Multi-Step Model Predictive Safety Filters: Reducing Chattering by Increasing the Prediction Horizon

TL;DR

This paper introduces a multi-step model predictive safety filter that extends the prediction horizon to significantly reduce chattering and oscillations near constraints, enhancing safety and smoothness in learning-based control systems.

Contribution

It proposes a novel multi-step safety filtering approach that considers longer horizons, with proven recursive feasibility under bounded uncertainties, and demonstrates substantial reduction in chattering in drone experiments.

Findings

Reduces chattering by over 4 times compared to previous methods.

Maintains safety guarantees with longer prediction horizons.

Validated through extensive simulation and quadrotor experiments.

Abstract

Learning-based controllers have demonstrated superior performance compared to classical controllers in various tasks. However, providing safety guarantees is not trivial. Safety, the satisfaction of state and input constraints, can be guaranteed by augmenting the learned control policy with a safety filter. Model predictive safety filters (MPSFs) are a common safety filtering approach based on model predictive control (MPC). MPSFs seek to guarantee safety while minimizing the difference between the proposed and applied inputs in the immediate next time step. This limited foresight can lead to jerky motions and undesired oscillations close to constraint boundaries, known as chattering. In this paper, we reduce chattering by considering input corrections over a longer horizon. Under the assumption of bounded model uncertainties, we prove recursive feasibility using techniques from robust MPC. We verified the proposed approach in both extensive simulation and quadrotor experiments. In experiments with a Crazyflie 2.0 drone, we show that, in addition to preserving the desired safety guarantees, the proposed MPSF reduces chattering by more than a factor of 4 compared to previous MPSF formulations.