Front Cover

Cellular Actuators

Copyright

Contents

List of figures

List of tables

Introduction

About this book

Motivation for biologically inspired actuation

Biological muscles and artificial muscle-type actuators

Cellular architecture

Outline of this book

Acknowledgment

Historical overview

Soft robots for unstructured environments

Robot actuators

Redundant actuators

Generation of natural movements

Cellular actuator concept

Inspiration from biological muscles

Binary control of an actuator array

Broadcast feedback with stochastic recruitment

Discussion

1 Structure of cellular actuators

1.1 Strain amplified piezoelectric actuators

1.1.1 Piezoelectric materials

1.1.2 Strain amplification mechanisms

1.1.3 MEMS-PZT cellular actuator

1.1.4 Discussion

1.2 Nested rhombus exponential strain amplification

1.2.1 Large effective strain piezoelectric actuators

1.2.2 Rhombus strain amplification mechanisms

1.2.3 Nested rhombus structure

1.2.4 Properties of ideal nested rhombus PZT actuators

1.2.5 Feasibility check for 20% effective strain

1.2.6 Discussion

1.3 Design of nested-rhombus cellular actuators

1.3.1 Nested rhombus mechanisms with structural flexibility

1.3.2 Verification and calibration of 3-spring lumped parameter model

1.3.3 Prototype two-layer actuator unit

1.3.4 Contractile two-layer mechanism design

1.3.5 Tweezer-style piezoelectric end-effector

1.3.6 Three-layer rhomboidal mechanism design and its application to a camera positioning mechanism

1.3.7 Discussion

2 Modeling of cellular actuators

2.1 Two-port networks for single cell modeling

2.1.1 Why a more involved model is necessary

2.1.2 Two-port models of strain amplifying compliant mechanisms

2.1.3 Finding expressions for the immittance parameters using Castigliano's theorem

2.1.4 Connecting strain amplifiers and amplified stacks together

2.1.5 Effectiveness of multiple layers and figures of merit

2.1.6 Amplifying still further with additional strain amplifying mechanisms

2.1.7 Discussion

2.2 Calibration of two-port network models

2.2.1 Model validation by finite element methods

2.2.2 Experimental results

2.2.3 Discussion

2.3 Modeling of actuator arrays: the nesting theorem: three-layer structure

2.3.1 Actuator compliance for nested amplified piezoelectric actuators

2.3.2 Antagonist pairs of compliant actuators

2.3.3 The first and second nesting theorem: evaluating the perceived stiffness based on the stiffness of each layer

2.3.4 The three-layer structure

2.3.5 Discussion

2.4 Representation and characterization of complex actuator arrays

2.4.1 Graph-theoretic modeling

2.4.2 Cell

2.4.3 Connecting structures

2.4.4 Incidence matrices

2.4.5 Fingerprint method basics

2.4.6 Fingerprint-to-incidence matrix relationship

2.4.7 Automatic generation of actuator array topologies

2.4.8 Incidence matrix identity and similarity transforms

2.4.9 Robustness analysis

2.4.10 Discussion

3 Control of cellular actuators

3.1 Minimum switching discrete switching vibration suppression

3.1.1 Control strategies for flexible mechatronic systems

3.1.2 Open-loop switching control methods

3.1.3 Redundantly actuated two-layer flexible cellular actuator

3.1.4 Determination of switching pattern

3.1.5 Illustrative example of switching algorithm

3.1.6 Experimental setup

3.1.7 Experimental results

3.1.8 Non-ideal effects and command robustness

3.1.9 Discussion

3.2 Broadcast control for cellular actuator arrays

3.2.1 Cellular control system

3.2.2 Broadcast feedback for cellular control system

3.2.3 Stability analysis of broadcast feedback

3.2.4 Simulation: uniform cellular array

3.2.5 Simulation: non-uniform cellular array

3.2.6 Discussion

3.3 Hysteresis loop control of hysteretic actuator arrays

3.3.1 Segmented binary control for hysteretic cellular actuator units

3.3.2 Implementation of hysteresis loop control of an SMA unit

3.3.3 Transition probability distribution and hysteresis loop

3.3.4 Localized stochastic transition

3.3.5 Broadcast control approach to the coordination of hysteric cellular actuator array

3.3.6 Centralized cell coordination

3.3.7 Simulation environment

3.3.8 Simulation results

3.3.9 Discussion

3.4 Supermartingale theory for broadcast control of distributed hysteretic systems

3.4.1 Anonymous control and stochastic recruitment

3.4.2 System representation

3.4.3 Aggregate state, internal dynamics, and observability

3.4.4 Control

3.4.5 Simulation

3.4.6 Robustness against cell failures

3.4.7 Contribution of preloading and refraction rule

3.4.8 Discussion

3.5 Signal-dependent variability of actuator arrays with floating-point quantization

3.5.1 Motor noise and cellular actuation

3.5.2 Floating-point quantization of cellular actuator arrays

3.5.3 Numerical example

3.5.4 Discussion

4 Application of cellular actuators

4.1 Variable stiffness cellular actuators

4.1.1 Variable stiffness actuators

4.1.2 Design of variable stiffness cellular architecture

4.1.3 Tunable resonant frequencies

4.1.4 Implementation of a PZT-based VSCA

4.1.5 Experimental results

4.1.6 Discussion

4.2 Bipolar buckling actuators

4.2.1 Strain amplification by structural buckling

4.2.2 Buckling for large displacement amplification

4.2.3 Redirecting stiffness

4.2.4 Dual buckling unit mechanism

4.2.5 Force-displacement analysis

4.2.6 Dynamic bipolar motion

4.2.7 Prototyping buckling actuators

4.2.8 Static performance

4.2.9 Dynamic performance

4.2.10 Discussion

4.3 Self-sensing piezoelectric grasper

4.3.1 Self-sensing of amplified PZT actuators

4.3.2 Force magnification for tweezer-style piezoelectric end-effector

4.3.3 Mechanical modeling

4.3.4 Combined electromechanical model of the tweezer device

4.3.5 On-site calibration procedure

4.3.6 Electrical circuit

4.3.7 Results

4.3.8 Discussion

4.4 Biologically inspired robotic camera orientation system

4.4.1 Robotic realization of saccades and smooth-pursuit

4.4.2 Dynamics-based oculomotor-visual coordination in rapid camera movements

4.4.3 Switching control of camera positioner

4.4.4 Dynamics-based blur kernel estimation for motion de-blurring

4.4.5 Dynamics-based fast panoramic image stitching

4.4.6 Discussion

5 Conclusion

5.1 Summary and future directions

5.1.1 Brief summary

5.1.2 Future work

Nomenclature

Appendix

A.1 Modeling of hysteresis

A.1.1 Hysteresis in piezoelectric actuators

A.1.2 Hysteresis modeling

A.2 Structural parameters of tweezer-style end-effector

A.3 Piezoelectric driving circuit and control system

A.3.1 Cédrat charge amplifiers

A.3.2 Discrete switching piezoelectric drive circuit

A.3.3 Hardware configuration of real-time controller

A.4 Compliance matrix elements in Section 2.2

A.5 SMA cellular actuators

A.5.1 SMA cellular actuator design

A.5.2 Damped SMA array

A.5.3 Dynamic SMA array

A.5.4 Implementation of floating-point quantization into dynamic SMA actuator array

A.5.5 Robotic arm with SMA cellular actuators

A.6 Deterministic analysis and stability of expectation

A.7 Proof of Lemma 2 in Section 3.4

A.8 Recursive computation of probability Pr(Xt|X0)

A.9 Proof of Lemma 2 in Section 4.1

Bibliography

Index

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