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Feasibility-Guided Safety-Aware Model Predictive Control for Jump Markov Linear Systems

Zakariya Laouar, Qi Heng Ho, Rayan Mazouz, Tyler Becker, Zachary N. Sunberg

TL;DR

Results indicate that the proposed technique of maximizing the robustness horizon, and the use of CBFs for safety awareness, improve the overall safety and performance of MPC for Jump Markov Linear Systems.

Abstract

In this paper, we present a controller framework that synthesizes control policies for Jump Markov Linear Systems subject to stochastic mode switches and imperfect mode estimation. Our approach builds on safe and robust methods for Model Predictive Control (MPC), but in contrast to existing approaches that either optimize without regard to feasibility or utilize soft constraints that increase computational requirements, we employ a safe and robust control approach informed by the feasibility of the optimization problem. We formulate and encode finite horizon safety for multiple model systems in our MPC design using Control Barrier Functions (CBFs). When subject to inaccurate hybrid state estimation, our feasibility-guided MPC generates a control policy that is maximally robust to uncertainty in the system's modes. We evaluate our approach on an orbital rendezvous problem and a six degree-of-freedom hexacopter under several scenarios and benchmarks to demonstrate the utility of the framework. Results indicate that the proposed technique of maximizing the robustness horizon, and the use of CBFs for safety awareness, improve the overall safety and performance of MPC for Jump Markov Linear Systems.

Feasibility-Guided Safety-Aware Model Predictive Control for Jump Markov Linear Systems

TL;DR

Results indicate that the proposed technique of maximizing the robustness horizon, and the use of CBFs for safety awareness, improve the overall safety and performance of MPC for Jump Markov Linear Systems.

Abstract

In this paper, we present a controller framework that synthesizes control policies for Jump Markov Linear Systems subject to stochastic mode switches and imperfect mode estimation. Our approach builds on safe and robust methods for Model Predictive Control (MPC), but in contrast to existing approaches that either optimize without regard to feasibility or utilize soft constraints that increase computational requirements, we employ a safe and robust control approach informed by the feasibility of the optimization problem. We formulate and encode finite horizon safety for multiple model systems in our MPC design using Control Barrier Functions (CBFs). When subject to inaccurate hybrid state estimation, our feasibility-guided MPC generates a control policy that is maximally robust to uncertainty in the system's modes. We evaluate our approach on an orbital rendezvous problem and a six degree-of-freedom hexacopter under several scenarios and benchmarks to demonstrate the utility of the framework. Results indicate that the proposed technique of maximizing the robustness horizon, and the use of CBFs for safety awareness, improve the overall safety and performance of MPC for Jump Markov Linear Systems.
Paper Structure (18 sections, 2 theorems, 15 equations, 3 figures, 4 tables, 1 algorithm)

This paper contains 18 sections, 2 theorems, 15 equations, 3 figures, 4 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Related Work
  3. Contribution
  4. System Setup
  5. Safety-aware Trajectory Planner Design
  6. Model Predictive Control
  7. Control Barrier Functions
  8. Robustness via Control Consensus across Modes
  9. Feasibility Analysis
  10. Adaptive Consensus Horizon Planning
  11. Computational Complexity
  12. Simulation Evaluation
  13. Case Studies
  14. Spacecraft Orbital Rendezvous
  15. Hazardous Mineshaft Inspection
  16. ...and 3 more sections

Key Result

Proposition 1

Let $F_h$ be the feasible set for problem:consensus with a consensus horizon $h$. Given two consensus horizons $h_1 < h_2 \leq H$, $F_{h_1} \supseteq F_{h_2}$.

Figures (3)

  • Figure 1: Feasibility-guided MPC for a multiple-model hexacopter subject to partially observable stochastic rotor faults. Our approach computes an adaptive robust control (consensus) horizon at each planning step to improve robustness and feasibility.
  • Figure 2: Spacecraft Orbital Rendezvous: example state trajectories for our approach and the baselines: First-Step Consensus, Full-Step Consensus, and Non-Robust. Only the in-track (y-direction) relative position is displayed to highlight the chaser spacecraft's (in)ability to stay behind the target satellite. The mode switch is induced at 35s and the estimation delay is 7s after. The simulation duration is 280s. Lower opacity illustrates problem infeasibility. When the problem is infeasible, the first control input from the mode with the highest likelihood is chosen and executed.
  • Figure 3: Hazardous Mineshaft Inspection: example state trajectories for our approach and the baselines: First-Step Consensus, Full-Step Consensus, and Non-Robust. The mode switch is induced at 0.9s and the estimation delay is 0.15s after. The simulation duration is 4 seconds. Lower opacity illustrates problem infeasibility. When the problem is infeasible, the first control input from the mode with the highest likelihood is chosen and executed.

Theorems & Definitions (9)

  • Example 1
  • Definition 1: Forward Invariance & Safety
  • Definition 2: Consensus Horizon
  • Proposition 1
  • proof
  • Definition 3: Feasible Consensus Horizon
  • Proposition 2
  • proof : Proof Sketch
  • Definition 4: Maximally Feasible Consensus Horizon