An NMPC Approach using Convex Inner Approximations for Online Motion Planning with Guaranteed Collision Freedom

Even though mobile robots have been around for decades, trajectory optimization and continuous time collision avoidance remains subject of active research. Existing methods trade off between path quality, computational complexity, and kinodynamic feasibility. This work approaches the problem using a model predictive control (MPC) framework, that is based on a novel convex inner approximation of the collision avoidance constraint. The proposed Convex Inner ApprOximation (CIAO) method finds a dynamically feasible and collision free trajectory in few iterations, typically one, and preserves feasibility during further iterations. CIAO scales to high-dimensional systems, is computationally efficient, and guarantees both kinodynamic feasibility and continuous-time collision avoidance. Our experimental evaluation shows that the approach outperforms state of the art baselines in terms of planning efficiency and path quality. Furthermore real-world experiments show its capability of unifying trajectory optimization and tracking for safe motion planning in dynamic environments.