An NC1 parallel 3D convex hull algorithm

In this paper we present an O(log n) time paridlel algorithm for computing the convex hull of n points in!)?3. This algorithm uses O (nl+a) processors on a CREW PRAM, for any constant O < cr <1. So far, all adequately documented parallel algorithms proposed for this problem use time at least 0(log2! n). In addition, the algorithm presented here is the first parallel algorithm for the three-dimensional convex hull problem that is not based on the serial divide-and-conquer algorithm of Preparat a and Hong, whose crucial operation is the merging of the convex hulls of two linearly separated point sets. The contributions of this paper are therefore (i) an O (log n) time parallel algorithm for the threedimensional convex hull problem, and (ii) a parallel algorithm for this problem that does not follow the traditional divide-and-conquer paradigm.

Asymptotically-Optimal Topological Nearest-Neighbor Filtering

Nearest-neighbor finding is a major bottleneck for sampling-based motion planning algorithms. The cost of finding nearest neighbors grows with the size of the roadmap, leading to a significant computational bottleneck for problems which require many configurations to find a solution. In this work, we develop a method of mapping configurations of a jointed robot to neighborhoods in the workspace that supports fast search for configurations in nearby neighborhoods. This expedites nearest-neighbor search by locating a small set of the most likely candidates for connecting to the query with a local plan. We show that this filtering technique can preserve asymptotically-optimal guarantees with modest requirements on the distance metric. We demonstrate the method’s efficacy in planning problems for rigid bodies and both fixed and mobile-base manipulators

An Optimal Algorithm for Determining the Separation of Two Nonintersecting Simple Polygons

Coordinated Science Laboratory was formerly known as Control Systems LaboratoryJoint Services Electronics Program / N00014-90-J-127

Improved Processor Bounds for Parallel Algorithms for Weighted Directed Graphs

Coordinated Science Laboratory was formerly known as Control Systems Laborator

Computing the Minimum Visible Vertex Distance Between Two Nonintersecting Simple Polygons

Coordinated Science Laboratory was formerly known as Control Systems Laborator

Hypergraph-based Multi-robot Motion Planning with Topological Guidance

We present a multi-robot motion planning algorithm that efficiently finds paths for robot teams up to ten times larger than existing methods in congested settings with narrow passages in the environment. Narrow passages represent a source of difficulty for sampling-based motion planning algorithms. This problem is exacerbated for multi-robot systems where the planner must also avoid inter-robot collisions within these congested spaces, requiring coordination. Topological guidance, which leverages information about the robot's environment, has been shown to improve performance for mobile robot motion planning in single robot scenarios with narrow passages. Additionally, our prior work has explored using topological guidance in multi-robot settings where a high degree of coordination is required of the full robot group. This high level of coordination, however, is not always necessary and results in excessive computational overhead for large groups. Here, we propose a novel multi-robot motion planning method that leverages topological guidance to inform the planner when coordination between robots is necessary, leading to a significant improvement in scalability.Comment: This work has been submitted for revie

Topology-Guided Roadmap Construction With Dynamic Region Sampling

Many types of planning problems require discovery of multiple pathways through the environment, such as multi-robot coordination or protein ligand binding. The Probabilistic Roadmap (PRM) algorithm is a powerful tool for this case, but often cannot efficiently connect the roadmap in the presence of narrow passages. In this letter, we present a guidance mechanism that encourages the rapid construction of well-connected roadmaps with PRM methods. We leverage a topological skeleton of the workspace to track the algorithm\u27s progress in both covering and connecting distinct neighborhoods, and employ this information to focus computation on the uncovered and unconnected regions. We demonstrate how this guidance improves PRM\u27s efficiency in building a roadmap that can answer multiple queries in both robotics and protein ligand binding applications

Hypergraph-based Multi-Robot Task and Motion Planning

We present a multi-robot task and motion planning method that, when applied to the rearrangement of objects by manipulators, produces solution times up to three orders of magnitude faster than existing methods. We achieve this improvement by decomposing the planning space into subspaces for independent manipulators, objects, and manipulators holding objects. We represent this decomposition with a hypergraph where vertices are substates and hyperarcs are transitions between substates. Existing methods use graph-based representations where vertices are full states and edges are transitions between states. Using the hypergraph reduces the size of the planning space-for multi-manipulator object rearrangement, the number of hypergraph vertices scales linearly with the number of either robots or objects, while the number of hyperarcs scales quadratically with the number of robots and linearly with the number of objects. In contrast, the number of vertices and edges in graph-based representations scale exponentially in the number of robots and objects. Additionally, the hypergraph provides a structure to reason over varying levels of (de)coupled spaces and transitions between them enabling a hybrid search of the planning space. We show that similar gains can be achieved for other multi-robot task and motion planning problems.Comment: This work has been submitted for revie