基于Legendre伪谱法的空间机器人姿态运动的最优控制

Attitude Optimal Control of Space Robot Based on the Legendre Pseudospectral Method

摘要: 采用Legendre伪谱法研究自由漂浮双臂空间机器人姿态运动最优控制问题。首先，根据系统动量矩守恒关系，对自由漂浮并带有双臂的平面型空间机器人建立动力学模型，并以系统关节的耗散能为性能指标，给出其最优控制问题描述。然后，利用Legendre伪谱法以多项式参数化近似状态变量与控制变量，微分方程用正交多项式近似，从而将连续最优控制问题转化为一组非线性规划问题求解。为解决空间机器人姿态规划问题提供了一种有效方法。最后，对自由漂浮双臂空间机器人姿态控制进行数值仿真，仿真结果表明Legendre伪谱法对解决该姿态运动最优控制问题的有效性。

Abstract: The optimal attitude control of free-floating space robot system with dual-arm is discussed in this paper by using Legendre pseudospectral method. The simplified robot system dynamics model is established based on the linear and angular momentum conservation of the system. And the system constraints and performance index function based on system joints dissipation energy are determined to describe the optimal control problem. Then the continuous trajectory optimization is transformed into a discrete nonlinear programming problem (NLP) by using Legendre pseudospectral method. And the energy-optimal solutions are obtained with a NLP solver. An optimal attitude control method for the space robot is obtained. At the end of this paper, numerical simulations on the free-floating space robot attitude control problems are given. And the results verify the effectiveness of Legendre pseudospectral method on solving the optimal attitude control problem.