Rapid Construction of Safe Search-Trees for Spacecraft Attitude Planning

This paper adapts the rapidly-exploring variant of invariant-set motion planner (ISMP) for spacecraft attitude motion planning and control. The ISMP is a motion-planning algorithm that uses positive-invariant sets of the closed-loop dynamics to find a constraint admissible path to a desired target through an obstacle filled environment. We present four mathematical results that enable the sub-routines used to rapidly construct a search-tree for the ISMP. These mathematical results describe how to uniformly sample safe quaternions, how to find the nearest orientation in the search-tree, how to move the sampled orientation to form an edge, and how to scale the invariant set to guarantee constraint admissibility. We present simulation results that demonstrate the ISMP for spacecraft attitude motion planning.