论文标题
多sparse高斯流程：基于学习的半参数控制
Multi-Sparse Gaussian Process: Learning based Semi-Parametric Control
论文作者
论文摘要
控制复杂的动态系统的关键挑战是准确对其进行建模。但是，在实践中，这一要求很难满足。通过采用基于回归的方法来捕获未建模的动力学效应，诸如高斯过程（GP）之类的数据驱动方法已被证明非常有效。但是，GPS与数据进行了立方体规模，并且通常是执行实时回归的挑战。在本文中，我们提出了一个半参数框架，以利用稀疏性进行基于学习的控制。我们将系统的参数模型与多个稀疏的GP模型相结合，以捕获任何未建模的动力学。 Multi-Sparse Gaussian过程（MSGP）将原始数据集分为多个稀疏模型，每个模型都有独特的超参数。从而保留每个稀疏模型的丰富性和独特性。对于查询点，根据$ n $相邻的稀疏模型执行加权稀疏后验预测。因此，预测复杂性从$ \ Mathcal {o}（n^3）$显着降低到$ \ Mathcal {o}（npu^2）$，其中$ p $和$ u $是每个稀疏模型的数据点和伪输入。我们使用模拟中的几何控制器来验证MSGP的学习成绩。与GP，稀疏GP和本地GP的比较表明，MSGP的预测准确性比稀疏和局部GP高，而时间复杂性明显低于所有三个。我们还验证了硬件四极管上的MSGP，以实现未建模的质量，惯性和干扰。实验视频可以看到：https：//youtu.be/zuk1isux6ao
A key challenge with controlling complex dynamical systems is to accurately model them. However, this requirement is very hard to satisfy in practice. Data-driven approaches such as Gaussian processes (GPs) have proved quite effective by employing regression based methods to capture the unmodeled dynamical effects. However, GPs scale cubically with data, and is often a challenge to perform real-time regression. In this paper, we propose a semi-parametric framework exploiting sparsity for learning-based control. We combine the parametric model of the system with multiple sparse GP models to capture any unmodeled dynamics. Multi-Sparse Gaussian Process (MSGP) divides the original dataset into multiple sparse models with unique hyperparameters for each model. Thereby, preserving the richness and uniqueness of each sparse model. For a query point, a weighted sparse posterior prediction is performed based on $N$ neighboring sparse models. Hence, the prediction complexity is significantly reduced from $\mathcal{O}(n^3)$ to $\mathcal{O}(Npu^2)$, where $p$ and $u$ are data points and pseudo-inputs respectively for each sparse model. We validate MSGP's learning performance for a quadrotor using a geometric controller in simulation. Comparison with GP, sparse GP, and local GP shows that MSGP has higher prediction accuracy than sparse and local GP, while significantly lower time complexity than all three. We also validate MSGP on a hardware quadrotor for unmodeled mass, inertia, and disturbances. The experiment video can be seen at: https://youtu.be/zUk1ISux6ao
