Safety-Critical Control of Nonlinear Systems via New Exponential Control Barrier Functions

In this paper, we design a new exponential control barrier function (NECBF) approach where the constraints with an arbitrarily high relative degree are expressed as equivalent constraints with a relative degree 1. The approach combines advantages of high order control barrier function (HOCBF) and conventional CBF, and thus can reduce the complexity of designing the control barrier function (CBF). We formulate an optimal control problem of an affine nonlinear system with constraints given by NECBF. Then we present a solution resolving the conflict between safety constraints and control limit constraints. The effectiveness of this control barrier function method is demonstrated through an adaptive cruise control problem.