Gradient-Enhanced Partitioned Gaussian Processes for Real-Time Quadrotor Dynamics Modeling
Xinhuan Sang, Adam Rozman, Sheryl Grace, Roberto Tron
TL;DR
The paper addresses the need for real-time, uncertainty-aware quadrotor dynamics under unsteady aerodynamics. It introduces a gradient-conditioned partitioned Gaussian Process with Schur-complement corrections, trained on mid-fidelity aerodynamic data from the CHARM solver to serve as a high-fidelity surrogate, while performing extensive offline precomputation to enable online 30 Hz updates. Key contributions include the near/far data partitioning with gradient information, Schur-based mean and covariance corrections, and dataset reduction via gradients, all enabling real-time inference with reduced memory. The results demonstrate improved accuracy over gradientless baselines, substantial speedups, and a practical path toward real-time aerodynamic prediction and control in complex, unsteady environments.
Abstract
We present a quadrotor dynamics Gaussian Process (GP) with gradient information that achieves real-time inference via state-space partitioning and approximation, and that includes aerodynamic effects using data from mid-fidelity potential flow simulations. While traditional GP-based approaches provide reliable Bayesian predictions with uncertainty quantification, they are computationally expensive and thus unsuitable for real-time simulations. To address this challenge, we integrate gradient information to improve accuracy and introduce a novel partitioning and approximation strategy to reduce online computational cost. In particular, for the latter, we associate a local GP with each non-overlapping region; by splitting the training data into local near and far subsets, and by using Schur complements, we show that a large part of the matrix inversions required for inference can be performed offline, enabling real-time inference at frequencies above 30 Hz on standard desktop hardware. To generate a training dataset that captures aerodynamic effects, such as rotor-rotor interactions and apparent wind direction, we use the CHARM code, which is a mid-fidelity aerodynamic solver. It is applied to the SUI Endurance quadrotor to predict force and torque, along with noise at three specified locations. The derivative information is obtained via finite differences. Experimental results demonstrate that the proposed partitioned GP with gradient conditioning achieves higher accuracy than standard partitioned GPs without gradient information, while greatly reducing computational time. This framework provides an efficient foundation for real-time aerodynamic prediction and control algorithms in complex and unsteady environments.