Iterative Relaxation of Constraints (IRC)

Can’t solve original Can solve relaxed

PRMs sample randomly but…

start

goal

C-obst

C-obst

C-obst

C-obst

difficult to sample points in small volume feasible regions

SolutionFind a solution to a relaxed version of the problem (larger volume feasible regions) and use that solution to help solve the original problem.

start

goal

C-obst

C-obst

C-obst

C-obst

start

goal

start

goal

start

goal

Relax constraints

Improve

Find aSolution

To relaxedVersion

•Relax feasibility constraints: set to minimal value

•Approximate solution: Find a valid solution for the current feasibility constraints

•Improve Solution:

•While (Original problem is not solved)• Strengthen feasibility constraints• Improve current solution

•End While

Feasibility Constraints:collision, penetration, energy

Enable the planner to concentrate on important areas by reducing region of C-space for planner to sample

• Virtual Prototyping• Check accessibility• Robot is rigid

• Deformable Objects• Avoid collisions by deforming• Robot changes its surface

• Ligand Binding• Generate candidate sites• Ligand is tree-like articulated robot

Applications of IRCAlgorithm

Virtual Prototyping – Domain I[Bayazit et.al. ICRA’00] [Bayazit.et.al. Autonomous Robots Journal‘01]

GIVEN A part in CAD/CAM DesignCHECK if the part is accessible from outside

Accessibility is checked by taking part outside the assembly

MotivationPhysical mock-ups are expensive and time consuming

•Approximate Solution: Find a path that may have collision ( solution to relaxed version)

•automated•manual

•Improving Approximate Solution: Push the colliding configurations to free space

• Use a scaled robot•Reduces the size of C-Space obstacles, increases the feasible regions

•Build a roadmap•Better connected then the original problem

•Query to find a path•Easier to find

obstacle

Original robot

Scaled robot (easier) Comparison

Automated Path Generation• User attaches haptic device to robot, and moves it around

•user feels when robot touches obstacles and adjusts trajectory•collision detection too slow (~10 Hz), so distribute process and use extrapolation techniques (almost all)

•Robot configurations passed to planner

• automatically sampled at regular intervals

C-obstacle

C-obstacle

pushedpath generated

by planner

approximatepath

• User or Planner generates approximate path P– it may contain collisions

• Planner “pushes” colliding portions of P to C-free– Both C-space and workspace techniques

are available

Ligand Binding – Domain II[Bayazit, Song, Amato, IEEE ICRA’01]

Given: a description of a ligand molecule (robot) and a protein (obstacle).

Find: a configuration of the ligand near the protein where geometric, electro-static and chemical constraints are satisfied.

protein

ligand

•Approximate Solution:

Generate sample nodes•automated•manual

•Improving Approximate Solution: Push nodes to local minima.

Use other researchers’ scoring functions to evaluate them.

•Generate a collision free base

•Find values for other joint angles for a collision free ligand

•Keep this configuration if the potential is less than Emax

Protein

Ligandbase

• Create a potential grid. Each grid cell contains contributions of protein atoms.

•Generate joint angles so that molecules stay in low potential grid cells.

•Keep this configuration if the potential is less than Emax.

• User attaches haptic device to ligand, and moves it around

• user feels the forces on ligand• ligand is rigid• force calculation is too slow, so use extrapolation techniques (grid potential)

• Ligand configurations (candidate sites) passed to planner

• automatically sampled at regular intervals when user indicated PHANToM

PHANToM haptic device gives a sense of touch through force feedback

0

1

2

3

4

5

6

7

5TIM

(6)

1ULB

(6)

3TPI(6

)

1A5Z(7

)

1LDM

(7)

2PHH(7

)

3PTB(7

)

6RSA(8

)

2CTC(9

)

5TLN

(10)

1STP(1

1)

4DFR(1

6)

1DW

C(17)

1DW

D(17)

4PHV(2

0)

Protein (dof)

RM

SD

Geometry-Based Energy-Based

Comparison of OBPRM-like generation methods for flexible ligandsDistance to Binding Configuration

*Tried by Singh et al.

• Able to generate conformations nearbinding conformation (usually < 4 Angstroms)

•No prior knowledge of protein is required

•Geometry-Based generation is usually better

* * *

• We have tested 15+ ligand/protein complexes– fully automated method is successful in generating

configurations in the binding site – the haptic user-input often helps speed up the

processing

• Next step is a more rigorous comparison to existing methods, and further refinement of our approach

• Need to refine haptic interface and understand potential benefit

• Need to score our conformations with existing scoring methods

• Our results (conformations) may be used as input to other automated docking programs - they are good at refining and ranking solutions

• Does a path contains valuable information related to destination configuration?

In all the applications, we first find an approximate solution and then improve it.

Manual Path Generation

Improving Solution

0

500

1000

1500

2000

2500

3000

3500

time (sec)

OBPRMhaptic pushiterative push

Flange Problem

0.85 0.95 1

Experimental Results

Automatic planners can effectively transform approximate paths to free paths

–faster than traditional PRMs

–iterative relaxation works well

Heuristic collision detection provides support for approximate path collection

–ok since we’re collecting approximate paths

Conclusion

Deformable Objects – Domain III[Bayazit, Lien, Amato, ICRA’02]

Given an object which can deform

Find a path taking object from start to goal. The object is allowed to deform to avoid collision.

•Approximate Solution: Find a path for rigid version, may have collision

•Improving Approximate Solution: Deform the robot to avoid collision

• Enable Penetration

– Use approximate C-Space penetration

• Use scaled robots

– More than one scaled model.

– Smaller (Bigger ) model needs more (less) deformation.

1. Build roadmap by relaxing collision free requirement

2. Extract Approximate Path

may not be feasible for the rigid robot

Bounding Box Deformation

build a 3D voxel bounding box.—Convert it to ChainMail bounding box (3D grid of springs)—Deform ChainMail Bounding box.—Deform objects using Free Form Deformation based of deformation of the bounding box.

Deformed ChainMail Bounding BoxObstacleChainMail Box Apply FFD

Geometric Deformation—Find the colliding surfaces —Move the colliding surfaces of the robot outside the obstacle—Smooth the robot

Colliding configurationBlue surface=obstacleRed surface=robot.

deformation

Approximate Solution

Automated Geometry Based

Automated Energy Based

Manual Node Generation

• Push nodes to local minima

• For each node sample n close nodes

• Choose the node with lowest potential among them

• Repeat until a local minima or iteration limit is reached

Improving Approximate Solution

Approximate Solution Improving Approximate Solution Experiments

Bounding Box

Geometric

Conclusion

Approximate Solution

Fully automated planner can only solve .85 scaled version. With user input, the solution time reduces.. 96 scaled version uses those results and solves the problem. The original problem is solved by using results of .95.

Goal

Robot

Start

Deformable VersionOriginal Problem

Penetration Scaled Robot

Experiments