Robot Modeling and Control / Edition 1

by Mark W. Spong, Seth Hutchinson, M. Vidyasagar

Overview

"The coverage is unparalleled in both depth and breadth. No other text that I have seen offers a better complete overview of modern robotic manipulation and robot control."
–– Bradley Bishop, United States Naval Academy

Based on the highly successful classic, Robot Dynamics and Control, by Spong and Vidyasagar (Wiley, 1989), Robot Modeling and Control offers a thoroughly up-to-date, self-contained introduction to the field. The text presents basic and advanced material in a style that is at once readable and mathematically rigorous.

Key Features

• A step-by-step computational approach helps you derive and compute the forward kinematics, inverse kinematics, and Jacobians for the most common robot designs.
• Detailed coverage of vision and visual servo control enables you to program robots to manipulate objects sensed by cameras.
• An entire chapter on dynamics prepares you to compute the dynamics of the most common manipulator designs.
• The most common motion planning and trajectory generation algorithms are presented in an elementary style.
• The comprehensive treatment of motion and force control includes both basic and advanced methods.
• The text’s treatment of geometric nonlinear control is more readable than in more advanced texts.
• Many worked examples and an extensive list of problems illustrate all aspects of the theory.

About the authors

Mark W. Spong is Donald Biggar Willett Professor of Engineering at the University of Illinois at Urbana-Champaign. Dr. Spong is the 2005 President of the IEEE Control Systems Society and past Editor-in-Chief of the IEEE Transactions on Control Systems Technology.

Seth Hutchinson is currently a Professor at the University of Illinois in Urbana-Champaign, and a senior editor of the IEEE Transactions on Robotics and Automation. He has published extensively on the topics of robotics and computer vision.

Mathukumalli Vidyasagar is currently Executive Vice President in charge of Advanced Technology at Tata Consultancy Services (TCS), India's largest IT firm. Dr. Vidyasagar was formerly the director of the Centre for Artificial Intelligence and Robotics (CAIR), under Government of India’s Ministry of Defense.

Product Details

ISBN-13:	9780471649908
Publisher:	Wiley
Publication date:	11/28/2005
Edition description:	Older Edition
Pages:	496
Product dimensions:	7.60(w) x 9.40(h) x 0.90(d)

About the Author

MARK W. SPONG has been researching and teaching robotics for over 35 years. He currently serves as a Professor, Excellence in Education Chair, in the Department of Systems Engineering at the University of Texas at Dallas. He has been recognized for outstanding achievements including the John R. Ragazzini Award for Control Education and the IEEE RAS Pioneer in Robotics Award. He is currently a Fellow of both IEEE and IFAC.

SETH HUTCHINSON received his Ph.D. from Purdue University in 1988, and is currently Professor and KUKA Chair for Robotics in the School of Interactive Computing at the Georgia Institute of Technology, where he also serves as Executive Director of the Institute for Robotics and Intelligent Machines. He was the Founding Editor-in-Chief of the IEEE Robotics and Automation Society's Conference Editorial Board, Editor-in-Chief of the IEEE Transactions on Robotics, and is a Fellow of the IEEE. His research in robotics spans the areas of planning, sensing, and control.

MATHUKUMALLI VIDYASAGAR received his Ph.D. in electrical engineering in 1969 from the University of Wisconsin in Madison. During his fifty-year career, he has worked in control theory, machine learning, robotics and cancer biology. Among the many honors he has received are Fellowship in The Royal Society and the IEEE Control Systems Award. At present he is a Distinguished Professor at the Indian Institute of Technology Hyderabad.

Table of Contents

	Preface
	Table of Contents
1	Introduction	1
1.1	Mathematical Modeling of Robots	3
1.1.1	Symbolic Representation of Robots	4
1.1.2	The Configuration Space	5
1.1.3	The State Space	6
1.1.4	The Workspace	6
1.2	Robots as Mechanical Devices	6
1.2.1	Classification of Robotic Manipulators	6
1.2.2	Robotic Systems	8
1.2.3	Accuracy and Repeatability	9
1.2.4	Wrists and End Effectors	10
1.3	Common Kinematic Arrangements	12
1.3.1	Articulated Manipulator (RRR)	12
1.3.2	Spherical Manipulator (RRP)	14
1.3.3	SCARA Manipulator (RRP)	15
1.3.4	Cylindrical Manipulator (RPP)	16
1.3.5	Cartesian Manipulator (PPP)	16
1.3.6	Parallel Manipulator	19
1.4	Outline of the Text	19
	Problems	27
	Notes and References	30
2	Rigid Motions and Homogeneous Transformations	35
2.1	Representing Positions	36
2.2	Representing Rotations	38
2.2.1	Rotation in the Plane	38
2.2.2	Rotations in Three Dimensions	41
2.3	Rotational Transformations	44
2.3.1	Similarity Transformations	47
2.4	Composition of Rotations	48
2.4.1	Rotation with Respect to the Current Frame	49
2.4.2	Rotation with Respect to the Fixed Frame	51
2.4.3	Rules for Composition of Rotational Transformations	52
2.5	Parameterizations of Rotations	53
2.5.1	Euler Angles	53
2.5.2	Roll, Pitch, Yaw Angles	56
2.5.3	Axis/Angle Representation	57
2.6	Rigid Motions	60
2.7	Homogeneous Transformations	61
2.8	Summary	63
	Problems	65
	Notes and References	72
3	Forward and Inverse Kinematics	73
3.1	Kinematic Chains	73
3.2	The Denavit-Hartenberg Convention	76
3.2.1	Existence and Uniqueness Issues	78
3.2.2	Assigning the Coordinate Frames	80
3.2.3	Examples	83
3.3	Inverse Kinematics	93
3.3.1	The General Inverse Kinematics Problem	93
3.3.2	Kinematic Decoupling	96
3.3.3	Inverse Position: A Geometric Approach	97
3.3.4	Articulated Configuration	98
3.3.5	Spherical Configuration	104
3.3.6	Inverse Orientation	105
3.4	Summary	110
	Problems	111
	Notes and References	117
4	Velocity Kinematics - The Jacobian	119
4.1	Angular Velocity: The Fixed Axis Case	120
4.2	Skew Symmetric Matrices	121
4.2.1	Properties of Skew Symmetric Matrices	122
4.2.2	The Derivative of a Rotation Matrix	124
4.3	Angular Velocity: The General Case	125
4.4	Addition of Angular Velocities	126
4.5	Linear Velocity of a Point Attached to a Moving Frame	128
4.6	Derivation of the Jacobian	129
4.6.1	Angular Velocity	130
4.6.2	Linear Velocity	131
4.6.3	Combining the Linear and Angular Velocity Jacobians	133
4.7	The Tool Velocity	138
4.8	The Analytical Jacobian	140
4.9	Singularities	141
4.9.1	Decoupling of Singularities	142
4.9.2	Wrist Singularities	144
4.9.3	Arm Singularities	144
4.10	Static Force/Torque Relationships	148
4.11	Inverse Velocity and Acceleration	150
4.12	Manipulability	153
4.13	Summary	156
	Problems	158
	Notes and References	160
5	Path and Trajectory Planning	163
5.1	The Configuration Space	164
5.2	Path Planning Using Potential Fields	168
5.2.1	The Attractive Field	170
5.2.2	The Repulsive Field	172
5.2.3	Mapping Workspace Forces to Joint Torques	175
5.2.4	Gradient Descent Planning	178
5.3	Escaping Local Minima	180
5.4	Probabilistic Roadmap Methods	182
5.4.1	Sampling the Configuration Space	183
5.4.2	Connecting Pairs of Configurations	183
5.4.3	Enhancement	185
5.4.4	Path Smoothing	186
5.5	Trajectory Planning	186
5.5.1	Trajectories for Point to Point Motion	188
5.5.2	Trajectories for Paths Specified by Via Points	196
5.6	Summary	199
	Problems	199
	Notes and References	201
6	Independent Joint Control	203
6.1	Actuator Dynamics	205
6.2	Independent Joint Model	208
6.3	Set-Point Tracking	210
6.3.1	PD Compensator	210
6.3.2	PID Compensator	213
6.3.3	The Effect of Saturation and Flexibility	215
6.4	Feedforward Control	217
6.5	Drive Train Dynamics	220
6.6	State Space Design	225
6.6.1	State Feedback Control	227
6.6.2	Observers	230
6.7	Summary	232
	Problems	234
	Notes and References	237
7	Dynamics	239
7.1	The Euler-Lagrange Equations	240
7.1.1	Motivation	240
7.1.2	Holonomic Constraints and Virtual Work	243
7.1.3	D'Alembert's Principle	248
7.2	Kinetic and Potential Energy	250
7.2.1	The Inertia Tensor	251
7.2.2	Kinetic Energy for an n-Link Robot	253
7.2.3	Potential Energy for an n-Link Robot	254
7.3	Equations of Motion	255
7.4	Some Common Configurations	257
7.5	Properties of Robot Dynamic Equations	267
7.5.1	Skew Symmetry and Passivity	267
7.5.2	Bounds on the Inertia Matrix	269
7.5.3	Linearity in the Parameters	270
7.6	Newton-Euler Formulation	271
7.6.1	Planar Elbow Manipulator Revisited	279
7.7	Summary	282
	Problems	285
	Notes and References	287
8	Multivariable Control	289
8.1	PD Control Revisited	290
8.1.1	The Effect of Joint Flexibility	292
8.2	Inverse Dynamics	294
8.2.1	Joint Space Inverse Dynamics	295
8.2.2	Task Space Inverse Dynamics	298
8.3	Robust and Adaptive Motion Control	299
8.3.1	Robust Inverse Dynamics	300
8.3.2	Adaptive Inverse Dynamics	305
8.4	Passivity-Based Motion Control	307
8.4.1	Passivity-Based Robust Control	308
8.4.2	Passivity-Based Adaptive Control	310
8.5	Summary	311
	Problems	315
	Notes and References	317
9	Force Control	319
9.1	Coordinate Frames and Constraints	320
9.1.1	Reciprocal Bases	321
9.1.2	Natural and Artificial Constraints	323
9.2	Network Models and Impedance	325
9.2.1	Impedance Operators	326
9.2.2	Classification of Impedance Operators	327
9.2.3	Thevenin and Norton Equivalents	328
9.3	Task Space Dynamics and Control	328
9.3.1	Task Space Dynamics	328
9.3.2	Impedance Control	329
9.3.3	Hybrid Impedance Control	331
9.4	Summary	334
	Problems	335
	Notes and References	337
10	Geometric Nonlinear Control	339
10.1	Background	340
10.1.1	Manifolds, Vector Fields, and Distributions	340
10.1.2	The Frobenius Theorem	345
10.2	Feedback Linearization	348
10.3	Single-Input Systems	350
10.4	Feedback Linearization for N-Link Robots	357
10.5	Nonholonomic Systems	360
10.5.1	Involutivity and Holonomy	362
10.5.2	Driftless Control Systems	363
10.5.3	Examples of Nonholonomic Systems	363
10.6	Chow's Theorem	367
10.7	Control of Driftless Systems	370
10.8	Summary	371
	Problems	372
	Notes and References	375
11	Computer Vision	377
11.1	The Geometry of Image Formation	378
11.1.1	The Camera Coordinate Frame	378
11.1.2	Perspective Projection	379
11.1.3	The Image Plane and the Sensor Array	380
11.2	Camera Calibration	381
11.2.1	Extrinsic Camera Parameters	381
11.2.2	Intrinsic Camera Parameters	382
11.2.3	Determining the Camera Parameters	382
11.3	Segmentation by Thresholding	385
11.3.1	A Brief Statistics Review	386
11.3.2	Automatic Threshold Selection	387
11.4	Connected Components	392
11.5	Position and Orientation	394
11.5.1	Moments	396
11.5.2	The Centroid of an Object and Central Moments	397
11.5.3	The Orientation of an Object	398
11.6	Summary	400
	Problems	401
	Notes and References	404
12	Vision-Based Control	407
12.1	Design Considerations	408
12.1.1	Camera Configuration	408
12.1.2	Image-Based vs. Position-Based Approaches	409
12.2	Camera Motion and the Interaction Matrix	410
12.3	The Interaction Matrix for Point Features	411
12.3.1	Velocity of a Fixed Point Relative to a Moving Camera	412
12.3.2	Constructing the Interaction Matrix	414
12.3.3	Properties of the Interaction Matrix for Points	416
12.3.4	The Interaction Matrix for Multiple Points	417
12.4	Image-Based Control Laws	418
12.4.1	Computing Camera Motion	419
12.4.2	Proportional Control Schemes	420
12.4.3	Performance of IBVS systems	423
12.5	End Effector and Camera Motions	423
12.6	Partitioned Approaches	425
12.7	Motion Perceptibility	427
12.8	Summary	430
	Problems	432
	Notes and References	434
A	Trigonometry	435
A.1	The Two-Argument Arctangent Function	435
A.2	Useful Trigonometric Formulas	435
B	Linear Algebra	437
B.1	Vectors	437
B.2	Differentiation of Vectors	440
B.3	Linear Independence	440
B.4	Matrices	440
B.5	Change of Coordinates	442
B.6	Eigenvalues and Eigenvectors	442
B.7	Singular Value Decomposition (SVD)	443
C	Dynamical Systems	445
D	Lyapunov Stability	449
D.1	Quadratic Forms and Lyapunov Functions	452
D.2	Lyapunov Stability	453
D.3	Global and Exponential Stability	455
D.4	Lyapunov Stability for Linear Systems	456
D.5	Lasalle's Theorem	456
	Index	470