1. PUMA 560 Architecture Main Page References Trajectories Control of manipulators Robots Opened Control Architecture Obtaining of Robots dynamic model by Gibbs- Appell formulation Movement simulation through the Dynamic Model Núria Rosillo Guerrero Study and Implementation of Industrial Robots Dynamic Controllers in Real-Time Name: Núria Rosillo Guerrero Faculty: Computer Science Engineering Department: Mathematics Science and Computation Universidad Cardenal Herrera CEU Halmstad, 27.06.15

2. PUMA 560 Architecture Main Page References Trajectories Control of manipulators Robots Opened Control Architecture Obtaining of Robots dynamic model by Gibbs- Appell formulation Movement simulation through the Dynamic Model Núria Rosillo Guerrero PUMA 560 Architecture Robot Arm Control Wardrobe Original Architecture

3. PUMA 560 Architecture Main Page References Trajectories Control of manipulators Robots Opened Control Architecture Obtaining of Robots dynamic model by Gibbs- Appell formulation Movement simulation through the Dynamic Model Núria Rosillo Guerrero PUMA 560 Architecture Robot Arm

4. PUMA 560 Architecture Main Page References Trajectories Control of manipulators Robots Opened Control Architecture Obtaining of Robots dynamic model by Gibbs- Appell formulation Movement simulation through the Dynamic Model Núria Rosillo Guerrero PUMA 560 Architecture Control Wardrobe Power Tray. Control Panel. Control Module. I/O Module. Amplifier Module.

5. PUMA 560 Architecture Main Page References Trajectories Control of manipulators Robots Opened Control Architecture Obtaining of Robots dynamic model by Gibbs- Appell formulation Movement simulation through the Dynamic Model Núria Rosillo Guerrero... PUMA 560 Architecture Original Architecture

6. PUMA 560 Architecture Main Page References Trajectories Control of manipulators Robots Opened Control Architecture Obtaining of Robots dynamic model by Gibbs- Appell formulation Movement simulation through the Dynamic Model Núria Rosillo Guerrero PUMA 560 Architecture Original Architecture LSI –11/02 Processor. Digital Servos. Analogical Servos. Amplifiers. Incremental encoders. Potentiometers....

7. PUMA 560 Architecture Main Page References Trajectories Control of manipulators Robots Opened Control Architecture Obtaining of Robots dynamic model by Gibbs- Appell formulation Movement simulation through the Dynamic Model Núria Rosillo Guerrero PUMA 560 Architecture Original Architecture

8. PUMA 560 Architecture Main Page References Trajectories Control of manipulators Robots Opened Control Architecture Obtaining of Robots dynamic model by Gibbs- Appell formulation Movement simulation through the Dynamic Model Núria Rosillo Guerrero Opened Control Architecture...

9. PUMA 560 Architecture Main Page References Trajectories Control of manipulators Robots Opened Control Architecture Obtaining of Robots dynamic model by Gibbs- Appell formulation Movement simulation through the Dynamic Model Núria Rosillo Guerrero Opened Control Architecture...

10. PUMA 560 Architecture Main Page References Trajectories Control of manipulators Robots Opened Control Architecture Obtaining of Robots dynamic model by Gibbs- Appell formulation Movement simulation through the Dynamic Model Núria Rosillo Guerrero Opened Control Architecture PCL-812. PCL-833. PCL-726....

11. PUMA 560 Architecture Main Page References Trajectories Control of manipulators Robots Opened Control Architecture Obtaining of Robots dynamic model by Gibbs- Appell formulation Movement simulation through the Dynamic Model Núria Rosillo Guerrero Opened Control Architecture...

12. PUMA 560 Architecture Main Page References Trajectories Control of manipulators Robots Opened Control Architecture Obtaining of Robots dynamic model by Gibbs- Appell formulation Movement simulation through the Dynamic Model Núria Rosillo Guerrero Opened Control Architecture Brake circuit Original braking system. Brake control by computer.

13. PUMA 560 Architecture Main Page References Trajectories Control of manipulators Robots Opened Control Architecture Obtaining of Robots dynamic model by Gibbs- Appell formulation Movement simulation through the Dynamic Model Núria Rosillo Guerrero Obtaining of Robots dynamic model by Gibbs-Appell formulation...

14. PUMA 560 Architecture Main Page References Trajectories Control of manipulators Robots Opened Control Architecture Obtaining of Robots dynamic model by Gibbs- Appell formulation Movement simulation through the Dynamic Model Núria Rosillo Guerrero Obtaining of Robots dynamic model by Gibbs-Appell formulation... Solve the Inverse Dynamic Problem Gibbs’s Function : Gibbs’s function for the solid i is given by

15. PUMA 560 Architecture Main Page References Trajectories Control of manipulators Robots Opened Control Architecture Obtaining of Robots dynamic model by Gibbs- Appell formulation Movement simulation through the Dynamic Model Núria Rosillo Guerrero Obtaining of Robots dynamic model by Gibbs-Appell formulation... Solve the Inverse Dynamic Problem If we express the tensorial and vectorial magnitudes considering a reference system located in the iesim bar. For a system consisting of n bodies, Gibbs’s function could be given by:

16. PUMA 560 Architecture Main Page References Trajectories Control of manipulators Robots Opened Control Architecture Obtaining of Robots dynamic model by Gibbs- Appell formulation Movement simulation through the Dynamic Model Núria Rosillo Guerrero Obtaining of Robots dynamic model by Gibbs-Appell formulation... Solve the Inverse Dynamic Problem The Gibbs-Appell’s movements equations are obtained leading respect to the generalized accelerations, of that way we obtain the inertial forces that correspond to the generalized external forces  j Operating:

17. PUMA 560 Architecture Main Page References Trajectories Control of manipulators Robots Opened Control Architecture Obtaining of Robots dynamic model by Gibbs- Appell formulation Movement simulation through the Dynamic Model Núria Rosillo Guerrero Obtaining of Robots dynamic model by Gibbs-Appell formulation Complexity n algorism From D-H and off-line: With a recursive way: A term: B term:...

18. PUMA 560 Architecture Main Page References Trajectories Control of manipulators Robots Opened Control Architecture Obtaining of Robots dynamic model by Gibbs- Appell formulation Movement simulation through the Dynamic Model Núria Rosillo Guerrero Obtaining of Robots dynamic model by Gibbs-Appell formulation Complexity n algorism AlgorismComplexityn=6 Luh, Walker and Paul (x) 121 n -112 (+) 90 n - 82 614 458 Proposed algorism(x) 121 n –136 (+) 91 n - 116 590 430...

19. PUMA 560 Architecture Main Page References Trajectories Control of manipulators Robots Opened Control Architecture Obtaining of Robots dynamic model by Gibbs- Appell formulation Movement simulation through the Dynamic Model Núria Rosillo Guerrero Obtaining of Robots dynamic model by Gibbs-Appell formulation... Direct Dynamic Problem Algorism that simulate the dynamic behavior of industrial robot. General form of the movement equation: Obtaining BIAS vector: Obtaining gravity vector:

20. PUMA 560 Architecture Main Page References Trajectories Control of manipulators Robots Opened Control Architecture Obtaining of Robots dynamic model by Gibbs- Appell formulation Movement simulation through the Dynamic Model Núria Rosillo Guerrero Obtaining of Robots dynamic model by Gibbs-Appell formulation Direct Dynamic Problem Obtaining the system inertias matrix.

21. PUMA 560 Architecture Main Page References Trajectories Control of manipulators Robots Opened Control Architecture Obtaining of Robots dynamic model by Gibbs- Appell formulation Movement simulation through the Dynamic Model Núria Rosillo Guerrero Movement simulation through the Dynamic Model Dynamic equation: DDP:IDP System to solve:  ControllerSimulator q, v, a qdqd...

22. PUMA 560 Architecture Main Page References Trajectories Control of manipulators Robots Opened Control Architecture Obtaining of Robots dynamic model by Gibbs- Appell formulation Movement simulation through the Dynamic Model Núria Rosillo Guerrero Movement simulation through the Dynamic Model Results

23. PUMA 560 Architecture Main Page References Trajectories Control of manipulators Robots Opened Control Architecture Obtaining of Robots dynamic model by Gibbs- Appell formulation Movement simulation through the Dynamic Model Núria Rosillo Guerrero Control of manipulators Robots... Development of a general expression to the controllers by passiveness and inverse dynamic  = M â + C + G

24. PUMA 560 Architecture Main Page References Trajectories Control of manipulators Robots Opened Control Architecture Obtaining of Robots dynamic model by Gibbs- Appell formulation Movement simulation through the Dynamic Model Núria Rosillo Guerrero Control of manipulators Robots... Control by passiveness The control based in the passiveness with point to point strategies can be seen as particular cases of this control law. We obtain the gravitational term a partir de: doing that and

25. PUMA 560 Architecture Main Page References Trajectories Control of manipulators Robots Opened Control Architecture Obtaining of Robots dynamic model by Gibbs- Appell formulation Movement simulation through the Dynamic Model Núria Rosillo Guerrero Controlgv PD + G(q) PD + G(qd) Compensador Lineal + G(q) Compensador Lineal + G(qd) Diferenciación Aproximativa + G(q) Diferenciación Aproximativa + G(qd) PID PI2D Control of manipulators Robots...

26. PUMA 560 Architecture Main Page References Trajectories Control of manipulators Robots Opened Control Architecture Obtaining of Robots dynamic model by Gibbs- Appell formulation Movement simulation through the Dynamic Model Núria Rosillo Guerrero Control of manipulators Robots Control by passiveness...

27. PUMA 560 Architecture Main Page References Trajectories Control of manipulators Robots Opened Control Architecture Obtaining of Robots dynamic model by Gibbs- Appell formulation Movement simulation through the Dynamic Model Núria Rosillo Guerrero Control of manipulators Robots Control by inverse dynamic We start from this equation We will establish a control over the trajectory, calculating a of that way Type of control over the trajectory a Point to point Follow-up of the trajectory Follow-up of the trajectory with integral action...

28. PUMA 560 Architecture Main Page References Trajectories Control of manipulators Robots Opened Control Architecture Obtaining of Robots dynamic model by Gibbs- Appell formulation Movement simulation through the Dynamic Model Núria Rosillo Guerrero Control of manipulators Robots Control by inverse dynamic

29. PUMA 560 Architecture Main Page References Trajectories Control of manipulators Robots Opened Control Architecture Obtaining of Robots dynamic model by Gibbs- Appell formulation Movement simulation through the Dynamic Model Núria Rosillo Guerrero Reference Trajectories Ramp entry Natural cubic spline...

30. PUMA 560 Architecture Main Page References Trajectories Control of manipulators Robots Opened Control Architecture Obtaining of Robots dynamic model by Gibbs- Appell formulation Movement simulation through the Dynamic Model Núria Rosillo Guerrero Reference Trajectories Fourier Series...

31. PUMA 560 Architecture Main Page References Trajectories Control of manipulators Robots Opened Control Architecture Obtaining of Robots dynamic model by Gibbs- Appell formulation Movement simulation through the Dynamic Model Núria Rosillo Guerrero ConclusionsConclusions