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

TL;DR

This paper introduces a modular optimal control framework for efficient collision avoidance with ellipsoidal obstacles in 3D space, applicable to UAVs, with demonstrated success in simulations and real-world Crazyflie quadrotor experiments.

Contribution

It presents a novel, computationally efficient collision detection method and a two-stage optimization approach for ellipsoidal obstacles in 3D, applied to UAV path-following MPC.

Findings

Effective collision avoidance demonstrated in simulations.

Successful real-world UAV experiments with Crazyflie.

First hardware implementation of this MPC approach for UAVs.

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.