基于Gauss伪谱法的移动机器人非完整运动规划  

Nonholonomic motion planning of mobile robot based on Gauss pseudospectral method

作　　者：董雪仰 戈新生[2] 陈凯捷 

机构地区：[1]北京信息科技大学机电工程学院,北京100192 [2]北京信息科技大学理学院,北京100192

出　　处：《北京信息科技大学学报（自然科学版）》2016年第1期23-27,共5页Journal of Beijing Information Science and Technology University

基　　金：国家自然科学基金项目(11472058)

摘　　要：针对轮式移动机器人中存在的非完整约束导致的系统控制及规划难度较高的问题,采用Gauss伪谱法求解最优控制的数值计算问题。通过建立移动机器人系统模型,确定系统约束及性能指标函数,将状态变量和控制变量在一系列Gauss点上离散,并以这些离散点为节点构造拉格朗日插值多项式来逼近状态变量和控制变量,对于性能指标中的积分项由Gauss积分计算,把非完整运动规划问题转化为一组有约束的非线性规划求解问题。通过建立最优控制输入和控制力矩关系,得到轮式机器人的最优控制力矩,数值仿真验证了方法的有效性。The nonholonomic constraint of wheeled mobile robots leads to system control and planning difficulty, so Gauss pseudospectral numerical method is used to solve the optimal control problem. Through the establishment of robot system model, the system constraints and performance index function are determined. The state variables and control variables are separated from one another in a series of Gauss point to make the Lagrange interpolation polynomial based on these nodes. Using the Gauss integral to calculate the integral of performance index, the nonholonomic motion planning problem is turned into a nonlinear programming problem with a set of constraints. By establishing the relationship between the optimal control input and the control torque, the optimal torque control of wheeled mobile robot is got. Finally, numerical simulation results verify the validity of the proposed method.

关 键 词：轮式机器人 非完整运动规划 GAUSS伪谱法 最优控制 

分 类 号：O313.7[理学—一般力学与力学基础]