自由下落猫姿态最优控制的混合优化策略

研究猫自由下落时的转体运动对探索宇航员在太空失重状态下的空间运动规律具有重要的参考价值.针对猫自由下落时四肢先着地现象的姿态最优控制问题,提出一种由Gauss伪谱法求解可行解与直接打靶法求解最优精确解相结合的混合优化策略.首先,根据猫在自由下落过程中的角动量守恒原理,推导出简化后的两对称刚体系统的非完整姿态运动方程;然后基于Gauss伪谱法将此无漂移系统的姿态非完整运动规划问题离散为非线性规划问题,并在不考虑实际性能指标函数的条件下利用序列二次规划算法求解此非线性规划问题在较少节点时对应的控制变量可行解,再通过三次样条插值获取较多节点时的控制变量值;最后基于直接打靶法将插值得到的控制值作为序列二次规划算法的初始猜测值,从而求解得到最优的控制输入,再代入系统姿态运动方程,通过数值积分得到落体猫的转体姿态运动曲线.通过数值仿真,求解得到的姿态运动曲线是光滑的,能以较高的精度到达预定的目标姿态;最优控制输入也能满足预先设计的零边界控制要求以及最大控制要求;结果表明了此混合优化策略具有较强的鲁棒性和有效性.

THE ATTITUDE OPTIMAL CONTROL WITH A HYBRID OPTIMAL STRATEGY FOR A FREE-FALLING CAT 1)

Researching the twist motion of a free fall cat has an important reference value for exploring the motion rules of astronauts under the condition of weightlessness in space. For the attitude optimal control problem of a free-falling cat which limbs is always land on floor firstly, a hybrid optimal strategy is presented, which combines the Gauss pseudo-spectral method for feasible solutions with the Direct Shooting Method for exact optimal solutions. Firstly, according to the conversation of angular momentum in the process of the cat free falling, the nonholonomic attitude motion equation of the simplified two symmetry rigid bodies can be deduced;then the attitude nonholonomic motion planning problem of non-drift system can be converted to a nonlinear programming problem by using Gauss pseudo-spectral method, and the feasible solutions of control can be solved through SQP algorithm at a lower LG points without considering the actual index function, and more nodes of control can be obtained through cubic spline interpolation;at last, with the theory of Direct Shooting Method, substituting these control values of interpolation into SQP algorithm as initial values to compute the optimal control inputting, then attitude motion of the cat can be obtained by applying the optimal control into motion equation of system. Through numerical simulating, the attitude motion is smooth, and can reach the predetermined target location at a higher accuracy;the optimal control can satisfy the requirements of zero boundaries control and maximum control. The results demonstrate the robustness and effectiveness of the hybrid optimal strategy.