勒让德伪谱法求解三维刚体摆姿态运动最优控制问题

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

研究伪谱法求解三维刚体摆姿态运动最优控制问题.针对三维刚体摆这类含有约束的力学模型,提出了基于勒让德伪谱法的三维刚体摆姿态最优控制方法.利用插值逼近设计了三维刚体摆姿态运动最优控制算法,得到了三维刚体摆的姿态最优控制轨迹,并结合松弛参数来控制插值点的取值,寻找满足的可行解.仿真结果表明,基于勒让德伪谱法的最优控制算法使得三维刚体摆能以较小的误差运动到期望的末端姿态,且计算速度快,能够获得精度较高的控制输入量.

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 pseudo- spectral 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.