LEGENDRE PSEUDO-SPECTRAL METHOD FOR SOLVING THE 3D RIGID PENDULUM MOTION OPTIMAL CONTROL PROBLEM

This paper studies the Legendre pseudo-spectral method for solving the 3D rigid pendulum motion optimal control problem. For the 3D rigid pendulum constrained mechanical model, a 3D Legendre pseudospectral method is proposed based on the rigid body posture and the optimal control method. By using the Legendre interpolation approximation method to design the 3D rigid pendulum motion optimal control algorithm, the optimal attitude control trajectory of the 3D rigid pendulum is obtained, and combined with the relaxation factor control, a satisfactory feasible solution can be found. The simulation results show that with the optimal Legendre pseudo-spectral method control algorithm, the 3D rigid pendulum goes to the end effector pose with a smaller error motion, at a fast calculation speed, and the control inputs can be obtained with a high precision. This paper also verifies the feasibility of the proposed optimal control algorithm.