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arXiv · 2305.10620

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

Pedram Rabiee·Jesse B. Hoagg
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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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Pedram Rabiee, Jesse B. Hoagg. 2023-05-18. Soft-Minimum and Soft-Maximum Barrier Functions for Safety with Actuation Constraints. https://doi.org/10.1016/j.automatica.2024.111921

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