  Recent work has shown that stabilizing an affine control system while
optimizing a quadratic cost subject to state and control constraints can be
mapped to a sequence of Quadratic Programs (QPs) using Control Barrier
Functions (CBFs) and Control Lyapunov Functions (CLFs). One of the main
challenges in this method is that the QPs could easily become infeasible under
safety and spatio-temporal constraints with tight control bounds. In our own
recent work, we defined Auxiliary-Variable Adaptive CBFs (AVCBFs) to improve
the feasibility of the CBF-based QP, while avoiding extensive parameter tuning.
In this paper, we consider spatio-temporal constraints as finite-time
reachability requirements. In order to satisfy these requirements, we
generalize AVCBFs to Auxiliary-Variable Adaptive Control Lyapunov Barrier
Functions (AVCLBFs) that work for systems and constraints with arbitrary
relative degrees. We show that our method has fewer conflicts with safety and
input constraints, and outperforms the state of the art in term of adaptivity
and feasibility in solving the QP. We illustrate our approach on an optimal
control problem for a unicycle.
