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Transcript of Randomized Motion Planning - College of Engineering · 1. Connect start and goal to roadmap Query...
http://parasol.tamu.edu
Randomized Motion Planning: From Intelligent CAD to Computer
Animation to Protein Folding
Nancy M. Amato Parasol Lab,Texas A&M University
Motion Planning
start
goal obstacles
(Basic) Motion Planning:
Given a movable object and a description of the environment, find a sequence of valid configurations that moves it from the start to the goal.
The Alpha Puzzle
(dis)Assembly Puzzle
Hard Motion Planning Problems: Intelligent CAD Applications
Using Motion Planning to Test Design Requirements: • Accessibility for servicing/assembly tested on physical “mock ups”. • Digital testing saves time and money, is more accurate, enables more extensive testing, and is useful for training (VR or e-manuals).
Maintainability Problems: Mechanical Designs from GE
Hard Motion Planning Problems: Highly Articulated (Constrained) Systems
Hard Motion Planning Problems: Group Behaviors for multiple agents
Traversing a Narrow Passage
A “shepherd” herding a flock of ducks
People evacuating a building
Hard Motion Planning Problems: Deformable Objects
Find a path for a deformable object that can deform to avoid collision with obstacles • deformable objects have infinite dof!
Hard Motion Planning Problems Computational Biology & Chemistry
• Drug Design - molecule docking
• Simulating Molecular Motions – study folding pathways & kinetics
Protein Folding
RNA Folding
Outline
• C-space, Planning in C-space (basic definitions)
• Probabilistic Roadmap Methods (PRMs) • PRM variants (OBPRM, MAPRM) • User-Input: Haptically Enhanced PRMs
• PRMs for more `complex’ robots • deformable objects • group behaviors for multiple robots • protein folding
Configuration Space (C-Space)
C-obst
C-obst
C-obst
C-obst
C-obst
C-Space
6D C-space (x,y,z,pitch,roll,yaw)
3D C-space (x,y,z) 3D C-space
(α,β,γ) α β γ
• “robot” maps to a point in higher dimensional space • parameter for each degree of freedom (dof) of robot • C-space = set of all robot placements • C-obstacle = infeasible robot placements
2n-D C-space (φ1, ψ1, φ2, ψ2, . . . , φ n, ψ n)
robot
obst
obst
obst
obst
x y
θ
C-obst
C-obst C-obst
C-obst
robot Path is swept volume
Motion Planning in C-space
Path is 1D curve
Workspace C-space Simple workspace obstacle transformed
Into complicated C-obstacle!!
Most motion planning problems of interest are PSPACE-hard [Reif 79, Hopcroft et al. 84 & 86]
The 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 - 6D for rigid body in 3-space • simple obstacles have complex C-obstacles impractical to compute explicit representation of freespace for more than 4 or 5 dof
So … attention has turned to randomized algorithms which • trade full completeness of the planner • for probabilistic completeness and a major gain in efficiency
The Complexity of Motion Planning
1. Connect start and goal to roadmap
Query processing start
goal
Probabilistic Roadmap Methods (PRMs) [Kavraki, Svestka, Latombe,Overmars 1996]
C-obst
C-obst
C-obst
C-obst
Roadmap Construction (Pre-processing)
2. Connect pairs of nodes to form roadmap - simple, deterministic local planner (e.g., straightline) - discard paths that are invalid
1. Randomly generate robot configurations (nodes) - discard nodes that are invalid
C-obst
C-space
2. Find path in roadmap between start and goal - regenerate plans for edges in roadmap
PRMs: Pros & Cons
PRMs: The Good News 1. PRMs are probabilistically complete 2. PRMs apply easily to high-dimensional C-space 3. PRMs support fast queries w/ enough preprocessing
Many success stories where PRMs solve previously unsolved problems
C-obst
C-obst
C-obst
C-obst
C-obst
start
goal
PRMs: The Bad News
1. PRMs don’t work as well for some problems: – unlikely to sample nodes in narrow passages – hard to sample/connect nodes on constraint surfaces
Our work concentrates on improving PRM performance for such problems.
start
goal
C-obst
C-obst
C-obst
C-obst
Smarter Sampling Methods
Goal: Sample nodes in Narrow Passages
• OBPRM: Obstacle-Based PRM • sampling around obstacles
• MAPRM: Medial-Axis PRM • sampling on the medial axis
• Repairing/Improving approximate paths • transforming invalid samples into valid samples
OBPRM: An Obstacle-Based PRM [IEEE ICRA’96, IEEE ICRA’98, WAFR’98]
start
goal
C-obst
C-obst
C-obst
C-obst
To Navigate Narrow Passages we must sample in them • most PRM nodes are where planning is easy (not needed)
PRM Roadmap
start
goal
C-obst
C-obst
C-obst
C-obst
Idea: Can we sample nodes near C-obstacle surfaces? • we cannot explicitly construct the C-obstacles... • we do have models of the (workspace) obstacles...
OBPRM Roadmap
1
3
2
4 5
OBPRM: Finding Points on C-obstacles
Basic Idea (for workspace obstacle S) 1. Find a point in S’s C-obstacle (robot placement colliding with S) 2. Select a random direction in C-space 3. Find a free point in that direction 4. Find boundary point between them using binary search (collision checks)
Note: we can use more sophisticated heuristics to try to cover C-obstacle
C-obst
Applications
Same Method: Diverse range of problems
• Intelligent CAD • digital testing, training, and servicing
• Simulating Group Behaviors • homing, covering, shepherding
• Modeling Molecular Motions • protein folding, RNA folding, protein/ligand binding
PHANToM 1. User collects approximate path using
haptic device • User insight identifies critical cfgs • User feels when robot touches obstacles
and adjusts trajectory 2. Approximate path passed to planner and
it fixes it • Planner is more efficient because search is
targeted to promising areas
Current Applications • Intelligent CAD Applications • Molecule Docking in drug design • Animation w/ Deformable Models
Hybrid Human/Planner System: Generating and Repairing Approximate Paths [IEEE ICRA 01, 0; PUG’99]
C-obstacle
C-obstacle approximate
path
repaired path
0
500
1000
1500
2000
2500
3000
3500
time (sec)
OBPRMhaptic pushiterative push
Hybrid Human/Planner System Haptic Hints Results
Flange Problem 0.85 0.95 1
1.0 (original size)
.95 (95% of original size)
Applications
Same Method: Diverse range of problems
• Intelligent CAD • digital testing, training, and servicing
• Simulating Group Behaviors • homing, covering, shepherding
• Modeling Molecular Motions • protein folding, RNA folding, protein/ligand binding
Group Behaviors J. Lien, B. Bayazit, S. Rodriguez, R. Sowell [PG’02,ALIFE’02,WAFR’02,ICRA04, ICRA05]
Solution: Roadmap-based flocking!
Flocking systems are good at simulating behaviors of groups of objects (schools of fish, crowds…) – flock formation is selfish, local,
decentralized, and efficient
Flocking systems are not good at complex navigation or customizing behavior in different regions – but roadmap-based planners are! ….
but generally just for one robot….
Roadmap-based Flocking
Roadmap – Map encoding global information (e.g., topology) – data structure for storing and accessing
information – supports implicit communication among group – Customize agent behavior in different regions
Agents – have traditional flocking behavior, local sensing
ability – have memory & reasoning – dynamically (locally) select routes in roadmap
edges selected based on edge weights Edge weights updated as agents traverse them (ant
pheromone)
?
?
Covering -50 flock members
- Environment size: 80 m *100 m
- 16 obstacles
- Sensory range: 5 m
Covering Movie.
Covering Rule
Go to the less visited edge
Group Behaviors: Roadmap-Based Flocking
Emergency Response • Evacuation Planning and Training
• placement of personnel and barriers
- 3 available exits - no directors or barriers
- 1 available exit (2 blocked) - 2 barriers placed at blocked exits
Applications
Same Method: Diverse range of problems
• Intelligent CAD • digital testing, training, and servicing
• Simulating Group Behaviors • homing, covering, shepherding
• Modeling Molecular Motions • protein folding, RNA folding, protein/ligand binding
Protein Folding We are interested in the folding process
- How the protein folds to its native, stable structure
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
Folding Landscapes
Each conformation has a potential energy – Native state is global
minimum Set of all conformations
forms landscape Shape of landscape
reflects folding behavior
Configuration space
Potential
Native state
Different proteins different landscapes different folding behaviors
Using Motion Planning to Map Folding Landscapes [RECOMB 01,02, 04, 06, 07; ISMB 07; JMB 08; PSB 03]
A conformation
Configuration space
Potential
Use Probabilistic Roadmap (PRM) method from motion planning to build roadmap
Roadmap approximates the folding landscape – Characterizes the main
features of landscape – Can extract multiple
folding pathways from roadmap
– Compute population kinetics for roadmap
Native state
Challenging Case Study [Thomas, Tang, Tapia, Amato - RECOMB 06 & 07, ISMB 07] Protein G
α, β3β4, β1β2, β1β4 [Kuszewski et al 1994, Orban et al. 1995]
Protein L
α, β1β2, β3β4, β1β4 L [Yi & Baker 1996, Yi et al 1997]; NuG1, NuG2 [Nauli, Kuhlman, Baker 2001]
NuG1 NuG2
• Proteins G, L and NuG1 & NuG2 (mutated forms of G) • All have similar structure (1 helix, 2 beta strands) • G & L have only 15% sequence identity (G, NuG1, NuG2 similar sequence) • In G beta 3-4 forms before beta 1-2, vice versa in L, NuG1, & NuG2
• Can our approach detect the difference? Yes! • When analyzing all (~10K) paths in our roadmaps
• 99% Protein G paths ,100% Protein L paths have “right” order • 98% and 97% paths in NuG1 and NuG2 have “right” order
Conclusions
Diverse problems can be addressed using appropriate adaptations of PRMs
• key is defining appropriate models and their C-spaces • validation check is very general - ranging from traditional collision detection to potential energy thresholds to ...
More info and Movies: http://parasol.tamu.edu/~amato [email protected]
Joint work with - my former students: O. Burchan Bayazit (WUSTL), Jyh-Ming Lien (George Mason), Marco Morales (ITAM, Mexico), Guang Song (Iowa State), Xinyu Tang (Google) - current students: Phil Coleman, Jory Denny, Roger Pearce, Sam Rodriguez, Robert Salazar, Lydia Tapia, Shawna Thomas, and the other members of our group - other colleagues: Ken Dill (UCSF), David Giedroc (Indiana), Marty Scholtz