  This paper presents a time-varying soft-maximum composite control barrier
function (CBF) that can be used to ensure safety in an a priori unknown
environment, where local perception information regarding the safe set is
periodically obtained. We consider the scenario where the periodically obtained
perception feedback can be used to construct a local CBF that models a local
subset of the unknown safe set. Then, we use a novel smooth time-varying
soft-maximum function to compose the N most recently obtained local CBFs into a
single CBF. This composite CBF models an approximate union of the N most
recently obtained local subsets of the safe set. Notably, this composite CBF
can have arbitrary relative degree r. Next, this composite CBF is used as a
rth-order CBF constraint in a real-time optimization to determine a control
that minimizes a quadratic cost while guaranteeing that the state stays in a
time-varying subset of the unknown safe set. We also present an application of
the time-varying soft-maximum composite CBF method to a nonholonomic ground
robot with nonnegligible inertia. In this application, we present a simple
approach to generate the local CBFs from the periodically obtained perception
data.
