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- Herausgeber: John Wiley & Sons
- Kategorie: Wissenschaft und neue Technologien
- Serie: Wiley-ASME Press Series
- Sprache: Englisch
Introduces a revolutionary, quadratic-programming based approach to solving long-standing problems in motion planning and control of redundant manipulators This book describes a novel quadratic programming approach to solving redundancy resolutions problems with redundant manipulators. Known as ``QP-unified motion planning and control of redundant manipulators'' theory, it systematically solves difficult optimization problems of inequality-constrained motion planning and control of redundant manipulators that have plagued robotics engineers and systems designers for more than a quarter century. An example of redundancy resolution could involve a robotic limb with six joints, or degrees of freedom (DOFs), with which to position an object. As only five numbers are required to specify the position and orientation of the object, the robot can move with one remaining DOF through practically infinite poses while performing a specified task. In this case redundancy resolution refers to the process of choosing an optimal pose from among that infinite set. A critical issue in robotic systems control, the redundancy resolution problem has been widely studied for decades, and numerous solutions have been proposed. This book investigates various approaches to motion planning and control of redundant robot manipulators and describes the most successful strategy thus far developed for resolving redundancy resolution problems. * Provides a fully connected, systematic, methodological, consecutive, and easy approach to solving redundancy resolution problems * Describes a new approach to the time-varying Jacobian matrix pseudoinversion, applied to the redundant-manipulator kinematic control * Introduces The QP-based unification of robots' redundancy resolution * Illustrates the effectiveness of the methods presented using a large number of computer simulation results based on PUMA560, PA10, and planar robot manipulators * Provides technical details for all schemes and solvers presented, for readers to adopt and customize them for specific industrial applications Robot Manipulator Redundancy Resolution is must-reading for advanced undergraduates and graduate students of robotics, mechatronics, mechanical engineering, tracking control, neural dynamics/neural networks, numerical algorithms, computation and optimization, simulation and modelling, analog, and digital circuits. It is also a valuable working resource for practicing robotics engineers and systems designers and industrial researchers.
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Veröffentlichungsjahr: 2017
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Table of Contents
Cover
Title Page
Copyright
Dedication
List of Figures
List of Tables
Preface
Acknowledgments
Acronyms
Part I: Pseudoinverse-Based ZD Approach
Chapter 1: Redundancy Resolution via Pseudoinverse and ZD Models
1.1 Introduction
1.2 Problem Formulation and ZD Models
1.3 ZD Applications to Different-Type Robot Manipulators
1.4 Chapter Summary
Part II: Inverse-Free Simple Approach
Chapter 2: G1 Type Scheme to JVL Inverse Kinematics
2.1 Introduction
2.2 Preliminaries and Related Work
2.3 Scheme Formulation
2.4 Computer Simulations
2.5 Physical Experiments
2.6 Chapter Summary
Chapter 3: D1G1 Type Scheme to JAL Inverse Kinematics
3.1 Introduction
3.2 Preliminaries and Related Work
3.3 Scheme Formulation
3.4 Computer Simulations
3.5 Chapter Summary
Chapter 4: Z1G1 Type Scheme to JAL Inverse Kinematics
4.1 Introduction
4.2 Problem Formulation and Z1G1 Type Scheme
4.3 Computer Simulations
4.4 Physical Experiments
4.5 Chapter Summary
Part III: QP Approach and Unification
Chapter 5: Redundancy Resolution via QP Approach and Unification
5.1 Introduction
5.2 Robotic Formulation
5.3 Handling Joint Physical Limits
5.4 Avoiding Obstacles
5.5 Various Performance Indices
5.6 Unified QP Formulation
5.7 Online QP Solutions
5.8 Computer Simulations
5.9 Chapter Summary
Part IV: Illustrative JVL QP Schemes and Performances
Chapter 6: Varying Joint-Velocity Limits Handled by QP
6.1 Introduction
6.2 Preliminaries and Problem Formulation
6.3 94LVI Assisted QP Solution
6.4 Computer Simulations and Physical Experiments
6.5 Chapter Summary
Chapter 7: Feedback-Aided Minimum Joint Motion
7.1 Introduction
7.2 Preliminaries and Problem Formulation
7.3 Computer Simulations and Physical Experiments
7.4 Chapter Summary
Chapter 8: QP Based Manipulator State Adjustment
8.1 Introduction
8.2 Preliminaries and Scheme Formulation
8.3 QP Solution and Control of Robot Manipulator
8.4 Computer Simulations and Comparisons
8.5 Physical Experiments
8.6 Chapter Summary
Part V: Self-Motion Planning
Chapter 9: QP-Based Self-Motion Planning
9.1 Introduction
9.2 Preliminaries and QP Formulation
9.3 LVIAPDNN Assisted QP Solution
9.4 PUMA560 Based Computer Simulations
9.5 PA10 Based Computer Simulations
9.6 Chapter Summary
Chapter 10: Pseudoinverse Method and Singularities Discussed
10.1 Introduction
10.2 Preliminaries and Scheme Formulation
10.3 LVIAPDNN Assisted QP Solution with Discussion
10.4 Computer Simulations
10.5 Chapter Summary
Appendix
Chapter 11: Self-Motion Planning with ZIV Constraint
11.1 Introduction
11.2 Preliminaries and Scheme Formulation
11.3 E47 Assisted QP Solution
11.4 Computer Simulations and Physical Experiments
11.5 Chapter Summary
Part VI: Manipulability Maximization
Chapter 12: Manipulability-Maximizing SMP Scheme
12.1 Introduction
12.2 Scheme Formulation
12.3 Computer Simulations and Physical Experiments
12.4 Chapter Summary
Chapter 13: Time-Varying Coefficient Aided MM Scheme
13.1 Introduction
13.2 Manipulability-Maximization with Time-Varying Coefficient
13.3 Computer Simulations and Physical Experiments
13.4 Chapter Summary
Part VII: Encoder Feedback and Joystick Control
Chapter 14: QP Based Encoder Feedback Control
14.1 Introduction
14.2 Preliminaries and Scheme Formulation
14.3 Computer Simulations
14.4 Physical Experiments
14.5 Chapter Summary
Chapter 15: QP Based Joystick Control
15.1 Introduction
15.2 Preliminaries and Hardware System
15.3 Scheme Formulation
15.4 Computer Simulations and Physical Experiments
15.5 Chapter Summary
References
Index
End User License Agreement
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Guide
Cover
Table of Contents
Preface
Begin Reading
Begin Reading
List of Illustrations
Chapter 1: Redundancy Resolution via Pseudoinverse and ZD Models
Figure 1.1 Block diagram of a kinematic-control system for a redundant robot manipulator by combining the MVN scheme (1.1) and ZD model, where .
Figure 1.2 Geometry of a five-link planar robot manipulator used in simulations.
Figure 1.3 Joint-angle and joint-velocity profiles of a five-link planar robot manipulator synthesized by pseudoinverse-based MVN scheme (1.1) aided with TDTZD-U model (1.14).
Figure 1.4 (a) Motion process and (b) position error of a five-link planar robot manipulator synthesized by the pseudoinverse-based MVN scheme (1.1) and aided by the TDTZD-U model (1.14).
Figure 1.5 Position error of a five-link planar robot manipulator synthesized by a pseudoinverse-based MVN scheme (1.1) aided with the EDTZD-K model (1.9) or Newton iteration (1.15).
Figure 1.6 Position errors of a three-link planar robot manipulator synthesized by a pseudoinverse-based MVN scheme (1.1) aided with EDTZD-K model (1.9) with .
Chapter 2: G1 Type Scheme to JVL Inverse Kinematics
Figure 2.1 (a) Motion process and (b) joint-angle profiles of a five-link redundant robot manipulator tracking the desired square path synthesized by the G1 type scheme (2.8).
Figure 2.2 (a) Desired path, actual trajectory, and (b) position error of a five-link redundant robot manipulator tracking square path synthesized by a G1 type scheme (2.8).
Figure 2.3 (a) Desired velocity and (b) velocity error of a five-link redundant robot manipulator tracking a square path synthesized by a G1 type scheme (2.8).
Figure 2.4 Motion process (a) and joint-angle profiles (b) of six-DOF redundant robot manipulator tracking the desired “Z”-shaped path synthesized by a G1 type scheme (2.8).
Figure 2.5 (a) Desired path, actual trajectory, and (b) position error of a six-DOF redundant robot manipulator tracking a “Z”-shaped path synthesized by a G1 type scheme (2.8).
Figure 2.6 (a) Desired velocity and (b) velocity error of a six-DOF redundant robot manipulator tracking a “Z”-shaped path synthesized by a G1 type scheme (2.8).
Figure 2.7 Hardware system (a) of six-DOF planar redundant robot manipulator with its structure platform (b).
Source:
Zhang et al. 2015. Reproduced from Y. Zhang, L. He, J. Ma et al., Inverse-free scheme of G1 type to velocity-level inverse kinematics of redundant robot manipulators, Figure 3, Proceedings of the Twelfth International Symposium on Neural Networks, pp. 99-108, 2015. ©Springer-Verlag 2015. With kind permission of Springer-Verlag (License Number 3978560065761).
Figure 2.8 “Z”-shaped-path-tracking experiment of six-DOF redundant robot manipulator synthesized by G1 type scheme (2.8) at joint-velocity level. Reproduced from Y. Zhang, L. He, J. Ma et al, Inverse-free scheme of G1 type to velocity-level inverse kinematics of redundant robot manipulators, Figure 4, Proceedings of the Twelfth International Symposium on Neural Networks, pp. 99-108, 2015. ©Springer-Verlag 2015. With kind permission of Springer-Verlag (License Number 3978560065761).
Chapter 3: D1G1 Type Scheme to JAL Inverse Kinematics
Figure 3.1 (a) Motion process, (b) desired path, and actual trajectory of a three-link redundant robot manipulator tracking a rhombus path synthesized by the D1G1 scheme (3.7) with .
Figure 3.2 Joint-angle profiles (a) and position error (b) of a three-link redundant robot manipulator tracking a rhombus path synthesized by the D1G1 scheme (3.7) with .
Figure 3.3 Joint-velocity profiles (a) and velocity error (b) of a three-link redundant robot manipulator tracking a rhombus path synthesized by the D1G1 scheme (3.7) with .
Figure 3.4 (a) Joint-acceleration profiles and (b) acceleration error of a three-link redundant robot manipulator tracking a rhombus path synthesized by the D1G1 scheme (3.7) with .
Figure 3.5 Position errors in rhombus-path-tracking task of a three-link robot manipulator synthesized by (a) pseudoinverse solution (3.4) and (b) inverse-free D1G1 scheme (3.7) with .
Figure 3.6 (a) Motion process and (b) joint-angle profiles of a three-link redundant robot manipulator tracking a desired triangle path synthesized by a D1G1 scheme (3.7) with .
Figure 3.7 Position errors in triangle-path-tracking task of the three-link robot manipulator synthesized by (a) pseudoinverse solution (3.4) and (b) inverse-free D1G1 scheme (3.7) with .
Chapter 4: Z1G1 Type Scheme to JAL Inverse Kinematics
Figure 4.1 (a) Motion process and (b) joint-angle profiles of a three-link planar robot manipulator tracking a desired isosceles-trapezoid path synthesized by the Z1G1 type scheme (4.5).
Figure 4.2 (a) Joint-velocity profiles and (b) joint-acceleration profiles of three-link planar robot manipulator tracking isosceles-trapezoid path synthesized by Z1G1 type scheme (4.5).
Figure 4.3 (a) Motion process and (b) joint-angle profiles of a four-link planar robot manipulator tracking a desired isosceles-triangle path synthesized by the Z1G1 type scheme (4.5).
Figure 4.4 (a) Joint-velocity profiles and (b) joint-acceleration profiles of a four-link planar robot manipulator tracking an isosceles-triangle path synthesized by the Z1G1 type scheme (4.5).
Figure 4.5 Simulation results of a three-link planar robot manipulator tracking an isosceles-trapezoid path synthesized by the Z1G1 type scheme (4.5) with an initial end-effector position not on the desired path.
Figure 4.6 “V”-shaped-path-tracking experiment of a six-DOF redundant robot manipulator synthesized by the Z1G1 type scheme (4.5) at joint-acceleration level.
Chapter 5: Redundancy Resolution via QP Approach and Unification
Figure 5.1 Contradicting situations in equality-based collision-free formulation.
Figure 5.2 QP-based approach to redundancy resolution and torque control.
Figure 5.3 PUMA560 transients synthesized by a QP-based MTN scheme.
Figure 5.4 PUMA560 transients synthesized by a QP-based MKE scheme.
Figure 5.5 Comparison of (a) conventional and (b) presented MTN schemes.
Figure 5.6 Joint-torque profiles synthesized by other QP-based resolution schemes of (a) IIWT and (b) MAN.
Figure 5.7 Joint-torque profiles synthesized by other QP-based resolution schemes of (a ) MKE and (b) MVN.
Chapter 6: Varying Joint-Velocity Limits Handled by QP
Figure 6.1 (a) Hardware system and (b) model of a six-DOF planar robot manipulator.
Figure 6.2 Local configuration of a six-DOF planar robot manipulator.
Figure 6.3 Relationship between (a) and as well as (b) the relationship between and .
Figure 6.4 Relationship between (a)
and
as well as (b) the relationship between
and
.
Figure 6.5 Relationship between (a) and as well as (b) the relationship between and .
Figure 6.6 Desired line-segment path to be tracked by the end-effector of a six-DOF planar robot manipulator.
Figure 6.7 Snapshots for an actual task execution of a six-DOF planar robot manipulator synthesized by a VJVL-constrained MVN scheme when a robot end-effector tracks a line-segment path. Reproduced from Z. Zhang, and Y. Zhang, Variable Joint-Velocity Limits of Redundant Robot Manipulators Handled by Quadratic Programming, Figure 5, IEEE/ASME Trans. Mechatronics, Vol. 18, No. 2, pp. 674-686, 2013.
Figure 6.8 Actual end-effector trajectory generated by a six-DOF planar robot manipulator synthesized by a VJVL-constrained MVN scheme.
Figure 6.9 Simulated six-DOF planar robot manipulator and its joints' trajectories synthesized by a VJVL-constrained MVN scheme when the robot end-effector tracks a line-segment path.
Figure 6.10 (a) PPS and (b) PPS transmitted to joint motors when the end-effector tracks a line-segment path.
Figure 6.11 (a) PPS
and (b) PPS
transmitted to joint motors when the end-effector tracks a line-segment path.
Figure 6.12 (a) PPS and (b) PPS transmitted to joint motors when the end-effector tracks a line-segment path.
Figure 6.13 (a) Joint-angle and (b) joint-velocity profiles of a six-DOF planar robot manipulator synthesized by a VJVL-constrained MVN scheme when the robot end-effector tracks a line-segment path.
Figure 6.14 End-effector position error of a six-DOF planar robot manipulator synthesized by a VJVL-constrained MVN scheme when the robot end-effector tracks a line-segment path.
Figure 6.15 Snapshots for actual task execution of a six-DOF planar robot manipulator synthesized by a VJVL-constrained MVN scheme when the robot end-effector tracks an elliptical path.
Figure 6.16 (a) Joint-angle and (b) joint-velocity profiles of a six-DOF planar robot manipulator synthesized by a VJVL-constrained MVN scheme when the robot end-effector tracks an elliptical path.
Figure 6.17 End-effector position error of a six-DOF planar robot manipulator synthesized by a VJVL-constrained MVN scheme when the robot end-effector tracks an elliptical path.
Figure 6.18 Joint-velocity profiles of (a) and (b) of a six-DOF planar robot manipulator synthesized by a VJVL-constrained MVN scheme when its end-effector tracks a line-segment path much faster.
Figure 6.19 Joint-velocity profiles of (a)
and (b)
of a six-DOF planar robot manipulator synthesized by a VJVL-constrained MVN scheme when its end-effector tracks a line-segment path much faster.
Figure 6.20 Joint-velocity profiles of (a) and (b) of a six-DOF planar robot manipulator synthesized by a the VJVL-constrained MVN scheme when its end-effector tracks a line-segment path much faster.
Figure 6.21 End-effector position error of a six-DOF planar robot manipulator synthesized by a VJVL-constrained MVN scheme when its end-effector tracks a line-segment path much faster.
Figure 6.22 Joint-velocity profiles of a robot synthesized by a VJVL-constrained MVN scheme when its end-effector tracks an elliptical path much faster, which includes a profile of joint velocity within and sometimes reaching limits of .
Figure 6.23 End-effector position error of a six-DOF planar robot manipulator synthesized by a VJVL-constrained MVN scheme when its end-effector tracks an elliptical path much faster.
Figure 6.24 Iteration number and computing time of a numerical algorithm 94LVI (6.17) per sampling period in a much faster elliptical-path tracking task.
Chapter 7: Feedback-Aided Minimum Joint Motion
Figure 7.1 (a) Desired “M”-shaped path and (b) motion process of a six-DOF planar robot manipulator synthesized by a FAMJM scheme (7.23)–(7.25).
Figure 7.2 Maximum error variation tendency of a six-DOF planar robot manipulator synthesized by FAMJM scheme (7.23)–(7.25) when increases from 0 to 100 during “M”-shaped-path-tracking execution.
Figure 7.3 Joint displacement variation tendency of a six-DOF planar robot manipulator synthesized by FAMJM scheme (7.23)–(7.25) when a robot end-effector tracks an “M”-shaped path.
Figure 7.4 Snapshots for actual task execution of a six-DOF planar robot manipulator synthesized by FAMJM scheme (7.23)–(7.25) when a robot end-effector tracks an “M”-shaped path.
Figure 7.5 (a) Joint-angle and (b) joint-velocity profiles of a six-DOF planar robot manipulator synthesized by FAMJM scheme (7.23)–(7.25) with and when a robot end-effector tracks an “M”-shaped path.
Figure 7.6 (a) Desired path, end-effector trajectory, and (b) position error for actual task execution of a six-DOF planar robot manipulator synthesized by FAMJM scheme (7.23)–(7.25) with and when a robot end-effector tracks an “M”-shaped path.
Figure 7.7 Snapshots of the actual task execution of a six-DOF planar robot manipulator synthesized by FAMJM scheme (7.23)–(7.25) when a robot end-effector tracks a “P”-shaped path.
Figure 7.8 Joint-angle profiles of (a) and (b) synthesized by PBMJM scheme (7.27) when a robot end-effector tracks a larger “M”-shaped path.
Figure 7.9 Joint-angle profiles of (a) and (b) synthesized by PBMJM scheme (7.27) when a robot end-effector tracks a larger “M”-shaped path.
Figure 7.10 Joint-angle profiles of (a) and (b) synthesized by PBMJM scheme (7.27) when a robot end-effector tracks a larger “M”-shaped path.
Figure 7.11 Joint-angle profiles of (a) and (b) synthesized by FAMJM scheme (7.23)–(7.25) when a robot end-effector tracks a larger “M”-shaped path.
Figure 7.12 Joint-angle profiles of (a)
and (b)
synthesized by FAMJM scheme (7.23)–(7.25) when a robot end-effector tracks a larger “M”-shaped path.
Figure 7.13 Joint-angle profiles of (a) and (b) synthesized by FAMJM scheme (7.23)–(7.25) when a robot end-effector tracks a larger “M”-shaped path.
Figure 7.14 Joint-angle profiles of (a) and (b) synthesized by PBMJM scheme (7.27) when robot end-effector tracks a larger “P”-shaped path.
Figure 7.15 Joint-angle profiles of (a)
and (b)
synthesized by PBMJM scheme (7.27) when a robot end-effector tracks a larger “P”-shaped path.
Figure 7.16 Joint-angle profiles of (a)
and (b)
synthesized by PBMJM scheme (7.27) when a robot end-effector tracks a larger “P”-shaped path.
Figure 7.17 Joint-angle profiles of (a)
and (b)
synthesized by FAMJM scheme (7.23)–(7.25) when a robot end-effector tracks a larger “P”-shaped path.
Figure 7.18 Joint-angle profiles of (a)
and (b)
synthesized by FAMJM scheme (7.23)–(7.25) when a robot end-effector tracks a larger “P”-shaped path.
Figure 7.19 Joint-angle profiles of (a) and (b) synthesized by FAMJM scheme (7.23)–(7.25) when a robot end-effector tracks a larger “P”-shaped path.
Chapter 8: QP Based Manipulator State Adjustment
Figure 8.1 (a) Joint-angle and (b) joint-velocity profiles of a six-DOF planar robot manipulator synthesized by state-adjustment scheme (8.1)–(8.3) without imposing a zero-initial-velocity constraint and with parameters and s.
Figure 8.2 (a) Joint-angle and (b) joint-velocity profiles of a six-DOF planar robot manipulator synthesized by state-adjustment scheme (8.1)–(8.3) without imposing a zero-initial-velocity constraint and with parameters and s.
Figure 8.3 (a) Motion process and (b) trajectories of a six-DOF planar robot manipulator synthesized by state-adjustment scheme (8.1)–(8.3) with a zero-initial-velocity constraint imposed (i.e., QP (8.13)–(8.14)) and with and s.
Figure 8.4 (a) Joint-angle and (b) joint-velocity profiles of a six-DOF planar robot manipulator synthesized by state-adjustment scheme (8.1)–(8.3) with zero-initial-velocity constraint imposed (i.e., QP (8.13)–(8.14)) and with and s.
Figure 8.5 (a) Joint-angle and (b) joint-velocity profiles of a six-DOF planar robot manipulator synthesized by state-adjustment scheme (8.1)–(8.3) with a zero-initial-velocity constraint imposed (i.e., QP (8.13)–(8.14)) and with and s.
Figure 8.6 (a) Joint-angle and (b) joint-velocity profiles of a six-DOF planar robot manipulator synthesized by state-adjustment scheme (8.1)–(8.3) with a zero-initial-velocity constraint imposed (i.e., QP (8.13)–(8.14)) and with and s.
Figure 8.7 (a) PPS and (b) PPS for controlling a six-DOF planar robot manipulator.
Figure 8.8 (a) PPS
and (b) PPS
for controlling a six-DOF planar robot manipulator.
Figure 8.9 (a) PPS and (b) PPS for controlling a six-DOF planar robot manipulator.
Figure 8.10 Motion transients of a physical six-DOF planar robot manipulator from initial state to desired state , which is synthesized by state-adjustment scheme (8.13)–(8.14) with s.
Chapter 9: QP-Based Self-Motion Planning
Figure 9.1 Three-dimensional motion trajectories of a PUMA560 robot manipulator performing self-motion from configurations A to B with .
Figure 9.2 (a) Joint-angle and (b) joint-velocity profiles of PUMA560 robot manipulator performing self-motion from configurations A to B with .
Figure 9.3 Three-dimensional motion trajectories of a PUMA560 robot manipulator performing self-motion from configurations A to C with .
Figure 9.4 (a) Joint-angle and (b) joint-velocity profiles of a PUMA560 robot manipulator performing self-motion from configurations A to C with .
Figure 9.5 (a) Three-dimensional motion trajectories and (b) maximal end-effector position error of a PUMA560 robot manipulator from configurations E to F with .
Figure 9.6 (a) Joint-angle and (b) joint-velocity profiles of a PUMA560 robot manipulator from configurations E to F with .
Figure 9.7 (a) Joint-angle and (b) joint-velocity profiles of a PUMA560 robot manipulator performing self-motion from configurations E to F with .
Figure 9.8 Three-dimensional motion trajectories of a PA10 manipulator performing self-motion (from to without moving the end-effector) with .
Figure 9.9 (a) Joint-angle and (b) joint-velocity profiles of a PA10 manipulator performing self-motion (from to without moving end-effector) with .
Figure 9.10 Resultant position error of a PA10 manipulator performing self-motion (from to theoretically without moving the end-effector) with .
Figure 9.11 (a) Joint-angle and (b) joint-velocity profiles of a PA10 manipulator performing self-motion (from to without moving the end-effector) with .
Figure 9.12 Three-dimensional motion trajectories of a PA10 manipulator performing self-motion (from to without moving the end-effector) with .
Figure 9.13 Resultant position error of a PA10 manipulator performing self-motion (from to theoretically without moving the end-effector) with .
Chapter 10: Pseudoinverse Method and Singularities Discussed
Figure 10.1 Block diagram of dynamic configuration of SMP for a redundant manipulator.
Figure 10.2 LVIAPDNN structure corresponding to dynamic equation (10.9).
Figure 10.3 Examples of three initial states of self-motion for a three-link redundant planar manipulator.
Figure 10.4 (a) Motion trajectories and (b) end-effector position error of a three-link robot performing self-motion with .
Figure 10.5 (a) Joint-angle and (b) joint-velocity profiles of a three-link robot performing self-motion with .
Figure 10.6 (a) Joint-velocity profiles and (b) motion trajectories of a three-link planar robot performing self-motion synthesized by the pseudoinverse-based method (10.12) with and without considering constraint (10.8).
Figure 10.7 (a) Joint-velocity profiles and (b) motion trajectories of a three-link planar robot performing self-motion synthesized by the pseudoinverse-based method (10.12) with and with constraint (10.8) imposed.
Figure 10.8 (a) Joint-velocity profiles and (b) motion trajectories of a three-link planar robot performing self-motion synthesized by LVIAPDNN solver (10.9) with and with constraint (10.8) imposed as well.
Figure 10.9 (a) Motion trajectories and (b) end-effector position error of PUMA560 robot performing self-motion.
Figure 10.10 (a) Joint-angle and (b) joint-velocity profiles of a PUMA560 robot performing self-motion with .
Figure 10.11 End-effector position errors of PUMA560 robot performing self-motion synthesized by LVIAPDNN solver (10.9) with different values of (i.e., (a) and (b) ).
Figure 10.12 End-effector position errors of a PUMA560 robot performing self-motion synthesized by LVIAPDNN solver (10.9) with different values of (i.e., (a) and (b) ).
Figure 10.13 (a) Motion trajectories and (b) end-effector position error of a PA10 robot performing self-motion with .
Figure 10.14 (a) Joint-angle and (b) joint-velocity profiles of a PA10 robot performing self-motion with .
Figure 10.15 (a) Motion trajectories and (b) -proximity of a PA10 robot performing self-motion with .
Chapter 11: Self-Motion Planning with ZIV Constraint
Figure 11.1 Safety device and limit-position indicators of a six-DOF planar robot manipulator.
Figure 11.2 Limits analysis of a six-DOF planar robot manipulator.
Figure 11.3 Block chart of zero-initial-velocity self-motion planning and control of a six-DOF planar robot manipulator.
Figure 11.4 Profiles of joint-velocity limits , velocity-level angle-converted bounds and corresponding bounds with of a six-DOF planar robot manipulator synthesized by QP (11.7)–(11.9) without imposing a zero-initial-velocity constraint.
Figure 11.5 Profiles of joint-velocity limits , velocity-level angle-converted bounds and corresponding bounds with of a six-DOF planar robot manipulator synthesized by QP (11.7)–(11.9) without imposing a zero-initial-velocity constraint.
Figure 11.6 Profiles of joint-velocity limits , velocity-level angle-converted bounds and final corresponding bounds with of a six-DOF planar robot manipulator synthesized by QP (11.10)–(11.12) with a zero-initial-velocity constraint imposed.
Figure 11.7 Profiles of joint-velocity limits , velocity-level angle-converted bounds , and final corresponding bounds with of a six-DOF planar robot manipulator synthesized by QP (11.10)–(11.12) with a zero-initial-velocity constraint imposed.
Figure 11.8 Joint-angle profiles of a six-DOF planar robot manipulator synthesized by self-motion schemes.
Figure 11.9 (a) PPS, (b) PPS, and (c) PPS for controlling a six-DOF planar robot manipulator.
Figure 11.10 (a) PPS, (b) PPS, and (c) PPS for controlling a six-DOF planar robot manipulator.
Figure 11.11 Self-motion task execution of a manipulator synthesized by the self-motion scheme (11.10)–(11.12).
Chapter 12: Manipulability-Maximizing SMP Scheme
Figure 12.1 Manipulability measures synthesized by MMSMP scheme (12.2)–(12.5) and SMMVA scheme [203].
Figure 12.2 (a) Joint-angle and (b) joint-velocity profiles of a six-DOF planar robot manipulator synthesized by the MMSMP scheme (12.2)–(12.5).
Figure 12.3 Manipulability measures of a six-DOF planar robot manipulator synthesized by the (a) MMSMP and (b) SMMVA schemes.
Figure 12.4 Self-motion task execution of a six-DOF planar robot manipulator synthesized by the MMSMP scheme (12.2)–(12.5).
Source
: IEEE 2012. Reproduced with permission of IEEE.
Chapter 13: Time-Varying Coefficient Aided MM Scheme
Figure 13.1 (a) Joint-angle and (b) joint-velocity profiles of a six-DOF planar robot manipulator synthesized by a manipulability-maximizing scheme with a constant coefficient .
Figure 13.2 (a) Motion trajectories as well as (b) end-effector path and trajectory of the end-effector of a six-DOF planar robot manipulator tracking an “R” path synthesized by time-varying coefficient aided manipulability-maximizing scheme (i.e., ).
Figure 13.3 (a) Joint-angle and (b) joint-velocity profiles of a six-DOF planar robot manipulator tracking an “R” path synthesized by a time-varying coefficient aided manipulability-maximizing scheme (i.e., ).
Figure 13.4 Comparison about manipulability index synthesized by schemes with , (i.e., an MVN scheme) and .
Figure 13.5 Joint-angle profiles (a) and (b) of corresponding limits of a six-DOF planar robot manipulator tracking an “R” path synthesized by TVCMM scheme with .
Figure 13.6 Joint-angle profiles (a)
and (b)
of corresponding limits of a six-DOF planar robot manipulator tracking an “R” path synthesized by TVCMM scheme with
.
Figure 13.7 Joint-angle profiles (a) and (b) of corresponding limits of a six-DOF planar robot manipulator tracking an “R” path synthesized by TVCMM scheme with .
Figure 13.8 Joint-velocity profiles (a) and (b) of corresponding limits and bounds of a six-DOF planar robot manipulator tracking an “R” path synthesized by a TVCMM scheme with .
Figure 13.9 Joint-velocity profiles (a)
and (b)
of corresponding limits and bounds of a six-DOF planar robot manipulator tracking an “R” path synthesized by TVCMM scheme with
.
Figure 13.10 Joint-velocity profiles (a) and (b) of corresponding limits and bounds of a six-DOF planar robot manipulator tracking an “R” path synthesized by a TVCMM scheme with .
Figure 13.11 Snapshots for actual end-effector task execution of a six-DOF planar robot manipulator tracking an “R” path synthesized by TVCMM scheme with .
Figure 13.12 (a) Top-view measurement result of “R” trajectory and (b) positioning error of robot end-effector synthesized by TVCMM scheme with .
Chapter 14: QP Based Encoder Feedback Control
Figure 14.1 Joint structure of Joint 2 through Joint 6.
Figure 14.2 (a) Motion trajectories. as well as (b) desired path and actual trajectory of a six-DOF planar robot manipulator tracking a petal-shaped path synthesized by an OMPFC scheme with L1.
Figure 14.3 (a) Position error and (b) joint-velocity profiles of a six-DOF planar robot manipulator tracking a petal-shaped path synthesized by a OMPFC scheme with L1.
Figure 14.4 (a) Joint-angle profiles and (b) joint-angle-limit constraint () of a six-DOF planar robot manipulator tracking a petal-shaped path synthesized by a OMPFC scheme with L1.
Figure 14.5 (a) Iteration numbers and (b) running times of numerical algorithm 94LVI for a six-DOF planar robot manipulator tracking a petal-shaped path.
Figure 14.6 (a) Motion trajectories and (b) position error of a six-DOF planar robot manipulator tracking a petal-shaped path synthesized by OMPFC scheme with L2.
Figure 14.7 (a) Joint-angle-limit constraint () and (b) running times of a six-DOF planar robot manipulator tracking a petal-shaped path synthesized by a OMPFC scheme with L2.
Figure 14.8 (a) Motion trajectories and (b) position error of a six-DOF planar robot manipulator tracking a petal-shaped path synthesized by a scheme equipped with the M4 algorithm and L1.
Figure 14.9 (a) Iteration numbers and (b) running times of a six-DOF planar robot manipulator tracking a petal-shaped path synthesized by a scheme equipped with the M4 algorithm and L1.
Figure 14.10 Simulation results of a six-DOF planar robot manipulator tracking a hexagonal path synthesized by an OMPFC scheme with L1.
Figure 14.11 Experimental end-effector position error synthesized by a OMPFC scheme with for tracking a petal-shaped path.
Figure 14.12 Snapshots for actual petal-shaped-path-tracking task execution of manipulator synthesized by OMPFC scheme with .
Figure 14.13 Top-view measurement for actual task execution results synthesized by OMPFC scheme with .
Figure 14.14 (a) Experimental end-effector trajectory and (b) position error synthesized by an OMPFC scheme with for tracking a petal-shaped path.
Figure 14.15 Comparison between actual-measured (with subscript ) and simulated (with subscript ) synthesized by an OMPFC scheme with for tracking a petal-shaped path ().
Figure 14.16 Comparison between actual-measured (with subscript ) and simulated (with subscript ) synthesized by an OMPFC scheme with for tracking a petal-shaped path ().
Figure 14.17 (a) Experimental end-effector trajectory and (b) position error synthesized by an OMPFC scheme with for tracking a hexagonal path.
Chapter 15: QP Based Joystick Control
Figure 15.1 Conceptual block diagram of a joystick-controlled robot system.
Figure 15.2 Joystick.
Source
: IEEE 2011. Reproduced with permission of IEEE.
Figure 15.3 Block diagram of cosine-aided position-to-velocity mapping.
Figure 15.4 Computing times used by numerical algorithm 94LVI for redundancy resolution in simulations of (a) forward and (b) backward movement.
Figure 15.5 Computing times used by numerical algorithm 94LVI for redundancy resolution in simulations of (a) leftward and (b) rightward movement.
Figure 15.6 Computing times used by numerical algorithm 94LVI for redundancy resolution in simulations of (a) upper-rightward and (b) lower-rightward movement.
Figure 15.7 Directional manipulation of joystick.
Source
: IEEE 2011. Reproduced with permission of IEEE.
Figure 15.8 Actual end-effector trajectories corresponding to Figure 15.7.
Source
: Zhang 2011. Reproduced with permission of IEEE.
Figure 15.9 Manipulation of joystick for writing “MVN”.
Source
: IEEE 2011. Reproduced with permission of IEEE.
Figure 15.10 Actual end-effector trajectories corresponding to Figure 15.9.
Source
: Zhang 2011. Reproduced with permission of IEEE.
List of Tables
Chapter 3: D1G1 Type Scheme to JAL Inverse Kinematics
Table 3.1 Position and velocity errors of a three-link robot manipulator's end-effector tracking rhombus and triangle paths synthesized by a inverse-free D1G1 scheme (3.7)
Chapter 4: Z1G1 Type Scheme to JAL Inverse Kinematics
Table 4.1 Maximum position, velocity, and acceleration errors when three planar robot manipulators track desired paths synthesized by Z1G1 type scheme (4.5)
Chapter 6: Varying Joint-Velocity Limits Handled by QP
Table 6.1 Parameters of a six-DOF planar robot manipulator hardware system
Table 6.2 Maximum and average position errors (m) of a six-DOF planar robot manipulator's end-effector for different paths tracked
Table 6.3 Iteration number and computing time within each sampling period when a robot tracks a line-segment or an elliptical path
Chapter 7: Feedback-Aided Minimum Joint Motion
Table 7.1 Actual joint-angle limits used in this chapter of six-DOF planar robot manipulator
Table 7.2 Maximum errors of a six-DOF planar robot manipulator synthesized by FAMJM scheme (7.23)–(7.25) when increases from 0 to 100 during task execution of “M”-shaped-path tracking
Chapter 8: QP Based Manipulator State Adjustment
Table 8.1 Joint-angle values with and s at different time instants
Table 8.2 Joint-angle errors of state-adjustment task for different and
Chapter 9: QP-Based Self-Motion Planning
Table 9.1 Initial configurations and desired configurations (rad) of PUMA560 robot manipulator involved in the simulations
Table 9.2 Joint values and errors of PUMA560 robot manipulator before and after self-motion from configurations A to B (rad)
Table 9.3 Joint-angle values and errors of PUMA560 robot manipulator before and after self-motion from configurations A to C (rad)
Table 9.4 Joint-angle values and errors of PUMA560 robot manipulator before and after self-motion from configurations E to F (rad)
Table 9.5 Joint-angle limits and joint-velocity limits used in this chapter for a PA10 manipulator
Table 9.6 Joint-angle values and errors of a PA10 manipulator before and after self-motion with (rad)
Table 9.7 Joint-angle values and errors of a PA10 manipulator before and after self-motion with (rad)
Chapter 10: Pseudoinverse Method and Singularities Discussed
Table 10.1 Joint values and errors (rad) of three-link robot before and after self-motion with
Table 10.2 Final joint values and errors (rad) of a three-link robot before and after self-motion with
Table 10.3 Final joint values and errors (rad) of a three-link robot before and after self-motion with
Table 10.4 Joint values and errors (rad) of a PUMA560 robot before and after self-motion with
Table 10.5 Joint values and errors (rad) of a PA10 robot before and after self-motion with
Chapter 14: QP Based Encoder Feedback Control
Table 14.1 Motor parameters of a six-DOF planar robot manipulator
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Robot Manipulator Redundancy Resolution
Yunong Zhang and Long Jin
Sun Yat-sen University Guangzhou, China
© 2018 John Wiley & Sons Ltd
This Work is a co-publication between ASME Press and John Wiley & Sons Ltd
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Library of Congress Cataloging-in-Publication Data
Names: Zhang, Yunong, 1973- author. | Jin, Long, 1988- author.
Title: Robot manipulator redundancy resolution / Yunong Zhang, Long Jin, Sun Yatsen University.
Description: Hoboken, New Jersey : Wiley, [2017] | Includes bibliographical references and index. |
Identifiers: LCCN 2017018502 (print) | LCCN 2017019566 (ebook) | ISBN 9781119381426 (pdf) | ISBN 9781119381433 (epub) | ISBN 9781119381235 (cloth)
Subjects: LCSH: Robots-Control systems. | Manipulators (Mechanism) | Redundancy (Engineering)
Classification: LCC TJ211.35 (ebook) | LCC TJ211.35 .Z44 2017 (print) | DDC 629.8/933-dc23
LC record available at https://lccn.loc.gov/2017018502
Cover image: © kynny/Gettyimages
To our parents and ancestors, as always
List of Figures
Figure 1.1
Block diagram of a kinematic-control system for a redundant robot manipulator by combining the MVN scheme (1.1) and ZD model, where .
Figure 1.2
Geometry of a five-link planar robot manipulator used in simulations.
Figure 1.3
Joint-angle and joint-velocity profiles of a five-link planar robot manipulator synthesized by pseudoinverse-based MVN scheme (1.1) aided with TDTZD-U model (1.14).
Figure 1.4
(a) Motion process and (b) position error of a five-link planar robot manipulator synthesized by the pseudoinverse-based MVN scheme (1.1) and aided by the TDTZD-U model (1.14).
Figure 1.5
Position error of a five-link planar robot manipulator synthesized by a pseudoinverse-based MVN scheme (1.1) aided with the EDTZD-K model (1.9) or Newton iteration (1.15).
Figure 1.6
Position errors of a three-link planar robot manipulator synthesized by a pseudoinverse-based MVN scheme (1.1) aided with EDTZD-K model (1.9) with .
Figure 2.1
(a) Motion process and (b) joint-angle profiles of a five-link redundant robot manipulator tracking the desired square path synthesized by the G1 type scheme (2.8).
Figure 2.2
(a) Desired path, actual trajectory, and (b) position error of a five-link redundant robot manipulator tracking square path synthesized by a G1 type scheme (2.8).
Figure 2.3
(a) Desired velocity and (b) velocity error of a five-link redundant robot manipulator tracking a square path synthesized by a G1 type scheme (2.8).
Figure 2.4
Motion process (a) and joint-angle profiles (b) of six-DOF redundant robot manipulator tracking the desired “Z”-shaped path synthesized by a G1 type scheme (2.8).
Figure 2.5
(a) Desired path, actual trajectory, and (b) position error of a six-DOF redundant robot manipulator tracking a “Z”-shaped path synthesized by a G1 type scheme (2.8).
Figure 2.6
(a) Desired velocity and (b) velocity error of a six-DOF redundant robot manipulator tracking a “Z”-shaped path synthesized by a G1 type scheme (2.8).
Figure 2.7
Hardware system (a) of six-DOF planar redundant robot manipulator with its structure platform (b).
Source:
Zhang et al. 2015. Reproduced from Y. Zhang, L. He, J. Ma et al., Inverse-free scheme of G1 type to velocity-level inverse kinematics of redundant robot manipulators, Figure 3, Proceedings of the Twelfth International Symposium on Neural Networks, pp. 99-108, 2015. ©Springer-Verlag 2015. With kind permission of Springer-Verlag (License Number 3978560065761).
Figure 2.8
“Z”-shaped-path-tracking experiment of six-DOF redundant robot manipulator synthesized by G1 type scheme (2.8) at joint-velocity level. Reproduced from Y. Zhang, L. He, J. Ma et al, Inverse-free scheme of G1 type to velocity-level inverse kinematics of redundant robot manipulators, Figure 4, Proceedings of the Twelfth International Symposium on Neural Networks, pp. 99-108, 2015. ©Springer-Verlag 2015. With kind permission of Springer-Verlag (License Number 3978560065761).
Figure 3.1
(a) Motion process, (b) desired path, and actual trajectory of a three-link redundant robot manipulator tracking a rhombus path synthesized by the D1G1 scheme (3.7) with .
Figure 3.2
Joint-angle profiles (a) and position error (b) of a three-link redundant robot manipulator tracking a rhombus path synthesized by the D1G1 scheme (3.7) with .
Figure 3.3
Joint-velocity profiles (a) and velocity error (b) of a three-link redundant robot manipulator tracking a rhombus path synthesized by the D1G1 scheme (3.7) with .
Figure 3.4
(a) Joint-acceleration profiles and (b) acceleration error of a three-link redundant robot manipulator tracking a rhombus path synthesized by the D1G1 scheme (3.7) with .
Figure 3.5
Position errors in rhombus-path-tracking task of a three-link robot manipulator synthesized by (a) pseudoinverse solution (3.4) and (b) inverse-free D1G1 scheme (3.7) with .
Figure 3.6
(a) Motion process and (b) joint-angle profiles of a three-link redundant robot manipulator tracking a desired triangle path synthesized by a D1G1 scheme (3.7) with .
Figure 3.7
Position errors in triangle-path-tracking task of the three-link robot manipulator synthesized by (a) pseudoinverse solution (3.4) and (b) inverse-free D1G1 scheme (3.7) with .
Figure 4.1
(a) Motion process and (b) joint-angle profiles of a three-link planar robot manipulator tracking a desired isosceles-trapezoid path synthesized by the Z1G1 type scheme (4.5).
Figure 4.2
(a) Joint-velocity profiles and (b) joint-acceleration profiles of three-link planar robot manipulator tracking isosceles-trapezoid path synthesized by Z1G1 type scheme (4.5).
Figure 4.3
(a) Motion process and (b) joint-angle profiles of a four-link planar robot manipulator tracking a desired isosceles-triangle path synthesized by the Z1G1 type scheme (4.5).
Figure 4.4
(a) Joint-velocity profiles and (b) joint-acceleration profiles of a four-link planar robot manipulator tracking an isosceles-triangle path synthesized by the Z1G1 type scheme (4.5).
Figure 4.5
Simulation results of a three-link planar robot manipulator tracking an isosceles-trapezoid path synthesized by the Z1G1 type scheme (4.5) with an initial end-effector position not on the desired path.
Figure 4.6
“V”-shaped-path-tracking experiment of a six-DOF redundant robot manipulator synthesized by the Z1G1 type scheme (4.5) at joint-acceleration level.
Figure 5.1
Contradicting situations in equality-based collision-free formulation.
Figure 5.2
QP-based approach to redundancy resolution and torque control.
Figure 5.3
PUMA560 transients synthesized by a QP-based MTN scheme.
Figure 5.4
PUMA560 transients synthesized by a QP-based MKE scheme.
Figure 5.5
Comparison of (a) conventional and (b) presented MTN schemes.
Figure 5.6
Joint-torque profiles synthesized by other QP-based resolution schemes of (a) IIWT and (b) MAN.
Figure 5.7
Joint-torque profiles synthesized by other QP-based resolution schemes of (a ) MKE and (b) MVN.
Figure 6.1
(a) Hardware system and (b) model of a six-DOF planar robot manipulator.
Figure 6.2
Local configuration of a six-DOF planar robot manipulator.
Figure 6.3
Relationship between (a) and as well as (b) the relationship between and .
Figure 6.4
Relationship between (a)
and
as well as (b) the relationship between
and
.
Figure 6.5
Relationship between (a) and as well as (b) the relationship between and .
Figure 6.6
Desired line-segment path to be tracked by the end-effector of a six-DOF planar robot manipulator.
Figure 6.7
