Planar space robots with coupled joints: differentially flat designs

The motion of free-floating space robots is characterized by nonholonomic, i.e., non-integrable rate constraint equations. These constraints originate from principles of conservation of linear and angular momentum. Trajectory planning of these systems is extremely challenging and computation intensive since the motion must satisfy differential constraints. However, under certain conditions, these drift-less control systems can be shown to be differentially flat. The property of flatness allows a computationally inexpensive way to plan trajectories for the dynamic system between two configurations as well as develop feedback controllers. In this paper, nonholonomic rate constraints for free-floating planar open-chain robots are studied together with auxiliary joint variable constraints to determine design conditions under which the system exhibits differential flatness. Sufficient conditions are derived for existence of flatness and are illustrated by examples.