Advances in Robot Kinematics 2022

✍ Scribed by Oscar Altuzarra, Andrés Kecskeméthy

• Publisher: Springer
• Year: 2022
• Tongue: English
• Leaves: 493
• Series: Springer Proceedings in Advanced Robotics, 24
• Category: Library

✦ Synopsis

This book reports on the latest scientific achievements on robot kinematics provided by the prominent researchers participating in the 18th International Symposium on Advances in Robot Kinematics ARK2022, organized in the University of the Basque Country, Bilbao, Spain. It is of interest to researchers wanting to know more about the latest topics and methods in the fields of the kinematics, control and design of robotic systems.

The book brings together 53 peer-reviewed papers. These cover the full range of robotic systems, including serial, parallel, flexible mechanisms, and cable-driven manipulators, and tackle problems such as: kinematic analysis of robots, robot modelling and simulation, theories and methods in kinematics, singularity analysis, kinematic problems in parallel robots, redundant robots, cable robots, kinematics in biological systems, flexible parallel manipulators, humanoid robots and humanoid subsystems.

✦ Table of Contents

Preface
Organization
Conference Chairman
Conference Co-chairman
Honorary Chairmen
Scientific Committee
Organizing Committee
Contents
I Theoretical Kinematics
Möbius Linkages
1 Introduction
2 Mathematical Basics
3 7R-Möbius Linkage
4 8R Möbius Linkage
5 9R Möbius Linkage
6 Conclusion
References
On Origami-Like Quasi-mechanisms with an Antiprismatic Skeleton
1 Introduction
2 Preliminary Considerations
3 Snapping Quasi-mechanisms
4 Shaky Quasi-mechanisms
5 Conclusion and Future Work
References
Line-Point Constraints and Robot Surgery
1 Introduction
2 The Displacement Variety
3 Two Ports
4 Conclusions
References
On the Use of Ternary Products to Characterize the Dexterity of Spatial Kinematic Chains
1 Introduction
2 Geometry of Spears
3 Real Products and Dual Products
4 Ternary Products
5 Ternary Product Matrices
6 Generalized Product Matrix and Indices
7 Conclusions
References
Extended Rotation Matrix for Kinematics of Pointing Mechanisms
1 Introduction
2 Extended Rotation Matrix and Alternative Coordinates
3 Geometric and Algebraic Properties of ERMs
4 A 2-DOF Pointing Mechanism
5 Example
6 Conclusions
References
A Linearization Method Based on Lie Algebra for Pose Estimation in a Time Horizon
1 Introduction
2 Fundamentals
2.1 Lie Groups and Algebras
2.2 Receding Horizon
3 Linear Pose Estimation
3.1 Pose Estimation in a Horizon
3.2 From the Magnus Expansion to an Estimate of the Logarithm Map
4 Results
5 Conclusions
References
Hyper-multidual Algebra and Higher-Order Kinematics
1 Introduction
2 Higher-Order Acceleration Field in Rigid Body Motion
3 Dual and Hyper-multidual Algebra
4 Differential HMD Transform of Dual Time Functions
5 Higher-Order Kinematics with Differential Transform
6 Higher-Order Kinematics of General mC Manipulator
7 Conclusion
References
Geometry Based Analysis of 3R Serial Robots
1 Introduction
2 Inverse Kinematic Model
2.1 Singularities
2.2 Degenerate Conic
3 Special Classes of Robots
3.1 Binary Robots
3.2 Quaternary Robot
4 Conclusions and Future Work
References
Synthesis of Gripper Mechanisms Derived from Baranov Chains
1 Introduction
2 Synthesis Process
3 Exploring the Synthesis Process of Grippers
4 Conclusion
References
6R Linkages with Hidden Singularities
1 Introduction
2 Notation and Terminology
3 Local Mobility Analysis
4 Synthesis Method for 1-DOF 6R Linkages with Hidden Singularities of Prescribed Rank
5 Examples
6 Conclusion
References
II Cable Driven Manipulators
Best Operation Regions in a Planar Cable Driven System
1 Introduction
2 Topology for the Studied Manipulator
3 Static Model for the Studied System
4 Proposed Method
5 Simulation Results
6 Conclusions
References
Stiffness and Transparency of a Collaborative Cable-Driven Parallel Robot
1 Introduction
2 CDPR Stiffness Modelling
3 Analysis of Factors Influencing Stiffness
3.1 Influence of the MP Pose on the Manipulator Stiffness
3.2 Influence of the Cable Tension Distribution
4 Transparency
5 Conclusion and Future Work
References
An Approach for Predicting the Calibration Accuracy in Planar Cable-Driven Parallel Robots
1 Introduction
2 CDPR Modelling
2.1 Kinematic Modelling
2.2 Sensors Accuracy Test
3 Identification Methodology
4 Simulation of 3-DoF, 2-Cable Planar CDPR
4.1 Results of the Simulated Identification Problem
4.2 Simulation of Sensor Effects on Identification Errors
4.3 Overall Simulation
5 Conclusions and Future Work
References
A Panorama of Methods for Dealing with Sagging Cables in Cable-Driven Parallel Robots
1 Cable-Driven Parallel Robots and Sagging Cables
2 Sagging Cables Model
3 Sagging and Kinematics Analysis
4 Sagging and Solving the IK/DK
5 Conclusion
References
Sensitivity of the Direct Kinematics of Underactuated Cable-Driven Parallel Robots to Redundant Sensor-Measurement Errors
1 Introduction
2 Kinematic Model
3 Sensitivity of Direct Kinematics with Redundant Measurements
4 Application on a 4-UACDPR
5 Conclusions
References
Stacked Tensegrity Mechanism for Medical Application
1 Introduction
2 Mechanism Design
3 Singularity Analysis
4 Stability Analysis
5 Optimization of One Segment
6 Conclusions and Future Work
References
Kinematic and Static Analysis of a Cable-Driven 2-X Tensegrity Manipulator for Two Actuation Strategies
1 Introduction
2 Manipulator Description and Kinematic Relations
3 Cable Actuation Schemes
4 Instantaneous Velocity Analysis
5 Static Force Analysis
6 Global Performance Inside the Task Space
7 Conclusion
References
III Computational Kinematics
Complete Inverse Geometric Model Computation of the Quattro Parallel Kinematic Robot
1 Introduction
2 Presentation of the Quattro Robot
3 Formalism Based on Joint Invariant
4 CIKM of the Quattro Robot
4.1 Inverse Kinematic Model
4.2 Complete Inverse Kinematic Model
5 Conclusion
References
A New Approach to Forward Kinematics for a SILS Robotic Orientation Platform Based on Perturbation Theory
1 Introduction
2 The 3-DOF Parallel Orientation Platform for SILS
3 Perturbation Theory Background
4 Solving the Forward Kinematics
5 Conclusions
References
Forward Kinematics of a Novel 6-DoF Spatial Hybrid Manipulator
1 Introduction
2 Geometry of the Manipulator
3 The Forward Kinematic Problem
4 Numerical Example
5 Conclusions
References
Structural and Dimensional Synthesis of Overconstraint Symmetric 3T2R Parallel Robots Using Tait-Bryan-Angle Kinematic Constraints
1 Introduction and State of the Art
2 Inverse Kinematic Model for 3T2R Parallel Robots
3 Combined Structural and Dimensional Synthesis of 3T2R PMs
4 Exemplary Results of the Combined Synthesis for 3T2R PMs
5 Conclusion
References
Inverse Kinematics for Functional Redundancy of Symmetric 3T1R Parallel Manipulators Using Tait-Bryan-Angle Kinematic Constraints
1 Introduction and State of the Art
2 Inverse Kinematic Model for 3T1R Parallel Robots
3 Functional Redundancy and Inverse Kinematics
4 Dimensional Synthesis of Functionally Redundant 3T1R PMs
5 Conclusion
References
IV Continuum Mechanisms
Analysis of a Compliant Parallel Manipulator for Torso Balance Rehabilitation
1 Introduction
2 Kinematic and Dynamic Requirements
3 Kinematic Model of the Manipulator
4 Results and Discussion
References
Design and Analysis of a Compliant Parallel Robot with Cardan Joints for a Cryogenic Working Environment
1 Introduction
1.1 Related Research
1.2 Previous Work
2 Constructive Implementation
2.1 Structure of a Single Kinematic Chain
2.2 Overall Construction of the Robot
3 Simulation of Static Deviations
3.1 Preconditions of the Simulations
3.2 Results of the Simulations
4 Summary and Outlook
References
Design and Inverse Kinematics of a Novel Tendon-Driven Continuum Manipulator Capable of Twisting Motion
1 Introduction
2 Design Concept and Proof-of-Concept
2.1 Remodeling of Conventional TCM
2.2 Proof-of-Concept
3 Inverse Kinematics
3.1 Nomenclature
3.2 Inverse Kinematics
3.3 Validation Experiment of the Inverse Kinematic Model
4 Conclusion
References
Geometric Insights into Kinematically-Singular Configurations of Planar Continuum Robots
1 Introduction
2 Kinematic Modeling for Continuum Robots: Preliminaries
2.1 Subsegment Kinematics
2.2 Multi-segment Kinematics
3 Instantaneous Screws of Motion
4 Singularity Condition
5 Simulation Study
6 Conclusion
References
A Gazebo Simulator for Continuum Parallel Robots
1 Introduction
2 Cosserat Rod Theory
3 Generic Modeling of CPRs
3.1 Assembly Constrains
3.2 Unique Solver
4 The Gazebo Simulator
5 Simulations Results
6 Conclusions
References
Exploring Electric Field Perturbations as the Actuator for Nanorobots and Nanomachines
1 Introduction
2 Kinematic Model
3 Defining Cyclic Peptide Energies
4 Force Field Perturbation Methods
5 Conclusion
References
V Mechanism Synthesis
General Procedure for Path Generation Synthesis Based on Kinematic Constraints
1 Introduction
2 Analytical Formulation of Partial Derivatives
2.1 Kinematic Constraints Formulation
2.2 Derivation of Kinematic Constraints
2.3 Automatic Calculation of Partial Derivatives
3 Optimization Method
4 Illustrative Example
5 Conclusions
References
Finding Straight Line Generators Through the Approximate Synthesis of Symmetric Four-Bar Coupler Curves
1 Introduction
2 Mathematical Formulation of Four-Bars
2.1 Symmetric Coupler Curves
3 Optimization Model for Approximating Straight Lines
4 Design of Experiments
5 Conclusion
References
A Method for the Complete Set of Solutions of the Finite-Position Synthesis Problem
1 Introduction
2 Methodology
3 The 2R Chain
4 The 3R Chain
5 The 4R and 5R Chain
6 Implementation and Results
7 Conclusions
References
Classification of Mobilities - New Insights on an Old Topic
1 Introduction
2 Davies' Method
3 Classification of Mobilities
4 Conclusions and Future Works
References
First and Second Order Centrodes of Slider-Crank Mechanisms by Using Instantaneous Invariants
1 Introduction
2 Instantaneous Invariants
3 First and Second Order Centrodes
4 Conclusions
References
Spherical 4R Linkage Algebraic Input-Output Equations
1 Introduction
2 Derivation of the Six Spherical IO Equations
3 Application
4 Conclusions
References
VI Spherical Mechanisms
Kinematics of a Gear-Based Spherical Mechanism
1 Introduction
2 The Proposed Mechanism
3 Inverse Kinematics
4 Forward Kinematics
5 Singularities
6 Example
7 Conclusion
References
Modeling of a Remote Center of Motion Spherical Parallel Tensegrity Mechanism for Percutaneous Interventions
1 Introduction
2 System Description
3 System Modeling
3.1 Inverse Kinematic Model
3.2 Direct Kinematic Model
3.3 Workspace
3.4 Prototype
4 Conclusion and Perspectives
References
Wriflex: Design and Kinematic Analysis of a Self-aligning Parallel Wrist
1 Introduction
2 Wriflex Geometry
3 Position Analysis
3.1 Forward Position Analysis
3.2 Inverse Position Analysis
4 Instantaneous Kinematics and Singularity Analysis
5 Simulation Results
6 Conclusion
References
Kinematic Analysis of a Novel Humanoid Wrist Parallel Mechanism
1 Introduction
2 Architecture and Constraint Equations
3 Kinematics
4 Performance Analysis
5 Conclusion
References
VII Biomechanics
Smooth Wrapping of Stretchable Thick Strands Over a Surface - The 2D Case
1 Introduction
2 Model Derivation
2.1 Description of the Stretchable Thick Strand
2.2 Implicit Velocity Constraints at A and B
2.3 Change of Wrap Length sOB for Infinitesimal Stretch Change d
3 Computational Results
4 Conclusions
References
Exploiting Reciprocity Between Constraints and Instantaneous Motion to Reconstruct Individual Knee Kinematics
1 Introduction
2 Materials and Metods
2.1 Experimental Acquisition
2.2 Numerical Model
3 Results
4 Discussion
5 Conclusions
References
Generation of Parametric Gait Patterns
1 Introduction
2 Motion Data
3 Kinematic Lower Body Model
4 Motion Mapping
5 Parametric Gait Generation
6 Results and Discussion
References
Parametrization of Compliant, Object-Level Controllers from Human Demonstrations
1 Introduction
2 Encoding Human Strategies
2.1 What We Have: Task Data
2.2 What We Want: A Parametrized Task-Space Robot Controller
2.3 What to Do: Define a Frame and Extract Parameters
3 Haptic Data Collection
4 Experimental Validation
4.1 Frame Selection
4.2 Primitive Parameters
4.3 Robot and Object Agnostic Behavior
5 Conclusions
References
VIII Linkages
Geometric Model for Serial-Chain Robot Inverse Kinematics in Case of Two Translational DoF, Spatial Rotation and Functional Redundancy
1 Introduction and State of the Art
2 Inverse Kinematic Model for Serial Chains
3 Inverse Kinematics and Functional Redundancy
4 Evaluation
5 Conclusion and Remark on Parallel Robots
References
The Distance Geometry of the Generalized Lobster's Arm
1 Introduction
2 A Distance-Based Formulation
3 The Resolution Process
4 Example
5 Conclusion
References
Degenerate Cases in the Inverse Kinematics Problem of a General 6R Serial Robot
1 Introduction
2 Mathematical Background
3 Degenerate Conditions
3.1 Analytical Determination of the Degenerate Conditions
3.2 The Generalised Lobster Arm
4 Conclusion
References
The Spatial Pantograph and Its Mass Balance
1 Introduction
2 General Kinematic Solution
3 Kinematic Solution with Solely Universal Joints
4 Conclusion
References
A New Family of Overconstrained P5R-Mechanisms
1 Introduction
2 Preliminaries
2.1 Dual Quaternions
2.2 Factorization of a Motion Polynomial
2.3 Bond Theory
3 Motivation
4 The Main Results
References
IX Motion Planning
Trajectory Planner for Type II Singularities Avoidance Based on Output Twist Screws
1 Introduction
2 Mathematical Foundation
2.1 Singularities
2.2 Angle Between Two Output Twist Screws
3 Methodology for Trajectory Planner
4 Results and Discussion
4.1 Experimentation Setup
4.2 Trajectory Planner Performance
5 Conclusion
References
Kinematically Adapted Sampling-Based Motion Planning Algorithm for Robotic Manipulators
1 Background
2 Kinematic Graph
3 Conclusive Notes
References
Robotic Analysation Methodology for Multidirectional Additive Manufacturing Process Configuration
1 Introduction to Multidirectional Additive Manufacturing
2 Configuration Analysation of MDAM Processes
3 Results
References
An Artificial Potential Field Algorithm for Path Planning of Redundant Manipulators Based on Navigation Functions
1 Introduction
2 Navigation Function for Path Planning Algorithm
3 Determination of Optimal Factors k
4 Results and Discussion
4.1 Example 1 - Upper Extremity Abduction for Hand Raising
4.2 Example 2 - Upper Extremity Flexion for Grasping
References
Reactive Locomotion of a Hexapod for Navigation Across Irregular Ground
1 Introduction
2 Model Description
3 Control Strategy
4 Results and Discussion
5 Conclusions
References
Trajectory Tracking by Fuzzy-Based Super-Twist Sliding Mode Control of a Parallel PnP Robot
1 Introduction
2 Parallel PnP Robot Under Study
3 Model-Based Control Design
3.1 Super-Twist Sliding Mode Control
3.2 Fuzzy Control Design
3.3 Integrated Controller Design
4 Experimental Evaluation of the Model-Based Control
5 Conclusions
References
Author Index