Presentation on theme: "By Lydia E. Kavraki, Petr Svestka, Jean-Claude Latombe, Mark H. Overmars Emre Dirican - 3440796."— Presentation transcript:
By Lydia E. Kavraki, Petr Svestka, Jean-Claude Latombe, Mark H. Overmars Emre Dirican - 3440796
Introduction Related Work The General Method Customization of the Method Experiments Results Conclusions and Assesments Questions
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
Experiments: robots with many DoFs Efficient, reliable, practical planner Local methods can be engineered further
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
Single shot roadmap methods ◦ Visibility graphs, Voronoi diagrams, Silhoutte ◦ Either, limited to low dimensional spaces ◦ Or, Less practical Differences/Extensions ◦ Many-DoF robots ◦ Connectivity
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
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.
Construction Algorithm D: a distance function Δ: a function to check whether a path exists or not
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
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
Choosing neighbor nodes: ◦ bounded by a max. number of neighbors The distance function (D): Where x is a point on the robot.
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.
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
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’
Connection failure ◦ Random-bounce walks Frequent query failures ◦ Connectivity on C-free ◦ Increase time spent on learning phase
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
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
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
Scene 3: 4 DoF articulated robot (left) Scene 4: 5 DoF articulated robot (right) Dark grey – Start configuration White – Goal configuration
Results for Scene 3 and 4 Results for Scene 1
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
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?
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
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
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