中文摘要：

带有被动轮的蛇形机器人在跟踪头部轨迹时，力矩输入具有无穷多解，其中振幅最小的解对应着电动机额定扭矩最小的情况，即为本文所指的优化力矩．由于带有被动轮的蛇形机器人侧向不打滑时轮子的法向速度为0，每个模块可以引入一个速度约束，此时蛇形机器人是一个非完整约束系统，而振幅最小的力矩对应着具有最小无穷范数的力矩．通过建立非完整约束动力学方程，将求解振幅最小的力矩转化为在动力学方程约束下求解最小无穷范数的问题．利用最小无穷范数的数值算法求得在蛇形机器人跟踪头部速度时的关节力矩最小无穷范数解，从而利用最小无穷范数解对蛇形机器人进行力矩控制，实现力矩振幅最小的最优力矩控制．动力学数值仿真结果证明了算法的有效性．

英文摘要：

When the snake-like robot with passive wheels tracks the trajectory of the head, there are infinite solutions for the input torque. The minimum amplitude torque corresponds to the minimum rated torque of the motor which is the optimal torque mentioned in this paper. When tile snake-like robot has no sideslip, the normal velocity of the snake-like robot is zero. So, a velocity constraint can be introduced into each module, and the snake-like robot is a nonholonomic system. The minimum amplitude torque corresponds to the torque with the minimum infinity norm. In this paper, the nonholonomic dynamics equations are developed, and the problem of solving the minimum amplitude torque is transformed into the problem of solving the minimum infinity norm under the constraints of dynamics equations. Using the numerical algorithm of the minimum infinity norm, the minimum infinity norm solution of the joint torque is derived when the snake-like robot tracks the head velocity. Using the minimum infinity norm solution, optimal torque control with minimum amplitude can be realized. The dynamics numerical simulation proves that the algorithm is valid.