Dynamic and Robust Local Clearance Triangulations

Abstract

The Local Clearance Triangulation (LCT) of polygonal obstacles is a cell decomposition designed for the efficient computation of locally shortest paths with clearance. This paper presents a revised definition of LCTs, new theoretical results and optimizations, and new algorithms introducing dynamic updates and robustness. Given an input obstacle set with n vertices, a theoretical analysis is proposed showing that LCTs generate a triangular decomposition of O(n) cells, guaranteeing that discrete search algorithms can compute paths in optimal times. In addition, several examples are presented indicating that the number of triangles is low in practice, close to 2n, and a new technique is described for reducing the number of triangles when the maximum query clearance is known in advance. Algorithms for repairing the local clearance property dynamically are also introduced, leading to efficient LCT updates for addressing dynamic changes in the obstacle set. Dynamic updates automatically handle intersecting and overlapping segments with guaranteed robustness, using techniques that combine one exact geometric predicate with adjustment of illegal floating point coordinates. The presented results demonstrate that LCTs are efficient and highly flexible for representing dynamic polygonal environments with clearance information.

Simplex Solutions for Optimal Control Flight Paths in Urban Environments

“…An extensive review of path planning through environments with clearances and algorithms developed to determine shortest paths while providing a minimum clearance to all constraints are provided by Kallmann [9,10]. These algorithms focus on computational efficiency while also providing a framework for dynamic addition and removal of constraints.…”

Multi‐group motion planning in virtual environments

“…Properties of corridors were studied in , which also developed approximate algorithms to compute near‐optimal corridors. Another approach developed the local clearance triangulation data structure in order to facilitate the computation of shortest paths with minimum clearance in dynamic environments . Subsequent work used the local clearance triangulation to plan paths for a group of agents .…”

Path planning for coherent and persistent groups

“…We represent navigable regions in the environment using a triangulation-based navigation mesh [1] with precomputed local clearance information in edge traversals, which enables the efficient computation of locally shortest paths with arbitrary clearance. We refer the readers to a detailed description in [1] and present a brief overview here.…”

“…The distance between two traversal edges can be computed based on the center of the respective triangles, the center of the edges etc. We use the edge centers and incorporate a visibility criterion [1] to compute the distance because it guarantees that straight line solutions are not missed. The distance cost c dis (s, s ) of transitioning between group states s and s is then computed as the average distance between the subgroups at each state.…”

“…This paper presents a path planning approach for coherent and persistent groups in arbitrarily complex environments. The navigable regions in the environment are represented using a triangulated navigation mesh [1] with precomputed local clearance information. A group is represented as a shape constrained area, which incurs a deformation penalty when it deviates from its rest shape, and can split (and reform) in necessary situations.…”