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Unformatted text preview: SplineBased Robot Navigation Evgeni Magid Applied Mathematics Technion  Israel Institute of Technology Haifa, Israel Email: evgenue@tx.technion.ac.il Daniel Keren Computer Science University of Haifa Haifa, Israel Email: dkeren@cs.haifa.ac.il Ehud Rivlin and Irad Yavneh Computer Science Technion  Israel Institute of Technology Haifa, Israel Email: { ehudr, irad } @cs.technion.ac.il Abstract This paper offers a path planning algorithm based on splines. The sought path avoids the obstacles, and is smooth and short. Smoothing is used as an integral part of the algorithm, and not only as a final improvement to a path found by other methods. In order to avoid a very difficult optimization over all the paths points, it is modeled by a sequence of splines defined by a gradually increasing number of knots. I. INTRODUCTION Motion planning is concerned with automatic planning of a collisionfree path between initial and final configurations. The classical motion planning problem, termed the piano movers problem , is defined for complete a priori information about the obstacles in the environment. The piano movers model is formulated as follows [15]. Given are a solid object of known size and shape in two or threedimensional space, its initial and target position and orientation, and a set of obstacles in the environment. The shapes, positions and orientations of the obstacles in space are fully described. The task is to find a continuous path for the object from its initial position to the target position, while avoiding collisions with obstacles along the way. Because full information is assumed, the whole operation of path planning is a onetime offline operation. The basic requirements become soundness (collision free path), completeness (guaranteed to find a path if it exists), optimality (being close to the optimal path) and complexity (time and space performance). The main difficulty of the piano movers model is to obtain a computationally efficient scheme. Searching is a fundamental component of piano movers conception. Given a search space, a set of possible problem states, and a state transition function to determine the states directly reachable from any given state, a search method is an algorithm to control the exploration of the state space in order to identify a path from an initial state to the goal. Given techniques to search a state space for a path, it remains to take an environment and to construct a state space to represent it [6]. A straightforward approach is to take a geometric representation of a free space and to discretize it (e.g., [2]). Other mechanisms of mapping the robots environment onto a discrete searchable space include visibility graph (e.g., [14]) and Voronoi diagram (e.g., [5]) construction techniques. Rather than searching through a discrete space that represent the state of the robot, an alternative is to model the configuration space of the robot as a continuous space. Path planning is considered as the appropriate trajectory within this continuum, modeled,...
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This note was uploaded on 08/03/2010 for the course MECHANIC 65921 taught by Professor Jons during the Spring '10 term at Tampa.
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