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					     CS 326A: Motion Planning

            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?

                                        ▪Collision with obstacle
                                        ▪Lack of visibility of an object
                                        ▪Lack of stability
          Valid region

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

                         Ladder problem

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

Valid region

               Forbidden region
   Tool: Configuration Space

• 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



            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


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



W1              G
Planning with Uncertainty in
    Sensing and Control



W1              G
Planning with Uncertainty in
    Sensing and Control



W1              G
Motion Planning for Deformable

[Kavraki] (Rice)
       Examples of Applications
• Manufacturing:             • Graphic animation of
   – Robot programming         “digital actors” for video
   – Robot placement           games, movies, and
   – 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
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

                                       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
                 Sensory-based locomotion
        Navigation Through Virtual
[Cheng-Chin U., UNC, Utrecht U.]

Building Code Verification
        Radiosurgical Planning

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”

         Continuous representation
(configuration space and related spaces + constraints)

   (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
each week in reading papers.
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
   listed as “required reading” in
D. Complete the programming project
E. Complete two homework assignments
          Website and Schedule
    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
    March 9       19   Radiosurgical planning
           Programming Project
• Navigate in virtual environment

• Simulate legged robot

• Inspection of structures

• Search and escape

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