Pseudo-admittance Bilateral Telemanipulation with Guidance Virtual Fixtures

1. Pseudo-admittanceBilateral Telemanipulationwith Guidance Virtual Fixtures By Jake J. Abbott and Allison M. Okamura Presenter In Lee, inism@postech.ac.kr 2010.05.17

2. MotivationOur Problem Problem: WAM has high joint friction that causes fatigue to the user Solution: Drive the WAM along the direction of motion so that it can aid the user! How? Admittance control

3. MotivationAdmittance Control / Admittance-type Device velocity force admittance Admittance Control New Problem: only specially designed devices called admittance-type device can be controlled by the admittance control, but WAM is not that kind of device. It’s animpedance-type device. Isn’t there any algorithm that makes impedance-type devices possible to be admittance-controlled? Pseudo-admittance Bilateral Telemanipulation of J. J. Abbott and A. M. Okamura

4. OverviewPseudo-admittance Bilateral Telemanipulation • An control algorithm for teleoperation • It makes the impedance-type master device to follow the admittance control law. • It only concerns about the position of the end effector. Hence, both master and slave are assumed to serial-link 3-DOF devices and all equations are represented in the Cartesian coordinate. • It is easy to implement virtual fixtures under the algorithm. • Contents • Introduction • Details on the algorithm • Virtual fixture implementation • Experiments

5. IntroductionTeleoperation • Teleoperation: to interact with a remote environment without actually being in that environment via a remote agent. • Application • Operations at hazardous or inaccessible places(e.g., explosive disposal, disaster relief, deep sea exploration) • Tasks that require better-than-human level operations(microsurgery, cell probing)

6. IntroductionTwo Control Schemes Pseudo-admittance is a sort of position control which allows fine motion tasks

7. Pseudo-admittance Bilateral Telemanipulation

8. Notations

9. Key Idea (Cont.) User position Slave Master Environment force (force feedback) Traditional Position Control Proxy Proxy position Net force Slave position Slave Master Environment force (force feedback) Pseudo-admittance Control Add a proxy that moves according to the admittance control law, and make the slave (master) follow the proxy (slave) instead of the master.

10. Key Idea • Admittance control law of proxy • Because the slave follows the proxy and the master does the slave, they eventually follows below equations: • A PD controller (for master) and a P controller with velocity feedback (for slave) are utilized to control the following motion.

11. Linearizing and Decoupling Control Because the dynamics of impedance-type device changes over the end-effector position, the same device force command can result in different motions. Dynamics of the device is assumed to be We can linearize the motion by changing the force command, , to

12. Actual Force Command to the Devices From the previous slide, the actual devices’ force command become In addition, the master should deliver the feedback force from the slave to the user

13. Net Force Approximation • The net force, , determines the proxy motion, and it can be approximated as follows: • From the device dynamics, . • If the device is in the equilibrium state or constant-velocity motion, the acceleration becomes zero; . • After few steps, we get • Algorithm summary: System Dynamics

14. Stability analysis

15. State-space Representation (cont.) Wikipedia says, “a state space representation is a mathematical model of a physical system as a set of input, output and state variables related by first-order differential equations”. Target variables: State-space representation of the system:

16. State-space Representation (cont.) It can be rewritten as follows,

17. Stability Concerns (Cont.) Linear and time-invariant (LTI). Eigenvalues are the PD-controller gains. We can set the gains to make the matrixto a Hurwitz matrix. We assume the machine is away from the singular points. -> is bounded. if is sufficiently small, from the continuity of eigenvalues,A(t) would still be Hurwitz. Hurwitz matrix: a matrix whose eigenvalues are strictly negative real numbers. if is Hurwitz, the differential equation is uniformly exponentially stable. x exponentially converges to zero We want the system to be stable ( ) with no error between the master and slave ( ) when it unforced ( ), and to be Bounded-input/bounded-output stable. is bounded if and are bounded.

18. Virtual fixture

19. Notations

20. Virtual Fixture Implementation First, find the projected direction of the net force on the subspace, Find the preferred direction of motion, Divide the net force into preferredand non-preferred components, Attenuate the non-preferred componentof the net force, and use it as an input tothe proxy dynamics.

21. Experiment

22. Constant Velocity Motion in Free Space

23. Pushing Soft Wall (Simulation)

24. Interaction with a Real Object

25. Virtual Fixture

26. So, How Can We Do the Admittance Control for WAM? Proxy Proxy position Net force Slave position Slave Master Environment force (force feedback) Pseudo-admittance Control Net force Proxy position Proxy Master Environment force (force feedback) For Our Purpose We have to expand the algorithm from 3-DOF to 7-DOF.

27. AppendixImpedance / Admittance Type Device

28. Stability Concerns Let’s return to the . is updated at a constant rate. -> For ‘th update, is just a constant matrix (i.e., LTI), . State change during an unit update period, , is If , the system will be exponentially stable.-> select system parameters, fix to an initial value, find the which results in the maximum over the workspace, and adjust to match the requirement.