An inverse dynamics-based trajectory planner for autonomous docking to a tumbling target

A trajectory planning algorithm for minimum-energy docking maneuvers between a controlled chaser spacecraft and an uncontrolled target vehicle is proposed. The key aspect of this method is that the shapes of both rotational and translational trajectories of the chaser spacecraft are parameterized using high-order polynomials. Some of the polynomial coefficients are constrained to satisfy the path constraints of the maneuver, whereas the rest are parameters to be optimized. By inverting the dynamics model of the system, the original optimal control problem for docking maneuvers is converted into an equivalent nonlinear programming problem with a limited number of varied parameters, being the free polynomial coefficients. This leads to fast computational speed. The trajectory planning algorithm is executed in closed-loop fashion using the current state of the spacecraft as initial conditions. The proposed guidance scheme is tested on different scenarios. By employing fifth-order polynomials for both translational and rotational trajectories, the resulting maneuvers are near-optimal: the translational components match the solution of the optimal control problem, whereas discrepancies are observed in the shape of the rotational trajectory. Several parameterizations for the attitude are employed to improve the optimality of the trajectory.