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Recursively Feasible Shrinking-Horizon MPC in Dynamic Environments with Conformal Prediction Guarantees

Charis Stamouli, Lars Lindemann, George J. Pappas

TL;DR

The paper tackles safe control in dynamic environments with uncontrollable stochastic agents by combining learning-based trajectory predictors with split conformal prediction to produce online high-confidence prediction regions for all future time steps. These regions are integrated into a shrinking-horizon MPC that gradually relaxes safety constraints over time to preserve recursive feasibility while maintaining probabilistic safety with confidence $1-\delta$. The authors prove recursive feasibility and safety guarantees, and demonstrate tighter prediction regions and maintained feasibility in a mobile-robot navigation case around pedestrians, comparing favorably against a state-of-the-art baseline. This approach enables tighter, data-driven safety envelopes for real-time autonomous systems operating in uncertain, dynamic environments.

Abstract

In this paper, we focus on the problem of shrinking-horizon Model Predictive Control (MPC) in uncertain dynamic environments. We consider controlling a deterministic autonomous system that interacts with uncontrollable stochastic agents during its mission. Employing tools from conformal prediction, existing works derive high-confidence prediction regions for the unknown agent trajectories, and integrate these regions in the design of suitable safety constraints for MPC. Despite guaranteeing probabilistic safety of the closed-loop trajectories, these constraints do not ensure feasibility of the respective MPC schemes for the entire duration of the mission. We propose a shrinking-horizon MPC that guarantees recursive feasibility via a gradual relaxation of the safety constraints as new prediction regions become available online. This relaxation enforces the safety constraints to hold over the least restrictive prediction region from the set of all available prediction regions. In a comparative case study with the state of the art, we empirically show that our approach results in tighter prediction regions and verify recursive feasibility of our MPC scheme.

Recursively Feasible Shrinking-Horizon MPC in Dynamic Environments with Conformal Prediction Guarantees

TL;DR

The paper tackles safe control in dynamic environments with uncontrollable stochastic agents by combining learning-based trajectory predictors with split conformal prediction to produce online high-confidence prediction regions for all future time steps. These regions are integrated into a shrinking-horizon MPC that gradually relaxes safety constraints over time to preserve recursive feasibility while maintaining probabilistic safety with confidence . The authors prove recursive feasibility and safety guarantees, and demonstrate tighter prediction regions and maintained feasibility in a mobile-robot navigation case around pedestrians, comparing favorably against a state-of-the-art baseline. This approach enables tighter, data-driven safety envelopes for real-time autonomous systems operating in uncertain, dynamic environments.

Abstract

In this paper, we focus on the problem of shrinking-horizon Model Predictive Control (MPC) in uncertain dynamic environments. We consider controlling a deterministic autonomous system that interacts with uncontrollable stochastic agents during its mission. Employing tools from conformal prediction, existing works derive high-confidence prediction regions for the unknown agent trajectories, and integrate these regions in the design of suitable safety constraints for MPC. Despite guaranteeing probabilistic safety of the closed-loop trajectories, these constraints do not ensure feasibility of the respective MPC schemes for the entire duration of the mission. We propose a shrinking-horizon MPC that guarantees recursive feasibility via a gradual relaxation of the safety constraints as new prediction regions become available online. This relaxation enforces the safety constraints to hold over the least restrictive prediction region from the set of all available prediction regions. In a comparative case study with the state of the art, we empirically show that our approach results in tighter prediction regions and verify recursive feasibility of our MPC scheme.
Paper Structure (12 sections, 2 theorems, 23 equations, 4 figures, 1 algorithm)

This paper contains 12 sections, 2 theorems, 23 equations, 4 figures, 1 algorithm.

Table of Contents

  1. Introduction
  2. Problem Formulation
  3. Online-updated Conformal Prediction Regions for Dynamic Agent Trajectories
  4. Trajectory Predictors
  5. Online-updated Conformal Prediction Regions based on Trajectory Predictors
  6. Recursively Feasible Shrinking-Horizon MPC in Dynamic Environments with Conformal Prediction Guarantees
  7. Case Study: Navigation of a Mobile Robot around Pedestrians
  8. Future Work
  9. Proofs
  10. Proof of Lemma \ref{['lemma1']}
  11. Proof of Theorem \ref{['theorem1']}
  12. Experiment Details

Key Result

Lemma 1

Fix a failure probability $\delta\in(0,1)$. Let $\widehat{Y}_{\tau|t}$ be the prediction of the joint agent state $Y_{\tau}$ at time $t$. Let the conformity scores $R^{(i)}$ be as in conformity_scores, with normalizing factors $\sigma_{\tau|t}$ as in normalization_factors. Then, if $R$ is the $\

Figures (4)

  • Figure 1: We predict trajectories of dynamic agents using arbitrary predictors (e.g., neural networks) and employ conformal prediction to bound the uncertainty in high-confidence prediction regions (blue squares).
  • Figure 2: Illustration of the constraint \ref{['relaxed_CP_agent_constraints']} for collision avoidance. The predicted unsafe areas for $x_2$ at times $0$ (pink set) and $1$ (gray set) are guaranteed to be valid. Consequently, their intersection can be used to define the predicted unsafe area for $x_{2|1}$. This leads to an expanded area of free space for system \ref{['system']} at time $1$.
  • Figure 3: Predicted unsafe areas corresponding to the final position of pedestrian $1$ at various times. In the proposed MPC, the target is deemed safe at all times. In the benchmark MPC, the target is deemed safe at time $0$ and unsafe at time $2$, rendering the controller recursively infeasible.
  • Figure 4: Proposed and benchmark MPC at time $2$. For the proposed MPC, there exists a safe trajectory (gray line) that allows the robot to reach the target at time $20$. In contrast, the benchmark MPC becomes infeasible, as the target is predicted to be unsafe with respect to pedestrian $1$.

Theorems & Definitions (4)

  • Lemma 1: Online-updated Conformal Prediction Regions for Trajectories
  • Remark 1
  • Theorem 1
  • Remark 2