Some Advanced Techniques in Reducing Time for Path Planning Based on Visibility Graph

This paper describes some techniques based on polygon aggregation in reducing time for visibility graph in case of many obstacles. In path planning, the approaches are commonly used such as search-based, sampling-based or combinatorial planning. And visibility graph is one of the roadmaps of combinatorial planning. Building a visibility graph is a main phase in the whole process and theoretically it takes θ(nlogn). However, with some practical applications, for example one which has a large number of obstacles, this phase is very time-consuming. With the techniques proposed, the experiment result shows that the computing time gets a reduction factor of one-third approximately when the aggregation are used in preprocessing of building visibility graph.

[1]  Samuli Laine.  A general algorithm for output-sensitive visibility preprocessing , 2005, I3D '05.

[2]  Joseph S. B. Mitchell,et al.  Two-point Euclidean shortest path queries in the plane , 1999, SODA '99.

[3]  Joseph S. B. Mitchell,et al.  Shortest paths among obstacles in the plane , 1993, SCG '93.

[4]  Andrew Chi-Chih Yao,et al.  On Constructing Minimum Spanning Trees in k-Dimensional Spaces and Related Problems , 1977, SIAM J. Comput..

[5]  M. H. Overmars.  Construction of sparse visibility graphs , 1987 .

[6]  Magnus Egerstedt,et al.  Oriented visibility graphs: low-complexity planning in real-time environments , 2006, Proceedings 2006 IEEE International Conference on Robotics and Automation, 2006. ICRA 2006..

[7]  Der-Tsai Lee.  Proximity and reachability in the plane. , 1978 .

[8]  Tomás Lozano-Pérez,et al.  An algorithm for planning collision-free paths among polyhedral obstacles , 1979, CACM.

[9]  Subhash Suri,et al.  Efficient computation of Euclidean shortest paths in the plane , 1993, Proceedings of 1993 IEEE 34th Annual Foundations of Computer Science.

[10]  J. Kitzinger.  The Visibility Graph Among Polygonal Obstacles: a Comparison of Algorithms , 2003 .

[11]  Mark H. Overmars,et al.  New methods for computing visibility graphs , 1988, SCG '88.

[12]  Se-Jong Oh,et al.  A New Concave Hull Algorithm and Concaveness Measure for n-dimensional Datasets , 2012, J. Inf. Sci. Eng..

[13]  H. Alt,et al.  Visibility graphs and obstacle-avoiding shortest paths , 1988, ZOR Methods Model. Oper. Res..

[14]  Xiaojun Shen,et al.  A Tight Lower Bound on the Size of Visibility Graphs , 1987, Inf. Process. Lett..

[15]  Emo WELZL,et al.  Constructing the Visibility Graph for n-Line Segments in O(n²) Time , 1985, Inf. Process. Lett..

[16]  David M. Mount,et al.  An Output Sensitive Algorithm for Computing Visibility Graphs , 1987, FOCS.