Motion Planning With Dynamic Obstacles Using Convexified Control Barrier Functions

Model Predictive Control (MPC) is a popular approach used for motion planning in dynamical systems. Given a finite horizon cost, we seek an optimal control law subject to safety constraints. However, in the presence of obstacles, existing MPC formulations are often slow and may lead to infeasibility. We propose a real-time implementable MPC formulation using control barrier functions (CBF) and successive convexification. We represent the non-convex obstacle avoidance constraints using CBFs that ensure that a feasible solution always exists. We then reformulate the non-convex optimal control problem using successive convexification to enable the use of computationally-efficient conic solvers. Our approach enables controller synthesis at real-time, which is difficult with existing approaches that rely on nonlinear solvers. We demonstrate the method in simulation, where we navigate a UAV to a target while avoiding dynamic obstacles in the environment.