Residual Neural Terminal Constraint for MPC-based Collision Avoidance in Dynamic Environments

TL;DR

This paper introduces a hybrid MPC local planner that leverages a neural network-approximated safe set, enhancing real-time collision avoidance in dynamic environments with improved success rates and safety guarantees.

Contribution

It presents a novel neural residual approach to approximate Hamilton-Jacobi reachability-based safe sets for MPC, enabling real-time collision avoidance with better safety and efficiency.

Findings

Achieves up to 30% higher success rates in simulations and hardware tests.

Provides real-time safe set approximation with comparable computational effort.

Produces low travel-time solutions with high safety guarantees.

Abstract

In this paper, we propose a hybrid MPC local planner that uses a learning-based approximation of a time-varying safe set, derived from local observations and applied as the MPC terminal constraint. This set can be represented as a zero-superlevel set of the value function computed via Hamilton-Jacobi (HJ) reachability analysis, which is infeasible in real-time. We exploit the property that the HJ value function can be expressed as a difference of the corresponding signed distance function (SDF) and a non-negative residual function. The residual component is modeled as a neural network with non-negative output and subtracted from the computed SDF, resulting in a real-time value function estimate that is at least as safe as the SDF by design. Additionally, we parametrize the neural residual by a hypernetwork to improve real-time performance and generalization properties. The proposed method is compared with three state-of-the-art methods in simulations and hardware experiments, achieving up to 30\% higher success rates compared to the best baseline while requiring a similar computational effort and producing high-quality (low travel-time) solutions.