  Optimal control problems with constraints ensuring safety and convergence to
desired states can be mapped onto a sequence of real time optimization problems
through the use of Control Barrier Functions (CBFs) and Control Lyapunov
Functions (CLFs). One of the main challenges in these approaches is ensuring
the feasibility of the resulting quadratic programs (QPs) if the system is
affine in controls. The recently proposed penalty method has the potential to
improve the existence of feasible solutions to such problems. In this paper, we
further improve the feasibility robustness (i.e., feasibility maintenance in
the presence of time-varying and unknown unsafe sets) through the definition of
a High Order CBF (HOCBF) that works for arbitrary relative degree constraints;
this is achieved by a proposed feasibility-guided learning approach.
Specifically, we apply machine learning techniques to classify the parameter
space of a HOCBF into feasible and infeasible sets, and get a differentiable
classifier that is then added to the learning process. The proposed
feasibility-guided learning approach is compared with the gradient-descent
method on a robot control problem. The simulation results show an improved
ability of the feasibility-guided learning approach over the gradient-decent
method to determine the optimal parameters in the definition of a HOCBF for the
feasibility robustness, as well as show the potential of the CBF method for
robot safe navigation in an unknown environment.
