generation so that the inertial terms are controllable. After the path has been generated, a gait algorithm that enables the walking machine to follow the path and maintain stability is developed. Two special cases—straight-line crab walking and turning about a fixed axis—are studied first. The general case that the walking machine is following an arbitrary curve is then studied. During walking, if the crab angle exceeds a certain limit, the gait needs to be changed in order to maintain stability. The methods for changing the gaits are discussed.     

Dynamic Effects in Statically Stable Walking Machines

Discontinuous gaits for walking machines present some advantages over wave gaits such as better stability margins and greater speed for small duty factors, for instance. The problem is that a machine using discontinuous gaits starts and stops its body motion several times per locomotion cycle. This means that high accelerations appear, therefore the theoretical static stability margin can be inadequate for measuring stability. This paper addresses how dynamic effects modify the measurement of the static stability of a discontinuous gait and determines the acceleration under which the criterion of using the static stability margin for measuring the stability is valid. For this study, a dynamic planar model of a four-legged walking machine was derived. Then, both the longitudinal and dynamic stability margins were computed and compared. Final results show that the static stability margin is an adequate measurement for studying stability in massless leg machines with the constraint that the acceleration of the body be smaller than the inversion acceleration. When the mass of the legs is significant, stability is determined by the dynamics of the legs and the distribution of the mass of the legs as well.     

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     

Dealing with internal and external perturbations on walking robots

Up to now, walking robots have been working outdoors under favorable conditions and using very large stability margins to cope with natural environments and intrinsic robot dynamics that can cause instability in these machines when they use statically-stable gaits. The result has been very slow robots prone to tumble down in the presence of perturbations. This paper proposes a novel gait-adaptation method based on the maximization of the Normalized Dynamic Energy Stability Margin. This method enables walking-machine gaits to adapt to internal (robot dynamics) and external (environmental) perturbations, including the slope of the terrain, by finding the gait parameters that maximize robot stability. The adaptation method is inspired in the natural gait adaptation carried out by humans and animals to balance external forces or the effect of sloping terrain. Experiments with the SILO4 quadruped robot are presented and show how robot stability is more robust when the proposed approach is used for different external forces and sloping terrains. Using the proposed gait-adaptation approach the robot is able to withstand external forces up to 58% the robot weight and 25-degree slopes.

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.     

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.     

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．     

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.     

仿蟹机器人步态分析与仿真

在仿蟹机器人的行走控制中,步态的选择对机器人的稳定快速行走具有至关重要的作用。本文对仿蟹八足机器人的基本步态进行了分类,并进一步对八足波形步态进行分析,得出八足步行机器人在采用双四足步态的行走方式时,既可以满足速度的要求,又可以保证机器人的稳定性。通过计算机软件ADAMS对所选步态进行全局仿真,结果验证了步态规划的合理性,同时得到了机器人相关物理量的变化曲线,为进一步选择电机,分析机器人系统的动态特性提供了依据。     

四足步行机跨沟前后的步态分析

本文针对四足步行机在直线行走时的跨沟步态进行了讨论.首先对步行机跨沟前周期步态的运动特性运用相位的概念作了阐述.在此基础上,分别对步行机的最大越沟能力的确定.越沟前初始位置的选取,姿态调整步态的规划和优化,以及稳定性的判别等问题作了分析和研究.并提出了解决此类问题的设想.最后,从简便、通用的角度制订了一套简易实用的跟随越沟步态,为四足步行机越为步态的实现提供了依据.     

Analysis of wave gaits for energy efficiency

In this paper an energy efficiency analysis of wave gaits is performed for a six-legged walking robot. A simulation model of the robot is used to obtain the data demonstrating the energy consumption while walking in different modes and with varying parameters. Based on the analysis of this data some strategies are derived in order to minimize the search effort for determining the parameters of the gaits for an energy efficient walk. Then, similar data is obtained from an actual experimental setup, in which the Robot-EA308 is used as the walking machine. The strategies are justified based on this realistic data. The analysis concludes the following: a phase modified version of wave gaits is more efficient than the (conventional) wave gaits, using the possible minimum protraction time results in more energy efficient gaits and higher velocity results in less energy consumption per traveled distance. A stability analysis is performed for the phase modification of the wave gaits, and the stability loss due to the modification is calculated. It is concluded that the loss in stability is insignificant.

Soft computing-based expert systems to predict energy consumption and stability margin in turning gaits of six-legged robots

Turning gaits are the most general and very important ones for omni-directional walking of a six-legged robot. Soft computing-based expert systems have been developed in the present work to predict specific energy consumption and stability margin of turning gait of a six-legged robot. Besides back-propagation neural network, three approaches based on adaptive neuro-fuzzy inference system have been developed and their performances are compared with each other. Genetic algorithm-tuned multiple adaptive neuro-fuzzy inference systems are found to perform better than other approaches. This could be due to a more exhaustive search conducted by the genetic algorithm in place of back-propagation algorithm and the use of two separate adaptive neuro-fuzzy inference systems for two different outputs.     

Passive dynamic turning in 3D biped locomotion: an extension to passive dynamic walking

Passive dynamic walking usually refers to a kind of walking where a biped walker is able to walk downhill, without any actuation or control, just due to the gravity. Although most of works done in this regard have concentrated on passive walking along a straight line, in this paper we extend this concept to a more general case of locomotion, i.e. turning or walking along curved path. We call the novel extension passive turning, and categorize it to two types of finite and infinite. We showed that the finite type is still applicable on a typical downhill or ramp, while the infinite type is only practical on a specific surface profile that we call it helical ramp. Furthermore, several stability and parameter analysis are also conducted to evaluate more aspects of this notion. We highlighted that surprisingly, the passive straight walking is actually a special case of passive turning, just with infinite radius of turn and less asymptotical stability. It should be noted that the present study is performed using a model of an arc-foot three-dimensional (3D) compass gait walker.     

Dynamic modeling,stability, and energy efficiency of a quadrupedal walking machine

In the past, the dynamics of walking machines was studied based on very simple or simplified leg structures. A more complete dynamic model is essential for the further development of a practical walking machine. In this paper, the dynamic model of a realistic quadrupedal walking machine is derived for simulation and real‐time control purposes. The walker has four cylindrical pantograph legs, and the whole system consists of twenty‐nine links. The walking gait is wave gait with at least three feet on the ground at any time. Significant efforts have been made to improve the computational efficiency of the inverse dynamics, and the required CPU time is less than 10 ms on an IBM 3090. The derived dynamic model is then applied to study two practical issues of walking: dynamic stability and mechanical efficiency of different legs and gaits. Simulation results show clear advantages of one leg type over another, and of some walking strategies in terms of adjusting velocities, strokes, and duty factors for greater efficiency. © 2001 John Wiley & Sons, Inc.     

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.     

Periodic gaits for the CMU Ambler

The configuration of the Carnegie-Mellon University Ambler, a six-legged autonomous walking vehicle for exploring Mars, enables the recovery of a trailing leg past the leading leg to reduce the energy expenditure in terrain interactions. In this article, gaits developed for this unprecedented configuration are described. A stability criterion has been developed that ensures stability of the vehicle in the event of failure of any one of the supporting legs. Periodic gaits developed for the Ambler utilize the Ambler's unique abilities and continuously satisfy the stability criterion.     

双足机器人自适应常值驱动与传感反馈结合的仿生行走控制

为了将双足机器人的混沌步态控制收敛到稳定的周期步态,提出一种控制策略。首先用庞卡莱截面法研究斜坡倾角变化对步态的影响,结果表明,坡度增大会导致倍周期步态到混沌步态的产生;然后以人类步行的生物力学为仿生依据,根据延迟反馈控制的基本思路,设计了自适应常值驱动与传感反馈相结合的仿生行走控制策略,并依据当前步和前两步初始状态对控制器参数进行逐步调节,最终将混沌步态控制收敛到周期步态。仿真结果表明了所提出算法的有效性。