Model Predictive Control approach for guidance of spacecraft rendezvous and proximity maneuvering

Abstract

Traditionally rendezvous and proximity maneuvers have been performed using open-loop maneuver planning techniques and ad hoc error corrections. In this paper, a Model Predictive Control (MPC) approach is applied to spacecraft rendezvous and proximity maneuvering problems in the orbital plane. We demonstrate that various constraints arising in these maneuvers can be effectively handled with the MPC approach. These include constraints on thrust magnitude, constraints on spacecraft positioning within Line-of-Sight (LOS) cone while approaching the docking port on a target platform, and constraints on approach velocity to match the velocity of the docking port. The two cases of a non-rotating and a rotating (tumbling) platform are treated separately, and trajectories are evaluated in terms of maneuver time and fuel consumption. For the case when the platform is not rotating and the docking port position is fixed with respect to the chosen frame, an explicit off-line solution of the MPC optimization problem is shown to be possible; this explicit solution has a form of a piecewise affine control law suitable for on-line implementation without an onboard optimizer. In the case of a fast rotating platform, it is, however, shown that the prediction of the platform rotation is necessary to successfully accomplish the maneuvers and to reduce fuel consumption. Finally, the proposed approach is applied to debris avoidance maneuvers with the debris in the spacecraft rendezvous path. The significance of this paper is in demonstrating that Model Predictive Control can be an effective feedback control approach to satisfy various maneuver requirements, reduce fuel consumption, and provide robustness to disturbances. International Journal of Robust and Nonlinear ControlThis work may not be copied or reproduced in whole or in part for any commercial purpose. Permission to copy in whole or in part without payment of fee is granted for nonprofit educational and research purposes provided that all such whole or partial copies include the following: a notice that such copying is by permission of Mitsubishi Electric Research Laboratories, Inc.; an acknowledgment of the authors and individual contributions to the work; and all applicable portions of the copyright notice. Copying, reproduction, or republishing for any other purpose shall require a license with payment of fee to Mitsubishi Electric Research Laboratories, Inc. All rights reserved. SUMMARYTraditionally rendezvous and proximity maneuvers have been performed using open-loop maneuver planning techniques and ad hoc error corrections. In this paper, a Model Predictive Control (MPC) approach is applied to spacecraft rendezvous and proximity maneuvering problems in the orbital plane. We demonstrate that various constraints arising in these maneuvers can be effectively handled with the MPC approach. These include constraints on thrust magnitude, constraints on spacecraft positioning within Line-of-Sight (LOS) cone while approaching the docking port on a target platform, and ...

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

“…To alleviate the concern of not meeting the problem's cone constraint as defined in Table 1, the cone range is extended in the IDVD formulation so that the original constraint is always met. Moreover, since the cone constraints are enforced on states, this issue could also be addressed by adding auxiliary slack variables in the cone constraints [7]. Figure 5 shows the simulated and experimental trajectories obtained with the re-tuned LQ-MPC controller.…”

“…This result is expected since the IDVD approach solves the full nonlinear optimization problem without approximating the obstacle keep-out zone. The LQ-MPC only considers a part of the trajectory (receding horizon) and approximates the nonlinear constraint through the rotating hyperplane method [7,37]. The linearization of the keep-out zone tends to overconstrain the problem, leading to a less optimal solution.…”

“…This type of optimization problems can be efficiently solved while enjoying deterministic convergence properties [6]. Implementation of MPC for spacecraft RPO maneuvers has been studied in the past [7]. A survey of guidance algorithms that can be used for onboard RPO trajectory planning is presented in [35], including an MPC implementation in simulation.…”

“…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.…”

“…This linearization may over-constrain the problem, providing a sub-optimal solution when compared to the solution of the original nonlinear problem. The use of MPC has been recently proposed for spacecraft RPO [7] and experimental evaluations using a kinematic test bed have already been conducted [8,9], but to the best knowledge of the authors, this is the first time that the use of MPC is experimentally demonstrated for spacecraft RPO in a dynamically representative test bed. After conducting the experiments presented in this paper, the authors have experimentally demonstrated the use of a nonlinear MPC approach for spacecraft docking maneuvers [10].…”