Dynamic Analysis Tool for Legged Robots

The paper introduces a systematic approach for dealing with legged robot mechanism analysis. First, we briefly summarize basic mathematical tools for studying the dynamics of these multi-loop and parallel mechanisms using a unified spatial formulation which is useful for computer algorithms. The dynamic behavior analysis is based on two stages. The first one deals with establishing the equations of motion of the whole mechanism including legs tip impact effects and allowing us to solve the direct and inverse dynamic problems. The second concerns the feet–ground interaction aspect which is one of the major problem in the context of dynamic simulation for walking devices. We focus on the phenomenon of contact by introducing a general model for dynamic simulation of contacts between a walking robot and ground. This model considers a force distribution and uses an analytical form for each force depending only on the known state of the robot system. Finally, some simulation results of biped robot are given. The simulation includes all phenomena that may occur during the locomotion cycle: impact, transition from impact to contact, contact during support with static friction, transition from static to sliding friction and sliding friction.     

Stealth walking with reduced double-limb support phase and its extension to careful legged locomotion

Stealth walking is an underactuated walking movement completing in one step for a stable and cautious walk on irregular terrains. The generated gait generally consists of the single- and double-limb support phases; during the former, the leg angles are strictly controlled to follow the desired trajectories to make the forefoot land on the ground stealthily, whereas during the latter, the upper body is controlled to return to the initial state while keeping the vertical ground reaction forces acting on both feet positive. This causes, however, the increase of the step period and deterioration of the energy efficiency. To solve this problem, this paper discusses some methods for achieving high-speed stealth walking based on a reduction of the double-limb support phase. First, a model of an underactuated rimless wheel with an upper body is introduced for analysis. Second, a method for generating a stealth walking gait of the linearized model is proposed, and the instability inherent in the gait is mathematically investigated. Third, two methods for extending the obtained results to the nonlinear model are discussed. Fourth, the method is also extended to generate a careful walking gait on the frictionless road surface; the importance and significance of this study are discussed through investigation of a strict stealth walking.     

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.     

仿人机器人双足行走模型研究

针对仿人机器人双足行走的稳定性问题,引入零力矩点理论,根据稳定行走必须满足地面反作用力位于稳定区域内这个条件,推导出仿人机器人在行走过程中单双腿支撑期的稳定区域面积和稳定裕量。建立2种不同形状的仿人机器人双足模型,在足底和地面间创建一系列接触力,并通过机械系统动力学自动分析软件得到行走过程中足底各个点的受力曲线并进行受力分析,得出合理的双足形状。     

Modeling and computational issues in the inverse dynamics simulation of triple jump

The triple jump is a demanding field event consisting of an approach run, and then followed by a hop, a bound, and a jump. The three consecutive takeoffs are executed at high speed, during which a jumper must absorb extremely large impact forces. The purpose of this paper is to develop an effective formulation for the inverse dynamics simulation of all the jump phases separately. A planar model of the jumper is used, composed of 14 rigid segments connected by 13 hinge joints, and actuated by muscle forces in the lower limbs and resultant muscle torques in the upper body joints. The equations of motion of the model are obtained using a projective technique, allowing for effective assessment of the ground reactions as well as muscle forces and joint reaction forces in the lower limbs. Some numerical results of the inverse dynamics simulation of a triple jump are reported.     

一种新的双足机器人模型设计与相关研究

针对双足机器人最简模型在行走过程中出现摆动腿足部擦地的问题,提出了一种通过摆动腿膝关节弯曲达到摆动腿缩短的新模型。当摆动腿开始摆动时,摆动腿膝关节弯曲锁定,摆动腿缩短;当摆动腿摆动到最大位置时,膝关节解锁,摆动腿伸直再锁定,此后摆动腿回摆,系统变为直腿模型。采用脚后跟冲击控制,在摆动腿落地前,拖后的支撑腿与地面接触处施加一指向髋关节的瞬时冲击力,冲击力可以减小摆动腿着地时能量的损耗,同时驱动被动机器人向前行走。设计了迭代学习控制算法,找到极限环与不动点,实现不同给定期望步长跟踪的冲击力的计算。仿真结果表明,迭代学习控制可以有效的实现不同期望步长的跟踪,可以很快的找到机器人系统的不动点,通过收敛的相平面,得到稳定的极限环,保证了机器人行走过程稳定。     

Producing alternating gait on uncoupled feline hindlimbs: muscular unloading rule on a biomimetic robot

Studies on decerebrate walking cats have shown that phase transition is strongly related to muscular sensory signals at limbs. To further investigate the role of such signals terminating the stance phase, we developed a biomimetic feline platform. Adopting link lengths and moment arms from an Acinonyx jubatus, we built a pair of hindlimbs connected to a hindquarter and attached it to a sliding strut, simulating solid forelimbs. Artificial pneumatic muscles simulate biological muscles through a control method based on EMG signals from walking cats (Felis catus). Using the bio-inspired muscular unloading rule, where a decreasing ground reaction force triggers phase transition, stable walking on a treadmill was achieved. Finally, an alternating gait is possible using the unloading rule, withstanding disturbances and systematic muscular changes, not only contributing to our understanding on how cats may walk, but also helping develop better legged robots.     

Human lifting simulation using a multi-objective optimization approach

This paper presents a multiobjective optimization (MOO) approach to predicting dynamic lifting for a three-dimensional, highly redundant digital human model with 55 degrees of freedom. The optimization problem is formulated to optimize two objective functions simultaneously—dynamic effort and stability—subject to basic physical and kinematical constraints. The predictive dynamics approach is used to solve for the joint angles, torque profiles, and ground reaction forces. The weighted sum approach of MOO is used to aggregate the two objective functions, and the Pareto optimal set for the problem is generated by systematically varying the weighting parameters for the objective functions. Experimental data are used to validate the final simulation. Several examples are presented to demonstrate the effect of the weighting parameters for the two objective functions on the predicted box-lifting strategies. The results show that the proposed MOO approach improves the simulation results compared to the single objective optimization formulation. Also, the formulation is less sensitive to the weighting coefficient for the stability criterion.     

基于圆弧模型的四足机器人步态规划

根据Aibo机器狗前腿的圆弧型结构建立了机器人腿部的二维实体模型，并通过两个直角三角形解算Aibo机器狗的逆运动学．在此模型的基础上进行前腿在地面滚动行走的同心圆步态规划，并通过机器学习得到了平稳、快速的行走步态参数．     

Control of a Biped Walking Robot during the Double Support Phase

This paper discusses the control problem of a biped walking robotduring the double-support phase. Motion of a biped robot during thedouble-support phase can be formulated as motion of robotmanipulators under holonomic constraints. Based on the formulation,the walking gait is generated by controlling the position of thetrunk of the robot to track a desired trajectory, referenced in theworld frame. Constrained forces at both feet were controlled suchthat firm contact is preserved between the feet and ground by using asimplified model of the double-support phase. The control scheme wasevaluated experimentally.     

Physics-based modeling and simulation of human walking: a review of optimization-based and other approaches

A review of human walking modeling and simulation is presented. This review focuses on physics-based human walking simulations in the robotics and biomechanics literature. The gait synthesis methods are broadly divided into five categories: (1) inverted pendulum model; (2) passive dynamics walking; (3) zero moment point (ZMP) methods; (4) optimization-based methods; and (5) control-based methods. Features of various methods are discussed, and their advantages and disadvantages are delineated. The modeling, formulation, and computation aspects of each method are reviewed.     

基于测力平台阵列的双足步行机器人实际零力矩点检测

提出一种多维力测力平台阵列系统,通过机器人行走过程中脚部与平台接触力的测量,并根据. vukobratovic关于ZMP的定义,得到机器人行走过程的ZMP实际轨迹信息,为双足步行机器人的稳态行走步态规划提 供参考依据.更进一步,该系统也可以用作双足步行机器人行走过程步态规划的实验平台.     

Comparison of different gaits with rotation of the feet for a planar biped

Fast human walking includes a phase where the stance heel rises from the ground and the stance foot rotates about the stance toe. This phase where the biped becomes under-actuated is not present during the walk of humanoid robots. The objective of this study is to determine if this phase is useful to reduce the energy consumed in the walking. In order to study the efficiency of this phase, six cyclic gaits are presented for a planar biped robot. The simplest cyclic motion is composed of successive single support phases with flat stance foot on the ground. The most complex cyclic motion is composed of single support phases that include a sub-phase of rotation of the stance foot about the toe and of finite time double support phase. For the synthesis of these walking gaits, optimal motions with respect to the torque cost, are defined by taking into account given performances of actuators. It is shown that for fast motions a foot rotation sub-phase is useful to reduce the criteria cost. In the optimization process, under-actuated phase (foot rotation phase), fully-actuated phase (flat foot phase) and over-actuated phase (double support phase) are considered.     

伸缩腿双足机器人半被动行走控制研究

研究半被动伸缩腿双足机器人行走控制和周期解的全局稳定性问题.使用杆长可变的倒立摆机器人模型,以支撑腿的伸缩作为行走动力源,采用庞加莱映射方法分析了双足机器人行走的不动点及其稳定性.当脚与地面冲击时,假设两腿间的夹角保持为常数,设计了腿伸缩长度的支撑腿角度反馈控制率.证明了伸缩腿双足机器人行走过程不动点的全局稳定性.仿真结果表明,本文提出的腿伸缩长度反馈控制可以实现伸缩腿双足机器人在水平面上的稳定行走,并且周期步态对执行器干扰和支撑腿初始角速度干扰具有鲁棒性.     

Development and motion control of a biped walking robot based on passive walking theory

This research aims to develop the biped walking robot that can walk on the horizontal ground and improve walking efficiency by utilizing the theory of the passive walking robot, namely the pendulum principle. For that, two motors were installed on the hip of the robot to generate the control torques to perform a walking motion. The computer simulations with dynamic model were carried out to investigate the walking capability of the system. Experimental robot was developed considering the calculated results. The proportional control law was used in walking experiment. The robot can walk on the horizontal ground with the proposed method.     

Backward walking simulation of humans using optimization

The objective of this study is to formulate, simulate and study the backward walking motion of a full-body skeletal digital human model using an optimization approach. Predictive dynamics is used to simulate the task in which joint angle profiles are treated as primary unknowns in the formulation. The joint torques are treated as dependent variables that are evaluated directly from the equations of motion. For the performance measure, the normalized dynamic effort represented by the integral of the squares of all the normalized joint torques is minimized subject to the associated physical constraints. Backward walking at different speeds is simulated and analyzed. The backward walking is validated with motion capture data and the available data in the literature. The results of the backward walking motion are compared to those of the forward walking motion in order to study the differences between the two walking patterns. It is seen that the joint torque profiles for hip and knee of backward walk are quite similar to those of forward walk with reverse sequence, but with different time duration of flexion and extension activations. These findings can impact many fields, such as improvement of human performance, rehabilitation from injuries, and others.     

Development of a Complete Dynamic Model of a Planar Five-Link Biped and Sliding Mode Control of Its Locomotion During the Double Support Phase

This paper presents a complete dynamic model of a planar five-link biped walking on level ground. The single support phase (SSP), double support phase (DSP) and double impact occurring at the heel strike are included in the model. By modifying the conventional definition of certain physical parameters of the biped system, it is shown that the procedure of the derivation of the dynamic equations and their final forms are significantly simplified. For motion regulation during the DSP, our dynamic model is formulated as the motion of biped system under holonomic constraints, and the hip position and the trunk orientation are selected as the independent generalized coordinates to describe the constraint system and to eliminate the constraint forces from the equations of motion. Based on the presented dynamic formulation, we develop a sliding mode controller for motion regulation during the DSP where the biped is treated as a redundant manipulator. The stability and the robustness of the controller are investigated, and its effectiveness is demonstrated by computer simulations. To the best of our knowledge, it is the first time that a sliding mode controller is developed for biped walking during the DSP. This work makes it possible to provide robust sliding mode control to a full range of biped walking and to yield dexterity and versatility for performing specific gait patterns.     

Simulated effect of driver and vehicle interaction on vehicle interior layout

Digital human modeling is an essential tool to reduce cost and to save time in a design process where humans take the part of users of the design. Considering this phenomenon for a vehicle interior, the importance of the seat track location and adjustment ranges become important. This paper presents the effect of driver and vehicle interaction on vehicle interior layout based on simulation approach. This simulation method includes two optimizations. The first optimization problem is the physics-based seated posture prediction. In order to represent physical drivers, 4,500 virtual drivers are generated based on an anthropometric database-ANSUR. Interaction forces between the digital human and pedal, seat, ground, and steering wheel are incorporated in the physics-based posture prediction. Three different pedal reaction moments (0, 20, and 40 N m) are implemented into the formulation to examine the effect of pedal reaction moment on driver seat location and adjustment ranges. To study the effect of shear forces, the physics-based posture prediction is compared to kinematics-based posture prediction. After posture predictions are completed, individuals' preferred seat locations are used in a second optimization problem to predict the seat track location and adjustment ranges. For a specific vehicle with 20 N m pedal reaction moment, adjustment ranges are predicted as 223 mm and 82 mm in horizontal and vertical directions, respectively. Also, it was shown that shear force due to the interaction between the driver and the seat pan and the pedal reaction moment are both influential to the seat track location and adjustment ranges.Relevance to industryThe simulation model presented in this paper is useful in vehicle and seat design and can be easily used for virtual design assessment in vehicle design.     

Passivity-Based Control of Bipedal Locomotion

In this article, we have shown how to design energy-based and passivity-based control laws that exploit the existence of passive walking gaits to achieve walking on different ground slopes, to increase the size of the basin of attraction and robustness properties of stable limit cycles, and to regulate walking speed. Many of the results presented in this are the compass gait are equally applicable to bipeds with knees and a torso. Practical considerations such as actuator saturation, ground reaction forces, and ground friction need to be addressed. The problem of foot rotation introduces an underactuated phase into the walking gait, which greatly challenges the application of energy shaping ideas. For walking in 3D, finding purely passive limit cycles, which is the first step in applying our energy control results, may be difficult. It was shown how ideas of geometric reduction can be used to generate 3D stable gaits given only 2D passive limit cycles.     

Reinforcement learning based compliance control of a robotic walk assist device

ABSTRACT

Millions of people around the globe have to deal with walking disability. Robotic walk assist devices can help people with walking disabilities, especially those with weak legs. However, safety, cost, efficiency and user friendliness are some of the key challenges. For robotic walk assist devices, light weight structure and energy efficient design as well as optimal control are vitally important. In addition, compliance control can help to improve the safety of such devices as well as contribute to their user friendliness. In this paper, an optimal adaptive compliance control is proposed for a Robotic walk assist device. The suggested scheme is based on bio-inspired reinforcement learning. It is completely dynamic-model-free scheme and employs joint position and velocity feedback as well as sensed joint torque (applied by user during walk) for compliance control. The efficiency of the controller is tested in simulation on a robotic walk assisting device model.