Related papers: Parameterization of configuration space obstacles …
This work studies path planning in two-dimensional space, in the presence of polygonal obstacles. We specifically address the problem of building a roadmap graph, that is, an abstract representation of all the paths that can potentially be…
Roadmaps constructed by many sampling-based motion planners coincide, in the absence of obstacles, with standard models of random geometric graphs (RGGs). Those models have been studied for several decades and by now a rich body of…
The determination of space layout is one of the primary activities in the schematic design stage of an architectural project. The initial layout planning defines the shape, dimension, and circulation pattern of internal spaces; which can…
We present a novel orbit parameterization in spherical coordinates. This parameterization enables the mixing of varying and invariant orbital parameters, and clarifies the physics of the orbit. It also simplifies the process of placing…
We present a mathematical and algorithmic scheme for learning the principal geometric elements in an image or 3D object. We build on recent work that convexifies the basic problem of finding a combination of a small number shapes that…
Understanding the geometry and topology of configuration or conformational spaces of molecules has relevant applications in chemistry and biology such as the proteins folding problem, drug design and the structure activity relationship…
This paper considers the collision avoidance problem in a multi-agent multi-obstacle framework. The originality in solving this intensively studied problem resides in the proposed geometrical view combined with differential flatness for…
We describe parametrised motion planning algorithms for systems controlling objects represented by points that move without collisions in an even dimensional Euclidean space and in the presence of up to three obstacles with \emph{a priori}…
Hard sphere systems are often used to model simple fluids. The configuration spaces of hard spheres in a three-dimensional torus modulo various symmetry groups are comparatively simple, and could provide valuable information about the…
3D object reconfiguration encompasses common robot manipulation tasks in which a set of objects must be moved through a series of physically feasible state changes into a desired final configuration. Object reconfiguration is challenging to…
Optimal control problems are formulated and efficient computational procedures are proposed for combined orbital and rotational maneuvers of a rigid body in three dimensions. The rigid body is assumed to act under the influence of forces…
The goal of robust motion planning consists of designing open-loop controls which optimally steer a system to a specific target region while mitigating uncertainties and disturbances which affect the dynamics. Recently, stochastic optimal…
Learning motion planners to move robot from one point to another within an obstacle-occupied space in a collision-free manner requires either an extensive amount of data or high-quality demonstrations. This requirement is caused by the fact…
This paper presents a two-stage prediction-based control scheme for embedding the environment's geometric properties into a collision-free Pythagorean Hodograph spline, and subsequently finding the optimal path within the parameterized free…
Stiffener layout optimization of complex surfaces is fulfilled within the framework of topology optimization. A combined parameterization method is developed in two aspects. One is to parameterize the material distribution of the stiffener…
We establish sharp upper bounds for the topological complexity of motion planning problem in spaces with small fundamental group, i.e. when it is finite of small order or has small cohomological dimension.
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…
The topological complexity TC(X) is a numerical homotopy invariant of a topological space X which is motivated by robotics and is similar in spirit to the classical Lusternik-Schnirelmann category of X. Given a mechanical system with…
For configurations of point-sets that are pairwise constrained by distance intervals, the EASAL software implements a suite of algorithms that characterize the structure and geometric properties of the configuration space. The algorithms…
In this series of papers, we present a motion planning framework for planning comfortable and customizable motion of nonholonomic mobile robots such as intelligent wheelchairs and autonomous cars. In this first one we present the…