From Robots to Molecules: Intelligent Motion Planning & Analysis

with Probabilistic Roadmaps Lydia Tapia

Department of Computer Science University of New Mexico

What is motion planning?   Find a valid path from a start to a goal for a movable

object

valid = collision-free

valid = low energy

start goal

obstacles

Motions: Robots, Graphics, Molecules   What do all of these have in

common?

Flocking Drug docking

Deformation

Shepherding

Protein folding Paper folding

Manipulators

  They are all examples of the motion planning problem   They can all be solved with the same framework!

Closed chains

Mobile robots

Molecular Motion Modeling Objective: Model Protein and RNA folding and kinetics; study kinetics-based functions; better understand diseases caused by misfolding

Project: Intelligent techniques to model and analyze Protein and RNA folding and kinetics

Motion Planning for many Problems My Projects

RNA Folding Protein Folding

[CIS 10,JMB 08, Bioinformatics 07; JCB 07; RECOMB 07; RECOMB 06]

Intelligent Robotic Movement in Complex Spaces Objective: Adapt based on complexity of space

Project: Integrating machine learning techniques with a library of planning methods in order to decide where and when to apply specific planners

[ICRA 09; ICRA 05; WAFR 04]

Why Study Folding Pathways?

Importance of Studying Pathways –  Insight into protein interactions & function

–  May lead to better structure prediction algorithms –  Diseases such as Alzheimer’s & Mad Cow

related to misfolded proteins

Computational Techniques Critical –  Hard to study experimentally (happens too fast) –  Can study folding for thousands of already

solved structures –  Help guide/design future experiments

normal - misfold

prion protein

Robot in plane

Motion Planning Framework Robot Abstraction   How can we develop a single framework to solve all of

these different problems?

Point in 3D m robots in plane Molecule

α β γ

Manipulator

(x,y,z,pitch,roll,yaw) (α,β,γ)

(x,y,z)

(x,y,θ) m*(x,y,θ)

(φ1, ψ1, φ2, ψ2, ..., φ n, ψ n)

Invalid

Invalid

Invalid

Invalid

Invalid

Configuration Space (C-space): the set of all object placements

Valid

α

β

α β

α

β

Rigid body in 3D

Most motion planning problems are PSPACE-hard [Reif 79, Hopcroft et al. 84 & 86]

PSPACE-complete [Canny 87]

Best deterministic algorithm known has running time that is exponential in the dimension of the robot’s C-space [Canny 86]

•  C-space has high dimension – spaceship (6), proteins (100+) •  simple obstacles have complex C-obstacles impractical to compute explicit

representation for more than 4 or 5 dof

Attention has turned to randomized algorithms which •  trade full completeness of the planner

•  for probabilistic completeness and a major gain in efficiency

Complexity of Motion Planning PSPACE

NP

P

Motion Planning Framework Probabilistic Roadmap Methods (PRMs) [Kavraki, Svestka, Latombe, Overmars 1996]   Idea: Build a model (roadmap) that approximates the

topology of the space of Configurations

Query processing

C-space

Invalid

Invalid

Invalid

Invalid

Invalid

Valid

Roadmap Construction 1. Randomly generate robot samples (nodes) - discard nodes that are invalid

1. Connect start and goal to roadmap start

goal

2. Find path(s) in roadmap between start and goal

2. Connect node pairs to form a roadmap - simple local planner - discard paths (edges) that are invalid

Strength: Solved many previously unsolvable problems Weakness: Doesn’t work well in complex spaces

Technique 1: Feature Sensitive Motion Planning (FSMP)

Technique 2: Map-Based Master Equation Calculation (MME)

Technique 3: Map-Based Monte Carlo (MMC)

Intelligent Map-Based Techniques

Density Low-------------------High

Algorithm Adapted from: Dale, Amato, “Probabilistic roadmaps: putting it all together”, ICRA 2001

Ariadne’s Clew Bessiere, Ahuactzin, Talbi, Mazer ’93

PRM Kavraki, Svestka, Latombe,Overmars ’96

OBPRM Amato, Wu, ’96

GaussianPRM Boor, Overmars, van der Stappen ’99

RRT LaValle, Kuffner, ’99

MAPRM Wilmarth, Amato, Stiller ’99

Planner for expansive spaces Hsu, Kavraki, Latombe, Motwani, Sorkin ’99

FuzzyPRM Nielsen,Kavraki ’00

LazyPRM Bohlin, Kavraki ’00

RNG Yang, LaValle ’00

Visibility Roadmap Laumond, Simèon ’00

ClosestVE Dale ’00

User Input Bayazit, Song, Amato ’00

Bridge Test, Hsu, Jiang, Reif, Sun, ’03

FSMP Motivation & Our Solution

  Challenges: –  Many randomized planners –  None is the best for all MP

problems –  Performance depends on the

environment –  The environment may contain

vastly different regions

  Our solution: –  Use machine learning to automate planning –  Adapt for the problem space: Identify regions –  Adapt during solution: Markov learning

FSMP Motivation & Our Solution

  Challenges: –  Many randomized planners –  None is the best for all MP

problems –  Performance depends on the

environment –  The environment may contain

vastly different regions

[Tapia, Thomas, Boyd, Amato ICRA 09; Morales, Tapia, Pearce, Rodriguez ICRA 05;

Morales, Tapia, Pearce, Rodriguez, Amato WAFR 04;]

FSMP Related Work

Use the environment’s features to adapt planning Adaptation can occur: over problem topology,

over sampler performance, with varying levels of interaction

Method User Intervention

Topology Adaptation

Sampler Adaptation

C-Space Type

Add New Sampler

UAS little yes, modeled yes any easy

Traditional PRM little none none any N/A

Basic FSMP [Morales et al. 2004]

supervised planner training yes, modeled yes, fixed mapping any difficult

Hybrid PRM [Hsu et al, 2005]

manual parameter tuning none yes any easy

InformationTheory-Based

IG/Entropy-based [Burns and Brock, 2005]

manual parameter tuning yes, implicit N/A any N/A

RESAMPL [Rodriguez et al, 2006]

manual parameter tuning yes, implicit N/A any N/A

Workspace Adaptation-

Based

Workspace Hybrid PRM [Kurniawati and Hsu, 2006] little yes, implicit yes restricted easy

Watershed-based Method [van den Berg et al, 2005]

manual parameter tuning yes, implicit yes, fixed mapping restricted N/A

FSMP Algorithm

①  Subdivide problem into homogeneous regions

②  Characterize regions and apply an appropriate planner

③  Final Solution is combination of regional solutions

[Tapia, Thomas, Boyd, Amato ICRA 09; Morales, Tapia, Pearce, Rodriguez ICRA 05;

Morales, Tapia, Pearce, Rodriguez, Amato WAFR 04;]

FSMP Algorithm: Subdivide Problem

①  Subdivide problem into homogeneous regions - Small roadmap to characterize the space - Automated method to identify regions: K-means - Identify the best number of regions: elbow criterion

FSMP Algorithm: Characterize Sub-problems and Solve

②  Characterize regions and apply an appropriate planner - Basic Method: Expert Mapping - Hybrid PRM [Hsu et al., ICRA ’05]: selects samplers based on success

- Reward: when it generates cc-create, cc-merge, and cc-expand nodes [Xie et al., WAFR ’06] - Penalty: a planner’s cost

cc-create cc-merge cc-expand cc-oversample

FSMP Algorithm: Combine Regional Solutions

①  Subdivide problem into homogeneous regions

②  Characterize regions and apply an appropriate planner

③  Final Solution is combination of regional solutions

FSMP Results: Regions

  Objective: 4 link robot must traverse through regions of different characteristics

  FSMP with Hybrid solved best –  16% less CD Calls

than Basic FSMP –  Hybrid not able to

solve in 5 runs of 5000 nodes

Method Nodes

Required CD Calls Basic

FSMP (expert

mapping in step 2)

Clustering 200 65842

Mapping 761 485537

Totals 962 551379

Hybrid (only step 2)

Not Solved

Not Solved

FSMP with Hybrid

Clustering 200 65842

Mapping 485 394613 Totals 685 460455

Step1: identify regions; Step 2: apply samplers in regions

FSMP Results: Cluttered

Method Nodes

Required CD Calls Basic

FSMP (expert

mapping in step 2)

Clustering 200 65842

Mapping 1761 192636

Totals 1961 205101 Hybrid

(only step 2) 2079 395380

FSMP with Hybrid

Clustering 200 12465 Mapping 2233 474975

Totals 2433 487440

  FSMP with Hybrid performance –  About 130% more CD

Calls and 24% more nodes than FSMP

–  About 23% more CD Calls and 17% more nodes than Hybrid

  Small amount of overhead compared to the gains in automation Step1: identify regions; Step 2: apply samplers in regions