This paper presents a strategy and case studies of spacecraft relative motion guidance and control based on the application of linear quadratic model predictive control (MPC) with dynamically reconfigurable constraints. The controller is designed to transition between the MPC guidance during a spacecraft rendezvous phase and MPC guidance during a spacecraft docking phase, with each phase having distinct requirements, constraints, and sampling rates. Obstacle avoidance is considered in the rendezvous phase, while a line-of-sight cone constraint, bandwidth constraints on the spacecraft attitude control system, and exhaust plume direction constraints are addressed during the docking phase. The MPC controller is demonstrated in simulation studies using a nonlinear model of spacecraft orbital motion. The implementation uses estimates of spacecraft states derived from relative angle and range measurements, and is robust to estimator dynamics and measurement noise.Index Terms-Constraints, model predictive control, obstacle avoidance, rendezvous and docking, spacecraft control.
1063-6536
Abstract-The concept of stochastic reachability allows for the assessment, before any maneuvers are initiated, of the probability of successfully implementing a rendezvous or docking procedure for spacecraft. The so-called reach-avoid problem lets us find the probability of reaching a target set while avoiding some unsafe or undesired set, despite uncertainty due to nonlinearity and disturbances. This paper examines two novel methods for the calculation of stochastic reachable sets, and specifically for rendezvous and docking problems. In particular, we examine a) particle (or scenario) approximations to expected values, and b) conversion of the reach-avoid probability to a chance-constrained convex optimization problem. Both methods allow for computation of the reach-avoid set in higher dimensions, as compared to other existing methods for computing stochastic reachable sets. We describe in detail both of these methods, and then apply them to spacecraft relative motion, a four-dimensional problem.
This paper presents an obstacle avoidance method for spacecraft relative motion control. In this approach, a connectivity graph is constructed for a set of relative frame points, which form a virtual net centered around a nominal orbital position. The connectivity between points in the virtual net is determined based on the use of safe positively invariant sets for guaranteed collision free maneuvering. A graph search algorithm is then applied to find a maneuver that avoids specified obstacles and adheres to specified thrust limits. As compared to conventional open-loop trajectory optimization, this approach enables the handling of bounded disturbances, which can represent the effects of perturbing forces and model uncertainty, while rigorously guaranteeing that nonconvex and possibly time-varying obstacle avoidance constraints are satisfied. Details for handling a single stationary obstacle, multiple stationary obstacles, moving obstacles, and bounded disturbances are reported and illustrated with simulation case studies.
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