locomotion and locomotion locomotion and...

Guest Lecture. Locomotion and

Manipulation

• Locomotion and Manipulation Duality • Locomotion Classification • Wheeled machines • Diff drive • Skid Steering • Omni wheels • Tricycle • Ackerman

• Non-holonomic constraints • Legged Robots • Static vs. Dynamic • Passive Dynamics

• Climbing Robots

Locomotion and Manipulation Locomotion

Amir Degani

Intro to Robotics – CS - Technion Winter 2012

1 Parts of slides taken from Howie Choset and Matt Mason

Guest Lecture. Locomotion and

Manipulation

• Locomotion and Manipulation Duality • Locomotion Classification • Wheeled machines • Diff drive • Skid Steering • Omni wheels • Tricycle • Ackerman

• Non-holonomic constraints • Legged Robots • Static vs. Dynamic • Passive Dynamics

• Climbing Robots

Today’s outline

• Locomotion and Manipulation Duality

• Locomotion Classification

• Wheeled machines Diff drive

Skid Steering

Omni wheels

Tricycle

Ackerman

• Non-holonomic constraints

• Legged Robots Static vs. Dynamic

Passive Dynamics

• Climbing Robots

2

Guest Lecture. Locomotion and

Manipulation

• Locomotion and Manipulation Duality • Locomotion Classification • Wheeled machines • Diff drive • Skid Steering • Omni wheels • Tricycle • Ackerman

• Non-holonomic constraints • Legged Robots • Static vs. Dynamic • Passive Dynamics

• Climbing Robots

Locomotion and Manipulation - Duality

3

Manipulation Locomotion

Moving “yourself” from place to place

Moving an object from place to place

Is a person walking on a globe or person is manipulating the globe with his feet

The two objects are moving relative to each other

Loaned in part from Mark Yim: http://ai.stanford.edu/users/mark/loco-loco.html

cars, trains, horses walking, a baby crawling, earthworms digging

Hand manipulation Robotics manipulators Juggling

Guest Lecture. Locomotion and

Manipulation

• Locomotion and Manipulation Duality • Locomotion Classification • Wheeled machines • Diff drive • Skid Steering • Omni wheels • Tricycle • Ackerman

• Non-holonomic constraints • Legged Robots • Static vs. Dynamic • Passive Dynamics

• Climbing Robots

Locomotion and Manipulation - Duality

Guest Lecture. Locomotion and

Manipulation

• Locomotion and Manipulation Duality • Locomotion Classification • Wheeled machines • Diff drive • Skid Steering • Omni wheels • Tricycle • Ackerman

• Non-holonomic constraints • Legged Robots • Static vs. Dynamic • Passive Dynamics

• Climbing Robots

Robotic Locomotion Classification

5

Ground Air Water

Guest Lecture. Locomotion and

Manipulation

• Locomotion and Manipulation Duality • Locomotion Classification • Wheeled machines • Diff drive • Skid Steering • Omni wheels • Tricycle • Ackerman

• Non-holonomic constraints • Legged Robots • Static vs. Dynamic • Passive Dynamics

• Climbing Robots

Robotic Locomotion Classification

6

Wheeled Legged

Ground

What about Rhex? or ModSnake?

Guest Lecture. Locomotion and

Manipulation

• Locomotion and Manipulation Duality • Locomotion Classification • Wheeled machines • Diff drive • Skid Steering • Omni wheels • Tricycle • Ackerman

• Non-holonomic constraints • Legged Robots • Static vs. Dynamic • Passive Dynamics

• Climbing Robots

Robotic Locomotion Classification

7

Ground

S.Roland, Introduction to autonomous mobile robots, , pp. 12-45, 2004

Legged

Wheeled on hard ground

Guest Lecture. Locomotion and

Manipulation

• Locomotion and Manipulation Duality • Locomotion Classification • Wheeled machines • Diff drive • Skid Steering • Omni wheels • Tricycle • Ackerman

• Non-holonomic constraints • Legged Robots • Static vs. Dynamic • Passive Dynamics

• Climbing Robots

Wheeled machines

Airtrax – omnidirectional forklift

Crusher - Carnegie Mellon University

8

Guest Lecture. Locomotion and

Manipulation

• Locomotion and Manipulation Duality • Locomotion Classification • Wheeled machines • Diff drive • Skid Steering • Omni wheels • Tricycle • Ackerman

• Non-holonomic constraints • Legged Robots • Static vs. Dynamic • Passive Dynamics

• Climbing Robots

Differential Drive

9

Guest Lecture. Locomotion and

Manipulation

• Locomotion and Manipulation Duality • Locomotion Classification • Wheeled machines • Diff drive • Skid Steering • Omni wheels • Tricycle • Ackerman

• Non-holonomic constraints • Legged Robots • Static vs. Dynamic • Passive Dynamics

• Climbing Robots

Differential Drive

10 Planning Algorithms, Steven M. LaValle, 2006 Great online book!

𝑢 = 𝑢𝑟 , 𝑢𝑙 Angular wheel velocities of right and left wheels

𝑢𝑟 = 𝑢𝑙 > 0 𝑢𝑙 = −𝑢𝑟 ≠ 0

Guest Lecture. Locomotion and

Manipulation

• Locomotion and Manipulation Duality • Locomotion Classification • Wheeled machines • Diff drive • Skid Steering • Omni wheels • Tricycle • Ackerman

• Non-holonomic constraints • Legged Robots • Static vs. Dynamic • Passive Dynamics

• Climbing Robots

Differential Drive

11 Planning Algorithms, Steven M. LaValle, 2006 Great online book!

𝑢𝑟 = 𝑢𝑙 > 0 𝑢𝑙 = −𝑢𝑟 ≠ 0

𝑥 =𝑟

2𝑢𝑙 + 𝑢𝑟 cos 𝜃

𝑦 =𝑟

2𝑢𝑙 + 𝑢𝑟 𝑠𝑖𝑛 𝜃

𝜃 =𝑟

𝐿𝑢𝑟 − 𝑢𝑙 .

Guest Lecture. Locomotion and

Manipulation

• Locomotion and Manipulation Duality • Locomotion Classification • Wheeled machines • Diff drive • Skid Steering • Omni wheels • Tricycle • Ackerman

• Non-holonomic constraints • Legged Robots • Static vs. Dynamic • Passive Dynamics

• Climbing Robots

Differential Drive (continued)

Advantages:

• Cheap to build

• Easy to implement

• Simple design

Disadvantages:

• Difficult straight line motion

12

Guest Lecture. Locomotion and

Manipulation

• Locomotion and Manipulation Duality • Locomotion Classification • Wheeled machines • Diff drive • Skid Steering • Omni wheels • Tricycle • Ackerman

• Non-holonomic constraints • Legged Robots • Static vs. Dynamic • Passive Dynamics

• Climbing Robots

Problem with Differential Drive: Knobbie Tires

Changing diameter makes for uncertainty in dead-reckoning error

Pictures from “Navigating Mobile Robots: Systems and Techniques” Borenstein, J.

13

Guest Lecture. Locomotion and

Manipulation

• Locomotion and Manipulation Duality • Locomotion Classification • Wheeled machines • Diff drive • Skid Steering • Omni wheels • Tricycle • Ackerman

• Non-holonomic constraints • Legged Robots • Static vs. Dynamic • Passive Dynamics

• Climbing Robots

Skid Steering

Advantages: •Simple drive system Disadvantages: •Slippage and poor odometry results •Requires a large amount of power to turn

MachineLAbs MMP-15 14

Guest Lecture. Locomotion and

Manipulation

• Locomotion and Manipulation Duality • Locomotion Classification • Wheeled machines • Diff drive • Skid Steering • Omni wheels • Tricycle • Ackerman

• Non-holonomic constraints • Legged Robots • Static vs. Dynamic • Passive Dynamics

• Climbing Robots

Omni Wheels

Advantages: •Allows complicated motions

Disadvantages: •No mechanical constraints to require straight-line motion •Complicated implementation

Pictures from “Navigating Mobile Robots: Systems and Techniques” Borenstein, J.

Morevac

Moravac

Airtrax 15

Guest Lecture. Locomotion and

Manipulation

• Locomotion and Manipulation Duality • Locomotion Classification • Wheeled machines • Diff drive • Skid Steering • Omni wheels • Tricycle • Ackerman

• Non-holonomic constraints • Legged Robots • Static vs. Dynamic • Passive Dynamics

• Climbing Robots

Tricycle

Advantages: •No sliding

Disadvantages: •Non-holonomic planning required

Pictures from “Navigating Mobile Robots: Systems and Techniques” Borenstein, J.

16

Guest Lecture. Locomotion and

Manipulation

• Locomotion and Manipulation Duality • Locomotion Classification • Wheeled machines • Diff drive • Skid Steering • Omni wheels • Tricycle • Ackerman

• Non-holonomic constraints • Legged Robots • Static vs. Dynamic • Passive Dynamics

• Climbing Robots

Ackerman Steering

Advantages: Simple to implement •Simple 4 bar linkage controls front wheels

Disadvantages: •Non-holonomic planning required

17

Guest Lecture. Locomotion and

Manipulation

• Locomotion and Manipulation Duality • Locomotion Classification • Wheeled machines • Diff drive • Skid Steering • Omni wheels • Tricycle • Ackerman

• Non-holonomic constraints • Legged Robots • Static vs. Dynamic • Passive Dynamics

• Climbing Robots

Non-holonomic constraint

So what does that mean? Your robot can move in some directions (forwards and backwards), but not others (side to side).

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

Taken from Principles of Robot Motion – Choset et al. MIT press 2005 And Matt Mason’s Mechanics of Manipulation

18

Definition: A non-holonomic constraint is a limitation on the allowable velocities of an object

This is most easily seen in wheeled robots.

Guest Lecture. Locomotion and

Manipulation

• Locomotion and Manipulation Duality • Locomotion Classification • Wheeled machines • Diff drive • Skid Steering • Omni wheels • Tricycle • Ackerman

• Non-holonomic constraints • Legged Robots • Static vs. Dynamic • Passive Dynamics

• Climbing Robots

Holonomic constraints

• Holonomic means the constraints can be written as equations independent of

• A mobile robot with no constraints is holonomic. • A mobile robot capable of arbitrary planar

velocities is holonomic. • A mobile robot capable of only translations is

holonomic.

q( , ) 0f q t

Holonomic does not mean unconstrained!!!

Definition (Holonomic constraint) A kinematic constraint is a holonomic constraint if it can be expressed in the form

( , ) 0f q t

19

Guest Lecture. Locomotion and

Manipulation

• Locomotion and Manipulation Duality • Locomotion Classification • Wheeled machines • Diff drive • Skid Steering • Omni wheels • Tricycle • Ackerman

• Non-holonomic constraints • Legged Robots • Static vs. Dynamic • Passive Dynamics

• Climbing Robots

Holonomic constraints

Definition (Holonomic constraint) A kinematic constraint is a holonomic constraint if it can be expressed in the form

( , ) 0f q t

• Suppose we have a constraint of the form:

Is it non-holonomic?

• Perhaps it can be expressed as

• in which case we say the constraint is integrable. It’s a holonomic constraint, disguised as a nonholonomic constraint.

20

𝑓 𝑞, 𝑡 = 0

𝑓 𝑞, 𝑞 , 𝑡 = 0

Guest Lecture. Locomotion and

Manipulation

• Locomotion and Manipulation Duality • Locomotion Classification • Wheeled machines • Diff drive • Skid Steering • Omni wheels • Tricycle • Ackerman

• Non-holonomic constraints • Legged Robots • Static vs. Dynamic • Passive Dynamics

• Climbing Robots

Non-holonomic constraint: The Unicycle

,

x x

q y q y

sin cos 0x y

( ) (sin , cos , 0 )w q

( ) 0w q q

nonholonomic constraint:

[sin cos 0 ] sin cos 0x x y

Non-integrable constraint

The unicycle cannot move sideways.

21

Guest Lecture. Locomotion and

Manipulation

• Locomotion and Manipulation Duality • Locomotion Classification • Wheeled machines • Diff drive • Skid Steering • Omni wheels • Tricycle • Ackerman

• Non-holonomic constraints • Legged Robots • Static vs. Dynamic • Passive Dynamics

• Climbing Robots

1

cos

sin

0

g

0

2 0

1

g

Rolling forward at unit speed Spinning counterclockwise at unit speed

1 2u u 1 2

q g g

Non-holonomic constraint: The Unicycle

The robot has two controls. How Many freedoms?

are the controls 1 2,u u R

x y

x y

22

,

x x

q y q y

The unicycle can move in two directions:

Guest Lecture. Locomotion and

Manipulation

• Locomotion and Manipulation Duality • Locomotion Classification • Wheeled machines • Diff drive • Skid Steering • Omni wheels • Tricycle • Ackerman

• Non-holonomic constraints • Legged Robots • Static vs. Dynamic • Passive Dynamics

• Climbing Robots

Lie Bracket

Definition (Lie Bracket) Let g1,g2 be two vector fields on C. Define the Lie bracket [g1,g2] to be the vector field

2 11 2 1 2[ , ]

g gg g g g

q q

23

What are 𝜕𝑔1

𝜕𝑞 and

𝜕𝑔2

𝜕𝑞?

Matrices! Each column is partial of velocity w.r.t. configuration variable.

Guest Lecture. Locomotion and

Manipulation

• Locomotion and Manipulation Duality • Locomotion Classification • Wheeled machines • Diff drive • Skid Steering • Omni wheels • Tricycle • Ackerman

• Non-holonomic constraints • Legged Robots • Static vs. Dynamic • Passive Dynamics

• Climbing Robots

x y

x y

Non-holonomic constraint: The Unicycle

1

cos

sin

0

g

0

2 0

1

g

Rolling forward at unit speed Spinning counterclockwise at unit speed

2 11 2 1 2Lie Bracket: [ , ]

g gg g g g

q q

1 2

0 0 0 cos 0 0 sin 0

[ , ] 0 0 0 sin 0 0 cos 0

0 0 0 0 0 0 0 1

g g

1

0 0 sin

0 0 cos

0 0 0

g

q

2

0 0 0

0 0 0

0 0 0

g

q

sin

cos

0

24

Guest Lecture. Locomotion and

Manipulation

• Locomotion and Manipulation Duality • Locomotion Classification • Wheeled machines • Diff drive • Skid Steering • Omni wheels • Tricycle • Ackerman

• Non-holonomic constraints • Legged Robots • Static vs. Dynamic • Passive Dynamics

• Climbing Robots

x y

x y

Non-holonomic constraint: The Unicycle

• Physically, this new lie bracket moves sideways.

• It is linearly independent of 𝑔1and 𝑔2 and it violates the constraint 𝑤.

• Physical significance and why is it important in robotics?

25

0

2 0

1

g

Rolling forward at unit speed Spinning counterclockwise at unit speed

2 11 2 1 2Lie Bracket: [ , ]

g gg g g g

q q

1

cos

sin

0

g

sin

cos

0

Guest Lecture. Locomotion and

Manipulation

• Locomotion and Manipulation Duality • Locomotion Classification • Wheeled machines • Diff drive • Skid Steering • Omni wheels • Tricycle • Ackerman

• Non-holonomic constraints • Legged Robots • Static vs. Dynamic • Passive Dynamics

• Climbing Robots

x y

x y

Non-holonomic constraint: The Unicycle 0

2 0

1

g

Rolling forward at unit speed Spinning counterclockwise at unit speed

2 11 2 1 2Lie Bracket: [ , ]

g gg g g g

q q

1

cos

sin

0

g

y

x

sin

cos

0

y

x

26

Guest Lecture. Locomotion and

Manipulation

• Locomotion and Manipulation Duality • Locomotion Classification • Wheeled machines • Diff drive • Skid Steering • Omni wheels • Tricycle • Ackerman

• Non-holonomic constraints • Legged Robots • Static vs. Dynamic • Passive Dynamics

• Climbing Robots

x y

x y

Non-holonomic constraint: The Unicycle 0

2 0

1

g

Rolling forward at unit speed Spinning counterclockwise at unit speed

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”

2 11 2 1 2Lie Bracket: [ , ]

g gg g g g

q q

1

cos

sin

0

g

y

x

y

x

sin

cos

0

27

Guest Lecture. Locomotion and

Manipulation

• Locomotion and Manipulation Duality • Locomotion Classification • Wheeled machines • Diff drive • Skid Steering • Omni wheels • Tricycle • Ackerman

• Non-holonomic constraints • Legged Robots • Static vs. Dynamic • Passive Dynamics

• Climbing Robots

Wheeled machines

• Problems with wheeled machines:

Maneuverability

Stability

Controllability

28

Guest Lecture. Locomotion and

Manipulation

• Locomotion and Manipulation Duality • Locomotion Classification • Wheeled machines • Diff drive • Skid Steering • Omni wheels • Tricycle • Ackerman

• Non-holonomic constraints • Legged Robots • Static vs. Dynamic • Passive Dynamics

• Climbing Robots

Legged Robots: Stability – Static vs. Dynamic

29

Leg Lab – Marc Raibert Honda Asimo

Dynamic Quasi-static

Guest Lecture. Locomotion and

Manipulation

• Locomotion and Manipulation Duality • Locomotion Classification • Wheeled machines • Diff drive • Skid Steering • Omni wheels • Tricycle • Ackerman

• Non-holonomic constraints • Legged Robots • Static vs. Dynamic • Passive Dynamics

• Climbing Robots

Walking/running machines

30

1 legged hoppers

From: Sayyad Single-legged hopping robotics research—A review Robotica 2007

Raibert’s 3D experimental prototype of one-legged hopping robot (Raibert, Brown)

Uniroo—Zeglin

ARL Monopod-I.

Guest Lecture. Locomotion and

Manipulation

• Locomotion and Manipulation Duality • Locomotion Classification • Wheeled machines • Diff drive • Skid Steering • Omni wheels • Tricycle • Ackerman

• Non-holonomic constraints • Legged Robots • Static vs. Dynamic • Passive Dynamics

• Climbing Robots

Walking/running machines

Boston Dynamics – Big Dog

31

Guest Lecture. Locomotion and

Manipulation

• Locomotion and Manipulation Duality • Locomotion Classification • Wheeled machines • Diff drive • Skid Steering • Omni wheels • Tricycle • Ackerman

• Non-holonomic constraints • Legged Robots • Static vs. Dynamic • Passive Dynamics

• Climbing Robots

Walking/running machines

Guest Lecture. Locomotion and

Manipulation

• Locomotion and Manipulation Duality • Locomotion Classification • Wheeled machines • Diff drive • Skid Steering • Omni wheels • Tricycle • Ackerman

• Non-holonomic constraints • Legged Robots • Static vs. Dynamic • Passive Dynamics

• Climbing Robots

Walking/running machines

Boston Dynamics LS3 400lbs, 20Miles, quiet…

4,700,000 Youtube hits!

33

Guest Lecture. Locomotion and

Manipulation

• Locomotion and Manipulation Duality • Locomotion Classification • Wheeled machines • Diff drive • Skid Steering • Omni wheels • Tricycle • Ackerman

• Non-holonomic constraints • Legged Robots • Static vs. Dynamic • Passive Dynamics

• Climbing Robots

Legged wheels

Rhex

Whegs 34

Guest Lecture. Locomotion and

Manipulation

• Locomotion and Manipulation Duality • Locomotion Classification • Wheeled machines • Diff drive • Skid Steering • Omni wheels • Tricycle • Ackerman

• Non-holonomic constraints • Legged Robots • Static vs. Dynamic • Passive Dynamics

• Climbing Robots

Passive Dynamic Walkers

35

Guest Lecture. Locomotion and

Manipulation

• Locomotion and Manipulation Duality • Locomotion Classification • Wheeled machines • Diff drive • Skid Steering • Omni wheels • Tricycle • Ackerman

• Non-holonomic constraints • Legged Robots • Static vs. Dynamic • Passive Dynamics

• Climbing Robots

Passive Dynamic Walkers

36

Collins, S. H., Wisse, M., Ruina, A., Cornell, 2001

Guest Lecture. Locomotion and

Manipulation

• Locomotion and Manipulation Duality • Locomotion Classification • Wheeled machines • Diff drive • Skid Steering • Omni wheels • Tricycle • Ackerman

• Non-holonomic constraints • Legged Robots • Static vs. Dynamic • Passive Dynamics

• Climbing Robots

Adhesive: Suction/Magnet/

”Electro-adhesion”, “Dry–adhesion”…

Spines “Grasping”/ ”Bracing”

“Brute force” grippers

Climbing Locomotion

37

Guest Lecture. Locomotion and

Manipulation

• Locomotion and Manipulation Duality • Locomotion Classification • Wheeled machines • Diff drive • Skid Steering • Omni wheels • Tricycle • Ackerman

• Non-holonomic constraints • Legged Robots • Static vs. Dynamic • Passive Dynamics

• Climbing Robots

Dynamics? Why? Maneuverability/Agility

38

Guest Lecture. Locomotion and

Manipulation

• Locomotion and Manipulation Duality • Locomotion Classification • Wheeled machines • Diff drive • Skid Steering • Omni wheels • Tricycle • Ackerman

• Non-holonomic constraints • Legged Robots • Static vs. Dynamic • Passive Dynamics

• Climbing Robots

Dynamics? Why Not?

39

Guest Lecture. Locomotion and

Manipulation

• Locomotion and Manipulation Duality • Locomotion Classification • Wheeled machines • Diff drive • Skid Steering • Omni wheels • Tricycle • Ackerman

• Non-holonomic constraints • Legged Robots • Static vs. Dynamic • Passive Dynamics

• Climbing Robots

Dynamics? Why? Minimalism

40

Vs.

g

Guest Lecture. Locomotion and

Manipulation

• Locomotion and Manipulation Duality • Locomotion Classification • Wheeled machines • Diff drive • Skid Steering • Omni wheels • Tricycle • Ackerman

• Non-holonomic constraints • Legged Robots • Static vs. Dynamic • Passive Dynamics

• Climbing Robots

Mechanism overview

41

Simulation – WorkingModel 2DTM

Guest Lecture. Locomotion and

Manipulation

• Locomotion and Manipulation Duality • Locomotion Classification • Wheeled machines • Diff drive • Skid Steering • Omni wheels • Tricycle • Ackerman

• Non-holonomic constraints • Legged Robots • Static vs. Dynamic • Passive Dynamics

• Climbing Robots

Experimental setup

42

Guest Lecture. Locomotion and

Manipulation

• Locomotion and Manipulation Duality • Locomotion Classification • Wheeled machines • Diff drive • Skid Steering • Omni wheels • Tricycle • Ackerman

• Non-holonomic constraints • Legged Robots • Static vs. Dynamic • Passive Dynamics

• Climbing Robots

Proof-of-concept Experiments

43

High friction/damping Low friction/damping

Low friction/damping

High friction/damping

Period-1 Period-2

Guest Lecture. Locomotion and

Manipulation

• Locomotion and Manipulation Duality • Locomotion Classification • Wheeled machines • Diff drive • Skid Steering • Omni wheels • Tricycle • Ackerman

• Non-holonomic constraints • Legged Robots • Static vs. Dynamic • Passive Dynamics

• Climbing Robots

Extensions – Miniature Tube Climber

44

Guest Lecture. Locomotion and

Manipulation

• Locomotion and Manipulation Duality • Locomotion Classification • Wheeled machines • Diff drive • Skid Steering • Omni wheels • Tricycle • Ackerman

• Non-holonomic constraints • Legged Robots • Static vs. Dynamic • Passive Dynamics

• Climbing Robots

Part Feeding

45

Guest Lecture. Locomotion and

Manipulation

• Locomotion and Manipulation Duality • Locomotion Classification • Wheeled machines • Diff drive • Skid Steering • Omni wheels • Tricycle • Ackerman

• Non-holonomic constraints • Legged Robots • Static vs. Dynamic • Passive Dynamics

• Climbing Robots

Part Feeding

46

Guest Lecture. Locomotion and

Manipulation

• Locomotion and Manipulation Duality • Locomotion Classification • Wheeled machines • Diff drive • Skid Steering • Omni wheels • Tricycle • Ackerman

• Non-holonomic constraints • Legged Robots • Static vs. Dynamic • Passive Dynamics

• Climbing Robots

ParkourBot

47

Guest Lecture. Locomotion and

Manipulation

• Locomotion and Manipulation Duality • Locomotion Classification • Wheeled machines • Diff drive • Skid Steering • Omni wheels • Tricycle • Ackerman

• Non-holonomic constraints • Legged Robots • Static vs. Dynamic • Passive Dynamics

• Climbing Robots

Difference between manipulation and locomotion

48

Aperiodic Periodic gaits Stable fixed point Stability?

Manipulation Locomotion