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# CS 326A: Motion Planning - PowerPoint PPT Presentation

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

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### CS 326A: Motion Planning

robotics.stanford.edu/~latombe/cs326/2004/index.htm

Jean-Claude Latombe

Computer Science Department

Stanford University

• 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

Are two given points connected by a path?

Valid region

Forbidden region

▪Collision with obstacle

▪Lack of visibility of an object

▪Lack of stability

Fundamental Question

Are two given points connected by a path?

Valid region

Forbidden region

• 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

Valid region

Forbidden region

• Problems:

• Geometric complexity

• Space dimensionality

Multiple robots

Movable objects

Assembly planning

Goal is to acquire information by sensing

Model building

Object finding/tracking

Inspection

Nonholonomic constraints

Dynamic constraints

Stability constraints

Optimal planning

Uncertainty in model, control and sensing

Exploiting task mechanics (sensorless motions, under-actualted systems)

Physical models and deformable objects

Integration of planning and control

Integration with higher-level planning

Some Extensions of Basic Problem

robot

obstacles

air thrusters

gas tank

air bearing

Total duration : 40 sec

[Feron] (MIT)

Where to move next?

video

[Lynch] (Northwestern)

[Kavraki] (Rice)

Robot programming

Robot placement

Design of part feeders

Design for manufacturing and servicing

Design of pipe layouts and cable harnesses

Autonomous mobile robots planetary exploration, surveillance, military scouting

Graphic animation of “digital actors” for video games, movies, and webpages

Virtual walkthru

Medical surgery planning

Generation of plausible molecule motions, e.g., docking and folding motions

Building code verification

Examples of Applications

General Motors

General Motors

General Electric

[Kuffner and Inoue, 2000] (U. Tokyo)

Casal and Yim, 1999

Xerox, Parc

[CMU, NASA]

Toy Story (Pixar/Disney)

Antz (Dreamworks)

A Bug’s Life (Pixar/Disney)

Tomb Raider 3 (Eidos Interactive)

The Legend of Zelda (Nintendo)

Final Fantasy VIII (SquareOne)

Manipulation

Sensory-based locomotion

[Cheng-Chin U., UNC, Utrecht U.]

video

Cross-firing at a tumor

while sparing healthy

critical tissue

Study of the Motion of Bio-Molecules

• Present a coherent framework for motion planning problems

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

Continuous representation

(configuration space and related spaces + constraints)

Discretization

(random sampling, criticality-based decomposition)

Graph searching

(blind, best-first, A*)

• 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.

• 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

• 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 each week in reading papers.

• Differential Geometry and Topology

• Kinematics and Dynamics

• Geometric Modeling

• … but it makes use of knowledge from all these areas

• Attend every class

• Prepare/give two presentations with ppt slides (20 minutes each)

• Complete the programming project

• Complete two homework assignments

robotics.stanford.edu/~latombe/cs326/2004/index.htm

• Navigate in virtual environment

• Simulate legged robot

• Inspection of structures

• Search and escape