Abstract

One of the most important problems in robotics is motion planning problem, which its basic controversy is to plan a collision-free path between initial and target configurations for a robot. In the framework of motion planning for nonholonomic systems, the wheeled robots have attracted a significant amount of interest. The path planner of a wheeled autonomous robot has to meet nonholonomic constraints and then the movement direction must always be tangent to its trajectory (Paromtichk et. al., 1998; Latombe, 1991, Murray & Sastry, 1993; Lamiraux & Laumond, 2001; Scheuer & Fraichard, 1996). If no obstacles exist on path of the robot, then the robot task is finding the shortest path connecting two given initial and final configurations. The shortest paths for a car like vehicle consist of a finite sequence of two elementary components: arcs of circle (with minimum turning radii) and straight line segments. In any case, the problem is that the curvature is discontinuous between two elementary components, so that these shortest paths cannot be followed precisely without stopping at each discontinuity point to reorient the front wheels. To avoid these stops, several authors have proposed continuous-curvature path planners using differential geometric methods. These planners generate clothoids, cubic spirals, ┚-splines, quintic polynomials, etc., which are then followed by using a path-tracking technique based on, for example, pure-pursuit or predictive control methods (Lamiraux & Laumond, 2001; Scheuer & Fraichard, 1996). Stabilization issues of path-tracking methods for car-like vehicles using the Lyapunov method have been reported in (Walsh et. al., 1994; Tayebi & Rachid, 1996). One of the key technologies of future automobiles is the parking assist or automatic parking control. Control problems of a car-like vehicle are not easy because of the nonholonomic velocity constraints. The truck backer-upper control is a typical nonlinear control problem that cannot be solved by the conventional control techniques. The goal of controller is to back up a truck to a loading dock from any initial position as quickly and precisely as possible. Backing a truck to the loading dock or parking spot is a difficult task even for a skilled truck driver. The research in parking problem is derived from the study of general motion planning for autonomous robots. In the past few decades, many algorithms have been developed for robot parking planning (Jiang & Seneviratne, 1999; Gomez-Bravo et. al., 2001; Cuesta et. al., 2004; Reeds & Shepp, 1990). The attempts to

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