1. By Lydia E. Kavraki, Petr Svestka, Jean-Claude Latombe, Mark H. Overmars Emre Dirican - 3440796

2.  Introduction  Related Work  The General Method  Customization of the Method  Experiments  Results  Conclusions and Assesments  Questions

3.  Collision-free paths for robots  Static workspace  Two phase approach  The learning phase ◦ Generate random free configurations ◦ Connect by a local planner  The query phase ◦ Find a path from start to goal

4.  Experiments: robots with many DoFs  Efficient, reliable, practical planner  Local methods can be engineered further

5.  Potential Field Methods ◦ Local minima ◦ Computationaly expensive solutions ◦ Impractical as the DoFs increase  Randomized Path Planner (RPP) ◦ To escape local minima ◦ Problems with narrow passages

6.  Single shot roadmap methods ◦ Visibility graphs, Voronoi diagrams, Silhoutte ◦ Either, limited to low dimensional spaces ◦ Or, Less practical  Differences/Extensions ◦ Many-DoF robots ◦ Connectivity

7.  The Learning Phase ◦ Construction Step: uniform undirected graph ◦ Expansion Step: increase connectivity  The Query Phase ◦ Connect start(s) and goal(g) positions ◦ Find a path between s and g ◦ Assumption: Query after the learning

8.  Construction Step ◦ The graph, R = (N,E) ◦ N: the set of configurations over C-free ◦ E: the edges (paths) between two configurations ◦ Repeatedly, generate random configurations ◦ By local planner, connect a node to some others and add them to E.

9.  Construction Algorithm D: a distance function Δ: a function to check whether a path exists or not

10.  Creating random configurations: ◦ Draw coordinates using uniform probability distribution over the intervals of DoFs ◦ Check for collisions:  An obstacle  Bodies of the robot ◦ Add to N if collision free

11.  Local Path Planner: ◦ Slow (powerful) vs. fast  Used also in query phase  Need fast response ◦ Deterministic vs. nondeterministic  Need to store local paths with nondeterministic ◦ Line segment between configurations  m discrete configurations on the line  Path is collision free if all m configurations are

12.  Choosing neighbor nodes: ◦ bounded by a max. number of neighbors  The distance function (D): Where x is a point on the robot.

13.  The Expansion Step ◦ Increase the density of the roadmap around difficult regions, i.e. narrow passages ◦ Short random-bounce walks  Pick a random direction from a configuration(c),  Move until a collision occurs,  Add new configuration and the edge to the graph,  Take new direction, repeat.

14.  Selection of configurations to expand ◦ For each node, a failure ratio is computed: ◦ Then, a weight, proportional to failure ratio is: n(c) : number of times tried to connect f(c) : number of times failed

15.  Connect start(s) and goal(g) configurations ◦ Similar to construction phase ◦ Try to connect, by an increasing distance:  s to s’ on R  g to g’ on R ◦ Recompute, concatenate the local paths from s’ to g’

16.  Connection failure ◦ Random-bounce walks  Frequent query failures ◦ Connectivity on C-free ◦ Increase time spent on learning phase

17.  Application to Planar Articulated Robots ◦ Customization with respect to joints at:  Local path planning  Distance computation ◦ Customization at collision checking  3D bitmaps to represent each link in 2D workspace  Check against the C-space bitmap

18.  Customized method with articulated robots ◦ 2-D Scenes ◦ Each scene with 8 different configurations ◦ Trying to connect to 30 generated roadmaps ◦ In 2.5 secs of query time ◦ Attempt to connect to largest component of the roadmap : Time spent on construction step  : Time spent on expansion step

19.  Scene 1: Fixed based 7-DoF articulated robot

20. With expansion and No expansion

21. Many collision checks, because of random-bounce walks before connection to roadmap Connecting configurations to one roadmap

22.  Scene 2: Free based 7-DoF articulated robot

23. With expansion and No expansion

24.  The general method with articulated robots ◦ 2-D scenes ◦ 2 scenes, start and goal configuration ◦ Attempt to connect to 30 roadmaps ◦ 2.5 secs of query times

25.  Scene 3: 4 DoF articulated robot (left)  Scene 4: 5 DoF articulated robot (right)  Dark grey – Start configuration  White – Goal configuration

26.  Results for Scene 3 and 4  Results for Scene 1

27.  Efficient in relatively complex 2D problems  Deals with many-DoF robots  Better query times compared to Randomized Path Planner (RPP) method  Customizable in local methods  Future work: Dynamic changes

28.  Assumption: Interwoven learning and query phases ◦ Not much detail or results.  Applicable to 3D environments? ◦ Learning time increases ( in order of minutes) ◦ Still efficient enough?

29.  Similar approach used for car-like robots by Svetska and Overmars, 1994 ◦ Flexible – local method customizations ◦ Efficient, but again in 2D ◦ Path planning with straight lines  Lack of smooth motions

30.  Comparative studies and analysis for PRM by Geraerts and Overmars, 2002 and 2007 ◦ Connectivity in difficult regions  Handled by random-bounce walks ◦ Choice of techniques on local methods becomes important  Dependant on scenes or robot  Easy to implement and use? ◦ Still needs customizations

31.  Thanks for your patience.  Any questions or remarks?