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CS 326A: Motion Planning

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  1. CS 326A: Motion Planning robotics.stanford.edu/~latombe/cs326/2004/index.htm Jean-Claude Latombe Computer Science Department Stanford University

  2. 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

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

  4. E.g.: ▪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

  5. 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

  6. Piano-mover problem  Examples with Rigid Object  Ladder problem

  7. Is It Easy?

  8. Example with Articulated Object

  9. Tool: Configuration Space

  10. Compare! Valid region Forbidden region

  11. Tool: Configuration Space • Problems: • Geometric complexity • Space dimensionality

  12. Moving obstacles 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

  13. Aerospace Robotics Lab Robot robot obstacles air thrusters gas tank air bearing

  14. Two concurrent planning goals: • Reach the goal • Reach a safe region Total duration : 40 sec

  15. Autonomous Helicopter [Feron] (MIT)

  16. Assembly Planning

  17. Map Building Where to move next?

  18. Target Tracking

  19. Planning for Nonholonomic Robots

  20. Under-Actuated Systems video [Lynch] (Northwestern)

  21. Planning with Uncertainty in Sensing and Control W2 I G W1

  22. Planning with Uncertainty in Sensing and Control W2 I G W1

  23. Planning with Uncertainty in Sensing and Control W2 I G W1

  24. Motion Planning for Deformable Objects [Kavraki] (Rice)

  25. Manufacturing: 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

  26. Robot Programming

  27. Robot Placement

  28. Design for Manufacturing/Servicing General Motors General Motors General Electric

  29. Assembly Planning and Design of Manufacturing Systems

  30. Part Feeding

  31. Part Feeding

  32. Cable Harness/ Pipe design

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

  34. Modular Reconfigurable Robots Casal and Yim, 1999 Xerox, Parc

  35. Military Scouting and Planet Exploration [CMU, NASA]

  36. 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)

  37. Motion Planning for Digital Actors Manipulation Sensory-based locomotion

  38. Navigation Through Virtual Environments [Cheng-Chin U., UNC, Utrecht U.] video

  39. Building Code Verification

  40. Radiosurgical Planning Cross-firing at a tumor while sparing healthy critical tissue

  41. Protein folding • Ligand binding Study of the Motion of Bio-Molecules

  42. 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

  43. Framework Continuous representation (configuration space and related spaces + constraints) Discretization (random sampling, criticality-based decomposition) Graph searching (blind, best-first, A*)

  44. 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.