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arXiv · 2510.26531

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

David Leprich·Mario Rosenfelder·Markus Herrmann-Wicklmayr·Kathrin Flaßkamp·Peter Eberhard·Henrik Ebel
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Abstract

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.

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David Leprich, Mario Rosenfelder, Markus Herrmann-Wicklmayr, Kathrin Flaßkamp, Peter Eberhard, Henrik Ebel. 2025-10-30. Efficient Collision-Avoidance Constraints for Ellipsoidal Obstacles in Optimal Control: Application to Path-Following MPC and UAVs. https://doi.org/10.1109/med70602.2026.11598421

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