Quadrupedal running with a flexible torso: control and speed transitions with sums-of-squares verification

This paper studies quadrupedal bounding in the presence of flexible torso and compliant legs with non-trivial inertia, and it proposes a method for speed transitions by sequentially composing locally stable bounding motions corresponding to different speeds. First, periodic bounding motions are generated simply by positioning the legs during flight via suitable (virtual) holonomic constraints imposed on the leg angles; at this stage, no control effort is developed on the support legs, producing efficient, nearly passive, bounding gaits. The resulting motions are then stabilized by a hybrid control law which coordinates the movement of the torso and legs in continuous time, and updates the leg touchdown angles in an event-based fashion. Finally, through sums-of-squares programming, formally verified estimates of the domain of attraction of stable fixed points are employed to realize stable speed transitions by switching among different bounding gaits in a sequential fashion.     

Gait optimization of step climbing for a hexapod robot

RHex-style hexapod robot is a type of legged robot which can perform multiple moving gaits according to different applications, due to its simple structure and strong mobility. However, traversing high obstacles has always been a big challenge for legged robots. In this paper, gait optimization of a hexapod robot is proposed for climbing steps at different heights, which even enables the robot to climb the step 3.9 times of the leg length. First, a previous step-climbing gait is optimized by adjusting body inclination when placing front legs on top of the step, which enables RHex with different sizes to perform the rising stage of the gait. Second, to improve the climbing heights, a novel quasi-static climbing gait is proposed by using the reversed claw-shape legs to reach the higher step. The nondeformable legs are used to raise the center of mass (COM) of the body by lifting the front and rear legs alternately so that the front legs can reach the top of the step, then the front and middle legs are lifted alternately to maneuver COM up onto the step. The simulations and dynamic analysis of climbing steps are utilized to verify the feasibility of the improved gait. Finally, the step-climbing experiments at different heights are performed with the optimized gaits to compare with the existing gaits. The results of simulations and experiments show the superiority of the proposed gaits due to climbing higher steps.     

基于静平衡的四足机器人直行与楼梯爬越步态

为提升四足机器人的障碍爬越能力,采用稳定裕度作为四足机器人静态稳定的判据,以落足点形成的 象限边界明确了不同初始位姿机器人的迈腿可能性．基于迈腿次序将所有步态划分为24 种类型．利用运动空间需 求最小、稳定裕度最大、步态协调性最好3 个基本评价指标,对四足机器人的24 种基本步态进行了对比分析．提出 了基于投影分析法结合平面静平衡步态理论的楼梯爬越步态研究方法,并以上述3 个特性参数最佳为要求,对楼梯 爬越步态进行了系统仿真,所得结果为四足机器人的直行与楼梯爬越步态选择提供了理论依据．实验表明了所研究 方法的有效性．     

Generation of discontinuous gaits for quadruped walking vehicles

Discontinuous gaits for walking machines have not yet been properly studied. Research has focused on the investigation, comprehension, and mathematical formulation of natural gaits. These gaits feature the fact that the body is in constant motion. The results have been significant, but they seem more adequate for animals than machines. On the other hand, discontinuous gaits, executed by animals under extreme conditions, exhibit excellent attributes for implementation in walking machines. This article presents a comparative study of continuous and discontinuous gaits with regard to their maximum achievable velocity and stability. Other aspects such as implementation in real machines, power requirements, and control under terrain difficulties are mentioned briefly. An elemental discontinuous gait is stated, and some variations on deriving crab and turning gaits are performed. Different methods for enlarging the achievable crab angle and improving stability are discussed for discontinuous crab gaits. A similar study is also done for turning gaits. (c) 1995 John Wiley & Sons, Inc.     

Gait transition and modulation in a quadruped robot: A brainstem-like modulation approach

In this article, we propose a bio-inspired architecture for a quadruped robot that is able to initiate/stop locomotion; generate different gaits, and to easily select and switch between the different gaits according to the speed and/or the behavioral context. This improves the robot stability and smoothness while locomoting.We apply nonlinear oscillators to model Central Pattern Generators (CPGs). These generate the rhythmic locomotor movements for a quadruped robot. The generated trajectories are modulated by a tonic signal, that encodes the required activity and/or modulation. This drive signal strength is mapped onto sets of CPG parameters. By increasing the drive signal, locomotion can be elicited and velocity increased while switching to the appropriate gaits. This drive signal can be specified according to sensory information or set a priori.The system is implemented in a simulated and real AIBO robot. Results demonstrate the adequacy of the architecture to generate and modulate the required coordinated trajectories according to a velocity increase; and to smoothly and easily switch among the different motor behaviors.     

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.

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。     

Integration of vision and walking skills together with high-level strategies for quadruped robots to play soccer

Legged robots taking part in real multi-agent activities represent a very innovative challenge. This domain of research requires developments in three main areas. First, without any feedback information from the environment, there is no way for robots to achieve some tasks autonomously. Fortunately, the quadruped 'Sony' prototypes on which all experiments are carried out are equipped with an enhanced vision system; thanks to its CCD camera located in its head, the robot can obtain color images of the scene around it. Extracting relevant information from the images captured is not easy since it must be done onboard in real time. Moreover, image treatment procedures should have high process rates for the robot to react quickly in front of unexpected events. A special vision module composed of three parts has been designed for these purposes. The second point to focus on is the walking ability of the robot. Quadrupeds are designed to move efficiently and rapidly on flat ground. The objective of the walking module is to generate appropriate walking patterns allowing the machine to walk in the desired direction. Walking gaits are produced like reflexes by the robot itself to adapt to the situation. With regard to the design of these gaits, emphasis has been put on increasing speed and mastering transitions. Finally, the machine should be given a minimum of intelligence since it has to manage vision information and its walking gaits by itself. When involved in situations of cooperation or competition or both, like in a soccer game, a high-level supervision task is welcome. This paper presents detailed developments of these three points and describes how they are implemented on a real robot.     

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.     

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.     

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.      

Generating high-speed dynamic running gaits in a quadruped robot using an evolutionary search

Over the past several decades, there has been a considerable interest in investigating high-speed dynamic gaits for legged robots. While much research has been published, both in the biomechanics and engineering fields regarding the analysis of these gaits, no single study has adequately characterized the dynamics of high-speed running as can be achieved in a realistic, yet simple, robotic system. The goal of this paper is to find the most energy-efficient, natural, and unconstrained gallop that can be achieved using a simulated quadrupedal robot with articulated legs, asymmetric mass distribution, and compliant legs. For comparison purposes, we also implement the bound and canter. The model used here is planar, although we will show that it captures much of the predominant dynamic characteristics observed in animals. While it is not our goal to prove anything about biological locomotion, the dynamic similarities between the gaits we produce and those found in animals does indicate a similar underlying dynamic mechanism. Thus, we will show that achieving natural, efficient high-speed locomotion is possible even with a fairly simple robotic system. To generate the high-speed gaits, we use an efficient evolutionary algorithm called set-based stochastic optimization. This algorithm finds open-loop control parameters to generate periodic trajectories for the body. Several alternative methods are tested to generate periodic trajectories for the legs. The combined solutions found by the evolutionary search and the periodic-leg methods, over a range of speeds up to 10.0 m/s, reveal "biological" characteristics that are emergent properties of the underlying gaits.     

Spine as an engine: effect of spine morphology on spine-driven quadruped locomotion

In quadruped animals, spinal movements contribute to locomotion in terms of controlling body posture and integrating limb and trunk actions. In this paper, we develop quadruped models with different numbers of spinal joints to demonstrate the spine-driven locomotion. Actuated spinal joint(s) are exclusively employed to these models with a minimalistic control strategy. We choose some typical individuals from two models and analyze them on gait properties. Results show that employing the spine morphology with two joints can greatly enhance the stability and speed of locomotion by readjusting the center of mass, increasing the stride length, and generating double flight phases similar to running cheetahs’ gait, which makes significant difference in the speed and the gait. Furthermore, we explore and compare models with more spinal joints. Results show that all gaits emerged from them can be categorized into three types (bounding, bounding with double flight phase, and stotting gaits). Overall, bounding gait with double flight phases is a more biologically inspired locomotive behavior; model with two spinal joints could be sufficient to emulate biological spine-driven locomotive behaviors.     

双手爪式仿生攀爬机器人的摇杆控制

探讨一种新型双手爪式5自由度仿生攀爬机器人(Climbot)的摇杆控制方法.首先,对机器人的运动学和可夹持空间问题进行了分析.然后,针对其双手爪交替夹持攀爬的特点,提出了直观的摇杆操作模式,包括对不同的攀爬步态设计了不同的操作坐标系,并利用建立变换矩阵的方法将交替夹持端前后的机器人描述在同一坐标系中.最后,通过尺蠖、扭转和翻转3种步态的路灯杆攀爬和应用示范实验结果证明了该摇杆控制方法的有效性.     

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．     

Online Optimization of Swimming and Crawling in an Amphibious Snake Robot

An important problem in the control of locomotion of robots with multiple degrees of freedom (e.g., biomimetic robots) is to adapt the locomotor patterns to the properties of the environment. This article addresses this problem for the locomotion of an amphibious snake robot, and aims at identifying fast swimming and crawling gaits for a variety of environments. Our approach uses a locomotion controller based on the biological concept of central pattern generators (CPGs) together with a gradient-free optimization method, Powell's method. A key aspect of our approach is that the gaits are optimized online, i.e., while moving, rather than as an off-line optimization process. We present various experiments with the real robot and in simulation: swimming, crawling on horizontal ground, and crawling on slopes. For each of these different situations, the optimized gaits are compared with the results of systematic explorations of the parameter space. The main outcomes of the experiments are: 1) optimal gaits are significantly different from one medium to the other; 2) the optimums are usually peaked, i.e., speed rapidly becomes suboptimal when the parameters are moved away from the optimal values; 3) our approach finds optimal gaits in much fewer iterations than the systematic search; and 4) the CPG has no problem dealing with the abrupt parameter changes during the optimization process. The relevance for robotic locomotion control is discussed.     

An energetic control based on limit cycles for stabilization of fast legged robots

Control of legged robots with fast gaits is addressed in this paper. These kind of systems interact intermittently with the environment. We propose a viable approach for the control of hopping gaits for legged robots. This control approach is based on controlled limit cycles (CLC) for stabilization of fast gaits (closed orbits) for legged robots. The designed control system generates the desired trajectories (on-line) and control inputs. Robustness of the proposed control with respect to parameter variation and disturbance is illustrated by numerical simulations. Viable definitions of gaits and their admissibility are introduced.     

A versatile locomotion mechanism for amphibious robots: eccentric paddle mechanism

Most of recently developed rescue robots can only be deployed to limited attacked regions after tsunami and the floods, due to their limited mobility on complex amphibious terrains. To access such amphibious environments with improved mobility, we propose a novel eccentric paddle mechanism (ePaddle) which has a set of paddles eccentrically placed in a wheel to perform multiple terrestrial, aquatic, and amphibious gaits. One of the advantages of our proposed ePaddle mechanism is its unique locomotion versatility introduced by the eccentric distance between the paddle shaft and the wheel center. We demonstrate this versatility by proposing five typical gaits for traveling on different terrains. For instance, wheeled rolling gait is used to achieve high-speed locomotion on even terrain. Legged gait is applied to travel on the rough terrains. To access the soft terrains where wheels slip and legs sink, a wheel-leg-integrated gait is performed by digging the paddle into the ground. To swim in the water, rotational paddling and oscillating paddling gaits are proposed. For each of these gaits, standard gait sequence is defined and joint parameters are calculated based on kinematics. An ePaddle prototype is then built and tested with the proposed gait sequences. Experimental results verify the design of the ePaddle mechanism as well as its versatile gaits.     

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.     

Generating gaits for snake robots: annealed chain fitting and keyframe wave extraction

Snake robots have many degrees of freedom, which makes them both extremely versatile and complex to control. They are often controlled with gaits, coordinated cyclic patterns of joint motion. Using gaits simplifies the design of high-level controllers, but shifts the complexity burden to designing the gaits. In this paper, we address the gait design problem by introducing two algorithms: Annealed chain fitting and Keyframe wave extraction. Annealed chain fitting efficiently maps a continuous backbone curve describing the three-dimensional shape of the robot to a set of joint angles for a snake robot. Keyframe wave extraction takes joint angles fit to a sequence of backbone curves and identifies parameterized periodic functions that produce those sequences. Together, they allow a gait designer to conceive a motion in terms three-dimensional shapes and translate them into easily manipulated wave functions, and so unify two previously disparate gait design approaches. We validate the algorithms by using them to produce rolling and sidewinding gaits for crawling and climbing, with results that match previous empirical investigations.