A locally optimal fast obstacle-avoiding path-planning algorithm (original) (raw)

Shortest Paths Among Obstacles in the Plane

International Journal of Computational Geometry & Applications, 1996

We give a subquadratic (O(n3/2+∊) time and O(n) space) algorithm for computing Euclidean shortest paths in the plane in the presence of polygonal obstacles; previous time bounds were at least quadratic in n, in the worst case. The method avoids use of visibility graphs, relying instead on the continuous Dijkstra paradigm. The output is a shortest path map (of size O(n)) with respect to a given source point, which allows shortest path length queries to be answered in time O( log n). The algorithm extends to the case of multiple source points, yielding a method to compute a Voronoi diagram with respect to the shortest path metric.

An efficient algorithm for Euclidean shortest paths among polygonal obstacles in the plane

Discrete and Computational …, 1997

1Department of Computer Science and Engineering, Indian Institute of Technology, Hauz Khas, New Delhi, India {skapoor, snm}@cse.iitd.ernet.in 2Department of Applied Mathematics and Statistics, State University of New York, Stony Brook, NY 11794–3600, USA ...

Computing Shortest Paths in the Plane with Removable Obstacles

2018

We consider the problem of computing a Euclidean shortest path in the presence of removable obstacles in the plane. In particular, we have a collection of pairwise-disjoint polygonal obstacles, each of which may be removed at some cost c_i > 0. Given a cost budget C > 0, and a pair of points s, t, which obstacles should be removed to minimize the path length from s to t in the remaining workspace? We show that this problem is NP-hard even if the obstacles are vertical line segments. Our main result is a fully-polynomial time approximation scheme (FPTAS) for the case of convex polygons. Specifically, we compute an (1 + epsilon)-approximate shortest path in time O({nh}/{epsilon^2} log n log n/epsilon) with removal cost at most (1+epsilon)C, where h is the number of obstacles, n is the total number of obstacle vertices, and epsilon in (0, 1) is a user-specified parameter. Our approximation scheme also solves a shortest path problem for a stochastic model of obstacles, where each ...

A Fast Algorithm for Planning Collision-Free Paths With Rotations

Journal of Mechanical Design, 1998

Motion planning is a major problem in robotics. The objective is to plan a collision-free path for a robot moving through a workspace populated with obstacles. In this paper, we present a fast and practical algorithm for moving a convex polygonal robot among a set of polygonal obstacles with translations and rotations. The running time is O(c((n + k)N + n log n)), 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 work builds upon the slabbing method proposed by Ahrikencheikh et al. [2], which finds an optimal motion for a point among a set of nonoverlapping obstacles. Here, we extend the slabbing method to the motion planning of a convex polygonal robot with translations and rotations, which also allows overlapping configuration space obstacles. This algorithm has been fully implemented an...

An Optimal Algorithm for Euclidean Shortest Paths in the Plane

SIAM Journal on Computing, 1999

We propose an optimal-time algorithm for a classical problem in plane computational geometry: computing a shortest path between two points in the presence of polygonal obstacles. Our algorithm runs in worst-case time O(n logn) and requires O(n logn) space, where n is the total number of vertices in the obstacle polygons. The algorithm is based on an e cient implementation of wavefront propagation among polygonal obstacles, and it actually computes a planar map encoding shortest paths from a xed source point to all other points of the plane; the map can be used to answer singlesource shortest path queries in O(logn) time. The time complexity of our algorithm is a signi cant improvement over all previously published results on the shortest path problem. Finally, we also discuss extensions to more general shortest path problems, involving non-point and multiple sources.

Rectilinear Shortest Paths Through Polygonal Obstacles in O(n (log n)2) Time

Symposium on Computational Geometry, 1987

The problem of finding a rectilinear shortest pathamongst obstacles may be stated as follows: Given a set ofobstacles in the plane find a shortest rectilinear (L 1 ) path from apoint s to a point t which avoids all obstacles. The path maytouch an obstacle but may not cross an obstacle. We study therectilinear shortest path problem for the case

Minimum-link paths among obstacles in the plane

Algorithmica, 1992

Given a set of nonintersecting polygonal obstacles in the plane, the link distance between two points s and t is the minimum number of edges required to form a polygonal path connecting s to t that avoids all obstacles. We present an algorithm that computes the link distance (and a corresponding minimum-link path) between two points in time O(E (n) log 2 n) (and space O(E)), where n is the total number of edges of the obstacles, E is the size of the visibility graph, and (n) denotes the extremely slowly growing inverse of Ackermann's function. We show how to extend our method to allow computation of a tree (rooted at s) of minimum-link paths from s to all obstacle vertices. This leads to a method of solving the query version of our problem (for query points t).

A Geometric Path-Planning Algorithm in Cluttered Planar Environments Using Convex Hulls

Volume 2B: 44th Design Automation Conference, 2018

The problem of finding a collision free path in an environment occupied by obstacles, known as path planning, has many applications in design of complex systems such as wire routing in automobile assemblies or motion planning for robots. Developing the visibility graph of the workspace is among the first techniques to address the path-planning problem. The visibility algorithm is efficient in finding the global optimal path. However, it is computationally expensive as it explores the entire workspace of the problem to create all non-intersecting segments of the graph. In this paper, we propose an algorithm based on the notion of convex hulls to generate the partial visibility graph from a given start point to a goal point in a 2D workspace cluttered with a number of disjoint polygonal convex or concave obstacles. The algorithm facilitates the attainment of the shortest path in a planar workspace while reducing the size of the visibility graph to explore.

Minimal Construct: Efficient Shortest Path Finding for Mobile Robots in Polygonal Maps

2018 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS)

With the advent of polygonal maps finding their way into the navigational software of mobile robots, the Visibility Graph can be used to search for the shortest collisionfree path. The nature of the Visibility Graph-based shortest path algorithms is such that first the entire graph is computed in a relatively time-consuming manner. Then, the graph can be searched efficiently any number of times for varying start and target state combinations with the A* or the Dijkstra algorithm. However, real-world environments are typically too dynamic for a map to remain valid for a long time. With the goal of obtaining the shortest path quickly in an ever changing environment, we introduce a rapid path finding algorithm-Minimal Construct-that discovers only a necessary portion of the Visibility Graph around the obstacles that actually get in the way. Collision tests are computed during an A* search only for lines that seem heuristically promising. This way, shortest paths can be found much faster than with a state-of-the-art Visibility Graph algorithm and as our experiments show, even grid-based A* searches are outperformed in most cases with the added benefit of smoother and shorter paths.