Data-Driven Risk-sensitive Model Predictive Control for Safe Navigation in Multi-Robot Systems

TL;DR

This paper introduces a data-driven, risk-sensitive model predictive control method for safe multi-robot navigation, robustly handling prediction errors and uncertainties using distributionally robust CVaR constraints, demonstrated in a multi-drone simulation.

Contribution

It develops a novel distributionally robust CVaR-based optimization framework for multi-robot navigation, accommodating prediction errors in both distributed and decentralized settings.

Findings

Successfully robustifies multi-drone navigation against prediction errors.

Provides tractable convex approximations for distributionally robust constraints.

Demonstrates effectiveness in Gazebo simulation environment.

Abstract

Safe navigation is a fundamental challenge in multi-robot systems due to the uncertainty surrounding the future trajectory of the robots that act as obstacles for each other. In this work, we propose a principled data-driven approach where each robot repeatedly solves a finite horizon optimization problem subject to collision avoidance constraints with latter being formulated as distributionally robust conditional value-at-risk (CVaR) of the distance between the agent and a polyhedral obstacle geometry. Specifically, the CVaR constraints are required to hold for all distributions that are close to the empirical distribution constructed from observed samples of prediction error collected during execution. The generality of the approach allows us to robustify against prediction errors that arise under commonly imposed assumptions in both distributed and decentralized settings. We derive tractable finite-dimensional approximations of this class of constraints by leveraging convex and minmax duality results for Wasserstein distributionally robust optimization problems. The effectiveness of the proposed approach is illustrated in a multi-drone navigation setting implemented in Gazebo platform.