A Convex Model Predictive Control Barrier Function Approach for Differentially Flat Systems

This brief provides a novel approach for online synthesis of predictive control barrier function (CBF)-based safety filters and controllers for differentially flat, input-constrained systems. A local convex approximation to the safe set is inflated around the current system state and used to formulate a set of discrete-time affine CBF constraints. These constraints are enforced over a finite prediction horizon using a discrete-time convex model predictive control (MPC) formulation that can be solved at each sample instant. This approach is tractable for cases when the original safe set is defined by one or more concave or convex-ellipsoidal barrier functions, and is applicable even when the number or configuration of these barriers can change during runtime. This methodology is extended to enable simultaneous control Lyapunov function (CLF) enforcement within the same MPC framework, and both approaches are demonstrated in simulation.