Time-Optimal Flight with Safety Constraints and Data-driven Dynamics

Time-optimal quadrotor flight is an extremely challenging problem due to the limited control authority encountered at the limit of handling. Model Predictive Contouring Control (MPCC) has emerged as a leading model-based approach for time optimization problems such as drone racing. However, the standard MPCC formulation used in quadrotor racing introduces the notion of the gates directly in the cost function, creating a multi-objective optimization that continuously trades off between maximizing progress and tracking the path accurately. This paper introduces three key components that enhance the MPCC approach for drone racing. First and foremost, we provide safety guarantees in the form of a constraint and terminal set. The safety set is designed as a spatial constraint which prevents gate collisions while allowing for time-optimization only in the cost function. Second, we augment the existing first principles dynamics with a residual term that captures complex aerodynamic effects and thrust forces learned directly from real world data. Third, we use Trust Region Bayesian Optimization (TuRBO), a state of the art global Bayesian Optimization algorithm, to tune the hyperparameters of the MPC controller given a sparse reward based on lap time minimization. The proposed approach achieves similar lap times to the best state-of-the-art RL and outperforms the best time-optimal controller while satisfying constraints. In both simulation and real-world, our approach consistently prevents gate crashes with 100% success rate, while pushing the quadrotor to its physical limit reaching speeds of more than 80km/h.