Efficient Collision-Avoidance Constraints for Ellipsoidal Obstacles in Optimal Control: Application to Path-Following MPC and UAVs

This article proposes a modular optimal control framework for local three-dimensional ellipsoidal obstacle avoidance, exemplarily applied to model predictive path-following control. Static as well as moving obstacles are considered. Central to the approach is a computationally efficient and continuously differentiable condition for detecting collisions with ellipsoidal obstacles. A novel two-stage optimization approach mitigates numerical issues arising from the structure of the resulting optimal control problem. The effectiveness of the approach is demonstrated through simulations and real-world experiments with the Crazyflie quadrotor. This represents the first hardware demonstration of an MPC controller of this kind for UAVs in a three-dimensional task.

Model Predictive Path-Following Control for a Quadrotor

Automating drone-assisted processes is a complex task. Many solutions rely on trajectory generation and tracking, whereas in contrast, path-following control is a particularly promising approach, offering an intuitive and natural approach to automate tasks for drones and other vehicles. While different solutions to the path-following problem have been proposed, most of them lack the capability to explicitly handle state and input constraints, are formulated in a conservative two-stage approach, or are only applicable to linear systems. To address these challenges, the paper is built upon a Model Predictive Control-based path-following framework and extends its application to the Crazyflie quadrotor, which is investigated in hardware experiments. A cascaded control structure including an underlying attitude controller is included in the Model Predictive Path-Following Control formulation to meet the challenging real-time demands of quadrotor control. The effectiveness of the proposed method is demonstrated through real-world experiments, representing, to the best of the authors' knowledge, a novel application of this MPC-based path-following approach to the quadrotor. Additionally, as an extension to the original method, to allow for deviations of the path in cases where the precise following of the path might be overly restrictive, a corridor path-following approach is presented.