Motion Planning CS121 – Winter 2003

Basic Problem Are two given points connected by a path?

From Robotics …

… to Graphic Animation …

… to Biology

How Do You Get There? ?

Configuration Space Problems: Geometric complexity Number of dimensions of space How to discretize the free space? Approximate the free space by random sampling

Digital Character q 2 q 1 q 3 q 0 q n q 4 Q(t) Parts DOF L H

Configuration Space Problems: Geometric complexity Number of dimensions of space How to discretize the free space? Approximate the free space by random sampling

Hierarchical Collision Checking

Example in 3D

Hierarchical Collision Checking

Performance Evaluation Collision checking takes between and.002 seconds for 2 objects of 500,000 triangles each on a 1-GHz Pentium III Collision checking is faster when objects collide or are far apart, and gets slower when they get closer without colliding Overall collision checking time grows roughly as the log of the number of triangles

Probabilistic Roadmap (PRM) free space mbmbmbmb mgmgmgmg milestone local path

Why It Works

Narrow Passage Issue Easy Difficult

Probabilistic Completeness Under the generally satisfied assumption that the free space is expansive, the probability that a PRM finds a path when one exists goes to 1 exponentially in the number of milestones (~ running time).

Multi-Query Sampling Strategies

Multi-stage strategies Obstacle-sensitive strategies Narrow-passage strategies

Single-Query Sampling Strategies mbmbmbmb mgmgmgmg

mbmbmbmb mgmgmgmg Diffusion strategies Adaptive-step strategies Lazy collision checking

Examples N robot = 5,000; N obst = 83,000 T av = 4.42 s N robot = 3,000; N obst = 50,000 T av = 0.17 s

Design for Manufacturing/Servicing General Electric General Motors [Hsu, 2000]

Modular Reconfigurable Robots Xerox, Parc Casal and Yim, 1999

Humanoid Robot [Kuffner and Inoue, 2000] (U. Tokyo) Stability constraints

Space Robotics air bearing gas tank air thrusters obstacles robot [Kindel, 2000] Dynamic constraints

Single-Query Sampling Strategies mbmbmbmb mgmgmgmg

Total duration : 40 sec

Autonomous Helicopter [Feron, 2000] (AA Dept., MIT)

Other goals The goal may not be to attain a given position, but to achieve a certain condition, e.g.: - Irradiate a tumor - Build a map of an environment - Sweep an environment to find a target

Radiosurgery: Irradiate a Tumor

Mobile Robots: Map Building

Next-Best View

Example

Scout Robot: Find an Evasive Target

Information State Example of an information state = (1,1,0) 0 : the target does not hide beyond the edge 1 : the target may hide beyond the edge

Critical Curve

More Complex Example

Example with Two Robots (Greedy algorithm)

Surgical Planning

Half-Dome, NW Face, Summer of 2010 … Tim Bretl

Rock-Climbing Robot