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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

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cs 326a motion planning

CS 326A: Motion Planning


Jean-Claude Latombe

Computer Science Department

Stanford University

goal of motion planning
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
Fundamental Question

Are two given points connected by a path?

Valid region

Forbidden region

fundamental question9


▪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
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

Valid region

Forbidden region

tool configuration space16
Tool: Configuration Space
  • Problems:
  • Geometric complexity
  • Space dimensionality
some extensions of basic problem
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
Aerospace Robotics Lab Robot



air thrusters

gas tank

air bearing


Two concurrent planning goals:

  • Reach the goal
  • Reach a safe region

Total duration : 40 sec

map building
Map Building

Where to move next?

under actuated systems
Under-Actuated Systems


[Lynch] (Northwestern)

examples of applications

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
Design for Manufacturing/Servicing

General Motors

General Motors

General Electric

humanoid robot
Humanoid Robot

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

modular reconfigurable robots
Modular Reconfigurable Robots

Casal and Yim, 1999

Xerox, Parc

digital actors
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)

motion planning for digital actors
Motion Planning for Digital Actors


Sensory-based locomotion

navigation through virtual environments
Navigation Through Virtual Environments

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


radiosurgical planning
Radiosurgical Planning

Cross-firing at a tumor

while sparing healthy

critical tissue

goals of cs326a
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

Continuous representation

(configuration space and related spaces + constraints)


(random sampling, criticality-based decomposition)

Graph searching

(blind, best-first, A*)

practical algorithms 1 2
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
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
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
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
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
website and schedule
Website and Schedule


programming project
Programming Project
  • Navigate in virtual environment
  • Simulate legged robot
  • Inspection of structures
  • Search and escape