Probab ilistic Roadmaps for Path Planning in High-Dimensional Configuration Spaces
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Transcript of Probab ilistic Roadmaps for Path Planning in High-Dimensional Configuration Spaces
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Probabilistic Roadmaps for Path Planning in
High-Dimensional Configuration Spaces
By Lydia E. Kavraki, Petr Svestka, Jean-Claude Latombe, Mark H. Overmars
Emre Dirican - 3440796
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Introduction Related Work The General Method Customization of the Method Experiments Results Conclusions and Assesments Questions
Outline
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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
Introduction
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Introduction Experiments: robots with many DoFs
Efficient, reliable, practical planner
Local methods can be engineered further
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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
Related Work
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Single shot roadmap methods◦ Visibility graphs, Voronoi diagrams, Silhoutte ◦ Either, limited to low dimensional spaces ◦ Or, Less practical
Differences/Extensions◦ Many-DoF robots◦ Connectivity
Related Work
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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
The Method
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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.
The Learning Phase - Step 1
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Construction Algorithm
The Learning Phase - Step 1
D: a distance function
Δ: a function to check whether a path exists or not
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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
The Learning Phase - Step 1
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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
The Learning Phase - Step 1
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Choosing neighbor nodes:
◦ bounded by a max. number of neighbors
The distance function (D):
The Learning Phase - Step 1
Where x is a point on the robot.
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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.
The Learning Phase - Step 2
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Selection of configurations to expand◦ For each node, a failure ratio is computed:
◦ Then, a weight, proportional to failure ratio is:
The Learning Phase - Step 2
n(c) : number of times tried to connectf(c) : number of times failed
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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’
The Query Phase
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Connection failure◦ Random-bounce walks
Frequent query failures◦ Connectivity on C-free◦ Increase time spent on learning phase
The Query Phase
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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
Customization of the Method
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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
Experiment
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Scene 1: Fixed based 7-DoF articulated robot
Results – Customized Method
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Results – Customized Method
With expansion and No expansion
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Results – Customized Method
•Many collision checks, because of random-bounce walks before connection to roadmap
• Connecting configurations to one roadmap
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Scene 2: Free based 7-DoF articulated robot
Results – Customized Method
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Results – Customized Method
With expansion and No expansion
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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
Experiment
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Scene 3: 4 DoF articulated robot (left) Scene 4: 5 DoF articulated robot (right)
Dark grey – Start configuration White – Goal configuration
Experiment
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Results – General Method Results for Scene 3 and 4
Results for Scene 1
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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
Conclusions and Assesments
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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?
Conclusions and Assesments
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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
Conclusions and Assesments
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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
Conclusions and Assesments
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Thanks for your patience.
Any questions or remarks?
Questions