Gradient-Enhanced Partitioned Gaussian Processes for Real-Time Quadrotor Dynamics Modeling

TL;DR

This paper introduces a real-time Gaussian Process model for quadrotor dynamics that incorporates gradient information and local partitioning, enabling fast and accurate aerodynamic predictions suitable for control applications.

Contribution

The paper presents a novel partitioned GP approach with gradient information and offline matrix inversion, achieving real-time inference for quadrotor dynamics including aerodynamic effects.

Findings

Achieves over 30 Hz inference on standard hardware

Higher accuracy than standard partitioned GPs without gradients

Effective modeling of aerodynamic effects using mid-fidelity simulations

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.