Flexible Robot Dynamics and Controls

by Robinett, Rush D., III; Dohrmann, Clark R.; Eisler, G. Richard; Feddema, John T.; Parker, Gordon G.; Wilson, David G.

• ISBN13: 9780306467240
• ISBN10: 0306467240
• Format: Hardcover
• Copyright: 2001-12-01
• Publisher: Kluwer Academic Pub

Summary

This volume will guide professional engineers whose disciplines include: robotics, controls, mechanical, electrical, computer science and electrical, etc., to a better, or first understanding of how to develop and control robotics or other systems with inherent or desirable structural flexibility. Furthermore, senior and graduate mechanical, electrical, and computer science engineering students, particular those new to a government or private sector research institution, will benefit from the academic study of this volume. In addition, it will guide the reader through a review and application of several necessary advanced mathematics, engineering and scientific principles.

Table of Contents

Introduction	1	(12)
Sandia National Laboratories	1	(1)
Flexible Robotics Research Historical Background	2	(3)
Milestones to Present Flexible Robotics Research	3	(2)
Outline of the Book	5	(5)
Chapter 1 Summary	10	(1)
Chapter 1 References	10	(1)
Chapter 1 Problems	11	(2)
Mathematical Preliminaries	13	(80)
Introduction	13	(1)
Linear Algebra	13	(4)
Linear Independence of Constant Vectors	14	(1)
Rank and Null Space of a Matrix	14	(1)
Eigenvalues and Eigenvectors	15	(2)
Linear Control Systems	17	(14)
Discontinuous Functions	18	(1)
Impulse Response Function	19	(1)
Laplace Transform	20	(3)
State-space Realization	23	(5)
Time Invariant Linear Systems	28	(2)
Controllability	30	(1)
Observability	30	(1)
Digital Systems	31	(11)
Introduction to Integration Algorithms	31	(2)
Explicit (Single Pass)	33	(1)
Implicit (Single Pass)	33	(1)
Second-order Runge-Kutta	34	(1)
Real-Time, Second-Order Runge-Kutta	35	(1)
Third-Order Runge-Kutta	35	(1)
Fourth-order Runge-Kutta (RK-4)	36	(1)
Stability	36	(1)
Z-transform	37	(2)
Unit data-point integrator	39	(2)
State-space methods	41	(1)
Calculus of Variations	42	(10)
Calculus of Several Variables	43	(3)
Lagrange Multipliers	46	(2)
Relationship Between Calculus of Variables and Calculus of Variations	48	(4)
Hamilton's Principle & Lagrange's Equations	52	(6)
Hamilton's Principle	53	(1)
Extended Hamilton's Principle	54	(2)
Newton's Equations of Motion	56	(1)
Gantry Robot Model	57	(1)
Analytical Optimization	58	(17)
Preliminaries	59	(1)
Positive Definite Matrices	59	(1)
Simple Parameter Minimization	60	(1)
Variational Conditions for Unconstrained Scalar Minimization	61	(1)
A Multivariable View of the Variational Conditions for Unconstrained Scalar Minimization	62	(2)
Variational Approach to Constrained Parameter Minimization	64	(2)
Optimal Control Problem	66	(2)
Derivation of the First Variation Conditions	68	(2)
First Integral and a Second Variation Condition	70	(3)
Free Final Time Problems	73	(2)
Numerical Optimization	75	(11)
Parameter Optimization - Themes	76	(1)
Development of a First-Order Method-Unconstrained Functions	77	(1)
Gradient Search - Stepping along the Search Direction	78	(1)
A Second-Order Method	79	(1)
Finite Differences	79	(1)
Second-Order Finite Differences	80	(1)
Penalty Functions	81	(1)
Parameterized Controls - the use of tabular functions u*(ξ	81	(5)
Chapter 2 Summary	86	(1)
Chapter 2 References	86	(2)
Chapter 2 Problems	88	(5)
Flexible Robot Dynamic Modeling	93	(40)
Introduction	93	(1)
Flexible Link Modeling Preliminaries	93	(10)
Linear Independence of Functions	94	(1)
Orthogonality of Functions	94	(2)
Beam Dynamic Analysis - Analytical Solution	96	(1)
Mode Shapes from Static Loading Conditions	97	(1)
Assumed Modes Method	98	(2)
The Finite Element Method	100	(1)
Mode Shape Discussion	101	(1)
Rotational Fundamentals	102	(1)
The Method of Quadratic Modes	103	(17)
An Introductory Example	103	(4)
Computing Quadratic Mode Shapes	107	(5)
Formal Quadratic Modes Equations	112	(7)
Multibody Quadratic Modes	119	(1)
Planar Flexible Robot Dynamics	120	(9)
Summary	125	(4)
Actuator Dynamics	129	(1)
Chapter 3 Summary	130	(1)
Chapter 3 References	130	(1)
Chapter 3 Problems	131	(2)
System Identification	133	(28)
Introduction	133	(1)
Linear Least Squares (LSS)	133	(3)
Nonlinear Least Squares	136	(9)
Gauss's Least Square Differential Correction Algorithm	137	(1)
Overhead Gantry Robot Example	138	(6)
Frequency Domain NLS	144	(1)
Homotopy Methods	145	(4)
Root Solving	145	(3)
Increase the Convergence Region	148	(1)
Robot and Actuator System ID	149	(6)
Chapter 4 Summary	155	(1)
Chapter 4 References	156	(1)
Chapter 4 Problems	157	(4)
Input Shaping for Path Planning	161	(72)
Introduction	161	(1)
Analytic Solutions for Input Shaping	161	(3)
Input Shaping Filters	164	(16)
Finite Impulse Response Filter	165	(4)
Infinite Impulse Response Filter Formulation	169	(7)
Flexible Two-Link Manipulator Example	176	(3)
Gantry Robot Example	179	(1)
Constrained Optimization with RQP	180	(24)
Quadratic Surfaces	181	(1)
Quadratic Approximation	182	(1)
A Second-Order Iterative Method for Unconstrained Minimization	182	(1)
Recursive Quadratic Programming - a method to handle constraints explicitly	183	(1)
RQP Equality Constraints - solving for the unknowns	184	(1)
Formalized solution methods for implementing RQP	184	(2)
Parameterized Controls - how to handle a changing final time	186	(1)
Parameterized Controls - treating fixed bounds on the controls	187	(1)
Examples with Parameterized Controls	188	(5)
Optimal Trajectories for Flexible Link Manipulators	193	(6)
Open Loop Input Shaping for a Slewing Flexible Rod	199	(5)
Dynamic Programming	204	(18)
The Principle of Optimality	205	(1)
Simple Application of Dynamic Programming	205	(1)
Application of Dynamic Programming to Data Smoothing	206	(3)
Application of Dynamic Programming to Discrete-Time Optimal Control Problems	209	(2)
Practical Issues	211	(6)
What Drove us to Dynamic Programming?	217	(5)
Chapter 5 Summary	222	(1)
Chapter 5 References	223	(2)
Chapter 5 Problems	225	(8)
Linear Feedback Control	233	(44)
Introduction	233	(1)
PD Control of a Gantry Robot	233	(7)
Lag-Stabilized Feedback Control	240	(5)
Non-collocated Controls	245	(5)
Feedforward Control	250	(5)
Linear Quadratic Regulator	255	(4)
Necessary Conditions for Optimality	256	(1)
Neighboring-Optimal Solutions	257	(2)
Linear Optimal Estimation	259	(3)
Linear Quadratic Gaussian (LQG) Control	262	(9)
Experimental Results	265	(6)
Chapter 6 Summary	271	(1)
Chapter 6 References	271	(2)
Chapter 6 Problems	273	(4)
Nonlinear Systems and Sliding Mode Control	277	(28)
Introduction	277	(2)
State-Space Representation of a Dynamic System	279	(3)
State Nonlinearities	280	(1)
Equilibrium Points	281	(1)
Stability	282	(6)
Stability Determination - Lyapunov's Direct Method	282	(2)
Formal Statement of Lyapunov Stability	284	(1)
Local Stability	285	(1)
Global Stability	285	(1)
Global Asymptotic Stability	285	(2)
Comments	287	(1)
Sliding Mode Control	288	(14)
SMC for Second-Order Systems	289	(1)
Stability Assessment	289	(1)
Sliding Mode Control for Tracking Control	290	(2)
Sliding Mode Control for Systems with Parameter Uncertainty	292	(1)
Augmented Sliding Mode Control	293	(3)
Output Feedback SMC	296	(4)
Control-Structure-Actuator Interaction	300	(2)
Chapter 7 Summary	302	(1)
Chapter 7 References	303	(1)
Chapter 7 Problems	303	(2)
Adaptive Sliding Mode Control	305	(20)
Introduction	305	(1)
Adaptive Sliding Mode Control	306	(2)
Examples	308	(13)
Chapter 8 Summary	321	(1)
Chapter 8 References	322	(1)
Chapter 8 Problems	322	(3)
Appendix A: VFO2AD Optimization	325	(2)
Appendix B: MATLAB® Optimization	327	(6)
Appendix C: Hardware & Software Support	333	(4)
Subject Index	337