Soft-Minimum and Soft-Maximum Barrier Functions for Safety with Actuation Constraints

• Published in: arXiv.org
• Main Authors: Rabiee, Pedram, Hoagg, Jesse B
• Format: Paper Journal Article
• Language: English
• Published: Ithaca Cornell University Library, arXiv.org 26.07.2024
• Subjects: Actuation; Actuators; Computer Science - Systems and Control; Control methods; Optimization; Quadratic programming; Safety
• ISSN: 2331-8422
• DOI: 10.48550/arxiv.2305.10620

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.