Model Predictive Control with Ellipsoid Obstacle Constraints for Spacecraft Rendezvous

The problem of spacecraft rendezvous with obstacle avoidance constraints is explored. A Model Predictive Control (MPC) approach is used to compute an optimal control strategy for a chaser attempting to rendezvous with a target spacecraft in Earth orbit. Given obstructions to the baseline optimal trajectory, such as orbital debris or other spacecraft, MPC attempts to update the trajectory in real time such that it evades these obstacles. In this work, obstacles are approximated or bounded by ellipsoids to both enable straightforward constraint evaluation and better represent statistical knowledge of the obstacle's position. A nonlinear optimization method, Sequential Quadratic Programming, is able to solve this quadratic optimal control problem with nonlinear obstacle avoidance constraints. Specifically, the cases of multiple and moving obstacles are handled well with this approach due to the flexibility of the nonlinear constraint formulation. Implementation of this algorithm and results from a MATLAB-based simulation are discussed. This ellipsoid constraint approach is compared to a previous method involving a convex, rotating hyperplane constraint. The nonlinear programming approach presented is more computationally expensive than previous methods seen in the literature, but shows markedly improved results in a few key areas.