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

• Published in: Automatica (Oxford) Vol. 171; p. 111921
• Main Authors: Rabiee, Pedram, Hoagg, Jesse B.
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 01.01.2025
• Subjects: Control of constrained systems; Nonlinear predictive control; Optimization-based controller synthesis; Safety; Nonlinear predictive control; Safety; Control of constrained systems; Optimization-based controller synthesis
• ISSN: 0005-1098
• DOI: 10.1016/j.automatica.2024.111921

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.