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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

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Cs 326a motion planning l.jpg

CS 326A: Motion Planning


Jean-Claude Latombe

Computer Science Department

Stanford University

Goal of motion planning l.jpg
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 l.jpg
Fundamental Question

Are two given points connected by a path?

Valid region

Forbidden region

Fundamental question9 l.jpg


▪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

Basic problem l.jpg
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 l.jpg

Piano-mover problem

Examples with Rigid Object

 Ladder problem

Compare l.jpg

Valid region

Forbidden region

Tool configuration space16 l.jpg
Tool: Configuration Space

  • Problems:

  • Geometric complexity

  • Space dimensionality

Some extensions of basic problem l.jpg

Moving obstacles

Multiple robots

Movable objects

Assembly planning

Goal is to acquire information by sensing

Model building

Object finding/tracking


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

Aerospace robotics lab robot l.jpg
Aerospace Robotics Lab Robot



air thrusters

gas tank

air bearing

Slide19 l.jpg

Total duration : 40 sec

Autonomous helicopter l.jpg
Autonomous Helicopter

[Feron] (MIT)

Map building l.jpg
Map Building

Where to move next?

Under actuated systems l.jpg
Under-Actuated Systems


[Lynch] (Northwestern)

Examples of applications l.jpg


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

Design for manufacturing servicing l.jpg
Design for Manufacturing/Servicing

General Motors

General Motors

General Electric

Humanoid robot l.jpg
Humanoid Robot

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

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Modular Reconfigurable Robots

Casal and Yim, 1999

Xerox, Parc

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Digital Actors

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)

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Motion Planning for Digital Actors


Sensory-based locomotion

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Navigation Through Virtual Environments

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


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Radiosurgical Planning

Cross-firing at a tumor

while sparing healthy

critical tissue

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Study of the Motion of Bio-Molecules

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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 l.jpg

Continuous representation

(configuration space and related spaces + constraints)


(random sampling, criticality-based decomposition)

Graph searching

(blind, best-first, A*)

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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 l.jpg
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 l.jpg
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 each week in reading papers.

Cs326a is not a course in l.jpg
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

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Work to Do

  • Attend every class

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

  • For each class read the two papers listed as “required reading” in advance

  • Complete the programming project

  • Complete two homework assignments

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Website and Schedule


Programming project l.jpg
Programming Project

  • Navigate in virtual environment

  • Simulate legged robot

  • Inspection of structures

  • Search and escape