Robust Time-Varying Control Barrier Functions with Sector-Bounded Nonlinearities

TL;DR

This paper introduces a robust, real-time safety filter for control systems with nonlinearities and time-varying constraints, ensuring safety while minimally altering baseline commands.

Contribution

It extends time-varying barrier functions to handle nonlinearities with quadratic bounds and derives an SOCP for online safety filtering.

Findings

Successfully applied to spacecraft docking maneuver.

Provides guaranteed bounds on nonlinear input-output behavior.

Ensures safety with minimal intervention from the baseline controller.

Abstract

This paper presents a novel approach for ensuring safe operation of systems subject to input nonlinearities and time-varying safety constraints. We extend the time-varying barrier function framework to address time-varying safety constraints and explicitly account for control-dependent nonlinearities at the plant input. Guaranteed bounds on the input-output behavior of these nonlinearities are provided through pointwise-in-time quadratic constraints. The result is a class of robust time-varying control barrier functions that define a safety filter. This filter ensures robust safety for all admissible nonlinearities while minimally modifying the command generated by a baseline controller. We derive a second-order cone program (SOCP) to compute this safety filter online and provide novel feasibility conditions for ball-constrained inputs. The proposed approach is demonstrated on a spacecraft docking maneuver.