Mobile Robots Part I.2 Robotics and Mechatronics
Description: Mobile Robots Part I.2 Robotics and Mechatronics a.a. 2020-2021 Mobile robot kinematics Mobile Robotics Robot kinematics Rolling constraints Sliding constraints Model Rolling constraints Sliding constraints Example: differential drive Same
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slide1. Mobile Robots Part I.2 Robotics and Mechatronics a.a. 2020-2021<br>
slide2. Mobile robot kinematics Mobile Robotics<br>
slide3. Robot kinematics<br>
slide4. Rolling constraints<br>
slide5. Sliding constraints<br>
slide6. Model Rolling constraints Sliding constraints<br>
slide8. Example: differential drive Same sliding constraint!<br>
slide9. Example: differential drive<br>
slide10. Example: bicycle<br>
slide11. Example: bicycle<br>
slide12. Exercise Bicycle<br>
slide13. Exercise Bicycle<br>
slide14. Exercise Bicycle Initialization Set the motor to the rear-wheel<br>
slide15. Exercise Bicycle Mainly for graphic purpose Plot<br>
slide16. Results!<br>
slide17. Exercises Mobile robot kinematics<br>
slide18. Differential drive robot: forward kinematics<br>
slide19. Bicycle drive robot: forward kinematics<br>
slide20. Mobility Mobile Robotics<br>
slide21. Kinematics: recap Rolling constraints Sliding constraints<br>
slide22. Mobility Motion vector Projection matrix Motion vector Sliding constraints<br>
slide23. Mobility Geometrical proof Zero motion lines Instantaneous Centre of Rotation
It is the single solution that allows mobility Solutions<br>
slide24. Mobility Examples<br>
slide25. Kinematics: Omnidirectional robot Necessary conditions:
No single point should exist where all the axes of the rollers intersect
Same with parallel axes
If not, then the system is labile.<br>
slide26. Mobility Unrestrained motion Unmovable Number of
independent
constraints<br>
slide27. Steerability<br>
slide28. Example Fixed wheels Steered wheels<br>
slide29. Maneuverability<br>
slide30. Mobile robot workspace This part not clear: C-space is the equiv of joint-space. WS is the space of poses so they are made of different stuff.
The point is that for a n-hol system we can have that every point in WS can be connected to a point in the C-space.
Thus, even if dim(C-space) = 2, dim(W) can be = 3.<br>
slide31. Example<br>
slide32. DDOF<br>
slide33. Mobile Robots Part I.07 Robotics a.a. 2020-2021<br>
slide34. Non-Holonomic constraints Mobile Robotics<br>
slide35. Non-holonomic Constraints<br>
slide36. Non-holonomic Constraints Any wheeled vehicle is subject to kinematic constraints that reduce in general its local mobility, while leaving intact the possibility of reaching arbitrary configurations by appropriate maneuvers.
Example:
It is impossible to move a car instantaneously in the direction orthogonal to the forward direction.
The same car can perform a S-manoeuver: the result is a displacement in the orthogonal direction!<br>
slide37. Holonomic/Non-holonomic constraints<br>
slide38. Holonomic Constraints Example: Point in space vs. point in plane<br>
slide39. Non-holonomic Constraints Dependent both on position and velocity!<br>
slide40. Non-holonomic Constraints Linear! Note: the proof of this is a little too involved for us: it revolves around the Frobenius Theorem and Lie brackets theory.<br>
slide41. Non-holonomic Constraints To summarize:
Non-holonomic constraints are representable only as constraints on velocities and not on positions.
Whatever kinematic constraint that is representable as a positional constraint is holonomic.<br>
slide42. Non-holonomic Constraints<br>
slide43. Model derivation<br>
slide44. Kinematics: unicycle<br>
slide45. Kinematics: differential steering<br>
slide46. Kinematics: bicycle Part 1<br>
slide47. Kinematics: bicycle Part 2<br>
slide48. Control Mobile Robotics<br>
slide49. Control problem<br>
slide50. Control problem<br>
slide51. Precomputed trajectory tracking<br>
slide52. Heading control Strictly bound to the kinematics<br>
slide53. Control basics<br>
slide54. Control basics<br>
slide55. Heading control: bicycle Part 1<br>
slide56. Heading control: bicycle Part 2 Linear control<br>
slide57. Forward speed controller<br>
slide58. Heading controller<br>
slide59. Heading control: differential steering Part 1<br>
slide60. Heading control: differential steering Part 2 Desired direction<br>
slide61. Exercises Mobile robot control<br>
slide62. Bicycle robot model: heading control (Proportional-Derivative controller)<br>
slide63. Differential drive model: heading control (Proportional-Derivative controller)<br>
slide64. Bicycle model: heading control (Proportional-Derivative controller)<br>
slide2. Mobile robot kinematics Mobile Robotics<br>
slide3. Robot kinematics<br>
slide4. Rolling constraints<br>
slide5. Sliding constraints<br>
slide6. Model Rolling constraints Sliding constraints<br>
slide8. Example: differential drive Same sliding constraint!<br>
slide9. Example: differential drive<br>
slide10. Example: bicycle<br>
slide11. Example: bicycle<br>
slide12. Exercise Bicycle<br>
slide13. Exercise Bicycle<br>
slide14. Exercise Bicycle Initialization Set the motor to the rear-wheel<br>
slide15. Exercise Bicycle Mainly for graphic purpose Plot<br>
slide16. Results!<br>
slide17. Exercises Mobile robot kinematics<br>
slide18. Differential drive robot: forward kinematics<br>
slide19. Bicycle drive robot: forward kinematics<br>
slide20. Mobility Mobile Robotics<br>
slide21. Kinematics: recap Rolling constraints Sliding constraints<br>
slide22. Mobility Motion vector Projection matrix Motion vector Sliding constraints<br>
slide23. Mobility Geometrical proof Zero motion lines Instantaneous Centre of Rotation
It is the single solution that allows mobility Solutions<br>
slide24. Mobility Examples<br>
slide25. Kinematics: Omnidirectional robot Necessary conditions:
No single point should exist where all the axes of the rollers intersect
Same with parallel axes
If not, then the system is labile.<br>
slide26. Mobility Unrestrained motion Unmovable Number of
independent
constraints<br>
slide27. Steerability<br>
slide28. Example Fixed wheels Steered wheels<br>
slide29. Maneuverability<br>
slide30. Mobile robot workspace This part not clear: C-space is the equiv of joint-space. WS is the space of poses so they are made of different stuff.
The point is that for a n-hol system we can have that every point in WS can be connected to a point in the C-space.
Thus, even if dim(C-space) = 2, dim(W) can be = 3.<br>
slide31. Example<br>
slide32. DDOF<br>
slide33. Mobile Robots Part I.07 Robotics a.a. 2020-2021<br>
slide34. Non-Holonomic constraints Mobile Robotics<br>
slide35. Non-holonomic Constraints<br>
slide36. Non-holonomic Constraints Any wheeled vehicle is subject to kinematic constraints that reduce in general its local mobility, while leaving intact the possibility of reaching arbitrary configurations by appropriate maneuvers.
Example:
It is impossible to move a car instantaneously in the direction orthogonal to the forward direction.
The same car can perform a S-manoeuver: the result is a displacement in the orthogonal direction!<br>
slide37. Holonomic/Non-holonomic constraints<br>
slide38. Holonomic Constraints Example: Point in space vs. point in plane<br>
slide39. Non-holonomic Constraints Dependent both on position and velocity!<br>
slide40. Non-holonomic Constraints Linear! Note: the proof of this is a little too involved for us: it revolves around the Frobenius Theorem and Lie brackets theory.<br>
slide41. Non-holonomic Constraints To summarize:
Non-holonomic constraints are representable only as constraints on velocities and not on positions.
Whatever kinematic constraint that is representable as a positional constraint is holonomic.<br>
slide42. Non-holonomic Constraints<br>
slide43. Model derivation<br>
slide44. Kinematics: unicycle<br>
slide45. Kinematics: differential steering<br>
slide46. Kinematics: bicycle Part 1<br>
slide47. Kinematics: bicycle Part 2<br>
slide48. Control Mobile Robotics<br>
slide49. Control problem<br>
slide50. Control problem<br>
slide51. Precomputed trajectory tracking<br>
slide52. Heading control Strictly bound to the kinematics<br>
slide53. Control basics<br>
slide54. Control basics<br>
slide55. Heading control: bicycle Part 1<br>
slide56. Heading control: bicycle Part 2 Linear control<br>
slide57. Forward speed controller<br>
slide58. Heading controller<br>
slide59. Heading control: differential steering Part 1<br>
slide60. Heading control: differential steering Part 2 Desired direction<br>
slide61. Exercises Mobile robot control<br>
slide62. Bicycle robot model: heading control (Proportional-Derivative controller)<br>
slide63. Differential drive model: heading control (Proportional-Derivative controller)<br>
slide64. Bicycle model: heading control (Proportional-Derivative controller)<br>