Table of Contents

  1. Cover
  2. Preface
  3. Acknowledgment
  4. About the CompanionWebsite
  5. Chapter 1: Introduction
    1. 1.1 Motivation
    2. 1.2 Origins of Robotic Systems
    3. 1.3 General Structure of Robotic Systems
    4. 1.4 Robotic Manipulators
    5. 1.5 Mobile Robotics
    6. 1.6 An Overview of Robotics Dynamics and Control Problems
    7. 1.7 Organization of the Book
    8. 1.8 Problems for Chapter 1
  6. Chapter 2: Fundamentals of Kinematics
    1. 2.1 Bases and Coordinate Systems
    2. 2.2 Rotation Matrices
    3. 2.3 Parameterizations of Rotation Matrices
    4. 2.4 Position, Velocity, and Acceleration
    5. 2.5 Angular Velocity and Angular Acceleration
    6. 2.6 Theorems of Kinematics
    7. 2.7 Problems for Chapter 2, Kinematics
  7. Chapter 3: Kinematics of Robotic Systems
    1. 3.1 Homogeneous Transformations and Rigid Motion
    2. 3.2 Ideal Joints
    3. 3.3 The Denavit–Hartenberg Convention
    4. 3.4 Recursive Formulation of Forward Kinematics
    5. 3.5 Inverse Kinematics
    6. 3.6 Problems for Chapter 3, Kinematics of Robotic Systems
  8. Chapter 4: Newton–Euler Formulations
    1. 4.1 Linear Momentum of Rigid Bodies
    2. 4.2 Angular Momentum of Rigid Bodies
    3. 4.3 The Newton–Euler Equations
    4. 4.4 Euler's Equation for a Rigid Body
    5. 4.5 Equations of Motion for Mechanical Systems
    6. 4.6 Structure of Governing Equations: Newton–Euler Formulations
    7. 4.7 Recursive Newton–Euler Formulations
    8. 4.8 Recursive Derivation of the Equations of Motion
    9. 4.9 Problems for Chapter 4, Newton–Euler Equations
  9. Chapter 5: Analytical Mechanics
    1. 5.1 Hamilton's Principle
    2. 5.2 Lagrange's Equations for Conservative Systems
    3. 5.3 Hamilton's Extended Principle
    4. 5.4 Lagrange's Equations for Robotic Systems
    5. 5.5 Constrained Systems
    6. 5.6 Problems for Chapter 5, Analytical Mechanics
  10. Chapter 6: Control of Robotic Systems
    1. 6.1 The Structure of Control Problems
    2. 6.2 Fundamentals of Stability Theory
    3. 6.3 Advanced Techniques of Stability Theory
    4. 6.4 Lyapunov's Direct Method
    5. 6.5 The Invariance Principle
    6. 6.6 Dynamic Inversion or Computed Torque Control
    7. 6.7 Approximate Dynamic Inversion and Uncertainty
    8. 6.8 Controllers Based on Passivity
    9. 6.9 Actuator Models
    10. 6.10 Backstepping Control and Actuator Dynamics
    11. 6.11 Problems for Chapter 6, control of Robotic Systems
  11. Chapter 7: Image Based Control of Robotic Systems
    1. 7.1 The Geometry of Camera Measurements
    2. 7.2 Image Based Visual Servo Control
    3. 7.3 Task Space Control
    4. 7.4 Task Space and Visual Control
    5. 7.5 Problems for Chapter 7
  12. Appendix A
    1. A.1 Fundamentals of Linear Algebra
    2. A.2 The Algebraic Eigenvalue Problem
    3. A.3 Gauss Transformations and Factorizations
  13. References
  14. Index
  15. End User License Agreement

List of Tables

  1. Chapter 2
    1. Table 2.1 Frames assignment for the detailed model of the leg assembly ...
    2. Table 2.2 The seven joints between adjacent pairs of rigid bodies illus...
  2. Chapter 3
    1. Table 3.1 DH parameters for the laser ranging scanner.
    2. Table 3.2 DH parameters for a humanoid leg.
    3. Table 3.3 DH parameters for the planar manipulator.
    4. Table 3.4 DH parameters for the robotic arm.
  3. Chapter 5
    1. Table 5.1 DH parameters for the two link robotic arm.
  4. Chapter 7
    1. Table 7.1 Table comparing rotation angle, range of motion, and singular...

List of Illustrations

  1. Chapter 1
    1. Figure 1.1 Fields of expertise associated with mechatronics.
    2. Figure 1.2 Structure of a typical mechatronic system.
    3. Figure 1.3 Fields contributing to robotics.
    4. Figure 1.4 Typical mobile robotic system components [4–6].
    5. Figure 1.5 Typical robotic manipulator system components.
    6. Figure 1.6 Ideal joints and their properties.
    7. Figure 1.7 Pantograph mechanism.
    8. Figure 1.8 Industrial Stewart platforms.
    9. Figure 1.9 Various workspace geometries.
    10. Figure 1.10 Cartesian robot by the Sepro Group. http://www.sepro-group.com...
    11. Figure 1.11 Cylindrical robot by ST Robotics. http://www.strobotics.com/in...
    12. Figure 1.12 Epson SynthisTM T3 all‐in‐one SCARA robot. http://www.epsonrob...
    13. Figure 1.13 Unimate spherical robot.
    14. Figure 1.14 PUMA Robot.
    15. Figure 1.15 Spherical wrist.
    16. Figure 1.16 Articulated robotic arm. http://www.kuka-robotics.com.
    17. Figure 1.17 Humanoid robot for RoboCup soccer competition. Created by stud...
    18. Figure 1.18 Humanoid robot CHARLI. Created by students at Virginia Tech un...
    19. Figure 1.19 Autonomous ground vehicle Odin. Created by students directed b...
    20. Figure 1.20 The autonomous remote controlled HMMWV, ARCH. Created by stude...
    21. Figure 1.21 Autonomous rotorcraft for radiation sensing. Created by studen...
    22. Figure 1.22 Fleet of SPAARO AAVs. Used in the research program of Professo...
    23. Figure 1.23 ASV. Created by students under the direction of Dr. Dan Stilwe...
    24. Figure 1.24 AUV Javelin. Created by students under the direction of Profes...
    25. Figure 1.25 Flapping wing robot.
    26. Figure 1.26 Robotic flapping using robot and joint variables images , and images ....
    27. Figure 1.27 AGV, iRobot PackBot, with manipulator arm.
  2. Chapter 2
    1. Figure 2.1 Space station with remote manipulator system.
    2. Figure 2.2 MULE autonomous vehicle, orientation.
    3. Figure 2.3 Humanoid robot.
    4. Figure 2.4 Cyclic permutations for vectors images .
    5. Figure 2.5 Detailed model of humanoid robot.
    6. Figure 2.6 Detailed model of leg assembly.
    7. Figure 2.7 Frames images and images and vector images for Example 2.2.
    8. Figure 2.8 Canonical single axis rotations. (a) About 1 axis. (b) About 2 ...
    9. Figure 2.9 General non‐commutation of rotation matrix multiplication.
    10. Figure 2.10 Orientation of an autonomous air vehicle, yaw‐pitch‐roll Euler...
    11. Figure 2.11 Yaw angle definition.
    12. Figure 2.12 Pitch angle definition.
    13. Figure 2.13 Roll angle definitions, 3D and 2D.
    14. Figure 2.14 Euler angles: precession, nutation, spin. (a) Precession. (b) ...
    15. Figure 2.15 Kinematic model of a satellite orbit around Earth. (a) Precess...
    16. Figure 2.16 Definition of direction of rotation images and angle of rotation
    17. Figure 2.17 Cylindrical robot, frames.
    18. Figure 2.18 Position Vectors.
    19. Figure 2.19 A Point images Fixed in Frame images .
    20. Figure 2.20 Definition of frames for leg assembly.
    21. Figure 2.21 Points images and images on the Same Rigid Body.
    22. Figure 2.22 Robotic arm and torso assembly.
    23. Figure 2.23 Frame definitions for cylindrical coordinates.
    24. Figure 2.24 Definition of frames on Rubik's cube.
    25. Figure 2.25 First sequence of rotations.
    26. Figure 2.26 Second sequence of rotations.
    27. Figure 2.27 Spherical Coordinates.
    28. Figure 2.28 Azimuth (images ) and elevation (images ) angles relative to an LVLH fra...
    29. Figure 2.29 Detail illustration of a two arm model.
    30. Figure 2.30 Definition of frames images .
    31. Figure 2.31 Definition of frames images .
    32. Figure 2.32 Definition of frames images .
    33. Figure 2.33 Definition of frames for PUMA robot.
    34. Figure 2.34 Definition of frames and points for the SCARA robot in Problem 2...
    35. Figure 2.35 Definition of frames for Problem 2.45.
  3. Chapter 3
    1. Figure 3.1 Two rigid bodies, body fixed frames, and position vectors.
    2. Figure 3.2 Articulating laser ranging sensor. (a) Commercial laser rangefi...
    3. Figure 3.3 Relative positioning of frames images .
    4. Figure 3.4 Two rigid bodies with joint coordinate systems prior to constra...
    5. Figure 3.5 Ideal prismatic joint. (a) Line drawing. (b) CAD example.
    6. Figure 3.6 Ideal revolute joint. (a) Line drawing. (b) CAD example.
    7. Figure 3.7 Universal joint frames.
    8. Figure 3.8 Body and joint numbering of a kinematic chain for the DH conven...
    9. Figure 3.9 Geometry of the DH convention.
    10. Figure 3.10 Intermediate frame images in the DH convention.
    11. Figure 3.11 Construction of the Homogeneous Transform in the DH Convention...
    12. Figure 3.12 DH procedure for kinematic chains.
    13. Figure 3.13 A laser ranging sensor assembly.
    14. Figure 3.14 Assignment of frames to the scanner assembly.
    15. Figure 3.15 Leg assembly of the humanoid robot.
    16. Figure 3.16 Definitions of degree of freedom axes images .
    17. Figure 3.17 Leg assembly joint images (a) and images (b) definitions.
    18. Figure 3.18 Leg assembly joint images (a) and images (b) definitions.
    19. Figure 3.19 Leg assembly joint images (a) and images (b) definitions.
    20. Figure 3.20 Body and joint numbering of a kinematic chain for the recursiv...
    21. Figure 3.21 Joint side labeling of a kinematic chain for the recursive for...
    22. Figure 3.22 Table Recursive algorithm for velocities and angular velocitie...
    23. Figure 3.23 Two link robotic arm.
    24. Figure 3.24 Recursive algorithm for calculation of accelerations and angul...
    25. Figure 3.25 Humanoid arm.
    26. Figure 3.26 Definition of frames consistent with the DH convention.
    27. Figure 3.27 Definition of frames in recursive images formulation of arm assem...
    28. Figure 3.28 Solvability for a planar workspace end effector (images ). (a) images
    29. Figure 3.29 Three degrees of freedom robotic arm. (a) Frames and coordinat...
    30. Example Figure 3.30 Schematic of a three degrees of freedom robotic arm.
    31. Figure 3.31 FANUC robot.
    32. Figure 3.32 Elbow manipulator.
    33. Figure 3.33 images ‐plane projection for calculating images .
    34. Figure 3.34 Planar kinematic chain for calculating images and images .
    35. Figure 3.35 Trigonometric analysis for images and images .
    36. Figure 3.36 Two minimizers of the error functional, configurations images and...
    37. Figure 3.37 Error contours of images .
    38. Figure 3.38 Error contours of images .
    39. Figure 3.39 Plot of images .
    40. Figure 3.40 Configurations of the flapping wing robot for a time varying o...
    41. Figure 3.41 SCARA robot and frame definitions.
    42. Figure 3.42 Cylindrical robot and frame definitions.
    43. Figure 3.43 Modular robot and frame definitions.
    44. Figure 3.44 Spherical joint.
    45. Figure 3.45 Universal Joint.
    46. Figure 3.46 Spherical robot.
    47. Figure 3.47 Humanoid arm assembly with revolute axes defined.
    48. Figure 3.48 Space Shuttle Remote Manipulator System (SSRMS).
    49. Figure 3.49 Industrial robot with frames illustrated.
    50. Figure 3.50 Industrial robot frames labeled.
    51. Figure 3.51 PUMA robot.
    52. Figure 3.52 The spherical wrist.
    53. Figure 3.53 Flapping wing robot.
    54. Figure 3.54 Cartesian robot frames and coordinates.
  4. Chapter 4
    1. Figure 4.1 Rigid body with differential mass element.
    2. Figure 4.2 SCARA robot.
    3. Figure 4.3 SCARA robot link 2 inertia estimation.
    4. Figure 4.4 Rectangular Prism.
    5. Figure 4.5 Rectangular prism.
    6. Figure 4.6 Rectangular Prisms with Body Fixed Frame at Center of Mass.
    7. Figure 4.7 Satellite with body fixed frame.
    8. Figure 4.8 Orbital plane definition.
    9. Figure 4.9 Frame definitions in the orbital plane.
    10. Figure 4.10 Single link rotated with respect to ground frame.
    11. Figure 4.11 Satellite with central body and solar panel fixed frames.
    12. Figure 4.12 Cylindrical Robot.
    13. Figure 4.13 PUMA link 1 with single plane of symmetry.
    14. Figure 4.14 Methodology to derive the equations of motion.
    15. Figure 4.15 Base body and inner arm of a PUMA robot.
    16. Figure 4.16 Link free body diagrams. (a) Link images . (b) Link images .
    17. Figure 4.17 Satellite with two solar arrays.
    18. Figure 4.18 Satellite free body diagrams. (a) Satellite body. (b) Solar pa...
    19. Figure 4.19 Composite joint, prismatic and revolute.
    20. Figure 4.20 Composite joint free body diagrams. (a) Yoke. (b) Collar.
    21. Figure 4.21 Composite joint rectangular bar free body diagram.
    22. Figure 4.22 Composite joint free body diagrams assuming massless collar. (...
    23. Figure 4.23 Composite joint, cylindrical and Revolute.
    24. Figure 4.24 Composite joint free body diagrams. (a) Yoke. (b) Collar.
    25. Figure 4.25 Composite joint cylindrical rod free body diagram.
    26. Figure 4.26 Composite joint free body diagrams assuming massless collar. (...
    27. Figure 4.27 Links 0–2 of a PUMA robotic arm.
    28. Figure 4.28 Links 0–2 of a SCARA robotic arm.
    29. Figure 4.29 Free body diagram of the outer arm.
    30. Figure 4.30 Free body diagram of the inner arm.
    31. Figure 4.31 Joint loading convention.
    32. Figure 4.32 Recursive algorithm for calculating forces and mome...
    33. Figure 4.33 Two link robotic arm.
    34. Figure 4.34 Free body diagrams for a two link robotic arm. (a) Link images . (...
    35. Figure 4.35 PUMA robot frame definitions.
    36. Figure 4.36 PUMA robot joint and mass center offsets.
    37. Figure 4.37 SCARA robot frame definitions.
    38. Figure 4.38 SCARA robot joint and mass center offsets.
    39. Figure 4.39 Cylindrical robot frame definitions.
    40. Figure 4.40 Cylindrical robot joint and mass center offsets.
    41. Figure 4.41 Industrial robot end effector component. (a) Detailed design. (b...
    42. Figure 4.42 Industrial robot fixed base component. (a) Detailed design. (b) ...
    43. Figure 4.43 Industrial robot mounting bracket component. (a) Detailed desi...
    44. Figure 4.44 Links images and images of an industrial robot. (a) Horizontal confi...
    45. Figure 4.45 Spherical joint frames.
    46. Figure 4.46 Universal joint frames.
  5. Chapter 5
    1. Figure 5.1 Point mass constrained to move on an inclined plane.
    2. Figure 5.2 Point on hemispherical surface.
    3. Figure 5.3 Two trajectories in configuration space.
    4. Figure 5.4 Two mass system.
    5. Figure 5.5 Two link robotic arm with point masses, absolute joint angles....
    6. Figure 5.6 Rigid body and differential mass element images .
    7. Figure 5.7 Spherical wrist frames and coordinates.
    8. Figure 5.8 Spherical wrist mass centers.
    9. Figure 5.9 Two link robotic arm.
    10. Figure 5.11 Actuation moment images and equivalent couple. (a) Moment. (b) Co...
    11. Figure 5.10 Reaction forces and moments. (a) Body images . (b) Body images .
    12. Figure 5.12 Couples for actuation moment images acting on bodies images (a) and
    13. Figure 5.13 Bodies images and images with shared revolute joint moving in images .
    14. Figure 5.14 Two link robotic arm with relative angles images .
    15. Figure 5.15 Two link revolute prismatic robot.
    16. Figure 5.16 Rigid link pinned to inertial frame origin.
    17. Figure 5.17 Two link robotic arm with point masses, relative joint angles.
    18. Figure 5.18 Translating mass with rotating pendulum.
    19. Figure 5.19 Point mass on solid cylinder.
    20. Figure 5.20 Point mass on solid cone.
    21. Figure 5.21 Point mass on hemispherical solid, spherical coordinates.
    22. Figure 5.22 Two spring loaded pistons connected by a massless coupler.
    23. Figure 5.23 Point mass on plane and suspended point mass.
    24. Figure 5.24 Two link revolute prismatic robot.
    25. Figure 5.25 PUMA robot frames.
    26. Figure 5.26 PUMA robot frame offsets.
    27. Figure 5.27 Cartesian robot with frames and coordinates.
    28. Figure 5.28 Spherical wrist frames and coordinates.
    29. Figure 5.29 Spherical wrist center of mass positions.
    30. Figure 5.30 SCARA robot frames.
    31. Figure 5.31 SCARA robot joint and mass center offsets.
    32. Figure 5.32 Cylindrical robot frames.
    33. Figure 5.33 Cylindrical robot joint and mass center offsets.
    34. Figure 5.34 Spherical robot frames.
    35. Figure 5.35 Spherical robot joint and mass center offsets.
  6. Chapter 6
    1. Figure 6.1 Graphic representation of stability.
    2. Figure 6.2 Plot of images for images , stable equilibrium marked with images , unstab...
    3. Figure 6.3 A dynamical system is attracted to the origin, but is not stabl...
    4. Figure 6.4 Examples of class images functions, images for images .
    5. Figure 6.5 Shifted sine function used in the Lyapunov function.
    6. Figure 6.6 Graphical interpretation of: (a) positive invariance: images for a...
    7. Figure 6.9 Spherical robot center of mass offsets.
    8. Figure 6.7 Architecture of computed torque control.
    9. Figure 6.8 Spherical robot frames.
    10. Figure 6.10 (a) Initial configurations and (b) final configurations.
    11. Figure 6.11 Time histories of generalized coordinates and actuation inputs...
    12. Figure 6.12 Input Torque Transients. (a) Input torque images and (b) input to...
    13. Figure 6.13 Time histories of generalized coordinates and actuation inputs...
    14. Figure 6.14 Actuation input transient response. (a) Actuation torque images a...
    15. Figure 6.15 Visualization of uniform ultimate boundedness.
    16. Figure 6.16 Time histories of generalized coordinates and actuation inputs...
    17. Figure 6.17 Actuator inputs transients response. (a) Input torque images and ...
    18. Figure 6.18 Time histories generated by discontinuous sliding mode control...
    19. Figure 6.19 Time histories generated by regularized sliding mode controlle...
    20. Figure 6.20 Time histories of generalized coordinates and actuation inputs...
    21. Figure 6.21 Permanent magnet DC motor.
    22. Figure 6.22 Loop of wire carrying a current in the magnetic field having f...
    23. Figure 6.23 Free body diagram of link images .
    24. Figure 6.24 Free body diagrams. (a) Link 1, (b) link 2.
    25. Figure 6.25 Schematic of an electromechanical linear motor.
  7. Chapter 7
    1. Figure7.1 Perspective pinhole camera, rear projected.
    2. Figure 7.2 Perspective pinhole camera, coordinate calculation.
    3. Figure 7.3 Perspective pinhole camera, front projected.
    4. Figure 7.4 Final configuration of the camera frame and feature points.
    5. Figure 7.5 Rotation about the images axis, images , focal plane trajectories.
    6. Figure 7.6 Rotation about the images axis, images , camera coordinate trajectorie...
    7. Figure 7.7 Initial condition configuration.
    8. Figure 7.8 Rotation about the images axis, images , focal plane trajectories.
    9. Figure 7.9 Rotation about the images axis, images , camera coordinate trajectorie...
    10. Figure 7.10 Rotation about the images axis, images , focal plane trajectories.
    11. Figure 7.11 Rotation about the images axis, images , camera coordinate trajectori...
    12. Figure 7.12 Rotation about the images axis, images , focal plane trajectories.
    13. Figure 7.13 Rotation about the images axis, images , camera coordinate trajectori...
    14. Figure 7.14 Rotation about the images axis, images , focal plane trajectories.
    15. Figure 7.15 Rotation about the images axis, images , camera coordinate trajectori...
    16. Figure 7.16 Rotation about the images axis, images , focal plane trajectories.
    17. Figure 7.17 Rotation about the images axis, images , camera coordinate trajectori...
    18. Figure 7.18 Rotation about the images axis, images , minimum singular value.
    19. Figure 7.19 Rotation about the images axis, images , minimum singular ...
    20. Figure 7.20 Rotation about the images axis, images , minimum singular ...
    21. Figure 7.21 Rotation about the images axis, images , minimum singular value.
    22. Figure 7.22 Initial Configuration: images rad, images rad, images m.
    23. Figure 7.23 Tracking error, images , Example 7.4.
    24. Figure 7.24 Tracking error, images , Example 7.4.
    25. Figure 7.25 Tip trajectory in inertial coordinates, images , Example 7.4.
    26. Figure 7.26 Actuation force, images , Example 7.4.
    27. Figure 7.27 Actuation moment, images , Example 7.4.
    28. Figure 7.28 Actuation moment, images , Example 7.4.
    29. Figure 7.29 Spherical robot configuration images and inertially fixed feature...
    30. Figure 7.30 Schematic of initial configuration of robot for case images .
    31. Figure 7.31 Isometric view of initial configuration of robot for case images ....
    32. Figure 7.32 Trajectory images , Example 7.5, case images .
    33. Figure 7.33 Trajectory images , Example 7.5, case images .
    34. Figure 7.34 Trajectory images , Example 7.5, case images .
    35. Figure 7.35 Tracking error images , Example 7.5, case images .
    36. Figure 7.36 Tracking error images , Example 7.5, case images .
    37. Figure 7.37 Actuation force images , Example 7.5, case images .
    38. Figure 7.38 Actuation moment images , Example 7.5, case images .
    39. Figure 7.39 Schematic of initial configuration of robot for case images .
    40. Figure 7.40 Isometric view of initial configuration of robot for case images ....
    41. Figure 7.41 Trajectory images , Example 7.5, case images .
    42. Figure 7.42 Trajectory images , Example 7.5, case images .
    43. Figure 7.43 Trajectory images , Example 7.5, case images .
    44. Figure 7.44 Tracking error images , Example 7.5, case images .
    45. Figure 7.45 Tracking error images , Example 7.5, case images .
    46. Figure 7.46 Actuation force images , Example 7.5, case images .
    47. Figure 7.47 Actuation moment images , Example 7.5, case images .
    48. Figure 7.48 Actuation moment images , Example 7.5, case images .
    49. Figure 7.49 Camera Calibration Pattern Configuration and Generated Image. (a...
    50. Figure 7.50 PUMA robot with attached camera.
    51. Figure 7.51 Spherical wrist with mounted camera
    52. Figure 7.52 SCARA robot with mounted camera.
    53. Figure 7.53 Cylindrical robot with mounted camera.
    54. Figure 7.54 Cylindrical robot and task space trajectory tracking.
    55. Figure 7.55 SCARA robot and task space trajectory tracking.
  8. Appendix
    1. Figure A.1 Gauss transformation, lower triangular form.
    2. Figure A.2 Gauss transformation, upper triangular form.
    3. Figure A.3 Progression of zeros below diagonal.
    4. Figure A.4 Gauss transformations to zero sub‐diagonal entries of images .
    5. Figure A.5 Progression of zeros above diagonal.
    6. Figure A.6 Gauss transformations for upper triangular factorization of images

Guide

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  3. Begin Reading

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