Collision-free path planning

Motion planning is an important challenge in robotics research. Efficient generation of collision-free motion is a fundamental capability necessary for autonomous robots;In this dissertation, a fast and practical algorithm for moving a convex polygonal robot among a set of polygonal obstacles with translations and rotations is presented. The running time is O(c((n + k)N + nlogn)), where c is a parameter controlling the precision of the results, n is the total number of obstacle vertices, k is the number of intersections of configuration space obstacles, and N is the number of obstacles, decomposed into convex objects. This dissertation exploits a simple 3D passage-network to incorporate robot rotations as an alternative to complex cell decomposition techniques or building passage networks on approximated 3D C-space obstacles;A common approach in path planning is to compute the Minkowski difference of a polygonal robot model with the polygonal obstacle environment. However such a configuration space is valid only for a single robot orientation. In this research, multiple configuration spaces are computed between the obstacle environment and the robot at successive angular orientations spanning [pi] . Although the obstacles do not intersect, each configuration space may contain intersecting configuration space obstacles (C-space obstacles). For each configuration space, the algorithm finds the contour of the intersected C-space obstacles and the associated passage network by slabbing the collision-free space. The individual configuration spaces are then related to one another by a heuristic called proper links that exploit spatial coherence. Thus, each level is connected to the adjacent levels by proper links to construct a 3D network. Dijkstra\u27s algorithm is used to search for the shortest path in the 3D network. Finally, the path is projected onto the plane to show the final locus of the path

Algorithmic Motion Planning and Related Geometric Problems on Parallel Machines (Dissertation Proposal)

The problem of algorithmic motion planning is one that has received considerable attention in recent years. The automatic planning of motion for a mobile object moving amongst obstacles is a fundamentally important problem with numerous applications in computer graphics and robotics. Numerous approximate techniques (AI-based, heuristics-based, potential field methods, for example) for motion planning have long been in existence, and have resulted in the design of experimental systems that work reasonably well under various special conditions [7, 29, 30]. Our interest in this problem, however, is in the use of algorithmic techniques for motion planning, with provable worst case performance guarantees. The study of algorithmic motion planning has been spurred by recent research that has established the mathematical depth of motion planning. Classical geometry, algebra, algebraic geometry and combinatorics are some of the fields of mathematics that have been used to prove various results that have provided better insight into the issues involved in motion planning [49]. In particular, the design and analysis of geometric algorithms has proved to be very useful for numerous important special cases. In the remainder of this proposal we will substitute the more precise term of algorithmic motion planning by just motion planning

An Algorithmic Framework for Robot Navigation in Unknown Terrains.

The problem of navigating a robot body through a terrain whose model is a priori known is well-solved problem in many cases. Comparatively, a lesser number of research results have been reported about the navigation problem in unknown terrains i.e., the terrains whose model are not a priori known. The focus of our work is to obtain an algorithmic framework that yields algorithms to solve certain navigational problems in unknown terrains. We consider a finite-sized two-dimensional terrain populated by a finite set of obstacles $O$ = \{O\sb1,O\sb2,\...,O\sb{n}\} where O\sb{i} is a simple polygon with a finite number of vertices. Consider a circular body R, of diameter $\delta\geq$ O, capable of translational and rotational motions. R houses a computational device with storage capability. Additionally, R is equipped with a sensor system capable of detecting all visible vertices and edges. We consider two generic problems of navigation in unknown terrains: the Visit Problem, VP, and the Terrain model acquisition Problem, TP. In the visit problem, R is required to visit a sequence of destination points d\sb1,d\sb2,\...,d\sb{M} in the specified order. In the terrain model acquisition problem, R is required to acquire the model of the terrain so that it can navigate to any destination without using sensors and by using only the path planning algorithms of known terrains. We present a unified algorithmic framework that yields correct algorithms to solve both VP and TP. In this framework, R \u27simulates\u27 a graph exploration algorithm on an incrementally-constructible graph structure, called the navigation course, that satisfies the properties of finiteness, connectivity, terrain-visibility and local-constructibility. Additionally, we incorporate the incidental learning feature in our solution to VP so as to enhance the performance. We consider solutions to VP and TP using navigation courses based two geometric structures, namely the visibility graph and the Voronoi diagram. In all the cases, we analyze the performance of the algorithms for VP and TP in terms of the number of scan operations, the distance traversed and the computational complexity