Robust model predictive control for multi-step short range spacecraft rendezvous

Abstract This work presents a robust model predictive control (MPC) approach for the multi-step short range spacecraft rendezvous problem. During the specific short range phase concerned, the chaser is supposed to be initially outside the line-of-sight (LOS) cone. Therefore, the rendezvous process naturally includes two steps: the first step is to transfer the chaser into the LOS cone and the second step is to transfer the chaser into the aimed region with its motion confined within the LOS cone. A novel MPC framework named after Mixed MPC (M-MPC) is proposed, which is the combination of the Variable-Horizon MPC (VH-MPC) framework and the Fixed-Instant MPC (FI-MPC) framework. The M-MPC framework enables the optimization for the two steps to be implemented jointly rather than to be separated factitiously, and its computation workload is acceptable for the usually low-power processors onboard spacecraft. Then considering that disturbances including modeling error, sensor noise and thrust uncertainty may induce undesired constraint violations, a robust technique is developed and it is attached to the above M-MPC framework to form a robust M-MPC approach. The robust technique is based on the chance-constrained idea, which ensures that constraints can be satisfied with a prescribed probability. It improves the robust technique proposed by Gavilan et al., because it eliminates the unnecessary conservativeness by explicitly incorporating known statistical properties of the navigation uncertainty. The efficacy of the robust M-MPC approach is shown in a simulation study.

[1]  Alberto Bemporad,et al.  Control of systems integrating logic, dynamics, and constraints , 1999, Autom..

[2]  Eric Rogers,et al.  Explicit Model Predictive Control Approach for Low-Thrust Spacecraft Proximity Operations , 2014 .

[3]  Sebastian Grimberg,et al.  Comprehensive Survey and Assessment of Spacecraft Relative Motion Dynamics Models , 2017 .

[4]  Ilya V. Kolmanovsky,et al.  Model Predictive Control for Spacecraft Rendezvous and Docking: Strategies for Handling Constraints and Case Studies , 2015, IEEE Transactions on Control Systems Technology.

[5]  Jonathan P. How,et al.  Spacecraft trajectory planning with avoidance constraints using mixed-integer linear programming , 2002 .

[6]  K. Yamanaka,et al.  New State Transition Matrix for Relative Motion on an Arbitrary Elliptical Orbit , 2002 .

[7]  Jonathan P. How,et al.  Robust variable horizon model predictive control for vehicle maneuvering , 2006 .

[8]  Jonathan P. How,et al.  Co‐ordination and control of distributed spacecraft systems using convex optimization techniques , 2002 .

[9]  Eduardo F. Camacho,et al.  Chance-constrained model predictive control for spacecraft rendezvous with disturbance estimation , 2012 .

[10]  Peng Li,et al.  Line-of-sight nonlinear model predictive control for autonomous rendezvous in elliptical orbit , 2017 .

[11]  Jonathan P. How,et al.  Safe Trajectories for Autonomous Rendezvous of Spacecraft , 2006 .

[12]  Borhan Beigzadeh,et al.  Robust control of spacecraft rendezvous on elliptical orbits: Optimal sliding mode and backstepping sliding mode approaches , 2016 .

[13]  Robin Larsson,et al.  Flight results from the PRISMA optical line of sight based autonomous rendezvous experiment , 2011 .

[14]  Shaoming He,et al.  Elliptical Orbital Spacecraft Rendezvous without Velocity Measurement , 2016 .

[15]  Ilya Kolmanovsky,et al.  Model Predictive Control approach for guidance of spacecraft rendezvous and proximity maneuvering , 2012 .

[16]  Georgia Deaconu,et al.  Minimizing the Effects of Navigation Uncertainties on the Spacecraft Rendezvous Precision , 2014 .

[17]  Shaoming He,et al.  Reliable spacecraft rendezvous without velocity measurement , 2018 .

[18]  Eduardo F. Camacho,et al.  Pulse-Width Predictive Control for LTV Systems with Application to Spacecraft Rendezvous , 2015, ArXiv.

[19]  Robin Larsson,et al.  System test results from the GNC experiments on the PRISMA in-orbit test bed , 2011 .