Convex Approach to Data-Driven Off-Road Navigation via Linear Transfer Operators

Abstract

We consider the problem of optimal control design for navigation on off-road terrain. We use a traversability measure to characterize the difficulty of navigation on off-road terrain. The traversability measure captures terrain properties essential for navigation, such as elevation maps, roughness, slope, and 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. We construct the finite-dimensional approximation of the optimization problem using data. We use a computational framework based on the data-driven approximation of the Koopman operator. This makes the proposed approach data-driven and applicable to cases where an explicit system model is unavailable. Finally, we apply the proposed navigation framework with single integrator dynamics and Dubin's car model.