论文标题
通过线性转移操作员，数据驱动的凸凸方法
Data-Driven Convex Approach to Off-road Navigation via Linear Transfer Operators
论文作者
论文摘要
我们考虑在越野地形上导航的最佳导航控制设计的问题。我们使用遍历性措施来表征越野地形上导航难度的程度。遍历度量捕获了导航所必需的地形的特性，例如高程图，地形粗糙度，坡度和地形纹理。存在或不存在障碍的地形成为拟议的遍历性措施的特殊情况。我们通过使用线性Perron-Frobenius（P-F）操作员将问题提升到密度空间来为越野导航问题提供凸公式。凸制配方导致用于控制合成的无限二维最佳导航问题。无限维凸问题的有限维近似是使用数据构建的。我们将涉及Koopman操作员的计算框架以及Koopman和P-F运算符之间的双重性来进行数据驱动的近似。这使我们提出的方法是数据驱动的，并且可以在不可用的系统模型的情况下应用。最后，我们演示了开发的框架在使用杜宾的汽车模型中导航车辆动力学的应用。
We consider the problem of optimal navigation control design for navigation on off-road terrain. We use traversability measure to characterize the degree of difficulty of navigation on the off-road terrain. The traversability measure captures the property of terrain essential for navigation, such as elevation map, terrain roughness, slope, and terrain texture. The terrain with the presence or absence of obstacles becomes a particular case of the proposed traversability measure. We provide a convex formulation to the off-road navigation problem by lifting the problem to the density space using the linear Perron-Frobenius (P-F) operator. The convex formulation leads to an infinite-dimensional optimal navigation problem for control synthesis. The finite-dimensional approximation of the infinite-dimensional convex problem is constructed using data. We use a computational framework involving the Koopman operator and the duality between the Koopman and P-F operator for the data-driven approximation. This makes our proposed approach data-driven and can be applied in cases where an explicit system model is unavailable. Finally, we demonstrate the application of the developed framework for the navigation of vehicle dynamics with Dubin's car model.
