Optimal Motion Planning and Control with Safety Guarantees for Aerial Robots

Autonomous aerial robots are expected to revolutionize many industries, such as construction, transportation or even space exploration. However, to target an industry where different robots and humans are meant to share the same space our algorithms need to provide safety and efficiency guarantees. Navigating autonomously in these kind of environments poses a great challenge. We may face a significant number of obstacles, and we can only estimate where they are and where they are expected to be, but not exactly. Dealing with these uncertainties is a challenging problem in most robotics applications, including motion planning and control. During the last decade, major contributions have established the theoretical basis upon which optimal motion planning and control with safety guarantees can be achieved. However, they involve a high computational cost that scales exponentially with the number of obstacles, rendering a limited domain of robotic applications. The main contribution of this thesis provides an efficient, scalable and safe approximation to this problem, allowing its application to embedded systems with fast dynamics such as aerial robots. This thesis also includes an additional contribution that allow these methods to plan longer trajectories with a minimal computational footprint, allowing to better anticipate evasive maneuvers. These contributions have been validated mathematically, in simulation and in real-time operation on aerial robots, handling uncertain dynamic obstacles such as pedestrians.