Two walking gaits for a planar bipedal robot equipped with a four-bar mechanism for the knee joint

The design of a knee joint is a key issue in robotics and biomechanics to improve the compatibility between prosthesis and human movements, and to improve the bipedal robot performances. We propose a novel design for the knee joint of a planar bipedal robot, based on a four-bar linkage. The dynamic model of the planar bipedal robot is calculated. Two kinds of cyclic walking gaits are considered. The first gait is composed of successive single support phases with stance flat-foot on the ground separated by impacts. The second gait is a succession of finite time double support phases, single support phases, and impacts. During the double support phase, both feet rotate. This phase is ended by an impact of the toe of the forward foot, while the rear foot is taking off. The single support phase is ended by an impact of the swing foot heel, the other foot keeping contact with the ground through its toe. For both gaits, the reference trajectories of the rotational joints are prescribed by cubic spline functions in time. A parametric optimization problem is presented for the determination of the parameters corresponding to the optimal cyclic walking gaits. The main contribution of this paper is the design of a dynamical stable walking gait with double support phases with feet rotation, impacts, and single support phases for this bipedal robot.     

双足机器人HEUBR-1 样机研制与实验研究

模拟人的肌肉驱动方式,为双足机器人HEUBR-1 设计了二自由度的空间并联机构,并将其应用于双 足机器人HEUBR-1 下肢关节,实现了一种新的串并混联的仿人下肢结构．在HEUBR-1 的足部增加了足趾关节,使 机器人能够模拟人的行走方式,实现真正的拟人步态行走．阐述了双足机器人HEUBR-1 稳定拟人行走的关键性技 术,提出了综合稳定性判据,分析了拟人的多种步态．通过拟人行走步态实验分析,验证了双足机器人HEUBR-1 串 并混联的仿人结构的设计合理性及拟人步态分析的准确性．     

Human like trajectory generation for a biped robot with a four-bar linkage for the knees

The design of a knee joint is a key issue in robotics to improve the locomotion and the performances of the bipedal robots. We study a design for the knee joints of a planar bipedal robot, based on a four-bar linkage. We design walking reference trajectories composed of double support phases, single support phases and impacts. The single support phases are divided in two sub-phases. During the first sub-phase the stance foot has a flat contact with the ground. During the second sub-phase the stance foot rotates on its toes. In the double support phase, both stance feet rotate. This phase is ended by an impact on the ground of the toe of the forward foot, the rear foot taking off. The single support phase is ended by an impact of the heel of the swing foot, the other foot keeping contact with the ground through its toes. A parametric optimization problem is presented for the determination of the parameters corresponding to the optimal cyclic walking gaits. In the optimization process this novel bipedal robot is successively, overactuated (double support with rotation of both stance feet), fully actuated (single support sub-phase with a flat foot contact), and underactuated (single support sub-phase with a rotation of the stance foot). A comparison of the performances with respect to a sthenic criterion is proposed between a biped equipped with four-bar knees and another with revolute joints. Our numerical results show that the performances with a four-bar linkage are bad for the smaller velocities and better for the higher velocities. These numerical results allows us to think that the four-bar linkage could be a good technological way to increase the speed of the future bipedal robots.     

Dynamics modeling and analysis of a biped walking robot actuated by a closed-chain mechanism

We developed a new type of human-sized biped walking robot (BWR) driven by the closed-chain type of joint actuator. Each leg of the robot is composed of three pitch joints and one roll joint. In all, a 15 degree-of-freedom robot including four arm joints and three joints for the head was developed. The BWR was developed to walk autonomously such that all leg joints are actuated by small 90 W dc motors/drivers and dc batteries and controllers which are boarded. The joint actuator for the BWR is composed of the four-bar-link mechanism driven by the ball screw which has high strength and high gear ratio. A dynamics modeling of the developed BWR for forward walking is presented in which the revolute joint dynamics are transformed into the prismatic joint dynamics of the ball screw. Also, an analysis on the four-bar-link mechanism applied to the joint actuator and on the structure of the BWR is shown. The design specification of the actuating motor for the BWR is analyzed through the torque analysis of the four-bar-link actuator. Through walking experiments of the BWR, the walking performance and trajectory tracking ability is shown. © 2004 Wiley Periodicals, Inc.     

理疗师交互下的下肢康复训练机器人个性化步态规划方法

针对偏瘫患者的个体差异及病况差异,提出了一种理疗师交互下的下肢康复训练机器人步态规划方法,在理疗师-减重悬吊式康复训练机器人-患者三者共存的复杂环境中,理疗师穿戴主控外骨骼直接行走实现步态时空参数规划,并融入理疗师的医学经验及对患者的评估.首先,基于旋量理论建立运动学模型,实现理疗师空间与机器人空间的运动映射;然后,统一规划机器人关节运动轨迹、减重机构重心调整轨迹及跑步机步速.最后,通过理疗师步态参数的实时采集、运动映射实验及机器人轨迹跟踪实验,验证了步态时空规划方法的有效性.结果表明,髋、膝关节规划角度在人体关节活动范围内,速度变化平稳,关节轨迹规划和重心调整规划均符合人体行走的生理特性.理疗师的参与实现了渐进康复训练中的个性化步态规划.     

Asymptotically Stable Walking of a Five-Link Underactuated 3-D Bipedal Robot

This paper presents three feedback controllers that achieve an asymptotically stable, periodic, and fast walking gait for a 3-D bipedal robot consisting of a torso, revolute knees, and passive (unactuated) point feet. The walking surface is assumed to be rigid and flat; the contact between the robot and the walking surface is assumed to inhibit yaw rotation. The studied robot has 8 DOF in the single support phase and six actuators. In addition to the reduced number of actuators, the interest of studying robots with point feet is that the feedback control solution must explicitly account for the robot's natural dynamics in order to achieve balance while walking. We use an extension of the method of virtual constraints and hybrid zero dynamics (HZD), a very successful method for planar bipeds, in order to simultaneously compute a periodic orbit and an autonomous feedback controller that realizes the orbit, for a 3-D (spatial) bipedal walking robot. This method allows the computations for the controller design and the periodic orbit to be carried out on a 2-DOF subsystem of the 8-DOF robot model. The stability of the walking gait under closed-loop control is evaluated with the linearization of the restricted PoincarÉ map of the HZD. Most periodic walking gaits for this robot are unstable when the controlled outputs are selected to be the actuated coordinates. Three strategies are explored to produce stable walking. The first strategy consists of imposing a stability condition during the search of a periodic gait by optimization. The second strategy uses an event-based controller to modify the eigenvalues of the (linearized) PoincarÉ map. In the third approach, the effect of output selection on the zero dynamics is discussed and a pertinent choice of outputs is proposed, leading to stabilization without the use of a supplemental event-based controller.      

An approach to analyzing biped locomotion dynamics and designing robot locomotion controls

An approach to analyzing biped locomotion problems is presented. This approach applies the principles of Lagrangian dynamics to derive the equations of motion of locomotion gaits, state-variable techniques to analyze locomotion dynamics, and multivariable feedback to design locomotion controls. A robot model which has no knee joints or feet and is constrained to motion in the sagittal plane is chosen as a sufficiently simple model of a biped to illustrate the approach. A goal of the analysis is the design of a locomotion control for the robot which produces a walking gait having a velocity and stride length similar to those of a human walking gait. The principle feature of the approach is a much deeper understanding of the dynamics of biped locomotion than previous approaches have provided.     

Mechanical Design of a Trunk with Redundant and Viscoelastic Joints for Rhythmic Quadruped Locomotion

Passive mechanisms, such as free joints and viscoelastic components, enable natural oscillation of the robot body, which allows rhythmic locomotion with low energy and computational costs. In particular, joint viscoelasticity can be a powerful candidate for changing natural oscillation and so influence the operation performance of locomotion. The present study considers the passive mechanism of a trunk, and investigates the contributions of a trunk mechanism with redundant joints and tunable viscoelasticity to quadruped locomotion. A physical quadruped robot with a trunk mechanism is developed, and the walking performance of this robot for various gait patterns and joint viscoelasticities is investigated. A simulation model is also constructed based on the physical robot, and the contribution of the viscoelasticity to trunk oscillation and the appropriate joint viscoelasticity and number of trunk joints are discussed. Experimental results obtained using the physical robot indicate that the proposed trunk mechanism contributes to successful locomotion as compared to a robot with a rigid trunk and that the velocity is influenced by not only the gait pattern, but also the joint viscoelasticity (i.e., there are appropriate couplings of the joint viscoelasticity and gait pattern). The simulation results indicate that the trunk mechanism requires joint viscoelasticity in order to achieve oscillation and that a greater number of joints having a smaller joint viscoelasticity enables higher velocity. These results suggest that, in addition to the leg mechanism and the controller design, the design of the trunk mechanism is also important.     

具有2DOF铰接式躯干的仿猎豹四足奔跑机器人

为了探索脊柱运动对腿运动的增强机理,设计了具有2自由度铰接式躯干的仿猎豹四足奔跑机器人。对带腾空相的跳跃（bound）步态奔跑运动的力学过程进行描述,采用阻尼型弹性负载倒立摆（D-SLIP）模型建立了四足机器人动力学模型。依据猎豹的奔跑运动模式,对四足机器人脊柱关节与腿关节的耦合运动进行了轨迹规划。提出一种改进的粒子群优化（PSO）算法,解决了机器人脊柱关节驱动机构尺寸和运动轨迹控制参数之间目标互斥的嵌套优化问题。对四足机器人跳跃奔跑运动进行动力学仿真,结果表明：脊柱与腿的协调运动可以增大奔跑步幅,使机器人产生腾空相,从而提高机器人的奔跑速度。     

Mechanical design of powered prosthetic leg and walking pattern generation based on motion capture data

In this paper, we describe the design procedure of an above-knee powered prosthetic leg and an algorithm to generate appropriate gait patterns that are synchronized with the movement of the user. The developed prosthetic leg has powered knee and ankle joints for transfemoral amputees, and its weight and dimensions were determined on the basis of human body data. In particular, two degrees of freedom (roll and pitch axes) were adopted in the ankle joint to achieve dynamic balance control on uneven ground, and passive toe joints using a crank-rocker mechanism and torsional springs were attached at the foot to increase the walking stability. In addition, we developed a walking pattern simulator that is able to test the walking patterns of the powered prosthetic leg in the air. By attaching two inertial sensors on both thighs of the user and measuring both thigh motions, the per cent of gait cycle is suitably calculated from the proposed algorithm, and smooth gait motions are generated according to the gait cycle percent. Finally, walking patterns of the powered prosthetic leg were successfully generated by synchronizing to the human gait, and the generated gaits were analyzed by comparing them to the human gait.     

Analytical development of dynamic equations of motion for a three-dimensional flexible link manipulator with revolute and prismatic joints

In this paper, a mathematical model capable of handling a three-dimensional (3D) flexible n-degree of freedom manipulator having both revolute and prismatic joints is considered. This model is used to study the longitudinal, transversal, and torsional vibration characteristics of the robot manipulator and obtain kinematic and dynamic equations of motion. The presence of prismatic joints makes the mathematical derivation complex. In this paper, for the first time, prismatic joints as well as revolute joints have been considered in the structure of a 3D flexible n-degree of freedom manipulator. The kinematic and dynamic equations of motion representing longitudinal, transversal, and torsional vibration characteristics have been solved in parametric form with no discretization. In this investigation, in order to obtain an analytical solution of the vibrational equations, a novel approach is presented using the perturbation method. By solving the equations of motion, it is shown that mode shapes of the link with prismatic joints can be modeled as the equivalent clamped beam at each time instant. As an example, this method is applied to a three degrees of freedom robot with revolute and prismatic joints. The obtained equations are solved using the perturbation method and the results are used to simulate vibrational behavior of the manipulator.     

肢体协调运动康复机器人的机构设计与实验

针对临床上缺少一种肢体协调运动康复训练设备的现状,研制了一款适用于偏瘫患者个性化训练的上下肢协调运动康复机器人.首先,在探究正常步态上下肢协调运动规律的基础上,选择以肩、膝关节角度协调变化规律作为机器人的设计目标;然后,基于五杆变胞机构设计了康复训练机构及主/辅传动链,并对训练机构进行了运动学分析;最后,在样机上进行了实验,结果表明该机器人能够满足设计目标.     

Reconfigurable main‐arm for assembly of all revolute‐only kinematically simple branches

Within previous work by Podhorodeski and Pittens,a class of kinematically simple (KS) joint layouts was defined for spatial serial joint‐assemblies consisting of revolute joints only. The identified KS class of layouts was comprised of main‐arms with three successively parallel and/or perpendicular revolute joints and end located spherical joint groups. Arguments of degeneracy and kinematic equivalency can be used to demonstrate that only five unique main‐arm layouts belong to the KS class. Within the current work, the design of a reconfigurable main‐arm (RMA) allowing the construction of all of the KS branches is examined. Sufficient joints are included within the RMA to allow, by the locking of certain joints and the freeing (actuation) of others, the kinematic attributes of each of the unique KS main‐arm layouts to be acquired. It is concluded that five successively perpendicular revolute joints are required within the RMA to allow such reconfiguration. Inverse kinematic solutions are presented for each of the five layouts. Potential RMA applications, use of the RMA for kinematically redundant layouts, and an RMA prototype are discussed. ©2000 John Wiley & Sons, Inc.     

Planar legged walking of a passive-spine hexapod robot

This paper proposes a new legged walking method for a novel passive-spine hexapod robot. This robot consists of several body segments connected by passive body joints. Each of the body segments carries two 1-DoF (degree of freedom) actuated legs. The robot is capable of achieving planar legged walking by rapidly abducting and adducting its legs. To model the mobility of a robot based on this simple design, the candidate configurations from all possible configurations are first selected in a mobility analysis of the robot based on the screw theory. All the feasible sequences of these candidate configurations are then searched to form planar locomotion gaits. Next, locomotive performance of the gaits is analyzed. Finally, the proposed locomotion design and gait planning methods are verified through simulations and experiments.     

Inverse kinematics of spherical wrist robot arms: Analysis and simulation

The spherical wrist robot arm is the most common type of industrial robot. This paper presents an efficient analytical computation procedure of its inverse kinematics. It is based on the decomposition of the inverse kinematic problem to two less complex problems; one concerns the robot arm basic structure and the other concerns its hand. The proposed computation procedure is used to obtain the inverse kinematic position models of two robot arms: one contains only revolute joints and the other contains both revolute and prismatic joints. The 1st and 2nd time derivatives of the obtained models give more accurate inverse kinematic velocity and acceleration models than numerical differentiation. These models are verified by simulation for two different trajectories. The obtained results demonstrate the effect of the proposed procedure on reducing the necessary computation time compared to other computation techniques.     

A Novel Six Degrees-of-Freedom Parallel Robot for MEMS Fabrication

This paper introduces a new architecture of a six degrees-of-freedom parallel robot suitable for microelectromechanical systems (MEMS) fabrication. The robot consists of only revolute joints for the passive joints, and linear actuators located at the base for the active ones, both of which are easier to manufacture in MEMS technology. The hybrid kinematic structure contains three single-loop submechanisms connected in parallel to the moving platform. The solutions of the inverse and direct kinematics problems are presented     

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.     

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.