Model Predictive Control of three dimensional spacecraft relative motion

Abstract

This paper further develops an approach for spacecraft relative motion control based on the application of linear quadratic Model Predictive Control (MPC) with dynamically reconfigurable constraints. Previous results for maneuvers confined to the orbital plane are extended to three dimensional maneuvers with three dimensional Line-of-Sight (LoS) constraint handling. The MPC controller is designed to prescribe ∆v impulsive velocity changes rather than piecewise constant thrust profiles. The ability to transition between MPC guidance in the spacecraft rendezvous phase and MPC guidance in the spacecraft docking phase, with requirements, constraints, and sampling rates specific to each phase, is demonstrated. Bandwidth constraints of the spacecraft attitude control system and exhaust plume direction constraints are also addressed. The MPC controller is validated on the full nonlinear model of spacecraft orbital motion and augmented with an Extended Kalman Filter (EKF) to estimate spacecraft states based on relative angles and relative range measurements.

Stochastic reachability for control of spacecraft relative motion

“…Both of the open loop methods described above are applied to the reachability problem for the final phase of in-plane space rendezvous, as described in [1]. First, we define the safe set K that the deputy should remain within for all time steps 0 to N − 1, and the target set T next to the chief, that should be reached at time N .…”

“…We compute the reachable sets over a period of N = 5 time steps, ∆ = 20 seconds per time step (as in [1]), and compare the particle approach to the convex optimization. Problem 2 is solved in CPLEX and Problem 4 using an active-set algorithm through fmincon in MATLAB's Optimization toolbox.…”

“…While there is extensive literature on control mechanisms for performing such maneuvers, particularly the use of model predictive control with approach and docking constraints for successful rendezvous (see, e.g. [1], [2], [3], [4]), almost no work has been done on characterizing the initial set of states from which such maneuvers can be performed safely.…”

Experimental evaluation of model predictive control and inverse dynamics control for spacecraft proximity and docking maneuvers

“…The experimental validation of an MPC algorithm presented in this paper provides further confidence in its ability to be implemented onboard real systems. Simulation results of applications of MPC to a constrained rendezvous problem have also been shown in [36,37]. The type of constraints enforced in these simulations include thrust constraints, a line-ofsight constraint linearized through polyhedral approximations [36], and an obstacle avoidance constraint linearized through a rotating hyperplane [7,37].…”

“…Simulation results of applications of MPC to a constrained rendezvous problem have also been shown in [36,37]. The type of constraints enforced in these simulations include thrust constraints, a line-ofsight constraint linearized through polyhedral approximations [36], and an obstacle avoidance constraint linearized through a rotating hyperplane [7,37]. These references provide the basic framework for the LQ-MPC formulation implemented for this experimental campaign.…”