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Motion Planning

Motion Planning. 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

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Motion Planning

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  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?

  4. Motion Planning for a robotic arm

  5. Motion Planning for a mobile robot

  6. Motion planning in a real world

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

  8. Motion Planning for unusual robots, reconfigurable robots

  9. Motion Planning in Medical and Chemical Applications

  10. Is It Easy?

  11. What is the fundamental question in motion planning?

  12. 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

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

  14. 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

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

  16. 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

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

  18. Example with Articulated Object

  19. Configuration Space

  20. Tool: Configuration Space

  21. Compare! Valid region Forbidden region

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

  23. Formalism for Configuration Space

  24. Notation for Configuration Space

  25. Point Robot in Configuration space

  26. Point robot in Three-Dimensional Configuration space

  27. Translation and rotation of a robot

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

  29. Representation of points in configuration space

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

  31. Free Space

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

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

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

  35. x Can we stay in 2D?

  36. x

  37. But is it good?

  38. Too conservative

  39. What is a Path?

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

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

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

  43. 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

  44. 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

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