Physics

Trajectory

Trajectory optimization

Pedagogy

Mathematics

Algorithm

Computer graphics (images)

Mathematical optimization

Astronomy

Engineering

Model predictive control

Artificial intelligence

Psychology

Systems engineering

Control (management)

Tracking (education)

Programming language

Path (computing)

Contouring

Computer science

Task (project management)

Control theory (sociology)

State (computer science)

Motion planning

Robot

Optimal control

IEEE Transactions on Robotics

In this article, we tackle the problem of flying time-optimal trajectories through multiple waypoints with quadrotors. State-of-the-art solutions split the problem into a planning task—where a global time-optimal trajectory is generated—and a control task—where this trajectory is accurately tracked. However, at the current state, generating a time-optimal trajectory that considers the full quadrotor model requires solving a difficult time allocation problem via optimization, which is computationally demanding (in the order of minutes or even hours). This is detrimental for replanning in the presence of disturbances. We overcome this issue by solving the time allocation problem and the control problem concurrently via Model Predictive Contouring Control (MPCC). Our MPCC optimally selects the future states of the platform at runtime, while maximizing the progress along the reference path and minimizing the distance to it. We show that, even when tracking simplified trajectories, the proposed MPCC results in a path that approaches the true time-optimal one, and which can be generated in real time. We validate our approach in the real world, where we show that our method outperforms both the current state of the art and a world-class human pilot in terms of lap time achieving speeds of up to 60 km/h.

Model Predictive Contouring Control for Time-Optimal Quadrotor Flight