Real-Time Multi-Convex Model Predictive Control for Occlusion Free Target Tracking

Abstract

This paper proposes a Model Predictive Control (MPC) algorithm for target tracking amongst static and dynamic obstacles. Our main contribution lies in improving the computational tractability and reliability of the underlying nonconvex trajectory optimization. The result is an MPC algorithm that runs real-time on laptops and embedded hardware devices such as Jetson TX2. Our approach relies on novel reformulations for the tracking, collision, and occlusion constraints that induce a multi-convex structure in the resulting trajectory optimization. We exploit these mathematical structures using the split Bregman Iteration technique, eventually reducing our MPC to a series of convex Quadratic Programs solvable in a few milliseconds. The fast re-planning of our MPC allows for occlusion and collision-free tracking in complex environments even while considering a simple constant-velocity prediction for the target trajectory and dynamic obstacles. We perform extensive bench-marking in a realistic physics engine and show that our MPC outperforms the state-of-the-art algorithms in visibility, smoothness, and computation-time metrics.1 Non-convex optimizations have the so-called trust-region (or line-search) constraints that limit the progress that the optimizer can make towards the individual solutions between subsequent iterations