in this paper we study the coprime graph of a group $g$. the coprime graph of a group $g$, is a graph whose vertices are elements of $g$ and two distinct vertices $x$ and $y$ are adjacent iff $(|x|,|y|)=1$. in this paper we classify all the groups which the coprime graph is a complete r-partite graph or a planar graph. also we study the automorphism group of the coprime graph.

In this paper, a new online robot motion planner is developed for systematically exploring unknown environ¬ments by intelligent mobile robots in real-time applications. The algorithm takes advantage of sensory data to find an obstacle-free start-to-goal path. It does so by online calculation of the Generalized Voronoi Graph (GVG) of the free space, and utilizing a combination of depth-first an...

in this paper, a new online robot motion planner is developed for systematically exploring unknown environâ¬ments by intelligent mobile robots in real-time applications. the algorithm takes advantage of sensory data to find an obstacle-free start-to-goal path. it does so by online calculation of the generalized voronoi graph (gvg) of the free space, and utilizing a combination of depth-first an...

Motion planning for mobile vehicles involves the solution of two disparate sub-problems: the satisfaction of highlevel logical task specifications and the design of low-level vehicle control laws. A hierarchical solution of these two sub-problems is efficient, but may not ensure compatibility between the highlevel planner and the dynamic constraints of the vehicle. To guarantee such compatibili...

We examine the issues that arise in extending an estimatedregression (ER) planner to reason about autonomous processes that run and have continuous and discrete effects without the planning agent’s intervention (although the planner may take steps to get processes running). An ER planner is a classical planner that searches situation space, using as a heuristic numbers derived from a backward s...

During the planning process, a planner may have many options for refinements to perform on the plan being developed. The planner’s efficiency depends on how it chooses which refinement to do next. Recent studies have shown that several versions of the popular “least commitment” plan refinement strategy are often outperformed by a fewest alternatives first (FAF) strategy that chooses to refine t...

| We describe a global motion planner for manipulating 3D objects by a dextrous multi-ngered robotic hand. We focus on the so-called re-connguration problem: nd a feasible quasi-static trajectory (motions and contact forces) that moves a hand-object system from an initial grasp to a nal desired connguration of the object. The planner is designed as a two-level process combining a graph search o...

In this article, we consider path planning for car-like robots in a new way, adding a continuous-curvature condition to the paths. As the optimal paths are too complex to be used, we deene a type of continuous-curvature paths inspired of the Dubins' curves. These paths contain at most seven pieces, each piece being either a line segment, a circular arc or a clothoid arc (a clothoid is a curve w...

| We describe a global motion planner for manipulating 3D objects by a dextrous robotic hand. We focus on the so-called re-connguration problem: nd a feasible trajectory (motions and contact forces) that moves a hand-object system from an initial grasp to a nal desired connguration of the object. The planner is designed as a three-level process combining a graph search on the conngu-ration spac...