8803 - Mobile Manipulation: Force Control Mike Stilman Robotics - - PDF document

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Mike Stilman (RIM@GT) 8803 Lecture 14 1

• Mike Stilman
• Robotics & Intelligent Machines @ GT
• Georgia Institute of Technology
• Atlanta, GA 30332-0760
• February 19, 2008

8803 - Mobile Manipulation: Force Control

2/21/2008 Mike Stilman (RIM@GT) 8803 Lecture 14 2

Force Control Strategies

• Logic Branching
• Continuous Force Control

– Direct Feedback – Position/Velocity Feedback

• Position Control & Force Control

– Impedance Control (Classic & Revised) – Hybrid Control

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2/21/2008 Mike Stilman (RIM@GT) 8803 Lecture 14 3

Logic Branching

Brief Description:

• Execute specified position/force commands
• Switch behavior on perceived input

Motivation:

• Handle Uncertainty
• Achieve Very Low Tolerances

Ernst ’61, Baber ’73, Inoue ‘74

2/21/2008 Mike Stilman (RIM@GT) 8803 Lecture 14 4

Peg I n Hole

Case 1: Loose Fit

.01” .068” Suppose our positioning error is < .068”

Inoue ‘74 Inoue ‘74

x z

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2/21/2008 Mike Stilman (RIM@GT) 8803 Lecture 14 5

Peg I n Hole

Case 1: Loose Fit

.01” .068” Suppose our positioning error is < .068” 1 2 3 1) Position Control X 2) PUSH-INTO

• Fz = Insert Force
• Fx = 0

Inoue ‘74 Inoue ‘74

x z

2/21/2008 Mike Stilman (RIM@GT) 8803 Lecture 14 6

Peg I n Hole

Case 2: Loose Fit with Uncertainty

.01” .068” Our positioning error is < .068” but Starting position is uncertain (± .1”)

Inoue ‘74 Inoue ‘74

x z

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2/21/2008 Mike Stilman (RIM@GT) 8803 Lecture 14 7

Peg I n Hole

Case 2: Loose Fit with Uncertainty

Inoue ‘74

.01” .068” Our positioning error is < .068” but Starting position is uncertain (± .1”)

Inoue ‘74

1 3 4 1) Z = Z-∆ Until Fz > 0 2) DROP-INTO

• X = X+∆
• Fz = Small Contact Force
• Fx = Small Sliding Force

Until Fx > Threshold 3) PUSH-INTO 2 x z

2/21/2008 Mike Stilman (RIM@GT) 8803 Lecture 14 8

Peg I n Hole

Case 3: Close Fit

Inoue ‘74

.01” Positioning error > .01 and Starting position is uncertain (± .1”)

Inoue ‘74

x z 1

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2/21/2008 Mike Stilman (RIM@GT) 8803 Lecture 14 9

Peg I n Hole

Case 3: Close Fit

Inoue ‘74

.01” Positioning error > .01 and Starting position is uncertain (± .1”)

Inoue ‘74

1 x z 2 4 3 1) Position Control θ to .1 2) DROP-INTO

2/21/2008 Mike Stilman (RIM@GT) 8803 Lecture 14 10

Peg I n Hole

Case 3: Close Fit

Inoue ‘74

.01” Positioning error > .01 and Starting position is uncertain (± .1”)

Inoue ‘74

1 x z 2 4 3 4 1) Position Control θ to .1 2) DROP-INTO 3) Torque θ until τ > threshold 4) PUSH-INTO

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2/21/2008 Mike Stilman (RIM@GT) 8803 Lecture 14 11

Continuous Strategies

• Discrete branching:

– Advantageous for handling Uncertainty/Tolerances – Very useful as part of a system – Could be more time efficient

• Continuous Strategies:

– Coordination of multi-axis motions – Responds to continuously changing force-torque information – Achieves forces with greater precision Nevins ‘73, Whitney ‘77 Raibert & Craig ‘81, Mason ‘81, Khatib ‘87…

2/21/2008 Mike Stilman (RIM@GT) 8803 Lecture 14 12

Continuous Force Control

• Feed-forward:

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2/21/2008 Mike Stilman (RIM@GT) 8803 Lecture 14 13

Continuous Force Control

• Feed-forward:
• How do we do Feedback?

τ = JTF

2/21/2008 Mike Stilman (RIM@GT) 8803 Lecture 14 14

Force-based Feedback Control

KF Arm

fd f

τ

+ −

ef

JT

eτ

τ = −KF JT (f − fd)

Is KF in Joint Space or Workspace? Whitney ‘85 Will it work well? F/T Sensor

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2/21/2008 Mike Stilman (RIM@GT) 8803 Lecture 14 15

Force-based Control (Linearization)

KF Arm

fd f

τ

+ −

ef

JT

eτ

τ = G − KF JT (f − fd)

+ +

F/T Sensor G

θ

2/21/2008 Mike Stilman (RIM@GT) 8803 Lecture 14 16

Force-based Control (Feed-forward)

KF Arm

fd f

τ

+ −

ef

JT

eτ

τ = JT fd + G − KF JT (f − fd)

Similar to Volpe ‘93 JT

+ +

F/T Sensor G

θ

+

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2/21/2008 Mike Stilman (RIM@GT) 8803 Lecture 14 17

Force-based Control (Feed-forward Term)

KF Arm

fd f

τ

+ −

ef

JT

eτ

τ = JT fd + G − KF JT (f − fd)

JT

+ +

F/T Sensor G

θ

+

• Non-zero steady-state error
• Can be oscillatory

Similar to Volpe ’93

2/21/2008 Mike Stilman (RIM@GT) 8803 Lecture 14 18

Options

• Integral Control
• Increase Feed-Forward Term

τ = JT fd + G − KF I Z t JT (f − fd)dt

Volpe ’93

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2/21/2008 Mike Stilman (RIM@GT) 8803 Lecture 14 19

Options

• Integral Control
• Increase Feed-Forward Term

τ = JT fd + G − KF I Z t JT (f − fd)dt

Volpe ’93

2/21/2008 Mike Stilman (RIM@GT) 8803 Lecture 14 20

Position-based Force Control

¯ G(q) = f

Workspace dynamics:

¯ G(q) = f + fE

Workspace dynamics with contact:

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2/21/2008 Mike Stilman (RIM@GT) 8803 Lecture 14 21

Position-based Force Control

¯ G(q) = f

Workspace dynamics:

¯ G(q) = f + fE

Workspace dynamics with contact: Generic Position Controller:

f = ¯ G(q) − Kp(x − xd) ¯ G(q) = ¯ G(q) − Kp(x − xd) + fE

Controlled System Dynamics:

2/21/2008 Mike Stilman (RIM@GT) 8803 Lecture 14 22

Position-based Force Control

¯ G(q) = f

Workspace dynamics:

¯ G(q) = f + fE

Workspace dynamics with contact: Generic Position Controller:

f = ¯ G(q) − Kp(x − xd) ¯ G(q) = ¯ G(q) − Kp(x − xd) + fE

Controlled System Dynamics:

Kp(x − xd) = fE xd = −K−1

p fE + x xd - x Kp

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2/21/2008 Mike Stilman (RIM@GT) 8803 Lecture 14 23

Position-based Force Control: Feedback

Position Control: Arm G

θ

Kin.

x

− +

xd

Kp

+ +

JT

FC

τC

xe

2/21/2008 Mike Stilman (RIM@GT) 8803 Lecture 14 24

Position-based Force Control: Feedback

Arm G

θ

Kin.

x

− +

xd

Kp

+ +

JT

FC

τC

fd f

+ −

F/T Sensor

xe

KIf

+ +

Force Control ∫ 1 s ∫ fe KlfKp

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2/21/2008 Mike Stilman (RIM@GT) 8803 Lecture 14 25

Position Control + Force Control

Impedance Control

• Continuous relationship between position/force
• Simulates behavior of a simple mechanical system

Hybrid Control

• Selection Matrix identifies directions for position/force
• Allows for precise positioning and force control

2/21/2008 Mike Stilman (RIM@GT) 8803 Lecture 14 26

I mpedance Control

Md¨ x − Dd ˙ xe − Kdxe = fE

How would the robot respond if its dynamics were actually:

• Position tracking when force = 0
• Compliance when force > 0
• Restoration to tracking when force is removed

xe = (x − xr)

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2/21/2008 Mike Stilman (RIM@GT) 8803 Lecture 14 27

I mpedance Control

Md¨ x − Dd ˙ xe − Kdxe = fE

How would the robot respond if its dynamics were actually:

• Position tracking when force = 0
• Compliance when force > 0
• Restoration to tracking when force is removed

xe = (x − xr) ¨ x = M−1

d (fE + Dd ˙

xe + Kdxe)

2/21/2008 Mike Stilman (RIM@GT) 8803 Lecture 14 28

I mpedance Control

Md¨ x − Dd ˙ xe − Kdxe = fE

How would the robot respond if its dynamics were actually:

• Position tracking when force = 0
• Compliance when force > 0
• Restoration to tracking when force is removed

xe = (x − xr) τ = JT( ¯ M(M−1

d (fE + Dd ˙

xe + Kdxe)) + ¯ C˙ x + ¯ G − fE) ¨ x = M−1

d (fE + Dd ˙

xe + Kdxe)

Notice the similarity to workspace computed torque:

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2/21/2008 Mike Stilman (RIM@GT) 8803 Lecture 14 29

Position-based I mpedance Control

Md¨ x − Dd ˙ xe − Kdxe = fE xe = (x − xr)

1) Simulate the system response to 2) Track simulated (possibly )

x

˙ x

fE ¨ x(t + ∆t) = M−1

d (fE + Dd ˙

x(t) + Kdx(t)) ˙ x(t + ∆t) = ˙ x(t) + ¨ x(t)∆t x(t + ∆t) = x(t) + ˙ x(t)∆t

2/21/2008 Mike Stilman (RIM@GT) 8803 Lecture 14 30

Hybrid Control

• Task Constraint: Restriction on the freedom of motion of the manipulator
• Cannot move in some direction
• Can control forces/moments in that direction
• Degrees of freedom are coordinates in a task frame
• Task frame is a transformed world frame

Ft = T0

tF 0

Ft

x = £ x1 · · · xn ¤T

Ft F0

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2/21/2008 Mike Stilman (RIM@GT) 8803 Lecture 14 31

Hybrid Control

• A motion constraint is described by a selection matrix:
• Coordinates – Cartesian + Fixed Axis (Roll, Pitch Yaw)
• Alternative Coordinates:

S = ⎡ ⎣ s1 · · · sn ⎤ ⎦

S˙ x = 0

x y z

Rt

B = R(zt, φ)R(yt, θ)R(xt, ψ)

SRPY = I[ sx sy sz sψ sθ sφ ]T

Ft

2/21/2008 Mike Stilman (RIM@GT) 8803 Lecture 14 32

Examples of Constraints

[ 0 1 1 1 1 1 ] [ 1 1 1 1 1 0 ] Parameterized [ 0 0 0 1 1 0 ] Parameterized [ 1 1 1 1 1 0 ]

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2/21/2008 Mike Stilman (RIM@GT) 8803 Lecture 14 33

Hybrid Control

x

f

−

xd

+

Motion Control S Force Control I-S Arm

− +

fd

+ +

Motion Force Rt Rt RtT RtT

2/21/2008 Mike Stilman (RIM@GT) 8803 Lecture 14 34

Best of Both Worlds

• Use task frame to set a center of compliance for impedance control
• Use Impedance Control (not motion control) in hybrid system
• Vary the parameters of Impedance Control according to direction

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2/21/2008 Mike Stilman (RIM@GT) 8803 Lecture 14 35

Summary

We looked at:

• Logic Branching
• Continuous Force Control (Force and Position Based)
• Hybrid Postion/Force Strategies

Your goal:

• Think about how these strategies can help you accomplish the task
• Which subtasks require which type of control?