Multi-rate Control Design under Input Constraints via Fixed-Time Barrier Functions

TL;DR

This paper presents a multi-rate control framework ensuring periodic safety through fixed-time barrier functions and model predictive high-level planning, effectively handling input constraints and outperforming exponential controllers in simulations.

Contribution

It introduces fixed-time barrier functions for low-level control and a high-level MPC policy for planning, ensuring periodic safety under input constraints.

Findings

Fixed-time barrier functions enable successful control objectives.

High-level MPC guarantees periodic safety.

Proposed method outperforms exponential stabilizing controllers.

Abstract

In this paper, we introduce the notion of periodic safety, which requires that the system trajectories periodically visit a subset of a forward-invariant safe set, and utilize it in a multi-rate framework where a high-level planner generates a reference trajectory that is tracked by a low-level controller under input constraints. We introduce the notion of fixed-time barrier functions which is leveraged by the proposed low-level controller in a quadratic programming framework. Then, we design a model predictive control policy for high-level planning with a bound on the rate of change for the reference trajectory to guarantee that periodic safety is achieved. We demonstrate the effectiveness of the proposed strategy on a simulation example, where the proposed fixed-time stabilizing low-level controller shows successful satisfaction of control objectives, whereas an exponentially stabilizing low-level controller fails.