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

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

1.2.2.1 Pick-and-Place (P&P) Tasks

1.2.2.2 Machining Tasks

1.2.2.3 Coordinate Measuring Machines

1.2.2.4 Medical Applications

1.2.2.5 Agriculture Applications

1.2.2.6 Motion Simulators

1.2.2.7 3D Printers

1.2.2.8 Haptic Devices

1.3 Control Problem Formulation

1.3.1 PKMs Control Challenges

1.3.1.1 Highly Nonlinear Dynamics

1.3.1.2 Unstructured and Structured Uncertainties

1.3.1.3 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

2.3.1.1 Newton-Euler Formulation

2.3.1.2 Virtual Work Principle

2.3.1.3 Euler-Lagrange Formulation

2.3.1.4 Simplification-based modelling method for delta-like PKMs

2.3.2 Dynamic modelling representation

2.3.2.1 The Inverse Dynamic Model in Joint Space

2.3.2.2 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

2.4.1.1 PD/PID Controllers

2.4.1.2 Nonlinear PD/PID Controllers

2.4.2 Non-model-based-adaptive controllers

2.4.2.1 L1 Adaptive Control

2.4.2.2 Active Disturbance Rejection Control

2.5 Overview of Model-Based Motion Controllers for PKMs

2.5.1 Model-based-non-adaptive controllers

2.5.1.1 Computed Torque Control

2.5.1.2 Augmented PD/PID Control

2.5.1.3 PD Computed Feedforward Control

2.5.1.4 Higher Order Sliding Mode Control

2.5.2 Model-based-adaptive controllers

2.5.2.1 Adaptive Computed Torque Control

2.5.2.2 PID with Adaptive Feedforward

2.5.2.3 Dual-Mode Adaptive Control

2.5.2.4 L1 Adaptive Control with Adaptive Feedforward

2.5.2.5 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

4.4.2.1 Controller design

4.4.2.2 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

4.5.2.1 Controller design

4.5.2.2 Adaptive criterion for feedback gains

4.5.2.3 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

5.2.3.1 Scenario 1 (nominal case)

5.2.3.2 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

5.5.2.1 Scenario 1 (nominal case)

5.5.2.2 Scenario 2 (Machining task case)

5.5.3 Experimental results of control solution 1

5.5.4 Experimental results of control solution 2

5.5.4.1 Machining path evaluation at low speed

5.5.4.2 Machining path evaluation at medium speed

5.5.4.3 Machining path evaluation at high-speed

5.6 Conclusion
General Conclusion
Appendices
A Proof of lemma 1
B Trajectory points for SPIDER4
B1 Trajectory points for Scenario 1
B2 Trajectory points for scenario 2
References