基于hp自适应伪谱法的空间机器人路径规划

针对空间机器人运动过程中基座姿态产生较大扰动的问题，基于hp自适应高斯伪谱法提出了一种以基座所受反作用力矩最小为目标函数的空间机器人路径规划方法.首先，综合考虑空间机器人运动过程中存在的关节角度约束、关节角速度约束、控制力矩约束及初始状态和终端状态约束等约束条件，将空间机器人路径规划问题看成满足一系列约束条件和边界条件并实现特定性能指标最优的最优控制问题.其次，结合hp自适应高斯伪谱法（hp-AGPM）与非线性规划技术，求解带有边界约束和路径约束的优化控制问题，得到满足约束且性能指标最优的空间机器人运动轨迹.最后，以平面2自由度空间机械臂为例对所设计方法进行仿真验证，并与其他伪谱法进行对比分析.仿真结果表明：本文算法能在10.6 s的时间内规划出满足各约束条件且容许偏差低于10^-6的最优运动轨迹，并且在计算速度和配点数量上都优于其他伪谱法.

Path Planning of Space Robot Based on hp-Adaptive Pseudospectral Method

For the problem that the motion of the space robot will cause a large disturbance to the attitude of the base, a path planning method based on hp-adaptive Gauss pseudospectral method is proposed, in which the minimum reaction torque of the base is taken as the objective function. Firstly, the path planning problem of the space robot is regarded as an optimal control problem which meets the boundary condition and a series of path constraints including joint angle constraint, joint angular velocity constraint, control torque constraint and initial and terminal state constraints, and simultaneously minimizes a special performance index. Secondly, the optimal problem with boundary constraints and path constraints is solved by combining the hp-adaptive Gauss pseudospectral method (hp-AGPM) and the nonlinear programming technique, and a space robot trajectory satisfying the constraints and the optimal performance index is obtained. Finally, a planar two degree-of-freedom space manipulator is taken as an example to simulate and verify the designed method, and different pseudospectral methods are compared and analyzed. The simulation results show that the proposed method can generate an optimal trajectory satisfying all constraints in 10.6 s with the tolerance less than 10^-6, and is better than other pseudospectral methods both in computation speed and the number of collocation points.