Semi-Analytic motion planning with actuator constraints on 3-D Lie groups

This paper describes a global motion planning method for vehicles with actuator constraints based on the semi-Analytic solution of minimum energy-Type curves on the frame bundle of connected surfaces of arbitrary cross sectional curvature. The method is semi-Analytic and solves the boundary-value problem arising from the geometric framing of the Pontryagin's maximum principle applied to the vehicle kinematics where the velocities are defined analytically in terms of three parameters. Numerical shooting on an iterative Lie group expression of the curve in the group is then employed to match the group boundary conditions. This approach has the advantage that an analytic description of the control accelerations can be derived and enables actuator constraints to be incorporated via time reparametrization. The method is applied to a practical example from space mechanics, the spacecraft docking problem with actuator constraints.