Optimal Guidance and Thruster Control in Orbital Approach and Rendezvous for Docking using Model Predictive Control

Abstract

In this paper, we present an integrated approach for proximal guidance and control of a docking vehicle during its terminal rendezvous and approach flight phases. The paper particularly focusses on one rendezvous orbit transfer sequence in the Space Shuttle's standard approach protocol of orbit-raising maneuvers during its approach to ISS: from MC4 (mid-course point 4) to MC5 directly beneath the Space Station. In addition to the relative position and velocity requirements in this transfer, optimal attitude pointing requirements are imposed on the shuttle, as this transfer is in close proximity and the shuttle must orient so that its Trajectory Control Sensor (TCS) can maintain line of sight to the ISS docking port to acquire ISS-relative navigation (relative position, velocity and attitude). The performance of the optimal relative translation and orientation guidance and control is shown in this paper utilizing the distinct, known mass properties and state dispersions from 7 recent shuttle missions (STS114-STS121).We use model-predictive control (MPC) to define and solve the optimal transfer guidance problem. The approach divides the problem into separate translational and associated attitude trajectory design phases that operate sequentially and replan at each guidance update period, consistent with MPC designs. To solve the attitude guidance problem, we introduce a method that analyzes a series of constrained optimal control problems at various candidate attitudes and torques to best achieve the desired translational trajectory synthesized in the previous step; the (optimal) attitude control problem is produced from a robust regression analysis of the optimal trajectory solutions.A linear programming solver selects and optimally schedules the vehicle jets to deliver the desired body force and torque commands subject to range-dependent plume impingement constraints imposed for safety of the ISS at ranges closer than 1000 ft.

Model Predictive Control of three dimensional spacecraft relative motion

“…The "rubber band" MPC approach was proposed in [6]. An application of MPC to spacecraft navigation in proximity of a space station is considered in [16], where an unconstrained MPC is proposed for guidance to the neighborhood of the space station, while the LoS between the station and the spacecraft sensors is maintained by a constrained spacecraft attitude controller, and a control allocation scheme to operate the thrusters. In a similar context, a receding horizon controller that uses the solutions of non-convex quadratically constrained quadratic programs has been proposed in [7] for passively safe proximity operations, where a statistical model of the uncertainty is used for improving robustness with respect to position uncertainty.…”

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

“…We assume that thrusters can be operated to generate prescribed propulsive forces in x and y directions and that the thrust magnitude is limited. The prescribed thrust forces can be physically realized by control allocation to appropriate thruster on–off times, see . For a single main thruster spacecraft configuration, we assume that the spacecraft orientation is changed appropriately by the attitude control system to realize the prescribed thrust vector.…”

“…The variable horizon approach is further extended in in the so‐called “rubber band” MPC, where the MPC controller is designed by inverse optimality by using techniques similar to with a horizon that first maintains a constant number of moves (as in standard MPC) and then decreases as in variable horizon MPC. An application of MPC to spacecraft navigation in proximity of a space station is considered in , where an unconstrained MPC is proposed for guidance to the neighborhood of the space station, while the LOS between the station and the spacecraft sensors is maintained by a constrained spacecraft attitude controller, and a control allocation scheme commands the thrusters. In a similar context, in , a receding horizon controller requiring the solutions of nonconvex quadratically constrained quadratic programs has been proposed for passively safe proximity operations, where a statistical model of the uncertainty is used for improving robustness with respect to position uncertainty.…”

A geometric framework for rigid body attitude estimation

“…This advantage is, however, associated with the accompanying weakness that it is not straightforward to incorporate nonlinear and nonholonomic constraints in the problem. For instance, in [13], the authors describe the attitude control of a spaceshuttle during a docking operation, when there is a hard constraint with respect to a nominal pitch angle in order to ensure that a trajectory control sensor is oriented towards the target platform. The attitude guidance module then estimates an optimal pitch attitude that complies with the hard constraint and minimizes the control effort.…”