  In this paper, we study a safe control design for dynamical systems in the
presence of uncertainty in a dynamical environment. The worst-case error
approach is considered to formulate robust Control Barrier Functions (CBFs) in
an optimization-based control synthesis framework. It is first shown that
environmentally robust CBF formulations result in second-order cone programs
(SOCPs). Then, a novel scheme is presented to formulate robust CBFs which takes
the nominally safe control as its desired control input in optimization-based
control design and then tries to minimally modify it whenever the robust CBF
constraint is violated. This proposed scheme leads to quadratic programs (QPs)
which can be easily solved. Finally, the effectiveness of the proposed approach
is demonstrated on an adaptive cruise control example.
