Indirect Collocation Method in Multiple Minimal Coordinates for Optimal Control of Constrained Mechanical Systems

This paper addresses the optimal control problem of constrained mechanical systems formulated in minimal coordinates. To avoid the underlying parameterization singularity issue of minimal coordinates, we derive the equivalent maximal principle in multiple minimal coordinates. With appropriate boundary transition conditions, they actually describe the same optimal trajectories and control inputs as the differential algebraic equations (DAEs) formulation in redundant coordinates. Based on the tangent space parameterization technique, a sequence of tangent charts is built along given initial trajectories. Furthermore, the collocation method in multiple minimal coordinates is proposed. The proposed formulation is more efficient to generate high‐accuracy optimal trajectories and control inputs, compared to two alternative methods in redundant coordinates. Simulations on two constrained mechanical systems verify the effectiveness of our approach.