MADR: MPC-guided Adversarial DeepReach

TL;DR

MADR introduces a novel framework combining MPC guidance with deep learning to efficiently approximate value functions and strategies in high-dimensional adversarial differential games, enhancing safety and robustness in robotic systems.

Contribution

It is the first to extend deep reachability methods to two-player zero-sum games using MPC guidance, improving convergence and solution quality.

Findings

Outperforms state-of-the-art baselines in simulation

Achieves robust safety policies for complex robotic agents

Demonstrates effectiveness on real hardware

Abstract

Hamilton-Jacobi (HJ) Reachability offers a framework for generating safe value functions and policies in the face of adversarial disturbance, but is limited by the curse of dimensionality. Physics-informed deep learning is able to overcome this infeasibility, but itself suffers from slow and inaccurate convergence, primarily due to weak PDE gradients and the complexity of self-supervised learning. A few works, recently, have demonstrated that enriching the self-supervision process with regular supervision (based on the nature of the optimal control problem), greatly accelerates convergence and solution quality, however, these have been limited to single player problems and simple games. In this work, we introduce MADR: MPC-guided Adversarial DeepReach, a general framework to robustly approximate the two-player, zero-sum differential game value function. In doing so, MADR yields the corresponding optimal strategies for both players in zero-sum games as well as safe policies for worst-case robustness. We test MADR on a multitude of high-dimensional simulated and real robotic agents with varying dynamics and games, finding that our approach significantly out-performs state-of-the-art baselines in simulation and produces impressive results in hardware.