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Chance-Constrained Sampling-Based MPC for Collision Avoidance in Uncertain Dynamic Environments

Ihab S. Mohamed, Mahmoud Ali, Lantao Liu

TL;DR

Uncertainty in perception and motion makes safe navigation in dynamic environments challenging. This work introduces C2U-MPPI, a chance-constrained extension of the Unscented MPPI that performs probabilistic collision checking and preserves real-time performance through a deterministic reformulation. It integrates a risk-sensitive trajectory cost, a layered dynamic obstacle representation, and an obstacle-prediction framework to enable scalable, multi-obstacle avoidance under uncertainty. Extensive simulations and real-world experiments demonstrate superior collision avoidance and robust trajectory quality compared with gradient-based MPC and baseline sampling-based methods, highlighting practical impact for autonomous navigation in crowds.

Abstract

Navigating safely in dynamic and uncertain environments is challenging due to uncertainties in perception and motion. This letter presents the Chance-Constrained Unscented Model Predictive Path Integral (C2U-MPPI) framework, a robust sampling-based Model Predictive Control (MPC) algorithm that addresses these challenges by leveraging the U-MPPI control strategy with integrated probabilistic chance constraints, enabling more reliable and efficient navigation under uncertainty. Unlike gradient-based MPC methods, our approach (i) avoids linearization of system dynamics by directly applying non-convex and nonlinear chance constraints, enabling more accurate and flexible optimization, and (ii) enhances computational efficiency by leveraging a deterministic form of probabilistic constraints and employing a layered dynamic obstacle representation, enabling real-time handling of multiple obstacles. Extensive experiments in simulated and real-world human-shared environments validate the effectiveness of our algorithm against baseline methods, showcasing its capability to generate feasible trajectories and control inputs that adhere to system dynamics and constraints in dynamic settings, enabled by unscented-based sampling strategy and risk-sensitive trajectory evaluation. A supplementary video is available at: https://youtu.be/FptAhvJlQm8.

Chance-Constrained Sampling-Based MPC for Collision Avoidance in Uncertain Dynamic Environments

TL;DR

Uncertainty in perception and motion makes safe navigation in dynamic environments challenging. This work introduces C2U-MPPI, a chance-constrained extension of the Unscented MPPI that performs probabilistic collision checking and preserves real-time performance through a deterministic reformulation. It integrates a risk-sensitive trajectory cost, a layered dynamic obstacle representation, and an obstacle-prediction framework to enable scalable, multi-obstacle avoidance under uncertainty. Extensive simulations and real-world experiments demonstrate superior collision avoidance and robust trajectory quality compared with gradient-based MPC and baseline sampling-based methods, highlighting practical impact for autonomous navigation in crowds.

Abstract

Navigating safely in dynamic and uncertain environments is challenging due to uncertainties in perception and motion. This letter presents the Chance-Constrained Unscented Model Predictive Path Integral (C2U-MPPI) framework, a robust sampling-based Model Predictive Control (MPC) algorithm that addresses these challenges by leveraging the U-MPPI control strategy with integrated probabilistic chance constraints, enabling more reliable and efficient navigation under uncertainty. Unlike gradient-based MPC methods, our approach (i) avoids linearization of system dynamics by directly applying non-convex and nonlinear chance constraints, enabling more accurate and flexible optimization, and (ii) enhances computational efficiency by leveraging a deterministic form of probabilistic constraints and employing a layered dynamic obstacle representation, enabling real-time handling of multiple obstacles. Extensive experiments in simulated and real-world human-shared environments validate the effectiveness of our algorithm against baseline methods, showcasing its capability to generate feasible trajectories and control inputs that adhere to system dynamics and constraints in dynamic settings, enabled by unscented-based sampling strategy and risk-sensitive trajectory evaluation. A supplementary video is available at: https://youtu.be/FptAhvJlQm8.
Paper Structure (27 sections, 14 equations, 3 figures, 7 tables)

This paper contains 27 sections, 14 equations, 3 figures, 7 tables.

Table of Contents

  1. Introduction and Related Work
  2. Preliminaries
  3. Robot Motion Model
  4. Dynamic and Static Obstacles Model
  5. Problem Formulation
  6. Overview of U-MPPI Control Strategy
  7. Proposed C2U-MPPI Framework
  8. Chance-Constrained U-MPPI Problem Formulation
  9. Robot-Obstacle Collision Avoidance Chance Constraints
  10. Cost Function Design
  11. Dynamic Obstacle Representation
  12. Results and Analysis
  13. Simulation-Based Evaluation
  14. Simulation Setup:
  15. Simulation Scenarios and Performance Metrics:
  16. ...and 12 more sections

Figures (3)

  • Figure 1: Handling dynamic obstacles by (a) predicting pedestrian positions using LKF and (b) structuring them into a layered representation for efficient trajectory evaluation over the prediction horizon $N$.
  • Figure 2: Collision-check behavior vs. $\!d_\text{ped}$ under two uncertainty levels: $\mathbf{\Sigma}^\mathbf{o} \!\!=\! \mathbf{I}_2$ (left) and $0.1\mathbf{I}_2$ (right), with $r_r \!\!=\!\! 0.3m$ and $\delta \!\!=\!\! 0.01$. Shaded regions denote constraint satisfaction (blue) and violation (red).
  • Figure 3: Snapshot of (a) our simulated corridor environment with 10 pedestrians moving at different speeds along the corridor, and (b) the velocity profiles of each pedestrian at 100% of their maximum speed.