Designing Control Barrier Functions Using a Dynamic Backup Policy
Victor Freire, Marco M. Nicotra
TL;DR
The paper tackles safe constrained control for nonlinear control-affine systems by constructing control barrier functions on an augmented state-reference space using dynamic safety margins. It develops a trajectory-based DSM that is parameterized by the equilibrium manifold and analyzed through flow-sensitivity of the prestabilized dynamics, with Clarke generalized Jacobians handling potential nonsmoothness. A finite-horizon, tractable DSM-CBF safety filter is proposed, including a QP formulation and guaranteed feasibility via a baseline prestabilizing policy. The inverted pendulum on a cart example demonstrates that the Traj-DSM-CBF approach achieves constraint satisfaction with superior performance relative to backup CBF, reference governor (RG) strategies, and Lyapunov-based DSM-CBF methods, illustrating its practical value for safety-critical nonlinear control.
Abstract
This paper presents a systematic approach to construct control barrier functions for nonlinear control affine systems subject to arbitrary state and input constraints. Taking inspiration from the reference governor literature, the proposed method defines a family of backup policies, parametrized by the equilibrium manifold of the system. The control barrier function is defined on the augmented state-and-reference space: given a state-reference pair, the approach quantifies the distance to constraint violation at any time in the future, should the current backup policy reference remain constant. Sensitivity analysis is then used to compute the (possibly nonsmooth) Jacobian with respect to the augmented state vector. To showcase its simple yet general nature, the proposed method is applied to an inverted pendulum on cart.