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

2025-10-30

AI Summary

This work addresses the real-time collision avoidance problem with static and dynamic ellipsoidal obstacles in three-dimensional optimal control. We propose a modular model predictive control (MPC) framework. Methodologically, (1) we derive a differentiable, closed-form ellipsoid–ellipsoid collision detection condition, significantly improving constraint modeling efficiency and gradient accuracy; and (2) we introduce a two-stage optimization strategy that decouples trajectory generation from obstacle avoidance refinement, mitigating numerical difficulties arising from nonconvexity. To the best of our knowledge, this is the first MPC-based approach achieving real-time 3D collision avoidance and path tracking on the Crazyflie quadrotor platform. Extensive simulations and flight experiments demonstrate stable, high-precision trajectory tracking and millisecond-level reactive obstacle avoidance in complex dynamic environments. The results validate the method’s computational efficiency, robustness, and engineering feasibility.

Technology Category

• Search and Optimization: Sampling/Simulation-based Search
• Intelligent Robots: State Estimation
• Planning, Routing, and Scheduling: Replanning and Plan Repair

Application Category

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• User Modeling, Personalization and Recommendation: Attacks and countermeasures in recommendation systems
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs

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.

Problem

• Develops efficient collision avoidance for ellipsoidal obstacles
• Addresses static and moving obstacles in optimal control
• Applies framework to UAV path-following with hardware validation

Innovation

• Modular optimal control framework for ellipsoidal obstacle avoidance
• Computationally efficient differentiable collision detection condition
• Two-stage optimization approach mitigating numerical issues