k-Color Multi-Robot Motion Planning

We present a simple and natural extension of the multi-robot motion planning problem where the robots are partitioned into groups (colors), such that in each group the robots are interchangeable. Every robot is no longer required to move to a specific target, but rather to some target placement that is assigned to its group. We call this problem k-color multi-robot motion planning and provide a sampling-based algorithm specifically designed for solving it. At the heart of the algorithm is a novel technique where the k-color problem is reduced to several discrete multi-robot motion planning problems. These reductions amplify basic samples into massive collections of free placements and paths for the robots. We demonstrate the performance of the algorithm by an implementation for the case of disc robots and polygonal robots translating in the plane. We show that the algorithm successfully and efficiently copes with a variety of challenging scenarios, involving many robots, while a simplified version of this algorithm, that can be viewed as an extension of a prevalent sampling-based algorithm for the k-color case, fails even on simple scenarios. Interestingly, our algorithm outperforms a well established implementation of PRM for the standard multi-robot problem, in which each robot has a distinct color.Comment: 2

Toggle PRM: A Coordinated Mapping of C-Free and C-Obstacle in Arbitrary Dimension

Abstract Motion planning has received much attention over the past 40 years. More than 15 years have passed since the introduction of the successful sampling-based approach known as the Probabilistic RoadMap Method (PRM). PRM and its many variants have demonstrated great success for some high-dimensional problems, but they all have some level of difficulty in the presence of narrow passages. Recently, an approach called Toggle PRM has been introduced whose performance does not degrade for 2-dimensional problems with narrow passages. In Toggle PRM, a si-multaneous, coordinated mapping of both C f ree and Cobst is performed and every connection attempt augments one of the maps – either validating an edge in the cur-rent space or adding a configuration ’witnessing ’ the connection failure to the other space. In this paper, we generalize Toggle PRM to d-dimensions and show that the benefits of mapping both C f ree and Cobst continue to hold in higher dimensions. In particular, we introduce a new narrow passage characterization, α-ε-separable nar-row passages, which describes the types of passages that can be successfully mapped by Toggle PRM. Intuitively, α-ε-separable narrow passages are arbitrarily narrow regions of C f ree that separate regions of Cobst, at least locally, such as hallways in an office building. We experimentally compare Toggle PRM with other methods in a variety of scenarios with different types of narrow passages and robots with up to 16 DOF.

CCQ: Efficient Local Planning Using Connection Collision Query

Abstract We introduce a novel proximity query, called connection collision query (CCQ), and use it for efficient and exact local planning in sampling-based motion planners. Given two collision-free configurations, CCQ checks whether these con-figurations can be connected by a given continuous path that either lies completely in the free space or penetrates any obstacle by at most ε, a given threshold. Our approach is general, robust, and can handle different continuous path formulations. We have integrated the CCQ algorithm with sampling-based motion planners and can perform reliable local planning queries with little performance degradation, as compared to prior methods. Moreover, the CCQ-based exact local planner is about an order of magnitude faster than prior exact local planning algorithms.

Homotopic Path Planning on Manifolds for Cabled Mobile Robots

We present two path planning algorithms for mobile robots that are connected by cable to a fixed base. Our algorithms efficiently compute the shortest path and control strategy that lead the robot to the target location considering cable length and obstacle interactions. First, we focus on cable-obstacle collisions. We introduce and formally analyze algorithms that build and search an overlapped configuration space manifold. Next, we present an extension that considers cable-robot collisions. All algorithms are experimentally validated using a real robot

Motion Planning via Manifold Samples

We present a general and modular algorithmic framework for path planning of robots. Our framework combines geometric methods for exact and complete analysis of low-dimensional configuration spaces, together with practical, considerably simpler sampling-based approaches that are appropriate for higher dimensions. In order to facilitate the transfer of advanced geometric algorithms into practical use, we suggest taking samples that are entire low-dimensional manifolds of the configuration space that capture the connectivity of the configuration space much better than isolated point samples. Geometric algorithms for analysis of low-dimensional manifolds then provide powerful primitive operations. The modular design of the framework enables independent optimization of each modular component. Indeed, we have developed, implemented and optimized a primitive operation for complete and exact combinatorial analysis of a certain set of manifolds, using arrangements of curves of rational functions and concepts of generic programming. This in turn enabled us to implement our framework for the concrete case of a polygonal robot translating and rotating amidst polygonal obstacles. We demonstrate that the integration of several carefully engineered components leads to significant speedup over the popular PRM sampling-based algorithm, which represents the more simplistic approach that is prevalent in practice. We foresee possible extensions of our framework to solving high-dimensional problems beyond motion planning.Comment: 18 page

A randomized attitude slew planning algorithm for autonomous spacecraft

The ability to autonomously generate and execute large angle attitude maneuvers, while operating under a number of celestial and dynamical constraints, is a key factor in the development of several future space platforms. In this paper we propose a ran-domized attitude slew planning algorithm for autonomous spacecraft, which is able to address a variety of pointing constraints, including bright object avoidance and ground link maintenance, as well as constraints on the control inputs and spacecraft states, and integral constraints such as those deriving from thermal control requirements. Moreover, through the scheduling of feedback control policies, the algorithm provides a consistent decoupling between low-level control and attitude motion planning, and is robust with respect to uncertainties in the spacecraft dynamics and environmental disturbances. Sim-ulation examples are presented and discussed

Efficient Clustering of Molecular Conformations

During the process of pharmaceutical drug design, computational chemists often compute different lowenergy conformations of small drug molecules (ligands). Such conformations are used in solving docking problems [5] and in pharmacophore identification [3]. Most methods that identify different low-energy conformations of ligands employ clustering to partition the generated conformations (typically tens of thousands) into sets that capture geometric similarity. Since the generation and clustering of conformations is a time-consuming operation [2], recent work focuses on devising faster algorithms for these problems. In this paper, we consider the problem of clustering conformations of ligands with 3-20 rotatable bonds. We report a number of experiments which indicate that while clustering based on distance measures defined over the workspace (W-space) has much better quality than clustering based on distance measures defined over the conformati..