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

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

Outline

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

Introduction 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

Related Work

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

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

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

Construction Algorithm

The Learning Phase - Step 1

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

The Learning Phase - Step 1

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

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.

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

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

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

Connection failure◦ Random-bounce walks

Frequent query failures◦ Connectivity on C-free◦ Increase time spent on learning phase

The Query 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

Customization of the Method

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

Scene 1: Fixed based 7-DoF articulated robot

Results – Customized Method

Results – Customized Method

With expansion and No expansion

Results – Customized Method

•Many collision checks, because of random-bounce walks before connection to roadmap

• Connecting configurations to one roadmap

Scene 2: Free based 7-DoF articulated robot

Results – Customized Method

Results – Customized Method

With expansion and No expansion

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

Scene 3: 4 DoF articulated robot (left) Scene 4: 5 DoF articulated robot (right)

Dark grey – Start configuration White – Goal configuration

Experiment

Results – General Method 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

Conclusions and Assesments

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

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

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

Thanks for your patience.

Any questions or remarks?

Questions