Cascaded Lyapunov Vector Fields for Acceleration-Constrained Spacecraft Path Planning

A variant of Lyapunov vector fields is presented for tracking trajectories within tumbling and accelerating reference frames. This extension is computationally light, and is acceleration constrained rather than velocity constrained, making it suitable for real-time use in spacecraft. A general stability analysis proves globally asymptotic stability given a set of conditions that are analogous to those of standard Lyapunov vector fields. A special case of this novel path-planning law (referred to as a cascaded Lyapunov vector field) is closely studied, and a simple set of conditions guaranteeing bounded acceleration commands for perfect tracking are derived. A design procedure is presented. Finally, a full design example for a spacecraft proximity inspection mission is presented. The simulations demonstrate stable behavior while respecting acceleration and path constraints. Furthermore, all constraints are met by judicious design of the path-planning field, without the need for computationally expensive algorithms running in real-time.