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```					     CS 326A: Motion Planning
robotics.stanford.edu/~latombe/cs326/2004/index.htm

Jean-Claude Latombe

Computer Science Department
Stanford University
Goal of Motion Planning
• Compute motion strategies, e.g.:
– geometric paths
– time-parameterized trajectories
– sequence of sensor-based motion commands
• To achieve high-level goals, e.g.:
–   go to A without colliding with obstacles
–   assemble product P
–   build map of environment E
–   find object O
Fundamental Question
Are two given points connected by a path?

Valid region

Forbidden region
Fundamental Question
Are two given points connected by a path?

E.g.:
▪Collision with obstacle
▪Lack of visibility of an object
▪Lack of stability
Valid region

Forbidden region
Basic Problem
Statement:
Compute a collision-free path for a rigid or
articulated object (the robot) among static obstacles
Inputs:
– Geometry of robot and obstacles
– Kinematics of robot (degrees of freedom)
– Initial and goal robot configurations (placements)
Output:
– Continuous sequence of collision-free robot
configurations connecting the initial and goal
configurations
Examples with Rigid Object

Piano-mover problem 
Is It Easy?
Example with Articulated Object
Tool: Configuration Space
Compare!

Valid region

Forbidden region
Tool: Configuration Space

Problems:
• Geometric complexity
• Space dimensionality
Some Extensions of Basic Problem
•   Moving obstacles            • Optimal planning
•   Multiple robots             • Uncertainty in model,
•   Movable objects               control and sensing
•   Assembly planning           • Exploiting task
•   Goal is to acquire            mechanics (sensorless
information by sensing        motions, under-
actualted systems)
– Model building
– Object finding/tracking   • Physical models and
– Inspection                  deformable objects
• Nonholonomic                  • Integration of planning
constraints                     and control
• Dynamic constraints           • Integration with higher-
level planning
• Stability constraints
Aerospace Robotics Lab Robot

robot

obstacles

air thrusters
gas tank

air bearing
Two concurrent planning goals:
• Reach the goal
• Reach a safe region

Total duration : 40 sec
Autonomous Helicopter

[Feron] (MIT)
Assembly Planning
Map Building

Where to move next?
Target Tracking
Planning for Nonholonomic Robots
Under-Actuated Systems

video

[Lynch] (Northwestern)
Planning with Uncertainty in
Sensing and Control

W2

I

W1              G
Planning with Uncertainty in
Sensing and Control

W2

I

W1              G
Planning with Uncertainty in
Sensing and Control

W2

I

W1              G
Motion Planning for Deformable
Objects

[Kavraki] (Rice)
Examples of Applications
• Manufacturing:             • Graphic animation of
– Robot programming         “digital actors” for video
– Robot placement           games, movies, and
webpages
– Design of part feeders
• Virtual walkthru
• Design for manufacturing
and servicing              • Medical surgery planning
• Generation of plausible
• Design of pipe layouts       molecule motions, e.g.,
and cable harnesses          docking and folding
• Autonomous mobile            motions
robots planetary           • Building code
exploration, surveillance,   verification
military scouting
Robot Programming
Robot Placement
Design for
Manufacturing/Servicing
General Motors    General Motors

General Electric
Assembly Planning and Design of
Manufacturing Systems
Part Feeding
Part Feeding
Cable Harness/ Pipe design
Humanoid Robot

[Kuffner and Inoue, 2000] (U. Tokyo)
Modular Reconfigurable Robots
Casal and Yim, 1999

Xerox, Parc
Military Scouting and Planet
Exploration

[CMU, NASA]
Digital Actors

A Bug’s Life (Pixar/Disney)         Toy Story (Pixar/Disney)                       Antz (Dreamworks)

Tomb Raider 3 (Eidos Interactive)                The Legend of Zelda (Nintendo)   Final Fantasy VIII (SquareOne)
Motion Planning for Digital Actors
Manipulation
Sensory-based locomotion
Environments
[Cheng-Chin U., UNC, Utrecht U.]

video
Building Code Verification

Cross-firing at a tumor
while sparing healthy
critical tissue
Study of
the Motion of Bio-Molecules

• Protein folding
• Ligand binding
Goals of CS326A
Present a coherent framework for
motion planning problems

Emphasis of “practical” algorithms with
some guarantees of performance over
“theoretical” or purely “heuristic”
algorithms
Framework

Continuous representation
(configuration space and related spaces + constraints)

Discretization
(random sampling, criticality-based decomposition)

Graph searching
(blind, best-first, A*)
Practical Algorithms (1/2)

A complete motion planner always returns a
solution plan when one exists and indicates that
no such plan exists otherwise.

Most motion planning problems are hard,
meaning that complete planners take
exponential time in # of degrees of freedom,
objects, etc.
Practical Algorithms (2/2)
Theoretical algorithms strive for completeness
and minimal worst-case complexity. Difficult to
implement and not robust.
Heuristic algorithms strive for efficiency in
commonly encountered situations. Usually no
performance guarantee.
 Weaker completeness
 Simplifying assumptions
 Exponential algorithms that work in practice
Prerequisites for CS326A
Ability and willingness to complete a
significant programming project with
graphic interface.
Basic knowledge and taste for geometry
and algorithms.
Interest in devoting reasonable time
CS326A is not a course in …
Differential Geometry and Topology
Kinematics and Dynamics
Geometric Modeling

… but it makes use of knowledge from
all these areas
Work to Do
A. Attend every class
B. Prepare/give two presentations with
ppt slides (20 minutes each)
C. For each class read the two papers
D. Complete the programming project
E. Complete two homework assignments
Website and Schedule
robotics.stanford.edu/~latombe/cs326/2004/index.htm
January 6     1    Overview
January 8     2    Path planning for point robot
January 13    3    Configuration space of a robot

January 15    4    Collision detection 1/2: Hierarchical methods

January 20    5    Collision detection 2/2: Feature-tracking methods

January 22    6    Probabilistic roadmaps 1/3: Basic techniques

January 27    7    Probabilistic roadmaps 2/3: Sampling strategies

January 29    8    Probabilistic roadmaps 3/3: Sampling strategies

February 3    9    Criticality-based motion planning: Assembly planning and target finding

February 5    10   Coordination of multiple robots

February 10   11   Kinodynamic planning

February 12   12   Humanoid and legged robots

February 17   13   Modular reconfigurable robots

February 19   14   Mapping and inspecting environments

February 24   15   Navigation in virtual environments

February 26   16   Target tracking and virtual camera

March 2       17   Motion of crowds and flocks

March 4       18   Motion of bio-molecules
Programming Project
• Navigate in virtual environment

• Simulate legged robot

• Inspection of structures

• Search and escape

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