Table of contents for Flexible robot dynamics and controls / Rush D. Robinett, III ... [et al.].


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1 Introduction
1.1. Sandia National Laboratories ..................
1.2. Flexible Robotics Research Historical Background  .........
1.2.1. Milestones To Present Flexible Robotics Research
1.3.  Outline  of the  Book  .......................
1.4.  Chapter 1 Summary  .......................
1.5. Chapter 1 References ..........................
1.6.  Chapter 1 Problems  .......................
2 Mathematical Preliminaries
2.1.  Introduction  .. .. .. . .. . .. .. .. .. . . . .. . . . . . . ..
2.2.  Linear Algebra  ........   ... .... ......
2.2.1. Linear Independence of Constant Vectors .....
2.2.2. Rank and Null Space of a Matrix ........
2.2.3. Eigenvalues and Eigenvectors ........
2.3. Linear Control Systems ................
2.3.1. Discontinuous Functions ....................
2.3.2. Impulse Response Function ..................
2.3.3. Laplace Transform ......           .........
2.3.4. State-space Realization  . . ........
2.3.5. Time Invariant Linear Systems ........
2.3.6.  Controllability  ...................
2.3.7.  Observability  ....................
2.4.  Digital Systems  .......................
2.4.1. Introduction to Integration Algorithms .............
2.4.2.  Explicit (Single Pass)  ...............
2.4.3.  Implicit (Single Pass)  ...............
2.4.4. Second-order Runge-Kutta ...........
2.4.5. Real-Time, Second-Order Runge-Kutta  .. ..  ..
2.4.6. Third-order Runge-Kutta ..............
2.4.7. Fourth-order Runge-Kutta (RK-4) ..............
2.4.8.  Stability  .................         ....
2.4.9.  Z-transform  .....................



2.4.10. Unit data-point integrator ....................
2.4.11. State-space methods ...........
2.5. Calculus of Variations ........................
2.5.1. Calculus of Several Variables ..................
2.5.2.  Lagrange Multipliers  .. . . ................
2.5.3. Relationship Between Calculus of Variables and Calculus of
Variations  . ...................
2.6. Hamilton's Principle & Lagrange's Equations ......
2.6.1. Hamilton's Principle ................
2.6.2. Extended Hamilton's Principle ........
2.6.3. Newton's Equations of Motion  ........
2.6.4. Gantry Robot Model ..............
2.7. Analytical Optimization ...............
2.7.1.  Preliminaries  ...........................
2.7.2. Positive Definite Matrices ............
2.7.3. Simple Parameter Minimization ...........
2.7.4. Variational Conditions for Unconstrained Scalar Minimization
2.7.5. A Multivariable View of the Variational Conditions for Un-
constrained Scalar Minimization ................
2.7.6. Variational Approach to Constrained Parameter Minimization
2.7.7. Optimal Control Problem  ....................
2.7.8. Derivation of the First Variation Conditions ..........
2.7.9. First Integral and a Second Variation Condition  .......
2.7.10. Free Final Time Problems  ....................
2.8. Numerical Optimization ......................
2.8.1. Parameter Optimization - Themes ............
2.8.2. Development of a First-Order Method-Unconstrained Functions
2.8.3. Gradient Search - Stepping along the Search Direction ....
2.8.4. A Second-Order Method    .     ..       .......
2.8.5.  Finite  Differences   .... . .. .......... .....
2.8.6. Second-Order Finite Differences ...   ........
2.8.7. Penalty Functions ........       ... ...
2.8.8. Parameterized Controls - the use of tabular functions u,(C)
2.9. Chapter 2 Summary .     ......... ..    ..    .    . . .......
2.10. Chapter 2 References ..       ..            ............
2.11. Chapter 2 Problems ......................
3 Flexible Robot Dynamic Modeling
3.1.  Introduction  ..............
3.2. Flexible Link Modeling Preliminaries . .... ..........
3.2.1. Linear Independence of Functions  ....      ......
3.2.2. Orthogonality of Functions .......
3.2.3. Beam Dynamic Analysis - Analytical Solution .. .....
3.2.4. Mode Shapes from Static Loading Conditions .  ....



3.2.5. Assumed Modes Method ..................
3.2.6. The Finite Element Method ................
3.2.7. Mode Shape Discussion ..................
3.2.8. Rotational Fundamentals .....
3.3. The Method of Quadratic Modes ...............
3.3.1. An Introductory Example ...............
3.3.2. Computing Quadratic Mode Shapes .........
3.3.3. Formal Quadratic Modes Equations ........
3.3.4. Multibody Quadratic Modes ............
3.4.  Planar Flexible Robot Dynamics ..............
3.4.1.  Summary  . .......................          ....
3.5.  Actuator Dynamics .  ....    ..................
3.6. Chapter 3 Summary ...................
3.7.  Chapter 3  References .....................
3.8.  Chapter 3 Problems  ...................
4  System Identification
4.1.  Introduction  ..........................
4.2.  Linear Least Squares (LSS)  .....................
4.3.  Nonlinear Least Squares  .......................
4.3.1. Gauss's Least Square Differential Correction
Algorithm ............................
4.3.2. Overhead Gantry Robot Example ............
4.3.3. Frequency Domain NLS ..................
4.4.  Homotopy Methods  ..........................
4.4.1.  Root  Solving  ..........................
4.4.2. Increase the Convergence Region ..........
4.5. Robot and Actuator System ID ...............
4.6. Chapter 4 Summary ....................
4.7.  Chapter 4 References .....................
4.8.  Chapter 4 Problems  .....................
5 Input Shaping for Path Planning
5.1.  Introduction  .............
5.2. Analytic Solutions for Input Shaping ..............
5.3.  Input Shaping  Filters .......................
5.3.1. Finite Impulse Response Filter .............
5.3.2. Infinite Impulse Response Filter Formulation
5.3.3. Flexible Two-Link Manipulator Example ..........
5.3.4. Gantry Robot Example ................
5.4. Constrained Optimization with RQP .............
5.4.1.  Quadratic Surfaces  ...................
5.4.2. Quadratic Approximation ..................



5.4.3. A Second-Order Iterative Method for Unconstrained Mini-
mization  . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..
5.4.4. Recursive Quadratic Programming - a method to handle con-
straints  explicitly  .. .. . .. .. .. . . .. . .. .. . .. ..
5.4.5. RQP Equality Constraints - solving for the unknowns ....
5.4.6. Formalized solution methods for implementing RQP .....
5.4.7. Parameterized Controls - how to handle a changing final time
5.4.8. Parameterized Controls - treating fixed bounds on the controls
5.4.9. Examples with Parameterized Controls ............
5.4.10. Optimal Trajectories for Flexible Link Manipulators .....
5.4.11. Open Loop Input Shaping for a Slewing Flexible Rod  . . .
5.5.  Dynamic Programming  ........................
5.5.1.  The Principle of Optimality  ..................
5.5.2. Simple Application of Dynamic Programming .......
5.5.3. Application of Dynamic Programming to Data
Smoothing  . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.5.4. Application of Dynamic Programming to
Discrete-Time Optimal Control Problems ...........
5.5.5.  Practical Issues  .....................
5.5.6. What Drove us to Dynamic Programming? ........
5.6.  Chapter 5 Summary  ......................
5.7. Chapter 5 References ......................
5.8.  Chapter 5 Problems  .....................
6 Linear Feedback Control
6.1. Introduction .......
6.2. PD Control of a Gantry Robot .....................
6.3. Lag-Stabilized Feedback Control ....................
6.4.  Non-collocated  Controls  .................
6.5.  Feedforward  Control  ................
6.6. Linear Quadratic Regulator ..............
6.6.1. Necessary Conditions for Optimality .......
6.6.2. Neighboring-Optimal Solutions . . .......
6.7. Linear Optimal Estimation  ...............
6.8. Linear Quadratic Gaussian (LQG) Control ......
6.8.1. Experimental Results ........
6.9.  Chapter 6 Summary  ......................
6.10. Chapter 6 References ......................
6.11. Chapter 6 Problems  .....................
7 Nonlinear Systems and Sliding Mode Control
7.1. Introduction .........................
7.2. State-Space Representation of a Dynamic System .......
7.2.1. State Nonlinearities .........



7.2.2.  Equilibrium   Points  .....................
7.3.  Stability  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
7.3.1. Stability Determination - Lyapunov's Direct Method ...
7.3.2. Formal Statement of Lyapunov Stability ........
7.3.3.  Local Stability  .....................
7.3.4.  Global Stability  ...    .....    .......    ..  ..
7.3.5. Global Asymptotic Stability ..............
7.3.6. Comments .     ............................
7.4.  Sliding  Mode Control......................
7.4.1. SMC for Second-Order Systems ...........
7.4.2.  Stability  Assessment  .....................
7.4.3. Sliding Mode Control for Tracking Control ........
7.4.4. Sliding Mode Control for Systems with Parameter Uncertainty
7.4.5. Augmented Sliding Mode Control................
7.4.6.  Output Feedback SMC  ......................
7.4.7. Control-Structure-Actuator Interaction  .....
7.5.   Chapter 7 Summary  ..........................
7.6.  Chapter  7  References  ..........................
7.7.  Chapter 7  Problems  .........................
8 Adaptive Sliding Mode Control
8.1.  Introduction  .........
8.2. Adaptive Sliding Mode Control .............
8.3.  Examples  .........................
8.4. Chapter 8 Summary ...................
8.5.  Chapter 8 References ...................
8.6.  Chapter 8 Problems  ...................








Library of Congress subject headings for this publication: Robots, Industrial, Flexible manufacturing systems