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A Contingency Model Predictive Control Framework for Safe Learning

Merlijne Geurts, Tren Baltussen, Alexander Katriniok, Maurice Heemels

TL;DR

The paper tackles safe learning for control-Hard safety constraints by introducing Contingency Model Predictive Control (CMPC), a two-horizon framework that merges robust MPC's constraint satisfaction with learning-based MPC's adaptivity. By proving robust recursive feasibility under standard RMPC assumptions, CMPC guarantees safety while leveraging data-driven residual dynamics through a learning horizon. A concrete implementation combines RMPC from existing robust MPC literature with Gaussian Process MPC to learn unmodeled dynamics, and applies this to automated lane merging, showing improved performance over standalone RMPC and preserved safety unlike standalone GP-MPC. The results indicate CMPC can achieve more assertive, efficient control in safety-critical applications without sacrificing feasibility, making it a promising approach for safe learning in autonomous systems.

Abstract

This research introduces a multi-horizon contingency model predictive control (CMPC) framework in which classes of robust MPC (RMPC) algorithms are combined with classes of learning-based MPC (LB-MPC) algorithms to enable safe learning. We prove that the CMPC framework inherits the robust recursive feasibility properties of the underlying RMPC scheme, thereby ensuring safety of the CMPC in the sense of constraint satisfaction. The CMPC leverages the LB-MPC to safely learn the unmodeled dynamics to reduce conservatism and improve performance compared to standalone RMPC schemes, which are conservative in nature. In addition, we present an implementation of the CMPC framework that combines a particular RMPC and a Gaussian Process MPC scheme. A simulation study on automated lane merging demonstrates the advantages of our general CMPC framework.

A Contingency Model Predictive Control Framework for Safe Learning

TL;DR

The paper tackles safe learning for control-Hard safety constraints by introducing Contingency Model Predictive Control (CMPC), a two-horizon framework that merges robust MPC's constraint satisfaction with learning-based MPC's adaptivity. By proving robust recursive feasibility under standard RMPC assumptions, CMPC guarantees safety while leveraging data-driven residual dynamics through a learning horizon. A concrete implementation combines RMPC from existing robust MPC literature with Gaussian Process MPC to learn unmodeled dynamics, and applies this to automated lane merging, showing improved performance over standalone RMPC and preserved safety unlike standalone GP-MPC. The results indicate CMPC can achieve more assertive, efficient control in safety-critical applications without sacrificing feasibility, making it a promising approach for safe learning in autonomous systems.

Abstract

This research introduces a multi-horizon contingency model predictive control (CMPC) framework in which classes of robust MPC (RMPC) algorithms are combined with classes of learning-based MPC (LB-MPC) algorithms to enable safe learning. We prove that the CMPC framework inherits the robust recursive feasibility properties of the underlying RMPC scheme, thereby ensuring safety of the CMPC in the sense of constraint satisfaction. The CMPC leverages the LB-MPC to safely learn the unmodeled dynamics to reduce conservatism and improve performance compared to standalone RMPC schemes, which are conservative in nature. In addition, we present an implementation of the CMPC framework that combines a particular RMPC and a Gaussian Process MPC scheme. A simulation study on automated lane merging demonstrates the advantages of our general CMPC framework.

Paper Structure

This paper contains 13 sections, 2 theorems, 19 equations, 3 figures, 1 table.

Table of Contents

  1. Introduction
  2. Problem Formulation
  3. CMPC Framework for Safe Learning
  4. Safety Guarantees
  5. Automated Lane Merging Application
  6. CMPC for Automated lane merging
  7. Robust MPC - Contingency Horizon
  8. Gaussian Process MPC - Performance Horizon
  9. Integration into CMPC Framework
  10. Numerical Results
  11. Merging scenario comparison
  12. Sensitivity analysis
  13. Conclusions

Key Result

Theorem 1

Let Ass. assum:terminal_set and assum:disturbance hold. If OCP eq:MPC_problem has a feasible solution $(\bar{x}_{k \mid k},\bar{U}_{k}, \hat{U}_{k})$ for $x_k$ at time $k\in\mathbb{N}$, then eq:MPC_problem is feasible for the next state $x_{k+1}=f(x_k, \kappa(x_k, \bar{x}_{k \mid k}) +\bar{u}_{k \mi

Figures (3)

  • Figure 1: A schematic of CMPC framework with circles indicating the admissible state constraint sets for each horizon.
  • Figure 2: Set-up of the lane-merging scenario.
  • Figure 3: Comparison of RMPC (left), CMPC (middle) and GP-MPC (right) for one lane merging scenario, see Sec. \ref{['sec:use_case']}. Shown are the trajectories of the path coordinate $s^i$, velocity $v^i$, acceleration $u^i$ and relative distance $|\Delta s|$ of Agent 1 and 2. The lower limit of $|\Delta s|$ is imposed by $D_{\text{safe}}$.

Theorems & Definitions (4)

  • Theorem 1
  • proof
  • Theorem 2
  • proof