  This study presents a framework to guarantee safety for a class of
second-order nonlinear systems under multiple state and input constraints. To
facilitate real-world applications, a safety-critical controller must consider
multiple constraints simultaneously, while being able to impose general forms
of constraints designed for various tasks (e.g., obstacle avoidance). With this
in mind, we first devise a zeroing control barrier function (ZCBF) using a
newly proposed nominal evading maneuver. By designing the nominal evading
maneuver to 1) be continuously differentiable, 2) satisfy input constraints,
and 3) be capable of handling other state constraints, we deduce an ultimate
invariant set, a subset of the safe set that can be rendered forward invariant
with admissible control inputs. Thanks to the development of the ultimate
invariant set, we then propose a safety-critical controller, which is a
computationally tractable one-step model predictive controller (MPC) with
guaranteed recursive feasibility. We validate the proposed framework in
simulation, where a fixed-wing UAV tracks a circular trajectory while
satisfying multiple safety constraints including collision avoidance, bounds on
flight speed and flight path angle, and input constraints.
