  We consider the problem of safely coordinating ensembles of identical
autonomous agents to conduct complex missions with conflicting safety
requirements and under noisy control inputs. Using non-smooth control barrier
functions (CBFs) and stochastic model-predictive control as springboards, and
by adopting an extrinsic approach where the ensemble is treated as a unified
dynamic entity, we devise a method to synthesize safety-aware control inputs
for uncertain collectives. Drawing upon stochastic CBF theory and recent
developments in Boolean CBF composition, our method proceeds by smoothing a
Boolean-composed CBF and solving a stochastic optimization problem where each
agent's forcing term is restricted to the affine subspace of control inputs
certified by the combined CBF. For the smoothing step, we employ a polynomial
approximation scheme, providing evidence for its advantage in generating more
conservative yet sufficiently-filtered control inputs than the smoother but
more aggressive equivalents produced from an approximation technique based on
the log-sum-exp function. To further demonstrate the utility of the proposed
method, we present an upper bound for the expected CBF approximation error,
along with results from simulations of a single-integrator collective under
velocity perturbations. Lastly, we compare these results with those obtained
using a naive state-feedback controller lacking safety filters.
