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

FMT* - Fast Marching Tree

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)

Online RRT* and Online FMT*

• Requirements
  • Allow both start and end points to move
  • Support dynamic cost
  • Sample indefinitely without becoming intractible
• 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

Move Start Point

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.