Motion Planning for Unlabeled Discs with Optimality Guarantees

We study the problem of path planning for unlabeled (indistinguishable) unit-disc robots in a planar environment cluttered with polygonal obstacles. We introduce an algorithm which minimizes the total path length, i.e., the sum of lengths of the individual paths. Our algorithm is guaranteed to find a solution if one exists, or report that none exists otherwise. It runs in time $\tilde{O}(m^4+m^2n^2)$, where $m$ is the number of robots and $n$ is the total complexity of the workspace. Moreover, the total length of the returned solution is at most $\text{OPT}+4m$, where OPT is the optimal solution cost. To the best of our knowledge this is the first algorithm for the problem that has such guarantees. The algorithm has been implemented in an exact manner and we present experimental results that attest to its efficiency

Comparative analysis of firefly algorithm for solving optimization problems

Firefly algorithm was developed by Xin-She Yang [1] by taking inspiration from flash light signals which is the source of attraction among fireflies for potential mates. All the fireflies are unisexual and attract each other according to the intensities of their flash lights. Higher the flash light intensity, higher is the power of attraction and vice versa. For solving optimization problem, the brightness of flash is associated with the fitness function to be optimized. The light intensity I (r) of a firefly at distance r is given by equation (1

06421 Abstracts Collection -- Robot Navigation

From 15.10.06 to 20.10.06, the Dagstuhl Seminar 06421 ``Robot Navigation\u27\u27generate automatically was held in the International Conference and Research Center (IBFI), Schloss Dagstuhl. During the seminar, several participants presented their current research, and ongoing work and open problems were discussed. Abstracts of the presentations given during the seminar as well as abstracts of seminar results and ideas are put together in this paper. The first section describes the seminar topics and goals in general. Links to extended abstracts or full papers are provided, if available

A motion planner for nonholonomic mobile robots

This paper considers the problem of motion planning for a car-like robot (i.e., a mobile robot with a nonholonomic constraint whose turning radius is lower-bounded). We present a fast and exact planner for our mobile robot model, based upon recursive subdivision of a collision-free path generated by a lower-level geometric planner that ignores the motion constraints. The resultant trajectory is optimized to give a path that is of near-minimal length in its homotopy class. Our claims of high speed are supported by experimental results for implementations that assume a robot moving amid polygonal obstacles. The completeness and the complexity of the algorithm are proven using an appropriate metric in the configuration space R^2 x S^1 of the robot. This metric is defined by using the length of the shortest paths in the absence of obstacles as the distance between two configurations. We prove that the new induced topology and the classical one are the same. Although we concentrate upon the car-like robot, the generalization of these techniques leads to new theoretical issues involving sub-Riemannian geometry and to practical results for nonholonomic motion planning

A Robot Navigation Algorithm for Moving Obstacles

In recent years, considerable progress has been made towards the development of intelligent autonomous mobile robots which can perform a wide variety of tasks. Although the capabilities of these robots vary significantly, each must have the ability to navigate within its environment from a starting location to a goal without experiencing collisions with obstacles in the process - a capability commonly referred to as robot navigation . Numerous algorithms for robot navigation have been developed which allow the robot to operate in static environments. However, little work has been accomplished in the development of algorithms which allow the robot to navigate in a dynamic environment. This thesis presents a mathematically-based navigation algorithm for a robot operating in a continuous-time environment inhabited by moving obstacles whose trajectories and velocities can be detected. In this methodology, the obstacles are represented as sheared cylinders to depict the areas swept out by the obstacle disks of influence over time. The robot is represented by the cone of positions it can reach by traveling at a constant speed in any direction. The methodology utilizes a three-dimensional navigation planning approach in which the search points, or tangent points, are the points in time at which the robot tangentially meets the obstacles. These tangent points are determined by calculating the intersection curves between the robot and the obstacles, and then using the first derivative of the intersection curves to make the tangent selections. Paths are created as sequences of these tangent points leading from the robot starting location to the goal, and are searched using the A* strategy, with a heuristic of the Euclidean distance from the tangent point to the goal. The main contribution of this thesis is the development of a methodology which produces optimal tangent paths to the goal for a dynamic robot environment. This feature is significant, since no other algorithm located in the literature survey as background to this thesis has shown the ability to produce paths with optimal properties