Optimal Trajectory Planning for a Space Robot Docking with a Moving Target via Homotopy Algorithms

The mathematical formulation of optimal trajectory planning for a space robot docking with a moving target is derived. The calculus of variations is applied to the problem so that the optimal robot trajectory can be obtained directlt from the target information without first planning the trajectory of the end-effector. The nonlinear two-point boundary value problem resulting from the problem formulation is solved numerically by a globally convergent homotopy algorithm. The algorithm guarantees convergence to a solution for an arbitrarily chosen initial guess. Numerical simulation for three examples demonstrates the approach.