Modelling and Nonlinear Robust Control of Delta-Like Parallel Kinematic Manipulators

Modelling and Nonlinear Robust Control of Delta-Like Parallel Kinematic Manipulators

1st Edition - January 1, 2023

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  • Authors: Jonatan Escorcia Hernandez, Ahmed Chemori, Hipolito Sierra
  • Paperback ISBN: 9780323961011

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Modelling and Nonlinear Robust Control of Delta-Like Parallel Kinematic Manipulators deals with the modeling and control of parallel robots. Its content will benefit students, researchers, and engineers in robotics with a simplified methodology to obtain the dynamic model of parallel robots with a delta-type architecture. Moreover, this methodology is compatible with the real-time implementation of model-based and robust control schemes. Besides, it can easily extend the proposed robust control solutions to other robotic architectures.

Key Features

  • Introduces a novel parallel robot designed for machining operations called SPIDER4
  • Presents a mathematical formulation of the kinematic and dynamic models of SPIDER4
  • Offers validation of the computed mathematical models and designed controllers through real-time experiments under different operating conditions


Ph.D. students and researchers in robotics centered around parallel robots. Robotics engineers, robotics researchers in general, and undergraduate, graduate, researchers from other robotics areas, since the control schemes presented in this book can be applied to other types of robotic manipulators

Table of Contents

  • Chapter 1: Introduction
    1.1 Classification of Robotic Manipulators
    1.2.1 Serial Robots
    1.2.2 Parallel Robots
    1.2.3 Serial Vs Parallel Robots
    1.2.4 Hybrid Manipulators
    1.2 Overview of Parallel Kinematic Manipulators (PKMs)
    1.2.1 History about Parallel Kinematic Manipulators
    1.2.2 Main applications of parallel kinematic manipulators Pick-and-Place (P&P) Tasks Machining Tasks Coordinate Measuring Machines Medical Applications Agriculture Applications Motion Simulators 3D Printers Haptic Devices
    1.3 Control Problem Formulation
    1.3.1 PKMs Control Challenges Highly Nonlinear Dynamics Unstructured and Structured Uncertainties Actuation Redundancy
    1.4 Conclusion
    Chapter 2: Literature review about modelling and control of PKMs
    2.1 Introduction
    2.2 Kinematic Modelling of Parallel Kinematic Manipulators
    2.2.1 Inverse Kinematic formulation
    2.2.2 Forward Kinematic formulation
    2.2.3 Jacobians
    2.2.4 Singularity analysis
    2.2.5 Workspace computation
    2.3 Dynamic Modelling of Parallel Kinematic Manipulators
    2.3.1 Dynamic Modelling approaches for PKMs Newton-Euler Formulation Virtual Work Principle Euler-Lagrange Formulation Simplification-based modelling method for delta-like PKMs
    2.3.2 Dynamic modelling representation The Inverse Dynamic Model in Joint Space The Inverse Dynamic Model in Cartesian Space
    2.4 Overview of Non-Model-Based Motion Controllers for PKMs
    2.4.1 Non-model-based non-adaptive controllers PD/PID Controllers Nonlinear PD/PID Controllers
    2.4.2 Non-model-based-adaptive controllers L1 Adaptive Control Active Disturbance Rejection Control
    2.5 Overview of Model-Based Motion Controllers for PKMs
    2.5.1 Model-based-non-adaptive controllers Computed Torque Control Augmented PD/PID Control PD Computed Feedforward Control Higher Order Sliding Mode Control
    2.5.2 Model-based-adaptive controllers Adaptive Computed Torque Control PID with Adaptive Feedforward Dual-Mode Adaptive Control L1 Adaptive Control with Adaptive Feedforward Adaptive Terminal Sliding Mode Control
    2.6 Motivations of advanced control solutions for PKMs
    2.6.1 Associated control challenges
    2.6.2 Why RISE feedback control?
    2.6.3 RISE versus classical feedback controllers
    2.7 Conclusion
    Chapter 3: Description and Modelling of Experimental platforms
    3.1 Introduction
    3.2 Kinematic Modelling for delta-like PKMs
    3.2.1 Inverse kinematic formulation
    3.2.2 Forward kinematic formulation
    3.3 Dynamic Modelling for delta-like PKMs
    3.3.1 Principle of modelling
    3.3.2 Torques and forces due to actuation
    3.3.3 Torques and forces due to traveling plate
    3.4 Application of modelling algorithms to a 3-DOF Delta PKM
    3.4.1 Inverse kinematic model
    3.4.2 Forward kinematic model
    3.4.4 Velocity relationship and Jacobian analysis
    3.4.5 Workspace computation
    3.4.6 Inverse dynamic model
    3.5 Application of modelling algorithms to the 5-DOF SPIDER4 RA-PKM
    3.5.1 Inverse kinematic model
    3.5.2 Forward kinematic model
    3.5.4 Velocity relationship and Jacobian analysis
    3.5.5 Workspace computation
    3.5.6 Inverse dynamic model of the delta-like positioning mechanism
    3.5.7 Inverse dynamic model of the wrist mechanism
    3.5.8 Whole inverse dynamic model of SPIDER4 RA-PKM
    3.6 The actuation redundancy issue in SPIDER4 RA-PKM
    3.7 Conclusion
    Chapter 4: Proposed Robust Control Solutions
    4.1 Introduction
    4.2 Background on RISE Feedback control
    4.2.1 Control law
    4.2.2 Application of standard RISE feedback control to PKMs
    4.4 Control solution 1: A RISE controller with Nominal Feedforward
    4.4.1 Motivation
    4.4.2 Proposed control law Controller design Stability analysis
    4.5 Control solution 2: A RISE Feedforward controller with Adaptive Feedback Gains
    4.5.1 Motivation
    4.5.2 Proposed control law Controller design Adaptive criterion for feedback gains Stability analysis
    4.8 Conclusion
    Chapter 5: Numerical simulations and Real-time experiments
    5.1 Introduction
    5.2 Performance evaluation criteria
    5.3 Tuning gains procedures
    5.3.1 Tuning gains procedure for control solution 1
    5.3.2 Tuning gains procedure for control solution 2
    5.4 Simulation results on Delta PKM
    5.4.1 Software settings for simulations
    5.4.2 Description of the simulation scenarios
    5.2.2 Evaluation scenarios Scenario 1 (nominal case) Scenario 2 (Pick-and-Place task case)
    5.2.3 Simulation results of control solution 1
    5.2.4 Simulation results of control solution 2
    5.5 Real-Time Experimental results on SPIDER4-RA-PKM
    5.5.1 Hardware and software description
    5.5.2 Description of the experimental scenarios
    5.5.2 Real-Time experimental scenarios Scenario 1 (nominal case) Scenario 2 (Machining task case)
    5.5.3 Experimental results of control solution 1
    5.5.4 Experimental results of control solution 2 Machining path evaluation at low speed Machining path evaluation at medium speed Machining path evaluation at high-speed
    5.6 Conclusion
    General Conclusion
    A Proof of lemma 1
    B Trajectory points for SPIDER4
    B1 Trajectory points for Scenario 1
    B2 Trajectory points for scenario 2

Product details

  • No. of pages: 200
  • Language: English
  • Copyright: © Academic Press 2023
  • Published: January 1, 2023
  • Imprint: Academic Press
  • Paperback ISBN: 9780323961011

About the Authors

Jonatan Escorcia Hernandez

Jonatan Martin Escorcia Hernández received his B.Sc in Robotic Engineering, M.Sc. in Automation and Control, and Ph.D. in Optomechatronics from the Polytechnic University of Tulancingo (UPT), Tulancingo de Bravo, Mexico in 2013, 2017, and 2020, respectively. He is currently working as a part time professor at the UPT, teaching classes in robotics engineering. His research interests include modeling, mechanical design, and nonlinear control of robotics systems.

Affiliations and Expertise

Polytechnic University of Tulancingo, Mexico

Ahmed Chemori

Ahmed Chemori CNRS, LIRMM received the M.Sc. and Ph.D. degrees both in automatic control from the Grenoble Institute of Technology, Grenoble, France, in 2001 and 2005, respectively. He has been a Postdoctoral Fellow with the Automatic Control Laboratory, Grenoble, France, in 2006. He is currently a tenured Research Scientist in automatic control and robotics with the Montpellier Laboratory of Informatics, Robotics and Microelectronics (LIRMM-CNRS). His research interests include nonlinear, robust , adaptive and predictive control and their real-time applications in complex robotic.

Affiliations and Expertise

University of Montpellier, France

Hipolito Sierra

Hipólito Aguilar Sierra received the B.Sc. degree in Mechatronics Engineering from UPIITA-IPN in 2009; and M.Sc. and Ph. D degrees both in Automatic Control from the CINVESTAV Zacatenco, Mexico City, Mexico, in 2011 and 2016, respectively. He is currently a Full-time professor at Faculty of Engineering from the La Salle Mexico University. His research interests include Medical robots, Rehabilitation robots, Exoskeleton robotics and Nonlinear control.

Affiliations and Expertise

La Salle University, Mexico

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