Off-Road Navigation of Legged Robots Using Linear Transfer Operators⋆

Abstract

This paper presents the implementation of of-road navigation on legged robots using convex optimization through linear transfer operators. Given a traversability measure that captures the of-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 of-road navigation are compared with a standard iterative planner, where we show how the linear operator approach generates a more traversable path for the legged robot compared to the suboptimal iterative planner.