Gaussian Processes (GPs) are expressive models for capturing signal statistics and expressing prediction uncertainty. As a result, the robotics community has gathered interest in leveraging these methods for inference, planning, and control. Unfortunately, despite providing a closed-form inference solution, GPs are non-parametric models that typically scale cubically with the dataset size, hence making them difficult to be used especially on onboard Size, Weight, and Power (SWaP) constrained aerial robots. In addition, the integration of popular libraries with GPs for different kernels is not trivial. In this paper, we propose GaPT, a novel toolkit that converts GPs to their state space form and performs regression in linear time. GaPT is designed to be highly compatible with several optimizers popular in robotics. We thoroughly validate the proposed approach for learning quadrotor dynamics on both single and multiple input GP settings. GaPT accurately captures the system behavior in multiple flight regimes and operating conditions, including those producing highly nonlinear effects such as aerodynamic forces and rotor interactions. Moreover, the results demonstrate the superior computational performance of GaPT compared to a classical GP inference approach on both single and multi-input settings especially when considering large number of data points, enabling real-time regression speed on embedded platforms used on SWaP-constrained aerial robots.

翻译：摘要：高斯过程（Gaussian Processes, GPs）是用于捕获信号统计特征并表达预测不确定性的表示模型。因此，机器人领域的研究人员对利用这些方法进行推理、规划和控制产生了浓厚兴趣。然而，尽管提供了闭式推理解，高斯过程作为非参数模型，其计算复杂度通常随数据集大小呈三次方增长，这使得它们在尺寸、重量与功耗（SWaP）受限的机载空中机器人上难以应用。此外，将常用函数库与不同核函数的高斯过程进行集成也并非易事。本文提出GaPT——一种新颖的工具包，它可将高斯过程转换为状态空间形式，并以线性时间复杂度执行回归。GaPT被设计为与机器人领域中多种主流优化器高度兼容。我们在单输入和多输入高斯过程设置下，对学习四旋翼动力学的方法进行了全面验证。GaPT能够准确捕获多个飞行状态和操作条件下的系统行为，包括产生高度非线性效应（如气动力和旋翼相互作用）的条件。此外，结果表明，与经典的高斯过程推理方法相比，GaPT在单输入和多输入设置下均展现出卓越的计算性能，尤其在处理大量数据点时优势显著，从而在SWaP受限空中机器人所使用的嵌入式平台上实现了实时回归速度。