1. A Randomized Approach to Robot Path Planning Based on Lazy Evaluation Robert Bohlin, Lydia E. Kavraki (2001) Presented by: Robbie Paolini

2. Robot Path Planning Goals Plan in new configuration spaces instantly – Avoid long preprocessing times Planning time should relate to difficulty Time should relate to quality of solution Planner should “learn” – Use info from previous queries to speed up subsequent plans

3. Probabilistic Roadmap Construct a network of paths (a roadmap) verified to be collision free Hard to find global strategy to plan efficiently Complex geometry and expensive collision checks => long planning times – A lot of it unnecessary PRMs satisfy most of our goals, but are still too slow

4. Lazy PRM Avoid local planners as much as possible – Keep a global view throughout planning Only check for collisions when we have to Theme: In terms of collision checking, it is ALWAYS advantageous to use a lazy evaluation, since we can never do more work than a basic PRM

5. Lazy PRM

6. Building the Initial Roadmap Distribute N nodes uniformly at random For PRM, choice of N is important For Lazy PRM, we only check for collisions on a small number of nodes, so less sensitive to N

7. Building the Initial Roadmap Where do we add edges? Add edges to nodes close enough together For a manipulator, use a weighted Euclidean metric

8. Searching for the Shortest Path A* to find the best path in the graph Authors use a weighted Euclidean Metric Could also consider other metrics – Power consumption, dynamic forces on joints, smooth paths…

9. Checking Paths for Collisions Want to remove colliding nodes and edges efficiently Remove nodes first, then edges Check nodes at ends of path and work towards the center 1 2 3 4 5 6

10. Checking Paths for Collisions Check edges in similar order as nodes Start at a given resolution, work inward, increase resolution, work inward Store all collision checks for later use 1 2 34 5

11. Lazy PRM in Action

13. Node Enhancement If no path is found, we need to create new nodes. Where? We can use leftover roadmap to guide us! Generate nodes around midpoints of removed edges To avoid overfitting, randomly add nodes as well

14. Multiple Queries Storing collision checks => immediate benefit Even in the long run, after many queries, many nodes may never be explored Lazy PRM will find the shortest feasible path with less collision checks than a PRM!

15. Both PRM and Lazy PRM give bounds on failure probability related to node density PRM: Node density in Lazy PRM: Node density in However, PRM generates nodes in and then checks if in, so density is the same AND: Lazy PRM doesn’t even check all nodes Probabilistic Completeness

16. Experiments Industrial manipulator in realistic environment Planning time breakdown: – Collision Checking: 79% – Graph Building: 19% – Graph Searching: 2% Entire roadmap: 500,000 collision checks – Lazy PRM (average): 92 to 693 checks (<0.1%) 27% of collision checks are on solution path

17. Discussion Lazy PRMs are especially good if collision checking is expensive – If cheap, should remove several nodes each collision check to reduce graph search time Excellent performance in low clutter – In high clutter, check collision of nodes before adding it to roadmap (but not edges) PRMs face same issues as Lazy PRMs, but they also collision check entire roadmap

18. Future Work Understand how N affects Lazy PRM Make algorithm more robust to decrease worst case performance More testing of node enhancement, see how it does in cheap collision checking, high clutter environments Trying many paths next to each other could be a waste… but then we’re at the mercy of heuristics.