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 ∞ight 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 deflne 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.