Two-dimensional motion-planning for nonholonomic robots using the bump-surfaces concept (original) (raw)

Flexible Path Planning for Nonholonomic Mobile Robots

This work presents a flexible path planning method for nonholonomic mobile robots. An intelligent planner based on a static map of the robot's environment has been developed. It comprises the possibility to set current robot properties on the fly and can therefore be used for many different mobile robots. The generated path is smoothened and eventually modified in reaction to dynamic obstacles or other external forces, using the method of elastic bands. This common algorithm has been extended for robots meeting the restrictions of a Dubin's car (nonholonomic robot that can only move forward).

Path Planning of Holonomic and Non-Holonomic Robots Using Bump-Surfaces

Computer-Aided Design and Applications, 2008

This paper presents a global solution to a general problem of planning an optimum path of a robot moving in two dimensional environments. The proposed method is able to deal with both holonomic and non-holonomic robots moving into dynamic 2D environments with static and/or moving obstacles. The proposed method is based on the Bump-Surfaces concept which is used to represent the entire robot's environment. The introduced method is general and easy to implement and can be applied virtually to any dimensional or point robot. The performance of the proposed method is investigated and discussed through selected simulated experiments.

Dynamic path modification for car-like nonholonomic mobile robots

Proceedings of International Conference on Robotics and Automation, 1997

In this paper, a method combining planning and reactive control for car-like nonholonomic mobile robots is discussed. Firstly, a "bubble" for a car-like mobile robot is defined as the locally reachable space from a given configuration considering the obstacles and using the appropriate metric. Then a flexible feasible trajectory, based on the elastic band concepts, is constructed. This trajectory is smoothed using Bezier curves satisfying a minimum curvature constraint, and a parameterization is proposed which satisfies the robot kinematics constraints.

A Shortest Path Based Path Planning Algorithm for Nonholonomic Mobile Robots

Journal of Intelligent and Robotic Systems - JIRS, 1999

A path planning algorithm for a mobile robot subject to nonholonomic constraints is presented. The algorithmemploys a global- local strategy, and solves the problem in the 2D workspace of the robot, without generating the complexconfiguration space. Firstly, a visibility graph is constructed for finding a collision-free shortest path for a point. Secondly,the path for a point is evaluated to find whether it can be used as a reference to build up a feasible path for the mobile robot.If not, this path is discarded and the next shortest path is selected and evaluated until a right reference path is found. Thirdly,robot configurations are placed along the selected path in the way that the robot can move from one configuration to the nextavoiding obstacles. Lemmas are introduced to ensure that the robot travels using direct, indirect or reversal manoeuvres. Thealgorithm is computationally efficient and runs in time O(nk + n log n) for k obstacles andn vertices. The path found is near opt...

Nonholonomic distance to polygonal obstacles for a car-like robot of polygonal shape

IEEE Transactions on Robotics, 2000

This paper shows how to compute the nonholonomic distance between a polygonal car-like robot and polygonal obstacles. The solution extends previous work of Reeds and Shepp by finding the shortest path to a manifold (rather than to a point) in configuration space. Based on optimal control theory, the proposed approach yields an analytic solution to the problem.

On motion planning of nonholonomic mobile robots

2000

ABSTRACT Mobile robots that consist of a mobile platform with one or many manipulators, are of great interest in a number of applications. This paper presents a methodology for generating paths and trajectories for both the mobile platform and the manipulator that will take a system from an initial configuration to a pre-specified final one, without violating the nonholonomic constraint. The generated paths are of polynomial nature and therefore are continuous and smooth.

Obstacle representation by Bump-surfaces for optimal motion-planning

Robotics and Autonomous Systems, 2005

This paper introduces a new method for global, near optimal, motion-planning of a robot (either mobile or redundant manipulator) moving in an environment cluttered with a priori known prohibited areas which have arbitrary shape, size and location. The proposed method is based on the novel notion of Bump-surfaces (or B-surfaces) which represent the entire robot environment through a single mathematical entity. The motion-planning solution is searched on a higher-dimension B-surface in such a way that its inverse image into the robot environment satisfies the given objectives and constraints. The computed solution for a mobile robot consists of a smooth curve without self-loops which connects the starting and destination points with the shortest possible path. The same approach is also used for nth degree-of-freedom manipulators where the end-effector reaches the destination position following a smooth short path avoiding the prohibited areas. For clarity reasons the proposed method is introduced in this paper for the case of a two-dimensional (2D) planar terrain with static obstacles, while a generalization to motion-planning problems on curved terrains is also discussed. Extensive experiments are presented and discussed to illustrate the efficiency and effectiveness of the proposed motion-planning method in a variety of complex environments.

Planning shortest bounded-curvature paths for a class of nonholonomic vehicles among obstacles

Journal of Intelligent and Robotic Systems, 1996

This paper describes a technique for path planning in environments cluttered with obstacles for mobile robots with nonholonomic kinematics and bounded trajectory curvature (i.e., limited turning radius). The method is inspired by the results of Reeds and Shepp regarding shortest paths of bounded curvature in absence of obstacles. It is proved that, under suitable assumptions, the proposed technique provides the shortest path of bounded curvature among polygonal objects for a particular class of vehicles (circular unicycles of radius h and minimum turning radius min h). Although the class of vehicles this theoretical result is restricted to is rather narrow, the proposed planner can be satisfactorily applied to other nonholonomic vehicles yielding good practical results.

Nonholonomic, bounded curvature path planning in cluttered environments

1995

The problem of planning a path for a robot vehicle amidst obstacles is considered. The kinematics of the vehicle being considered are of the unicycle or car-like type, i.e. are subject to nonhcJonomic constraints. Moreover, the trajectories of the robot are supposed not to exceed a iven bound on curvature, that incorporates physical limitations of the allowable minimum turning radius for the vehicle. The presented method attempts at extending Reeds and Shepp's results on shortest paths of bounded curvature in absence of obstacles, to the case where obstacles are present in the workspace. The method does not require explicit construction of the configuration space, nor employs a preliminary phase of holonomic trajectory planning. Successfull outcomes of the proposed technique are paths consisting of a simple composition of Reeds/Shepp paths that solves the problem. For a particular vehicle shape, the path provided by the method, if regular, is also the shortest feasible path. In its original version, however, the method may fail to find a path, even though one may exist (path-completeness not guaranteed). Most such empasses can be overcome by use of a few simple heuristics suggested in the text. Applications to both unicycle and car-like (bicycle) mobile robots of general shape are described and their performance and practicality discussed.

Nonholonomic Motion Planning Using the Fast Marching Square Method

International Journal of Advanced Robotic Systems, 2015

This research presents two novel approaches to nonholonomic motion planning. The methodologies presented are based on the standard fast marching square path planning method and its application to car-like robots. Under the first method, the environment is considered as a three-dimensional C-space, with the first two dimensions given by the position of the robot and the third dimension by its orientation. This means that we operate over the configuration space instead of the bi-dimensional environment map. Moreover, the trajectory is computed along the C-space taking into account the dimensions of the vehicle, and thus guaranteeing the absence of collisions. The second method uses the standard fast marching square, and takes advantage of the vector field of the velocities computed during the first step of the method in order to adapt the motion plan to the control inputs that a car-like robot is able to execute. Both methods ensure the smoothness and safety of the calculated paths in...