Trajectory Planning for Hopping Rover on Small Bodies Under Pre-Collision Attitude Adjustment Modulation

Abstract

A novel pre-collision attitude adjustment (PCAA) modulation based on angular velocity and quaternions control is developed to more controllable and reliably adjust the non-spherical hopping rover's trajectory on small bodies. This corresponds to a hopping trajectory planning (HTP) framework that addresses inherent technical challenges, including attitude-trajectory coupled features, hard-to-depicting near-truth gravity and continues dynamical contact models, difficult-to-predetermine collision times with the small bodies’ surface, and complex judgments regarding whether the period of attitude adjustment is sufficient in current hops. Two main contributions are proposed, focusing on modeling and planning. To achieve a more realistic modeling of the rover's motion, its attitude-trajectory coupling dynamic model is researched, including a ground-truth irregular gravity model and continuous dynamical contact model. Additionally, a collision detection method based on the local surface smoothing technique is proposed for rapid and exact switching between the ballistic and contact motions for the subsequent planning purpose. On the other hand, redundancy planning and binary event-trigger techniques are combined for handling unpredictable available dimensions of optimization variables of PCAA-based HTP, which arise from the indeterminate scale of collision times and potential deficiency in ballistic flight time required for completing attitude maneuvers. Specifically, the solution space is preset to guarantee the unchanging dimensions of the design variables, which are activated or deactivated by coupling binary event variables for each dimension. These newly introduced events are triggered by comparing the realistic rebound time of the current hop with the necessary time for attitude maneuver, which is accurately computed by designing a first-order sliding mode controller. This approach enables an equivalent and easily implementable version of the problem to be obtained. Logically and numerically, the application of PCAA modulation is found to significantly enlarge or contract the area of the reachable region of the hopping rover and contribute to improving the convergence and reducing the relative final position error of the hopping trajectory planning problem.