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

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 pseudospectral 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.