Navigation in Unknown Environments Using Safety Velocity Cones

TL;DR

This paper introduces a novel navigation method for unknown environments using safety velocity cones and Nagumo's invariance theorem, ensuring safe and convergent robot movement based solely on local measurements.

Contribution

It develops a projection-based controller onto safety velocity cones that guarantees safety and convergence without prior global environment knowledge.

Findings

Guarantees safety and convergence to the target.

Works with local measurements like LiDAR or stereo vision.

Applicable to environments of arbitrary dimension.

Abstract

We rely on Nagumo's invariance theorem to develop a new approach for navigation in unknown environments of arbitrary dimension. The idea consists in projecting the nominal velocities (that would drive the robot to the target in the absence of obstacles) onto Bouligand's tangent cones (referred to as the safety velocity cones) when the robot is close to the boundary of the free space. The proposed projection-based controller is explicitly constructed to guarantee safety and convergence to a set of Lebesgue measure zero that contains the target. For specific free spaces such as Euclidean sphere worlds, the convergence to the target is guaranteed from almost all initial conditions in the free space. We provide a version of the controller (generating a continuous and piecewise smooth closed-loop vector field) relying on the robot's current position and local range measurements (e.g., from LiDAR or stereo vision) without global prior knowledge about the environment.