MPCC++: Model Predictive Contouring Control for Time-Optimal Flight with Safety Constraints

TL;DR

This paper tackles time-optimal quadrotor flight in drone racing under safety constraints by enriching Model Predictive Contouring Control (MPCC) into MPCC++. The approach adds a track-based safety constraint in a Euclidean framework, augments the dynamics with a data-driven residual to capture aerodynamic effects, and automatically tunes controller hyperparameters with Trust Region Bayesian Optimization (TuRBO). Empirically, MPCC++ achieves comparable lap times to the best RL policies while delivering robust 100% safety against gate collisions across both simulation and real-world flights, reaching speeds over 80 km/h and enabling a tunable safety-performance trade-off via tunnel width. The work demonstrates that integrating safety constraints, learned dynamics, and efficient hyperparameter optimization yields a powerful, dependable alternative to purely learning-based methods for high-speed quadrotor racing.

Abstract

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 promising 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 state-of-the-art MPCC approach for drone racing. First and foremost, we provide safety guarantees in the form of a track constraint and terminal set. The track constraint 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 MPCC controller given a sparse reward based on lap time minimization. The proposed approach achieves similar lap times to the best-performing RL policy and outperforms the best model-based 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 limits reaching speeds of more than 80km/h.

Figures (5)

• Figure 1: Spatial constraint forming a tunnel around the centerline. The width and height are parameterized by $W(\theta_k)$ and $H(\theta_k)$, respectively.
• Figure 2: Parameter exploration using TuRBO and WML. We plot two of the tuning parameters - $Q_c$ and $\mu$ - over the number of episodes. TuRBO's trust regions enhance exploration of the entire parameter space, while WML randomly restarts the exploration every 100 episodes.
• Figure 3: Simulation experiments of MPCC with the proposed MPCC++, both tuned using TuRBO.
• Figure 4: Real world flight trajectories on the Split-S track for the baseline MPCC mpcc, MPCC++ and the best-performing RL policy Song23Reaching. Both MPCC and MPCC++ were tuned using TuRBO.
• Figure 5: Real world thrust and velocity profiles for MPCC, MPCC++ and RL.

Theorems & Definitions (1)

• Proposition 1