Keywords: Control , Detailes description of H-infinity design process, Design criteria

New fideity measure: quantifies ability to transmit changes of the compliance of the environment. (important for tasks like tumor detection)

1. Introduction
The stability- performance trade-of is the main determinant of the control design for teleoperation systems. Both performance and stability are inherently dependent on the task for which the system is designed.

Three important deswign points:
a) Iit is important to have task-based performance goals rather than trying to achieve a marginally stable, physically unachievable ideal teleoperator response.
b) Teleoperator control design should be explicitly formulated as an optimization to accommodate task-based
performance metrics.
c) Design of the teleoperation system must be oriented towards improving performance with respect to human
perceptual capabilities. It is necessary to experimentally quantify human perceptual capabilities and to develop control design methodologies which will provide the means to include this in the control design.

2. Formulation
Two-port I/O model of teleoperation system.

3. Fidelity
Old fidelity measure from Lawrence: transparancy: the ratio between the transmitted and the environment
impedances. Lawrence's design goal was to keep this ratio close to one over a maximal bandwidth.
Fidelity measure used in article: We would like to explicitly distinguish the term fidelity in teleoperation. We define fidelity as a task dependent measure of performance which will be optimized during teleoperator controller design. In robotic telesurgery one would like to improve the abiity to detect compliance changes in the environment. The measure of fidelity proposed in this paper is therefore the sensitivity of the transmitted impedance to changes in the environmental impedance.

Examples when compliance change is important:
a) feel when needle entersor leaves tissue
b) feel stuctures hidden in tissue like blood vessels, nerves and tumors

4. Task-Based optimization of the tele-operation controller
1) Stability: Any teleoperation system must maintain stability under operator and environment variations. Robust
stability of the closed loop system under unstructured uncertainty can be used to check this by properly mod-
eling the operator and environment variations as uncertainty in the system.
2) Tracking: The tracking requirement is necessary to prevent the
nal controller parameter optimization from yielding
trivial solutions.
3) Optimizing fidelity: The controller gains are chosen to optimize the fidelity among the set of controller values which satisfy stability and tracking requirements.

5. Comparing controller architectures and sensors

For better performance, it is almost always desirable to put additional sensors on the manipulators, however, as this sensor will be located on the part of the instrument which will be inside the body, it is a source of complications in the manipulator design, sterilization requirements, and adds to the cost of the final product.

Three different controller architectures are studied: PERR, KFF, P+KF
PERR and KFF are the limit cases of the more general P+FF controller.Therefore it is possible to quantify the improvement due to using a force sensor for a given task by looking at how the fidelity of the P+FF architecture
changes as the force gain is changed.

The alpha-curve is designed: highest fidelity achievable with the P+FF controller as a function of the force gain alpha, subject to the stability and tracking constraints.
The location of the maximum fidelity indicates which controller architecture is the best (eg. If the KFF end is the maximum, then it is better to use purely the force sensor output as the source of force feedback. Finally, if the maximum is located at an intermediate point, it is possible to have better performance by using a combination of position error and the force measurements to generate force feedback. The relative value of the peak value of the curve to the PERR value can be used to judge if the amount of performance improvement justifies the use of the force sensor.)

6. Case study
The analysis described above was evaluated with a system with two identical 3-DOF robotic manipulators: two PHANToM 1.5 haptic interfaces. The local linear model was determined by using a black-box identification technique. The upper bounds of the uncertainy terms were determined emperically.
Figure 8 and 9 show the fidelity plot and resulting alpha curve: the KFF algorithm performs the best.

7. Discussion and conclusion
We are currently working on using linear fractional transformations to develop a better uncertainty model..
The authors are also working on a more detailed system model: For example, absence of noise in the force sensor model gives an unfair advantage to the KFF algorithm in the alpha-curve analysis.