This paper presents the implementation of off-road navigation on legged robots using convex optimization through linear transfer operators. Given a traversability measure that captures the off-road environment, we lift the navigation problem into the density space using the Perron-Frobenius (P-F) operator. This allows the problem formulation to be represented as a convex optimization. Due to the operator acting on an infinite-dimensional density space, we use data collected from the terrain to get a finite-dimension approximation of the convex optimization. Results of the optimal trajectory for off-road navigation are compared with a standard iterative planner, where we show how our convex optimization generates a more traversable path for the legged robot compared to the suboptimal iterative planner.

翻译：本文介绍了通过线性传递算子结合凸优化方法，在足式机器人上实现越野导航的具体实现。基于反映越野环境的可通行性度量，我们利用Perron-Frobenius（P-F）算子将导航问题提升至密度空间。这使得问题公式化可表示为凸优化形式。由于该算子作用于无穷维密度空间，我们利用从地形采集的数据获得凸优化的有限维近似。将越野导航最优轨迹的结果与标准迭代规划器进行对比，结果表明：相较于次优的迭代规划器，我们的凸优化方法能为足式机器人生成更具可通行性的路径。