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This paper presents a new approach for guaranteed safety subject to inputconstraints (e.g., actuator limits) using a composition of multiple controlbarrier functions (CBFs). First, we present a method for constructing a singleCBF from multiple CBFs, which can have different relative degrees. Thisconstruction relies on a soft minimum function and yields a CBF whose$0$-superlevel set is a subset of the union of the $0$-superlevel sets of allthe CBFs used in the construction. Next, we extend the approach to systems withinput constraints. Specifically, we introduce control dynamics that allow us toexpress the input constraints as CBFs in the closed-loop state (i.e., the stateof the system and the controller). The CBFs constructed from input constraintsdo not have the same relative degree as the safety constraints. Thus, thecomposite soft-minimum CBF construction is used to combine the input-constraintCBFs with the safety-constraint CBFs. Finally, we present a feasiblereal-time-optimization control that guarantees that the state remains in the$0$-superlevel set of the composite soft-minimum CBF. We demonstrate theseapproaches on a nonholonomic ground robot example.

Composition of Control Barrier Functions With Differing Relative Degrees for Safety Under Input Constraints