Using Wave Variables for System Analysis and Robot Control

1. Using Wave Variables for System Analysis and Robot Control MSc. Lei Ma 27 May, 2004

2. Contents • Introduction to teleoperation • Concept of passivity • Wave variable: idea, definition, characteristics • conclusion

3. Telerobotics: System construction • A master (local) device, • A slave (remote) device, • A communication channel. Communication channel

4. General description • Human operator as present of high-level control of activities; • Both master and salve have own control systems; • Human operator requires information: • Proper user interface; • Data feedback from the slave site: • forces applied to the environment, • relevant positions of the slave, • graphical video data, • tactile or acoustic information.

5. The master • Typical features of the master are: • Capability of assigning tasks to the slave and providing the operator with relevant information about the task development—TELEPRESENCE: • Implementative solutions: joysticks and/or consoles; • Different types of signals may be reflected by these devices to the operator. • Capability of acquiring and processing data from both the operator and the slave.

6. The slave • directly interacts with environment for task execution. • A robotic system for the interaction with the environment and the execution of the task planned by the operator; • Signal acquisition and processing; • Capability data processing.

7. The communication channel • represents the link between the master and slave sites. • Main drawback. Time delay in the transmission of signals: • physical delay in the transmission line (e.g. in a long satellite communication), • limited bandwidth of the hardware. • The time delay, in some case not constant, can originate noticeable instability problems. • A very common choice in practical applications is to transmit velocity to the slave and force to the master.

8. Application • space • underwater • hazardous environments • production • security • simulators • …

9. Rotex: ROboter Technology EXperiment • Robotic arm for intra-vehicular activities developed by DLR, Germany. • Successfully used in the mission of the space-shuttle COLUMBIA in 1993. • Variety of operational modes: teleoperation on board ,teleoperation from ground using predictive graphics, sensor-based off-line programming. • Performing three significant tasks: assembly of a grid, connection/disconnection of an electrical plug, grasp of a flying object.

10. Transmission delay over Internet • Discussion of time delay of 0.1~several seconds because: • Human operator as slowest element has reaction time of ~0.1 sec; • Teleoperation not possible with delay more than 10 sec

11. Problem statment • Slave manipulator follows motion of the master properly. • Force applied to the environment fedback to mater properly.

12. Problem statement: stability • A control system is in equilibrium if, in the absence of any disturbance or input, the output stays in the same state. • A control system is stable if the output eventually comes back to its equilibrium state when the system is subject to an initial condition. • Example: inverted pendulum.

13. Problem statement: passivity Estore: energy storage • Loosely said, a system is passive if it absorbs more energy than it produces. • “Power” entering the system: P = xTy • A system is said to be Passive if : P = xTy = dEstore/dt+Pdiss The power is either stored or dissipated. Or: the system cannot generate energy and provide only as much as stored initially.

14. Passivity Say if a system “absorbs” energy then P is positive, otherwise P is negative. • A system ispassiveif energy supplied by it is limited to the initial stored : Or: the system itself can not “produce” any energy.

15. Properties of passive systems • A passive system is stable; • Connection of passive elements remains passive; • A passive system is said to be lossless if Pdiss=0; • It is dissipative if Pdiss>0.

16. Passivity of communication channel in teleoperation Assume no initial energy stored in the communication channel, the channel is passive if P not lower than zero.

17. Time delay causes instability P is no longer guaranteed to be semi-negative, thus passivity Is also not guaranteed.

18. Wave variable: idea • Virtual tool for modifying the entire dynamics of the teleoperator system into a simple and well know form; • Shows both basic physical characteristics like inertia and stiffness ; • Delay presents as a passive element in the system; • As the delay increases the tool becomes softer and / or heavier; • A large delay can thus be tuned into either a heavy drill or a soft sponge. Both provide a heavy versus soft tradeoff appears naturally as a tuning parameter; • In real time, if no contact is made, for example during a virtual inspection, the virtual tool should be tuned to a soft sponge making quick motions easy; • In close proximity to a desired contact location, the tool should be adjusted to a heavy and stiff appearance, allowing good force clarity under slow speed.

19. Wave variable: definition • U denote the forward (right moving) wave; • V denote the backward (left moving) wave.

20. Passivity of wave systems • Assume uprovides input and v contains output, and there is no energy stored initially, the system is passive if • If v=u(t-T) True if v is limited to bound of u Energy due to delay T is stored,  time delay is a passive element

21. Wave variables in teleoperation

22. Passivity in telemanipulation Energy stored, communication channel is passive and lossless.

23. Remarks • Wave variables themselves have no physical meaning. • Symmetry – u and v are distinguished due to sign of F. • Hybrid encoding: • When in contact, wave command produces force, • When in free space, causes motion. • Move or push commands – energy may be converted to either potential or kinetic energy as needed. • Wave impedance • e.g. given u, lager b leads to higher weight for velocity dx/dt, so that more force and lower velocity reconstructed, system appears more damped.

24. Comparison of power and wave variables

25. Wave response: Extreme example of a string v = -u v=u

26. More wave responses

27. Conclusion Wave variable method • Applies well to inherently passive system – robots; • Shows power gain with non-passive systems, there for possible to design power reduction element to counteract energy production and force global passivity; • A delay is passive when it occurs in wave variables while not passive when it effects power variables; • In case of teleoperation delay effectively occurs in software level, “wrap” delay with proper encoding to achieve passivity; • Provides new perspective on system and makes further methods possible (filtering, prediction,…).

28. References and links: • A detailed and intuitive introduction to passivity, wave method and teleoperation: http://telerobotics.stanford.edu/publications/Niemeyer_PhD_Thesis.pdf • Univ. Bologna: http://www-lar.deis.unibo.it • The Haptics Community Web Site: http://haptic.mech.northwestern.edu/ • Rotex: http://www.robotic.dlr.de/telerobotics/rotex.html

29. Thank You !Question ?