Mechanics and control of soft-fingered manipulation

"Mechanics and Control of Soft-fingered Manipulation" introduces a new approach to the modeling of fingertips that have a soft pad and a hard back plate, similar to human fingers. Starting from the observation of soft-fingered grasping and manipulation, the book provides a parallel distributed model that takes into account tangential deformation of the fingertips. The model is supported with many experimental verifications and simulation results. Statics and dynamics in soft-fingered grasping and manipulation are also formulated based on this new model. The book uniquely investigates how soft fingertips with hard back plates enhance dexterity in grasping and manipulation, theoretically and experimentally, revealing the differences between soft-fingered and rigid-fingered manipulation. Researchers involved in object manipulation by robotic hands, as well as in human dexterity in object manipulation, will find this text enlightening.

Author Notes

Takahiro Inoue received his MSc and PhD degrees from Ritsumeikan University, Japan. He has received funding from the Japan Society of the Promotion of Science and his current research interests include soft-fingered manipulation, soft object modeling, and MEMS technology.

Shinichi Hirai received his BSc, MSc and doctoral degrees from Kyoto University. He is now a professor in the Department of Robotics at Ritsumeikan University. His previous positions include visiting researcher at Massachusetts Institute of Technology and assistant professor at Osaka University. His current research interests are the modeling and control of deformable structures, real-time computer vision, and soft-fingered manipulation.

1 Introduction	p. 1
1.1 Goal	p. 1
1.2 A Brief History of Articulated Robot Hands	p. 2
1.2.1 The 1970s	p. 2
1.2.2 The 1980s	p. 4
1.3 Overview	p. 11
2 Observation of Soft-fingered Grasping and Manipulation	p. 13
2.1 Introduction	p. 13
2.2 Object Pinching by a Pair of 1-DOF Fingers	p. 14
2.3 Rotation of a Pinched Object by External Force	p. 16
2.4 Concluding Remarks	p. 17
3 Elastic Model of a Deformable Fingertip	p. 19
3.1 Introduction	p. 19
3.2 Static Elastic Model of a Hemispherical Soft Fingertip	p. 21
3.2.1 Fingertip Stiffness	p. 21
3.2.2 Elastic Force	p. 24
3.2.3 Elastic Potential Energy	p. 25
3.2.4 Relationship Between Elastic Force and Elastic Energy	p. 25
3.3 Comparison with Hertzian Contact	p. 27
3.4 Measurement of Young's Modulus	p. 28
3.5 Compression Test	p. 29
3.6 Concluding Remarks	p. 32
4 Fingertip Model with Tangential Deformation	p. 33
4.1 Introduction	p. 33
4.2 Two-dimensional Elastic Energy Model	p. 34
4.2.1 Derivation of the Energy Equation	p. 34
4.2.2 Local Minimum of Elastic Potential Energy (LMEE)	p. 36
4.2.3 Restoring Moment for a Contacted Object	p. 37
4.2.4 Boundary Condition of Slip Motion	p. 38
4.3 Formulation of Geometric Constraints	p. 39
4.3.1 Normal Constraints	p. 39
4.3.2 Tangential Constraints	p. 40
4.3.3 LMEE with Constraints (LMEEwC)	p. 43
4.4 Concluding Remarks	p. 43
5 Variational Formulations in Mechanics	p. 45
5.1 Introduction	p. 45
5.2 Variational Principles	p. 45
5.2.1 Variational Principle in Statics	p. 45
5.2.2 Variational Principle in Dynamics	p. 48
5.3 Numerical Optimization of Energy Functions	p. 51
5.3.1 Nelder-Mead Method	p. 51
5.3.2 Multiplier Method	p. 55
5.4 Numerical Integration of Equations of Motion	p. 60
5.4.1 Runge-Kutta Method	p. 60
5.4.2 Constraint Stabilization Method	p. 63
5.4.3 Stabilization of Pfaffian Constraints	p. 66
5.5 Concluding Remarks	p. 70
6 Statics of Soft-fingered Grasping and Manipulation	p. 71
6.1 Introduction	p. 71
6.2 Static Analysis Based on Force/Moment Equilibrium	p. 71
6.2.1 Internal Energy Function	p. 71
6.2.2 Numerical Analysis	p. 72
6.3 Simulation	p. 72
6.3.1 Analysis Without Gravity	p. 72
6.3.2 Analysis Under Gravity	p. 75
6.3.3 Degrees of Freedom Desired for Stable Manipulation	p. 78
6.4 Experiments	p. 78
6.5 Concluding Remarks	p. 81
7 Dynamics of Soft-fingered Grasping and Manipulation	p. 83
7.1 Introduction	p. 83
7.2 Dynamics of Soft-fingered Grasping and Manipulation	p. 83
7.3 Simulation of Soft-fingered Grasping and Manipulation	p. 86
7.3.1 Numerical Integration of Lagrange Equations of Motion Under Geometric Constraints	p. 86
7.3.2 Computation of Equations of Motion	p. 87
7.4 Simulation Results	p. 91
7.5 Experimental Results	p. 95
7.6 Discussion	p. 98
7.7 Conclusion and Research Perspective	p. 98
8 Control of Soft-fingered Grasping and Manipulation	p. 101
8.1 Introduction	p. 101
8.2 Equations of Motion of the Two-fingered Hand	p. 102
8.3 Simulations I: Posture Control of a Grasped Object	p. 103
8.3.1 Serially-coupled Two-phased Object Orientation Controller	p. 103
8.3.2 Examples of Failure	p. 106
8.3.3 Available Range of the Biased Torque	p. 108
8.3.4 Passivity Analysis	p. 111
8.4 Simulations II: Responses for Time Delay	p. 113
8.5 Experiments I: Posture Control of a Grasped Object	p. 118
8.5.1 Object Orientation Control Under Constant Biased Torque (Exp. 1)	p. 119
8.5.2 Open-loop Control of Biased Torque (Exp. 2)	p. 121
8.5.3 Object Orientation Control Under Variable Biased Torque (Exp. 3)	p. 121
8.6 Experiments II: Responses for Time Delay	p. 124
8.7 Concluding Remarks	p. 132
9 Geometric and Material Nonlinear Elastic Model	p. 135
9.1 Introduction	p. 135
9.2 Hertzian Contact and Kao's Elastic Model	p. 135
9.3 Identification of Nonlinear Young's Modulus	p. 136
9.4 Comparison with Hertzian Contact	p. 138
9.5 Force Comparison	p. 139
9.6 Concluding Remarks	p. 141
10 Non-Jacobian Control of Robotic Pinch Tasks	p. 143
10.1 Introduction	p. 143
10.2 Kinematic Thumb Models in Previous Studies	p. 144
10.3 Equations of Motion	p. 147
10.4 Simulations	p. 149
10.4.1 A Serial Two-phased Controller	p. 149
10.4.2 Revolute Joint vs. Prismatic Joint (RP Joints)	p. 150
10.4.3 Revolute Joint vs. Revolute Joint (RR Joints)	p. 162
10.4.4 Prismatic 1-DOF Hand (P Joint)	p. 167
10.4.5 Rotational 1-DOF Hand (R Joint)	p. 169
10.5 Observations and Discussions	p. 181
10.6 Concluding Remarks	p. 183
11 Three-dimensional Grasping and Manipulation	p. 185
11.1 Introduction	p. 185
11.2 Quaternions	p. 185
11.3 Spatial Geometric Constraints Between an Object and a Fingertip	p. 192
11.4 Potential Energy of a Fingertip in Three-dimensional Grasping	p. 197
11.5 Grasping and Manipulation by Three 1-DOF Fingers	p. 201
11.5.1 Observation	p. 201
11.5.2 Mathematical Description	p. 202
11.5.3 Lagrange Equations of Motion	p. 207
11.5.4 Simulation	p. 214
11.6 Concluding Remarks	p. 217
12 Conclusions	p. 219
12.1 Main Contribution	p. 219
12.2 Future Work	p. 221
A Static Modeling of Fingertips	p. 223
A.1 Contact Plane Formula	p. 223
A.2 Spring Constant Formulation	p. 223
A.3 Coordinate Conversion to Derive Fingertip Stiffness	p. 224
A.4 Approximation Method for a Nonlinear Curve	p. 226
B Three-dimensional Modeling of Fingertips	p. 229
B.1 Derivatives of Angular Velocity Matrix	p. 229
B.2 Bilinear Form of the Outer Product Matrix	p. 230
B.3 Derivatives of Relative Angle with Respect to Quaternion Elements	p. 231
B.4 Derivatives of Relative Angle with Respect to Finger Angle	p. 232
B.5 Derivative of the Arctangent Function	p. 233
References	p. 235
Index	p. 243

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