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.

翻译：本文提出一种融合梯度信息的四旋翼动力学高斯过程模型，该模型通过状态空间分区与近似方法实现实时推理，并利用中保真度势流模拟数据捕捉空气动力学效应。传统基于高斯过程的方法虽能提供可靠的贝叶斯预测及不确定性量化，但计算成本高昂，难以适用于实时仿真。为解决此问题，我们集成梯度信息以提升精度，并引入创新的分区与近似策略以降低在线计算开销。具体而言，我们在每个非重叠区域关联一个局部高斯过程；通过将训练数据划分为局部近场与远场子集，并利用舒尔补方法，证明了推理所需的大部分矩阵求逆运算可离线完成，从而在标准桌面硬件上实现高于30 Hz的实时推理频率。为生成包含空气动力学效应（如旋翼间相互作用与表观风向）的训练数据集，我们采用中保真度空气动力学求解器CHARM代码，将其应用于SUI Endurance四旋翼飞行器以预测力、力矩及三个指定位置的噪声。梯度信息通过有限差分法获取。实验结果表明，所提出的梯度增强分区高斯过程相较于无梯度信息的标准分区高斯过程具有更高精度，同时显著降低了计算时间。该框架为复杂非定常环境下的实时空气动力学预测与控制算法提供了高效基础。