Occlusion-Aware Path Planning to Promote Infrared Positioning Accuracy for Autonomous Driving in a Warehouse

Infrared positioning is a critical module in an indoor autonomous vehicle platform. In an infrared positioning system, the ego vehicle is equipped with an infrared emitter while the infrared receivers are fixed onto the ceiling. The infrared positioning result is accurate only when the number of valid infrared receivers is more than three. An infrared receiver easily becomes invalid if it does not receive light from the infrared emitter due to indoor occlusions. This study proposes an occlusion-aware path planner that enables an autonomous vehicle to navigate toward the occlusion-free part of the drivable area. The planner consists of four layers. In layer one, a homotopic A* path is searched for in the 2D grid map to roughly connect the initial and goal points. In layer two, a curvature-continuous reference line is planned close to the A* path using numerical optimal control. In layer three, a Frenet frame is constructed along the reference line, followed by a search for an occlusion-aware path within that frame via dynamic programming. In layer four, a curvature-continuous path is optimized via quadratic programming within the Frenet frame. A path planned within the Frenet frame may violate the curvature bounds in a real-world Cartesian frame; thus, layer four is implemented through trial and error. Simulation results in CarSim software show that the derived paths reduce the poor positioning risk and are easily tracked by a controller.

Remarks on Manifolds with Two-Sided Curvature Bounds

We discuss folklore statements about distance functions in manifolds with two-sided bounded curvature. The topics include regularity, subsets of positive reach and the cut locus.

Dilation Type Inequalities for Strongly-Convex Sets in Weighted Riemannian Manifolds

In this paper, we consider a dilation type inequality on a weighted Riemannian manifold, which is classically known as Borell’s lemma in high-dimensional convex geometry. We investigate the dilation type inequality as an isoperimetric type inequality by introducing the dilation profile and estimate it by the one for the corresponding model space under lower weighted Ricci curvature bounds. We also explore functional inequalities derived from the comparison of the dilation profiles under the nonnegative weighted Ricci curvature. In particular, we show several functional inequalities related to various entropies.