Safety-Critical Control under Multiple State and Input Constraints and Application to Fixed-Wing UAV

TL;DR

This paper introduces a safety-critical control framework for nonlinear systems with multiple constraints, using a novel zeroing control barrier function and a one-step model predictive controller, demonstrated on a fixed-wing UAV.

Contribution

It develops a new zeroing control barrier function based on a nominal evading maneuver and proposes a computationally efficient safety-critical MPC for systems with multiple constraints.

Findings

Successfully guarantees safety constraints in simulation

Enables fixed-wing UAV to track trajectories while avoiding obstacles

Ensures recursive feasibility of the control strategy

Abstract

This study presents a framework to guarantee safety for a class of second-order nonlinear systems under multiple state and input constraints. To facilitate real-world applications, a safety-critical controller must consider multiple constraints simultaneously, while being able to impose general forms of constraints designed for various tasks (e.g., obstacle avoidance). With this in mind, we first devise a zeroing control barrier function (ZCBF) using a newly proposed nominal evading maneuver. By designing the nominal evading maneuver to 1) be continuously differentiable, 2) satisfy input constraints, and 3) be capable of handling other state constraints, we deduce an ultimate invariant set, a subset of the safe set that can be rendered forward invariant with admissible control inputs. Thanks to the development of the ultimate invariant set, we then propose a safety-critical controller, which is a computationally tractable one-step model predictive controller (MPC) with guaranteed recursive feasibility. We validate the proposed framework in simulation, where a fixed-wing UAV tracks a circular trajectory while satisfying multiple safety constraints including collision avoidance, bounds on flight speed and flight path angle, and input constraints.