Locomotion. Amir Degani. Intro to Robotics CS - Technion Winter Guest Lecture. Locomotion and Manipulation. Locomotion and. Manipulation Duality

Transcription

1 Locomotion Amir Degani Intro to Robotics CS - Technion Winter 2012 Duality Parts of slides taken from Howie Choset and Matt Mason 1

2 Today s outline Duality Duality 2

3 - Duality Locomotion cars, trains, horses walking, a baby crawling, earthworms digging Moving yourself from place to place Hand manipulation Robotics manipulators Juggling Moving an object from place to place Is a person walking on a globe or person is manipulating the globe with his feet Duality The two objects are moving relative to each other Loaned in part from Mark Yim: 3

4 - Duality Duality

5 Robotic Locomotion Ground Air Water Duality 5

6 Robotic Locomotion Wheeled Ground Legged Duality What about Rhex? or ModSnake? 6

7 Robotic Locomotion Wheeled on hard ground Ground Legged Duality S.Roland, Introduction to autonomous mobile robots,, pp ,

8 Wheeled machines Crusher - Carnegie Mellon University Duality Airtrax omnidirectional forklift 8

9 Differential Drive Duality 9

10 Differential Drive u = u r, u l Angular wheel velocities of right and left wheels Duality u r = u l > 0 u l = u r 0 Planning Algorithms, Steven M. LaValle, 2006 Great online book! 10

11 Differential Drive u r = u l > 0 u l = u r 0 x = r 2 u l + u r cos θ y = r 2 u l + u r sin θ Duality θ = r L u r u l. Planning Algorithms, Steven M. LaValle, 2006 Great online book! 11

12 Differential Drive (continued) Advantages: Cheap to build Easy to implement Simple design Disadvantages: Difficult straight line motion Duality 12

13 Problem with Differential Drive: Knobbie Tires Pictures from Navigating Mobile Robots: Systems and Techniques Borenstein, J. Duality Changing diameter makes for uncertainty in dead-reckoning error 13

14 Skid Steering Advantages: Simple drive system Disadvantages: Slippage and poor odometry results Requires a large amount of power to turn Duality MachineLAbs MMP-15 14

15 Omni Wheels Morevac Moravac Advantages: Allows complicated motions Disadvantages: No mechanical to require straight-line motion Complicated implementation Pictures from Navigating Mobile Robots: Systems and Techniques Borenstein, J. Duality Airtrax 15

16 Tricycle Advantages: No sliding Pictures from Navigating Mobile Robots: Systems and Techniques Borenstein, J. Disadvantages: Non-holonomic planning required Duality 16

17 Ackerman Steering Advantages: Simple to implement Simple 4 bar linkage controls front wheels Duality Disadvantages: Non-holonomic planning required 17

18 Non-holonomic constraint Definition: A non-holonomic constraint is a limitation on the allowable velocities of an object So what does that mean? Your robot can move in some directions (forwards and backwards), but not others (side to side). This is most easily seen in wheeled robots. The robot can instantly move forward and back, but can not move to the right or left without the wheels slipping. To go to the right, the robot must first turn, and then drive forward Duality Taken from Principles of Robot Motion Choset et al. MIT press 2005 And Matt Mason s Mechanics of 18

19 Holonomic Definition (Holonomic constraint) A kinematic constraint is a holonomic constraint if it can be expressed in the form f ( q, t) 0 Holonomic does not mean unconstrained!!! Holonomic means the can be written as equations independent of q f ( q, t) 0 A mobile robot with no is holonomic. A mobile robot capable of arbitrary planar velocities is holonomic. A mobile robot capable of only translations is holonomic. 19 Duality

20 Holonomic Definition (Holonomic constraint) A kinematic constraint is a holonomic constraint if it can be expressed in the form f ( q, t) 0 Suppose we have a constraint of the form: f q, q, t = 0 Is it non-holonomic? Perhaps it can be expressed as f q, t = 0 in which case we say the constraint is integrable. It s a holonomic constraint, disguised as a nonholonomic constraint. Duality 20

21 Non-holonomic constraint: The Unicycle x x q y, q y The unicycle cannot move sideways. nonholonomic constraint: wq ( ) (sin, cos, 0 ) w( q) q 0 x sin ycos 0 Duality [sin cos 0 ] x x sin y cos 0 Non-integrable constraint 21

22 Non-holonomic constraint: The Unicycle The unicycle can move in two directions: g 1 cos sin 0 Rolling forward at unit speed x q ug u g u1, u2r are the controls The robot has two controls. How Many freedoms? y 0 g2 0 1 Spinning counterclockwise at unit speed x y x x q y, q y 22 Duality

23 Lie Bracket Definition (Lie Bracket) Let g 1,g 2 be two vector fields on C. Define the Lie bracket [g 1,g 2 ] to be the vector field g2 g1 [ g1, g2] g1 g2 q q What are g 1 q and g 2 q? Matrices! Each column is partial of velocity w.r.t. configuration variable. Duality 23

24 Non-holonomic constraint: The Unicycle g 1 cos sin 0 Rolling forward at unit speed 0 g2 0 1 Spinning counterclockwise at unit speed x y x y g g Lie Bracket: [ g, g ] g g q q sin g1 0 0 cos g q q Duality cos 0 0 sin 0 [ g1, g2] sin 0 0 cos sin cos 0 24

25 Non-holonomic constraint: The Unicycle g 1 cos sin 0 Rolling forward at unit speed x y x Physically, this new lie bracket moves sideways. It is linearly independent of g 1 and g 2 and it violates the constraint w. Physical significance and why is it important in robotics? 0 g2 0 1 Spinning counterclockwise at unit speed g g Lie Bracket: [ g, g ] g g q q y sin cos 0 25 Duality

26 Non-holonomic constraint: The Unicycle g 1 cos sin 0 Rolling forward at unit speed 0 g2 0 1 Spinning counterclockwise at unit speed x y x y g g Lie Bracket: [ g, g ] g g q q y x sin cos 0 Duality y x 26

27 Non-holonomic constraint: The Unicycle g 1 cos sin 0 Rolling forward at unit speed x y x 0 g2 0 1 Spinning counterclockwise at unit speed g g Lie Bracket: [ g, g ] g g q q y y x y sin cos 0 The Lie Brackets tells us if infinitesimal motions along these vector fields can be used to locally generate motion in a direction not contained in original field Duality x 27

28 Wheeled machines Problems with wheeled machines: Maneuverability Stability Controllability Duality 28

29 Legged Robots: Stability Static vs. Dynamic Quasi-static Honda Asimo Dynamic Leg Lab Marc Raibert Duality 29

30 Walking/running machines 1 legged hoppers Raibert s 3D experimental prototype of one-legged hopping robot (Raibert, Brown) Uniroo Zeglin Duality ARL Monopod-I. From: Sayyad Single-legged hopping robotics research A review Robotica

31 Walking/running machines Duality Boston Dynamics Big Dog 31

32 Walking/running machines Duality

33 Walking/running machines Boston Dynamics LS3 400lbs, 20Miles, quiet 4,700,000 Youtube hits! Duality 33

34 Legged wheels Rhex Duality Whegs 34

35 Passive Dynamic Walkers Duality 35

36 Passive Dynamic Walkers Duality Collins, S. H., Wisse, M., Ruina, A., Cornell,

37 Climbing Locomotion Adhesive: Suction/Magnet/ Electro-adhesion, Dry adhesion Spines Brute force grippers Grasping / Bracing Duality 37

38 Dynamics? Why? Maneuverability/Agility Duality 38

39 Dynamics? Why Not? Duality 39

40 Dynamics? Why? Minimalism Vs. g Duality 40

41 Mechanism overview Simulation WorkingModel 2D TM Duality 41

42 Experimental setup Duality 42

43 Proof-of-concept Experiments High friction/damping High friction/damping Low friction/damping Duality Period-1 Low friction/damping Period-2 43

44 Extensions Miniature Tube Climber Duality 44

45 Part Feeding Duality 45

46 Part Feeding Duality 46

47 ParkourBot Duality 47

48 Difference between manipulation and locomotion Aperiodic Stable fixed point Locomotion Periodic gaits Stability? Duality 48