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

On the Power of Manifold Samples in Exploring Configuration Spaces and the Dimensionality of Narrow Passages

We extend our study of Motion Planning via Manifold Samples (MMS), a general algorithmic framework that combines geometric methods for the exact and complete analysis of low-dimensional configuration spaces with sampling-based approaches that are appropriate for higher dimensions. The framework explores the configuration space by taking samples that are entire low-dimensional manifolds of the configuration space capturing its connectivity much better than isolated point samples. The contributions of this paper are as follows: (i) We present a recursive application of MMS in a six-dimensional configuration space, enabling the coordination of two polygonal robots translating and rotating amidst polygonal obstacles. In the adduced experiments for the more demanding test cases MMS clearly outperforms PRM, with over 20-fold speedup in a coordination-tight setting. (ii) A probabilistic completeness proof for the most prevalent case, namely MMS with samples that are affine subspaces. (iii) A closer examination of the test cases reveals that MMS has, in comparison to standard sampling-based algorithms, a significant advantage in scenarios containing high-dimensional narrow passages. This provokes a novel characterization of narrow passages which attempts to capture their dimensionality, an attribute that had been (to a large extent) unattended in previous definitions.Comment: 20 page

Cell Representations of the Configuration Space for Planning Optimal Paths

This paper proposes sampling techniques to approximate the configuration space for optimal motion planning. We sample valid configurations in the workspace and construct path subconvex cells in the free configuration space. The radius of each cell is calculated using lower bounds on the robot’s minimum time to collision. Using theorems about path convexity, the shortest paths found between any two points in the decomposed space are guaranteed to be safe. Experimental results are provided for a planar arm

Distributed cooperation of multiple robots under operational constraints via lean communication

Η αυτόνομη λειτουργία των ρομπότ εντός περίπλοκων χώρων εργασίας αποτελεί ένα επίκαιρο θέμα έρευνας και η αυτόνομη πλοήγηση είναι αναμφισβήτητα ένα θεμελιώδες κομμάτι αυτής. Επιπλέον, καθώς οι εργασίες που τα ρομπότ καλούνται να εκπληρώσουν αυξάνονται σε πολυπλοκότητα μέρα με τη μέρα, η χρήση πολύ-ρομποτικών συστημάτων, τα οποία εμφανίζουν γενικά υψηλότερη ευρωστία και ευελιξία, αυξάνεται προοδευτικά. Ως εκ τούτου, τα προβλήματα αυτόνομης πλοήγησης που πρέπει να επιλυθούν γίνονται όλο και πιο απαιτητικά, αυξάνοντας την ανάγκη για πιο αποτελεσματικά και σθεναρά σχήματα σχεδιασμού πορείας και κίνησης