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MPC for Tracking applied to rendezvous with non-cooperative tumbling targets ensuring stability and feasibility

Jose Antonio Rebollo, Rafael Vazquez, Ignacio Alvarado, Daniel Limon

Abstract

A Model Predictive Controller for Tracking is introduced for rendezvous with non-cooperative tumbling targets in active debris removal applications. The target's three-dimensional non-periodic rotational dynamics as well as other state and control constraints are considered. The approach is based on applying an intermediate coordinate transformation that eliminates the time-dependency due to rotations in the constraints. The control law is then found as the solution to a QP problem with linear constraints and dynamics, as derived from the HCW equations, that provides feasibility and stability guarantees by means of a terminal LQR and dead-beat region. The proposed control algorithm performs well in a realistic simulation scenario, namely a near rendezvous with the Envisat spacecraft.

MPC for Tracking applied to rendezvous with non-cooperative tumbling targets ensuring stability and feasibility

Abstract

A Model Predictive Controller for Tracking is introduced for rendezvous with non-cooperative tumbling targets in active debris removal applications. The target's three-dimensional non-periodic rotational dynamics as well as other state and control constraints are considered. The approach is based on applying an intermediate coordinate transformation that eliminates the time-dependency due to rotations in the constraints. The control law is then found as the solution to a QP problem with linear constraints and dynamics, as derived from the HCW equations, that provides feasibility and stability guarantees by means of a terminal LQR and dead-beat region. The proposed control algorithm performs well in a realistic simulation scenario, namely a near rendezvous with the Envisat spacecraft.
Paper Structure (14 sections, 3 theorems, 107 equations, 7 figures, 1 table)

This paper contains 14 sections, 3 theorems, 107 equations, 7 figures, 1 table.

Table of Contents

  1. Introduction
  2. Problem formulation
  3. MPCT-based rendezvous
  4. Brief review of the optimization problem
  5. Definition of state and control variables
  6. Equilibrium parameter and equilibrium trajectory
  7. Design of the controller
  8. Terminal controllers design
  9. Feasibility constraint derivation
  10. Definition of weighting matrices
  11. Implementation and properties of the controller
  12. Case study and simulation results
  13. Conclusions and future lines of work
  14. Supplementary Proofs

Key Result

Lemma 1

The dimension of the space of equilibrium points for the LTV system given in EqsOfMotion is constant and equal to $n_\theta(k) = 3$. Furthermore, it is possible to define $M(k)$ such that $\theta$ is equal to the position of the considered equilibrium point in $B$, $\theta = \bm{r}^B_e$, which is co

Figures (7)

  • Figure 1: Rendezvous operation considering debris body (B) and LVLH (L) reference frames.
  • Figure 2: Real and virtual controller layout with feasibility and stability guarantees.
  • Figure 3: Modified LOS region considering feasibility constraints.
  • Figure 4: Construction of a feasible solution at $k+1$ given a solution at $k$.
  • Figure 5: Chaser controlled rendezvous path in LVLH axes.
  • ...and 2 more figures

Theorems & Definitions (6)

  • Lemma 1
  • Lemma 2
  • Lemma 3
  • proof : Proof of Lemma 1
  • proof : Proof of Lemma 2
  • proof : Proof of Lemma 3