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

7. 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

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

9. Fundamental Question Are two given points connected by a path? Valid region Forbidden region E.g.: ▪Collision with obstacle ▪Lack of visibility of an object ▪Lack of stability

10. 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

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

12. Is It Easy?

13. Example with Articulated Object

14. Tool: Configuration Space

15. Compare! Valid region Forbidden region

16. Tool: Configuration Space Problems: Geometric complexity Space dimensionality

17. 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 –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

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

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

20. Autonomous Helicopter [Feron] (MIT)

21. Assembly Planning

22. Map Building Where to move next?

23. Target Finding

24. Target Tracking

25. Planning for Nonholonomic Robots

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

27. Planning with Uncertainty in Sensing and Control I G W1W1W1W1 W2W2W2W2

28. I G W1W1W1W1 W2W2W2W2

29. I G W1W1W1W1 W2W2W2W2

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

31. Examples of Applications 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

32. Robot Programming

33. Robot Placement

34. Design for Manufacturing/Servicing General Electric General Motors

35. Assembly Planning and Design of Manufacturing Systems

36. Part Feeding

38. Cable Harness/ Pipe design

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

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

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

43. Digital Actors A Bug’s Life (Pixar/Disney) Toy Story (Pixar/Disney) Tomb Raider 3 (Eidos Interactive)Final Fantasy VIII (SquareOne)The Legend of Zelda (Nintendo) Antz (Dreamworks)

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

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

46. Building Code Verification

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

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

49. 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

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

51. 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.

52. 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

53. 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.

54. 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

55. 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 advance D.Complete the programming project E.Complete two homework assignments

56. Website and Schedule robotics.stanford.edu/~latombe/cs326/2004/index.htm January 61Overview January 82Path planning for point robot January 133Configuration space of a robot January 154Collision detection 1/2: Hierarchical methods January 205Collision detection 2/2: Feature-tracking methods January 226Probabilistic roadmaps 1/3: Basic techniques January 277Probabilistic roadmaps 2/3: Sampling strategies January 298Probabilistic roadmaps 3/3: Sampling strategies February 39Criticality-based motion planning: Assembly planning and target finding February 510Coordination of multiple robots February 1011Kinodynamic planning February 1212Humanoid and legged robots February 1713Modular reconfigurable robots February 1914Mapping and inspecting environments February 2415Navigation in virtual environments February 2616Target tracking and virtual camera March 217Motion of crowds and flocks March 418Motion of bio-molecules March 919Radiosurgical planning

57. Programming Project Navigate in virtual environment Simulate legged robot Inspection of structures Search and escape