1. Motion Planning

2. 154 slides • What is the motion planning problem? • What is the fundamental question in motion planning problem? • What is the basic problem formulation? • Configuration Space. • Formalism for Configuration Space. • What is a Path? • Extensions to the Basic Motion Planning Probem • Examples of Applications of Motion Planning • Examples of Practical Algorithms: Bug 2. • Examples : Probabilistic Roadmaps.

3. What is the motion planning problem?

6. Motion Planning for a robotic arm

7. Motion Planning for a mobile robot

8. Motion planning in a real world

9. Motion Planning for a Humanoid Robot with Many Degrees of Freedom in real world environment

10. Motion Planning for unusual robots, reconfigurable robots

11. Motion Planning in Medical and Chemical Applications

12. Is It Easy?

13. What is the fundamental question in motion planning?

14. 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

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

16. 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

17. What is the formulation of the basic problem of path finding ?

18. Basic Problem of Path planning • 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

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

20. Example with Articulated Object

21. Configuration Space

22. Tool: Configuration Space

23. Compare! Valid region Forbidden region

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

25. Formalism for Configuration Space

26. Notation for Configuration Space

27. Point Robot in Configuration space

28. Point robot in Three-Dimensional Configuration space

29. Translation and rotation of a robot

30. Example of simple configuration space for a robot with 2DOF in planar space

31. Representation of points in configuration space

32. In presence of obstacles, where the robot can actually move?

37. Free Space

38. Think of R as a robot and P as an obstacle

39. Robot that can translate and rotate in 2D space gives another dimension to the problem

40. C-obstacle in Three-Dimensional Space This is twisted

41. x Can we stay in 2D?

42. x

43. But is it good?

44. Too conservative

45. What is a Path?

46. What is a Path? Path is a very general concept considered from the point of view of computational geometry, time and search

47. Tool: Configuration Space(C-Space C)

48. Configuration Space qn q=(q1,…,qn) q3 q1 q2 In real problems configuration space is highly dimensional

49. Definition of Robot Configuration • A robot configuration is a specification of the positions of all robot points relative to a fixed coordinate system • Usually a configuration is expressed as a “vector” of position/orientation parameters

50. Rigid Robot Example • 3-parameter representation: q = (x,y,q) • In a 3-D workspace q would be of the form (x,y,z,a,b,g) workspace robot reference direction q y reference point x Like you need six-dimensional space to describe the airplane in the air