软体尺蠖爬行机器人建模与仿真分析

Modeling and Simulation of an Inchworm-Like Soft Robot

高效计算并整体分析软体尺蠖机器人的运动规律和行进步态是个具有挑战性的难题.在准静态条件下,建立了一个由刚性滑块和曲梁构成的简化力学模型,对该类机器人进行准静态的建模与仿真分析.首先基于欧拉-伯努利梁理论,给出了曲梁的总势能表达式.其次,利用变分原理,由总势能推导出控制方程,联立边界条件,建立了常微分方程组,并对其进行离散化以及无量纲化,给出了用于数值求解的非线性代数方程组.然后,根据曲梁和地面的接触情况以及系统的黏滞与滑移状况,将机器人的整个运动过程分为三个阶段,通过数值计算,得到在不同阶段下曲梁随初始曲率幅值变化的不同构型,描述出软体机器人在一个周期内的运动规律、步态变化和净位移量,解决了软体机器人在不同阶段的运动衔接问题.准静态方法的特点是计算效率较高,更加适用于对软体机器人的运动构型进行分析.

It is a challenging problem to efficiently calculate and systematically analyze the motion laws and working gait of the inchworm-like soft robot.A simple mechanical model consisting of a rigid slider and a curved beam is established under quasi-static conditions,in order to realize quasi-static modeling and simulation analysis of the inchworm-like soft robot.First,based on the Euler-Bernoulli beam theory,the total potential energy expression of the beam is obtained.Next,combining the boundary conditions and the governing equation derived from the total potential energy based on the variational principle,a set of ordinary differential equations are established.Then,through discretization and dimensionlessness of those equations,a class of nonlinear algebraic equations for numerical solution is proposed.Finally,in the light of the contact situation between curved beam and ground as well as the viscous and slip condition of the system,the motion of the robot is divided into three stages.Through numerical calculations,the different configurations of the curved beam in different stages with the change of the initial curvature amplitude are obtained,which makes it possible to describe the law,the gait,and the net displacement of the soft robot in a motion cycle and solve the problem of movement connection of soft robots at different stages.The quasi-static method is characterized by high computational efficiency,which is more suitable for analyzing the motion configuration of soft robots.