1.4 LIST OF APPENDICES
Page
APPENDIX A: KINEMATICS OF TWO LINK MANIPULATOR................................ 210
A.1 Forward Kinematics .............................................................................. 210
A.2 Inverse Kinematics ................................................................................ 211
APPENDIX B: DYNAMICS OF TWO LINK MANIPULATOR .................................. 213
B.1 Equations of Motion .............................................................................. 213
B.2 Formulation of Equations of Motion ..................................................... 213
B.3 Lagrange-Euler Formulation ................................................................. 214
B.4 Macsyma ............................................................................................... 217
B.5 Using Macsyma on the Lagrange-Euler Problem .................................. 218
B.6 Macsyma Batch File .............................................................................. 219
B.7 The Results From Macsyma .................................................................. 225
B.8 Verifying the Results ............................................................................. 226
B.9 Macsyma Output ................................................................................... 226
APPENDIX C: NEURAL NETWORK SUBROUTINES .............................................. 238
C.1 Introduction ........................................................................................... 238
C.2 SubRoutine Architecture ....................................................................... 238
C.3 Example Subroutines ............................................................................ 241
C.4 Neural Network Initialization ................................................................ 241
C.5 Network Definition and Application Tools ............................................ 241
C.6 Neural Network Calculation Subroutines .............................................. 242
C.7 Neural Network Background Utilities ................................................... 243
C.8 User Defined Global Variable ................................................................ 243
C.9 Program Listing ..................................................................................... 244
APPENDIX D: ADAPTIVE TIME STEP RUNGE-KUTTA INTEGRATION .............. 255
D.1 Introduction .......................................................................................... 255
D.2 The Runge-Kutta Algorithm for Robot Motion Integration .................. 256
D.3 The Fourth Order Runge-Kutta Method ................................................ 256
D.4 Variable Step Size Estimation ............................................................... 258
D.5 Implementation ..................................................................................... 259
D.6 Subroutines ........................................................................................... 260
D.7 Program Listing .................................................................................... 262
APPENDIX E: GLOBAL DEFINITIONS FOR SOFTWARE ....................................... 267
E.1 Introduction ........................................................................................... 267
E.2 Program Listing ..................................................................................... 269
APPENDIX F: DYNAMICS MODULE ........................................................................ 272
F.1 Introduction ........................................................................................... 272
F.2 Subroutines ............................................................................................ 272
F.3 Program Listing ..................................................................................... 274
APPENDIX G: OPTIMIZATION ALGORITHMS ........................................................ 278
G.1 Introduction .......................................................................................... 278
G.2 Sample Application Subroutines ........................................................... 279
G.3 Hookes and Jeeves Subroutines ............................................................ 280
G.4 Common Optimization Support Routines ............................................. 280
G.5 Program Listing .................................................................................... 282
APPENDIX H: PATH OPTIMIZATION SUBROUTINES ............................................ 295
H.1 Introduction .......................................................................................... 295
H.2 Example Subroutines ............................................................................ 296
H.3 Spline Subroutines ................................................................................ 296
H.4 Path Generation Subroutines ................................................................. 296
H.5 Utility Subroutines ................................................................................ 297
H.6 Program Listing .................................................................................... 299
APPENDIX I: NEURAL NETWORK MOTION PLANNING MODULE .................... 311
I.1 Introduction ............................................................................................ 311
I.2 Simulation Subroutines .......................................................................... 312
I.3 Training and Testing Subroutines ........................................................... 312
I.4 Training Trajectory and Neural Network Maintenance ........................... 315
I.5 Program Listing ...................................................................................... 316
APPENDIX J: PATH PLANNING FUNCTION MODULE .......................................... 337
J.1 Introduction ............................................................................................ 337
J.2 Endpoint Buffer Subroutines .................................................................. 338
J.3 Training Data Subroutines ...................................................................... 339
J.4 Robot Specific Subroutines .................................................................... 339
J.5 Path Planning Subroutines ...................................................................... 340
J.6 Program Listing ...................................................................................... 342
APPENDIX K: NEURAL NETWORK BATCH TRAINING PROGRAM ................... 359
K.1 Introduction .......................................................................................... 359
K.2 Program Listing .................................................................................... 360
APPENDIX L: USER INTERFACE PROGRAM .......................................................... 361
L.1 Introduction ........................................................................................... 361
L.2 Description of Functions in Neural Network Window ........................... 362
L.3 Description of Functions in Path Endpoint Window .............................. 364
L.4 Description of Functions in Robot Window ........................................... 365
L.5 Description of Functions in Graphing Window ..................................... 367
L.6 Windows and Applications Setup Subroutines ...................................... 368
L.7 Graphing Subroutines ............................................................................ 370
L.8 Path Endpoint Maintenance Subroutines ............................................... 371
L.9 Training Trajectory Array Subroutines .................................................. 372
L.10 Robot Maintenance Subroutines .......................................................... 372
L.11 Neural Network Maintenance Subroutines .......................................... 373
L.12 Sunview Interface Subroutines ............................................................ 375
L.13 Program Listing ................................................................................... 376