Gait Generation and Stabilization for Nearly Passive Dynamic Walking Using Auto‐distributed Impulses

We propose a state feedback control design via linearization for flexible walking on flat ground. First, we generate nearly passive limit cycles, being stable or not, using impulsive toe‐off actuations. The term ‘nearly passive’ means that the dynamics is completely passive almost everywhere except at the toe‐off moment. A feature of our gait generation method is that walking gaits are characterized only by amounts of supplied energy, and we observe that other variables, including input torques, are auto‐balanced via our method. After gait generation, we design a feedback controller considering robustness and input saturation. As a result, each limit cycle can be matched with its respective controller classified only by energy levels. We have verified that walking speeds monotonically increase by adding more energy, and the ankle joint plays a significant role in compass‐gait walking. Finally, instead of applying impulsive torques, we discuss a practical issue regarding realistic control inputs that ensure stable gait transitions as energy levels are elevated.     

High-speed dynamic gait generation for limit cycle walkers based on forward-tilting impact posture

This paper proposes a novel method for generating a dynamic gait based on anterior-posterior asymmetric impact posture tilting the robot’s center of mass forwards. The primary purpose of this method is to make the impact posture become asymmetrical by actuating the robot’s telescopic legs to easily overcome the potential barrier at mid-stance, accordingly restoring the mechanical energy. First, we introduce a planar rimless wheel model with telescopic legs, and investigate the validity of the stance-leg extension control. The basic properties and efficiency of the generated gait are also numerically analyzed. Second, we extend the method to a planar telescopic-legged biped model, and investigate the validity through numerical simulations. We also discuss the role of asymmetric shape of human foot through efficiency analysis from the point of view of the brake effect, taking the ankle-joint actuation into account.     

Efficiency and Optimality of Two-Period Limit Cycle Walking

This paper investigates the efficiency of a two-period gait from the kinetic energy viewpoint. First, we formulate a steady two-period gait for a compass-like bipedal robot by using a simple recurrence formula for the kinetic energy of an asymmetric rimless wheel. Then, we theoretically show that, in the case where the mean value of the hip angle is constant, the generated two-period steady gait is less efficient than a one-period symmetric gait in terms of kinetic energy. We also show that the symmetric gait is not always optimal from another viewpoint. We then extend the analysis to biped walking and investigate the validity of the derived method through numerical simulations of virtual passive dynamic walking.     

Robust pseudo virtual passive dynamic walking with control of swing-leg retraction

This paper proposes a simplified method of underactuated virtual passive dynamic walking without having any singularities in the control input, which is termed as the pseudo virtual passive dynamic walking (PVPDW), and analyzes the gait properties considering quasiconstraint on the impact posture. First, we introduce a planar underactuated biped model that added an upper body by means of a bisecting hip mechanism and formulate the method of PVPDW based on the concept of pseudo center of mass. Second, we introduce a control law for inhibiting swing-leg retraction and analyze the effect on the gait stability. The simulation results show that falling down as a 1-DOF rigid body dramatically increases the stable domain even though the hip angle at impact is not precisely kept constant. Finally, we discuss the mechanism from the energy-loss coefficient point of view.     

Biped Gait Generation and Control Based on a Unified Property of Passive Dynamic Walking

Principal mechanisms of passive dynamic walking are studied from the mechanical energy point of view, and novel gait generation and control methods based on passive dynamic walking are proposed. First, a unified property of passive dynamic walking is derived, which shows that the walking system's mechanical energy increases proportionally with respect to the position of the system's center of mass. This yields an interesting indeterminate equation that determines the relation between the system's control torques and its center of mass. By solving this indeterminate equation for the control torque, active dynamic walking on a level can then be realized. In addition, the applications to the robust energy referenced control are discussed. The effectiveness and control performances of the proposed methods have been investigated through numerical simulations.     

Wave CPG model for autonomous decentralized multi-legged robot: Gait generation and walking speed control

In this paper, we propose a method to control gait generation and walking speed control for an autonomous decentralized multi-legged robot by using a wave Central Pattern Generator (CPG) model. The wave CPG model is a mathematical model of nonlinear oscillators and generates rhythmic movements of the legs. The gait generation and the walking speed control are achieved by controlling the virtual energy of the oscillators (Hamiltonian). A real robot experiment showed the relationship to the Hamiltonian, the actual energy consumption and the walking speed, and the effectiveness of the proposed method was verified.     

Transition to an optimal periodic gait by simultaneous input and parameter optimization method of Hamiltonian systems

This paper is concerned with a gait transition to an optimal periodic gait by a simultaneous input and parameter optimization technique of Hamiltonian systems. First, a continuous-time dynamics of a passive walking/running robot between the touchdown and lift-off is considered as a Hamiltonian system. Then, the control input and some robot parameters, such as the mass, inertia, link length, and so on, are optimized using learning optimal control of Hamiltonian systems, which has been developed by the authors. This method allows one to simultaneously obtain an optimal feedforward input and optimal parameters, which (at least locally) minimize a given cost function. The main advantage is that the precise model of the dynamics of the plant system is not required using a symmetric property of Hamiltonian systems, called variational symmetry. We formulate an optimal gait generation scheme via the learning optimal control, where the robot keeps walking and the gait is optimized with respect to the control input and some adjustable robot parameters simultaneously. As a result, the gait transition to an optimal periodic one is achieved.     

Energy-Efficient and High-Speed Dynamic Biped Locomotion Based on Principle of Parametric Excitation

We clarified that the common necessary condition for generating a dynamic gait results from the requirement to restore mechanical energy through studies on passive dynamic walking mechanisms. This paper proposes a novel method of generating a dynamic gait that can be found in the mechanism of a swing inspired by the principle of parametric excitation using telescopic leg actuation. We first introduce a simple underactuated biped model with telescopic legs and semicircular feet and propose a law to control the telescopic leg motion. We found that a high-speed dynamic bipedal gait can easily be generated by only pumping the swing leg mass. We then conducted parametric studies by adjusting the control and physical parameters and determined how well the basic gait performed by introducing some performance indexes. Improvements in energy efficiency by using an elastic-element effect were also numerically investigated. Further, we theoretically proved that semicircular feet have a mechanism that decreases the energy dissipated by heel-strike collisions. We provide insights throughout this paper into how zero-moment-point-free robots can generate a novel biped gait.      

Simulation verification for the robustness of passive compass gait with a joint stiffness adjustment

A passive walking robot can achieve a smooth gait without any sensory feedback while walking down a slope. This phenomenon is based on the transformation of potential energy into kinetic energy in the legs. Although the entrainment is observed in a passive gait motion, there is a possibility that the passive gait cannot be achieved in the case of variations in physical parameters, initial conditions, and disturbances. To realize a robust passive gait against variations in physical parameters, this paper proposes a passive gait system that possesses a joint stiffness adjustment. Targeting a compass model, this paper investigates the effectiveness of the proposed method for a passive gait against variations in slope angle and hip joint mass through simulation. As a result, the simulation results show that this method especially has strong robustness against the slope angle variation.     

The standard circular gait of a quadruped walking vehicle

A quadruped walking vehicle has the potential capability of being developed into a vehicle of high mobility and adaptability to terrain by making use of its high degree of motion freedom. The authors have investigated the gait control problems of a walking vehicle, i.e. the straightforward or crab walk of the vehicle on rough terrains. This paper introduces a more generalized gait, namely, a circular gait around an arbitrarily located turn center, and discusses a standard circular gait. The standard circular gait is the one which maximizes the speed of walking and the rotational angle in a circular walk, and this consideration forms the basis of the discussion on advanced gait control problems. This paper formalizes the problems and analyses them by using mathematical optimization methods such as non-linear programming. Computations are carried out on a TITAN III, the quadruped walking vehicle model constructed by the authors. Several characteristics of the optimum gait and the final gait selection chart are derived. The validity of these conditions was verified by a circular walking experiment using the TITAN III.     

基于矢状面质心角动量的人类行走步态周期阶段划分方法

认知人类的步行机理是双足机器人开发的重要基础.在人类行走过程中,外力力矩是影响行走稳定性的决定性因素,步态与外力力矩的相互作用是人类步行机理研究中的关键问题.尽管质心角动量可反映人体受到的外力力矩变化,但会随步态的演化呈现不同的变化规律.以人类自然行走步态为研究目标,通过准确获取人体行走过程中实时运动信息与质心角动量的变化,根据人体行走过程中的外力力矩与质心角动量的角度对人体步态进行力学分析,并结合人体行走过程中的足地关系与矢状面质心角动量变化规律,得出角动量特征点与步态特征点在时间上具有高度一致性的结论,最终实现基于矢状面质心角动量的人类步态周期阶段的精准划分.研究结果对于认知人类步行机理,指导行走康复医疗和双足机器人研发具有重要意义.     

双足步行机器人能量成型控制

为了使双足被动行走机器人的行走步态符合仿生规律,且当路面坡度变化后,迅速进入新的稳定步态行走,提出了角度不变能量成型控制策略.研究了欠驱动双足机器人能量匹配条件和能量成型控制器的求解;由于动能相对于旋转变换不具有对称性,通过在能量成型控制中附加一个辅助控制量,实现角度不变控制.仿真结果表明,该算方法可实现仿生控制,既能扩大吸引域,又改善系统的鲁棒性.     

Power Consumption Optimization for a Hexapod Walking Robot

Power consumption is one of the main operational restrictions on autonomous walking robots. In this paper, an energy efficiency analysis is performed for a hexapod walking robot to reduce these energy costs. To meet the power-saving demands of legged robots, the torque distribution algorithm required to minimize the system’s energy costs was established with an energy-consumption model formulated. In contrast to the force distribution method, where the objective function is related to the tip-point force components, the torque distribution scheme is based on minimization of the mechanical energy cost and heat loss power. The simulation results show that this scheme could reduce the system energy costs with use of the appropriate walking velocities and duty factors for the robot. The paper also discusses the effects of the gait patterns and the mechanical structure on the system energy costs. For this purpose, the prescribed periodic walking gait of the robot is described in terms of several parameters, including the duty factor, the stride length, the body height, and the foot trajectory lateral offset. The numerical results indicate some analogies between the characteristics of the simulated walking robot and those of animals in nature. The optimized parameters derived here are intended for robot platform development applications.     

Application of Genetic Algorithms for biped robot gait synthesis optimization during walking and going up-stairs

Selecting an appropriate gait can reduce consumed energy by a biped robot. In this paper, a Genetic Algorithm gait synthesis method is proposed, which generates the angle trajectories based on the minimum consumed energy and minimum torque change. The gait synthesis is considered for two cases: walking and going up-stairs. The proposed method can be applied for a wide range of step lengths and step times during walking; or step lengths, stair heights and step times for going up-stairs. The angle trajectories are generated without neglecting the stability of the biped robot. The angle trajectories can be generated for other tasks to be performed by the biped robot, like going down-stairs, overcoming obstacles, etc. In order to verify the effectiveness of the proposed method, the results for minimum consumed energy and minimum torque change are compared. A Radial Basis Function Neural Network is considered for the real-time application. Simulations are realized based upon the parameters of the 'Bonten-Maru I'humanoid robot, which is under development in our laboratory. The evaluation by simulations shows that the proposed method has a good performance.     

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.     

How to optimize the slope walking motion by the quadruped walking robot

Reduction of the energy consumption is one of the most important problems to utilize quadruped walking robots for various works on rugged terrain. The authors have studied basic strategy to achieve high energy efficiency when the quadruped walking robot do the motion essentially requires positive power by the analysis of body rising motion. This paper discusses the energy efficiency of the slope walking motion by the quadruped walking robot. First, we investigate the walking posture in consideration of ideal actuator characteristics where the robot consumes few negative powers at each joint which causes the main energy loss of the walking robot. Then, we investigate optimal walking posture in consideration of DC motor characteristics by the full search of three gait parameters which define the crawl gait. Furthermore, we derive the optimal walking motion by the optimization of three gait parameters which are kept constant during one cycle gait and instantaneous parameters such as body velocity and supporting forces changed at each moment simultaneously.     

The effects of variable mechanical parameters on peak power and energy consumption of ankle-foot prostheses at different speeds

In recent years, powered ankle-foot prostheses are developed to restore human ankle behaviour. Compared with common passive ankle prostheses, a powered ankle-foot prosthesis can provide amputees with better performance on walking gait by providing additional energy. However, the electrical peak power of powered ankle-foot prostheses at high speed is still a big challenge for the current actuation system. While most researchers focus on the energy consumption on one walking speed, we investigate the influences of several variable mechanical parameters to reduce electrical peak power during different locomotion speeds. Then we apply this concept to current ankle-foot models. It's found that the variable mechanical parameters can significantly reduce the demand of electrical peak power at different speeds. Meanwhile, the reduction of the electrical peak power does not lead to a large increment of the energy consumption. The results also show that every variable mechanical parameter has a different influence on the peak power and energy consumption of the ankle-foot prosthesis. It means the most effective and sensitive variable mechanical parameter need to be found for a specific ankle prosthesis system.     

Gait generation for a biped robot with knees and torso via trajectory learning and state-transition estimation

The proposed method can generate an optimal feedforward control input and the corresponding optimal walking trajectory minimizing the \(L_2\) norm of the control input by iteration of laboratory experiments. Since a general walking motion involves discontinuous velocity transitions caused by the collision with the ground, the proposed method consists of the combination of a trajectory learning part and an estimation part of the discontinuous state transition mapping using the stored experimental data. We apply the proposed method to a kneed biped robot with a torso, where we also provide a technique to generate an optimal gait not only being energy-efficient but also avoiding the foot-scuffing problem.     

仿人机器人步态平衡泛化模型的建立与仿真

通过人体示教计算零力矩点(zero moment point, ZMP),并通过补偿关节角度对其矫正的方法可以解决机器人步行不稳定的问题,但仍存在算法复杂度过高等问题。本文提出一种人体示教与机器学习相结合的方法,基于支持向量回归算法建立机器人的步态平衡泛化模型,通过该模型可以实现对模型输入人体示教的关节角度和ZMP信息后直接得到经稳定性补偿的关节角度,并以此驱动机器人完成步行动作。引入鲸鱼优化算法(whale optimization algorithm, WOA)优化模型的参数以使模型得到最优的泛化效果,完善步态平衡模型的性能。WEBOTS仿真平台下,使用模型输出的补偿后的关节角度驱动NAO机器人,其动作自然、稳定且算法复杂度较低,验证了本文方法的可行性。     

Experimental studies on passive dynamic bipedal walking

Passive dynamic walking is a gait developed, partially or in whole, by the energy provided by gravity. The research on passive dynamic bipedal walking helps create an understanding of walking mechanics. Moreover, the experimental passive dynamic research provides a base to compare and validate computer simulation results. An improved kneed bipedal walking mechanism was designed and built to study the passive gait patterns. The first aim of this study is to determine the equivalency of testing a passive dynamic biped walker on a treadmill to testing on a ramp. Based on the small difference between the gait patterns measured on the two test platforms, testing on a treadmill was found equivalent to testing on a ramp. Gait measurements were then conducted on the treadmill to evaluate the effects of the treadmill inclination angle, mass distribution of the biped, and the length of flat feet on the gait pattern. Results show that most of these parameters had significant effects on the step length, step period and hip velocity of the passive walker. Our experimental results are also compared with previous experimental results.