Soft-minimum and soft-maximum barrier functions for safety with actuation constraints

Pedram Rabiee; Jesse B. Hoagg

doi:10.1016/j.automatica.2024.111921

Soft-minimum and soft-maximum barrier functions for safety with actuation constraints

Pedram Rabiee, Jesse B. Hoagg

Mechanical and Aerospace Engineering

Research output: Contribution to journal › Article › peer-review

7 Scopus citations

Abstract

This paper presents two new control approaches for guaranteed safety (remaining in a safe set) subject to actuator constraints (the control is in a convex polytope). The control signals are computed using real-time optimization, including linear and quadratic programs subject to affine constraints, which are shown to be feasible. The first control method relies on a soft-minimum barrier function that is constructed using a finite-time-horizon prediction of the system trajectories under a known backup control. The main result shows that the control is continuous and satisfies the actuator constraints, and a subset of the safe set is forward invariant under the control. Next, we extend this method to allow from multiple backup controls. This second approach relies on a combined soft-maximum/soft-minimum barrier function, and it has properties similar to the first. We demonstrate these controls on numerical simulations of an inverted pendulum and a nonholonomic ground robot.

Original language	English
Article number	111921
Journal	Automatica
Volume	171
DOIs	https://doi.org/10.1016/j.automatica.2024.111921
State	Published - Jan 2025

Bibliographical note

Publisher Copyright:
© 2024 Elsevier Ltd

Funding

This work is supported in part by the National Science Foundation ( 1849213 , 1932105 ) and the Air Force Office of Scientific Research ( FA9550-20-1-0028 ). The material in this paper was partially presented at the 2023 American Control Conference (ACC), May 31–June 2, 2023, San Diego, California, USA. This paper was recommended for publication in revised form by Associate Editor Daniele Casagrande under the direction of Editor Florian Dorfler.

Funders	Funder number
National Science Foundation Arctic Social Science Program	1849213, 1932105
Air Force Office of Scientific Research, United States Air Force	FA9550-20-1-0028

Keywords

Control of constrained systems
Nonlinear predictive control
Optimization-based controller synthesis
Safety

ASJC Scopus subject areas

Control and Systems Engineering
Electrical and Electronic Engineering

Access to Document

10.1016/j.automatica.2024.111921

Cite this

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abstract = "This paper presents two new control approaches for guaranteed safety (remaining in a safe set) subject to actuator constraints (the control is in a convex polytope). The control signals are computed using real-time optimization, including linear and quadratic programs subject to affine constraints, which are shown to be feasible. The first control method relies on a soft-minimum barrier function that is constructed using a finite-time-horizon prediction of the system trajectories under a known backup control. The main result shows that the control is continuous and satisfies the actuator constraints, and a subset of the safe set is forward invariant under the control. Next, we extend this method to allow from multiple backup controls. This second approach relies on a combined soft-maximum/soft-minimum barrier function, and it has properties similar to the first. We demonstrate these controls on numerical simulations of an inverted pendulum and a nonholonomic ground robot.",

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KW - Optimization-based controller synthesis

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Soft-minimum and soft-maximum barrier functions for safety with actuation constraints

Abstract

Bibliographical note

Funding

Keywords

ASJC Scopus subject areas

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