Learning Model Predictive Control for Quadrotors

TL;DR

This work addresses time-critical quadrotor control by formulating a Learning Model Predictive Control (LMPC) framework on the nonlinear manifold $SO(3)\times \mathbb{R}^3$ that leverages past successful iterations to improve performance while respecting dynamics and actuator limits. To render LMPC tractable for real-time quadrotor control, the authors introduce convex relaxations of the safety set and a local, sparse safety subset, along with a RK4-based discretization that preserves the $SO(3)$ structure. A concrete instantiation demonstrates learning minimum-time trajectories along corridors, using a sigmoid-based surrogate for the terminal cost and linear corridor constraints, solved efficiently with an SQP solver through ACADOS. Simulation and indoor real-world experiments validate that the LMPC progressively discovers faster paths within track constraints, achieving significant reductions in travel time and demonstrating real-time feasibility on a laptop. The approach contributes a practical LMPC toolkit for quadrotors facing complex dynamics and environmental constraints, with potential extensions to drone racing and dynamics-based refinements via Bayesian learning.

Abstract

Aerial robots can enhance their safe and agile navigation in complex and cluttered environments by efficiently exploiting the information collected during a given task. In this paper, we address the learning model predictive control problem for quadrotors. We design a learning receding--horizon nonlinear control strategy directly formulated on the system nonlinear manifold configuration space SO(3)xR^3. The proposed approach exploits past successful task iterations to improve the system performance over time while respecting system dynamics and actuator constraints. We further relax its computational complexity making it compatible with real-time quadrotor control requirements. We show the effectiveness of the proposed approach in learning a minimum time control task, respecting dynamics, actuators, and environment constraints. Several experiments in simulation and real-world set-up validate the proposed approach.

Figures (7)

• Figure 1: The LMPC iterates over the same task while learning minimum time trajectories and improving its performances.
• Figure 2: System convention with $\mathcal{I}$ and $\mathcal{B}$ denoting inertial and body frames respectively.
• Figure 3: Illustrative example on creating a local safety set in the X-Y position only. At time $t-1$ in $j^{th}$ iteration, the LMPC forecasts states over the horizon, $N$, including the terminal predicted state $\mathbf{x}_{N|t-1}$ (green $\times$ in this figure). The local safety set, $SS_t^{j-1}$, at time $t$ (red circles with blue outline) is made up of $\mathbf{x}_{N|t-1}$'s nearest neighbors in $SS^{j-1}$.
• Figure 4: Iteration trajectories for the L-shaped track in simulation.
• Figure 5: Trajectory and velocity profiles across several iterations for the L-shaped track in simulation.