Real-time Trajectory Generation for Multiple Drones using Bézier Curves
Bahareh Sabetghadam, Rita Cunha, A. Pascoal
Abstract
Practical applications of drones are expanding into many new areas due to their fast-evolving technology. Looking further into the future, it is very likely that applications will require more than one drone to tackle a specific task, calling for reliable and efficient algorithms that can generate collision-free trajectories for multiple drones, under timing constraints of real-time applications. In this paper, we study a motion planning method based on the Bézier parametrization of spatial paths with a special focus on the less addressed issue in this method, (inefficient) constraint evaluation, that might hinder its use in real-time trajectory generation for multi-drone applications. We take advantage of the Bézier curves properties to obtain a small-scale optimization problem and find a finite set of inequalities that guarantee constraints satisfaction. We also propose a method to lower the conservatism in the resulting set of inequalities without the need to use unnecessary high-degree Bézier curves. Numerical results illustrate the efficacy of the presented method in reducing the computational costs associated with generating collision-free trajectories for multiple drones and re-planning them online with a receding horizon.