Rapid Path Planning for Zero Propellant Maneuvers Based on Flatness

Abstract

A rapid path planning (RPP) method that fast generates suboptimal zero propellant maneuver (ZPM) paths was proposed previously, and to further enhance the planning performance, the differential flatness of the model is studied in this paper. For the crucial issue of singularity in flatness planning, the equivalence between the state transformation singularity and the control transformation singularity is proved for the feedback-linearizable multi-input multi-output (MIMO) affine system, which simplifies the singularity investigation of the ZPM problem. The question of searching suitable flat outputs for specific types of large-angle maneuvers is raised before path planning. Four sets of flat output candidates, which are biased to different types of maneuvers, are examined, and it is shown that only the large-angle yaw maneuver is achievable. The essentially singular attitudes (ESAs), for which no outputs could linearize the model, are presented, and it is found that the large-angle pitch or roll maneuver path planning easily encounters singularity in the flat output space no matter what output functions are constructed. To the regular mission of large-angle yaw maneuvers, the flatness is utilized in the RPP method. A simultaneous reconstruction method is proposed to solve the large amount of implicit equations in the planning, and rapid planning for the ZPM path is achieved.