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

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.

• The paper introduces the C2U-MPPI framework that leverages unscented transformations and probabilistic chance constraints for robust collision avoidance.
• It employs risk-assessed trajectory sampling and a layered dynamic obstacle representation to maintain real-time performance in uncertain environments.
• Simulations and real-world experiments demonstrate enhanced collision avoidance and trajectory efficiency compared to baseline approaches.

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

Introduction

Autonomous Ground Vehicles (AGVs) operating in dynamic, uncertain environments must navigate safely while avoiding obstacles, both static and dynamic, under conditions of uncertainty. Traditional methods for collision avoidance fall into reactive, optimization, and learning-based approaches, each with limitations in dealing with the complex constraints of dynamic environments. The presented approach, C\textsuperscript{2}U-MPPI, builds upon sampling-based Model Predictive Control (MPC), specifically leveraging the Unscented Model Predictive Path Integral (U-MPPI) framework, introducing probabilistic chance constraints that enhance collision avoidance capabilities under uncertainty, and maintaining computational tractability and real-time performance.

Methodology

The C\textsuperscript{2}U-MPPI framework integrates unscented transformations in its MPC to handle uncertainties in an environment populated with dynamic and static obstacles. This method allows for efficient trajectory sampling without linearizing system dynamics, instead incorporating non-linear chance constraints directly. The control strategy employs a layered representation of dynamic obstacles, which enhances the computational efficiency of trajectory evaluations over time. Key elements include probabilistic reformulation of collision avoidance constraints into deterministic forms, enabling the incorporation of risk-sensitive trajectory evaluations and assessment of multi-horizon predictions of dynamic obstacles.

The algorithm modifies traditional Unscented Kalman Filtering to create sigma points, facilitating the prediction of mean and covariance states over time. These sigma points undergo risk-assessed trajectory evaluations to guide the optimizer toward safer navigation decisions. Dynamic costs related to obstacle avoidance are integrated, including exponential, repulsive, and probabilistic environments considerations, highlighting the probabilistic and deterministic evaluations under uncertainty.

Implementation Details

In implementing C\textsuperscript{2}U-MPPI, practitioners must account for:

1. State Propagation: Ensure accurate estimation of dynamic obstacles using Linear Kalman Filters (LKF) and map these onto a predictive layered structure, facilitating real-time assessments.
2. Chance Constraints: Formulate and integrate probabilistic collision checking as deterministic constraints, using adaptive calculations based on system covariance. Ensure collision buffers adequately cover trajectory deviations due to uncertainties.
3. Optimization Parameters: Deploy suitable scaling parameters for the UT, risk-sensitivity adjustments, and control weights to effectively balance risk and reward, adapting to specific environments and speed settings inline with AGV capabilities.
4. Computational Workload: Utilize GPU-based parallelization for efficient computation of trajectory samples and state predictions, ensuring real-time applicability even within dense obstacle environments.

Results and Performance

Simulations and real-world experiments highlight the performance of C\textsuperscript{2}U-MPPI over baseline methods like MPCC and log-MPPI. The framework displays superior collision avoidance and trajectory efficiency, particularly in high-speed and dense obstacle scenarios. Execution times remain within real-time constraints, bolstered by probabilistic yet deterministic constraint formulations that enable faster trajectory resolutions without sacrificing safety.

Conclusion

C\textsuperscript{2}U-MPPI represents a significant step forward in enabling robust, efficient, and real-time navigation for AGVs in complex environments. Through sampling-based trajectory optimizations with integrated chance constraints, the method achieves high standards of safety and energy efficiency, offering a balanced solution for environments characterized by uncertainty and dynamic interactions. Future work involves extending the approach to multi-AGV systems and further refinement of real-time prediction methodologies to enhance adaptability in increasingly complex environments.