  Receding horizon control (RHC) is a popular procedure to deal with optimal
control problems. Due to the existence of state constraints, optimization-based
RHC often suffers the notorious issue of infeasibility, which strongly shrinks
the region of controllable state. This paper proposes a generalized control
barrier function (CBF) to enlarge the feasible region of constrained RHC with
only a one-step constraint on the prediction horizon. This design can reduce
the constrained steps by penalizing the tendency to move towards the constraint
boundary. Additionally, generalized CBF is able to handle high-order equality
or inequality constraints through extending the constrained step to nonadjacent
nodes. We apply this technique on an automated vehicle control task. The
results show that compared to multi-step pointwise constraints, generalized CBF
can effectively avoid the infeasibility issue in a larger partition of the
state space, and the computing efficiency is also improved by 14%-23%.
