Online RRT* and Online FMT*: Rapid Replanning with Dynamic Cost

Bryant Chandler and Michael A Goodrich


Computer Science Department

Brigham Young University

How do you plan for this?

RRT - Rapidly Exploring Random Tree

  1. Randomly sample a point
  2. Find the nearest neighbor
  3. Create a new node, no longer than max segment from nearest neighbor in the direction of the sampled point
  4. Connect to nearest neighbor as parent

RRT* (* for optimal)

  1. A point is sampled and all nodes in a neighborhood are found
  2. The neighbor that would provide the lowest cost is selected and becomes parent of sampled point
  3. All other neighbors are checked to see if they would reduce cost by rewiring to the new node as their parent

RRT* Replanning Limitation

  1. Robot starts at red headed to purple
  2. At green it realizes that it really wants to go to blue
  3. The only way to get there is to replan (expensive)

FMT* - Fast Marching Tree

Online RRT* and Online FMT*

  • Requirements
    • Allow both start and end points to move
    • Sample indefinitely without becoming intractible
    • Support dynamic cost
  • Solution
    • Run RRT* or FMT* to saturate configuration space
      • A fixed threshold based on area
    • Continue sampling and rewiring without adding new nodes

Online Rewiring

Sample a point (highlighted in pink) and find all nodes in its neighborhood

Find the node in the neighborhood that has the lowest cost (blue)

Rewire all neighbors to the best node if it would improve their cost

Move Start Point

A tree with the start node as a square

A new start node (blue square) is made parent of the original and its neighbors are found

Neighbors are rewired to the new start node

Impact on # of Nodes

  • Moving the start point acts like a memory leak
  • Eventually becomes a significant problem

Online Pruning

Prune a leaf node in the vicinity of the new root after moving start

Is it fast enough?

The performance of OFMT* and ORRT* is comparable to A* on a visibility graph

Does pruning create bias?

The best pruning radius was 0.7 units

Time-Varying Cost

Hide from others

High cost of being seen

Fixed start and end point

How close to optimal?

ORRT*

OFMT*

Both algorithms do quite well, but OFMT* appears to be more efficient at adjusting the tree

Conclusions

  • Developed path planning algorithms that extend RRT* and FMT* by:
    • Affording rapid replanning with a moving start
    • Affording path adjustment to account for time-varying cost
  • Complete and approximately optimal

Acknowledgement

This work has been partially funded by the Center for Unmanned Aircraft Systems (C-UAS), a National Science Foundation-sponsored industry/university cooperative research center (I/UCRC) under NSF Award No. IIP-1161036 along with significant contributions from C-UAS industry members.

 

The work was also partially funded by the Robotics Collaborative Technology Alliance.

ORRT* and OFMT*

By Mike Goodrich

Source: Bryant Chandler

ORRT* and OFMT*

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