基于拟牛顿算法的自由下落猫的非完整运动规划

Nonholonomic Motion Planning for Free-Falling Cat Using Quasi-Newton Method

研究猫在自由下落时四肢着地的姿态运动规划问题。自由落体的猫在空中转体运动由于角动量守恒,姿态运动方程呈现为非完整形式。系统的控制问题可转化为无漂移系统的非完整运动规划问题。首先导出由两个对称刚体组成的力学模型的非完整姿态运动方程。利用最优控制理论和最优化技术,采用输入参数化的方法将连续的最优控制问题转化为离散的最优控制问题,基于拟牛顿方法,给出自由落体猫在空中姿态非完整运动规划算法。最后对自由落体猫作了数值仿真试验,仿真结果验证了该算法的有效性。

The motion planning problem of a free-falling cat was investigated. Nonholonomicity arises in a free-falling cat subject to nonintegrable velocity constraints or nonintegrable conservation laws. When the total angular momentum is zero, the attitude motion equations take on nonholonornic constraint. The control of system can be converted to the motion planning problem for a driftless system. The equation of dynamics of a free-falling cat wasobtained by using the model of two symmetric rigid bodies. Based on the input parameterization, the continuous optimal control problem was transformed into the discrete one. The quasi-Newton method of motion planning for nonholonomic multibody system was proposed. The effectiveness of the numerical algorithm is demonstrated by numerical simulation.