Safety in Augmented Importance Sampling: Performance Bounds for Robust MPPI

TL;DR

This paper introduces a novel safety-enhanced augmented importance sampling method for model predictive control, demonstrating improved safety, efficiency, and theoretical bounds in cluttered navigation with disturbances.

Contribution

It presents a new safety-focused augmented importance sampling algorithm using embedded barrier states, improving efficiency and safety in constrained control tasks.

Findings

More sample-efficient collision-free trajectories

Better safety performance in cluttered navigation

Derivation of a new free energy bound for the system

Abstract

This work explores the nature of augmented importance sampling in safety-constrained model predictive control problems. When operating in a constrained environment, sampling based model predictive control and motion planning typically utilizes penalty functions or expensive optimization based control barrier algorithms to maintain feasibility of forward sampling. In contrast the presented algorithm utilizes discrete embedded barrier states in augmented importance sampling to apply feedback with respect to a nominal state when sampling. We will demonstrate that this approach of safety of discrete embedded barrier states in augmented importance sampling is more sample efficient by metric of collision free trajectories, is computationally feasible to perform per sample, and results in better safety performance on a cluttered navigation task with extreme un-modeled disturbances. In addition, we will utilize the theoretical properties of augmented importance sampling and safety control to derive a new bound on the free energy of the system.