Abstract

In this paper, based on the linear inverted pendulum (LIP) model, the multi-walking of biped robot is analogous to the multi-swing of a three-dimensional inverted pendulum. In terms of the concept of 'divergent component of motion (DCM)', the dynamic equations expressed by using Center of Mass (COM) and DCM are studied. Two DCM closed-loop controllers are designed:one-step DCM terminal invariant disturbance rejection controller and real-time DCM trajectory tracking closed-loop controller. Both controllers can effectively suppress the disturbance, so that the DCM of the actual robot does not diverge, and which is used to plan the COM trajectory of the biped walking process. Based on the COM trajectory and biped end trajectory, the numerical method for solving inverse kinematics of biped robot is studied. The whole set of solving problems from input footprint to output joint angle in biped walking process is completed, and systematize the method of biped gait planning. Finally, combining with a ubiquitous robot model, all the algorithms in this paper are simulated via MATLAB platform. The simulation results verify the effectiveness of the method.

Highlights

  • In this paper, based on the linear inverted pendulum ( LIP) model, the multi⁃walking of biped robot is analogous to the multi⁃swing of a three⁃dimensional inverted pendulum

  • In terms of the concept of 'divergent compo⁃ nent of motion ( DCM) ', the dynamic equations expressed by using Center of Mass ( COM) and DCM are studied

  • Combining with a ubiquitous robot model, all the algorithms in this paper are simulated via MATLAB platform

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Summary

Introduction

Vukobratovic 等[4] 1972 年提出了 ZMP ( zero mo⁃ ment point) 的概念,ZMP 作为脚与地之间的垂直压 力分布的抽象描述,可以有效地判定双足行走的稳 定性。 结合 LIP 模型,Wieber[5] 提出了一种无轨迹 模型预测控制器( MPC) ,该控制器最小化 COM 抖 2.2 一步 DCM 终值不变抗扰动控制 针对 LIP 动力学方程的不稳定部分,有必要设 式中,ξk→k+1( t) 为第 k 步系统规划出的 DCM 轨迹,为 一时间序列,ξx( t) 为实时系统反馈 ξ 值,b = edT,dT 为系统跟踪上目标 ξ 值所需要的时间,注意 dT 和一

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