An Application of Robust Control for Force Communication Systems over Inferior Quality Network

The developments of computer and network technologies have provided a virtual reality environment and ubiquitous network systems. Especially audio-visual devices play an important role in communication. For example, voice communication by telephone, audio-visual communication, streaming technology, digital television system and so on. However, we know that the human makes communication not only by audio-visual information but also by using all five-senses (touch, taste, hearing, eyesight, and smell). The realization of the five-senses communication system is one of the prospected technologies. Especially force communication is a hopeful application in the coming e-world. Several kinds of gimmicks can be considered for transmitting or exchanging the sense of touch, haptic, tactile, force and kinesthetic. In the area of the wearable computing technologies some force-like communication system is realized by using pressure, tension, bending, stress sensors and vibration or pressure actuators, which give the illusion of force communication. On the other hand, robotic researchers have discussed on bilateral tele-operation systems, which realizes remote-manipulations with the sense of reaction forces caused by collision or touching of remote objects and environments. An aim of the technology is that the communication channel between two terminals simulates as if a rigid rod or tight rope. In this article, we consider the bilateral tele-operation systems as a force communication device. It is a well-known that the computer network has inevitable time-delay and jitter in the transmission of the data. And in control engineering deterioration of the stability and performance of the closed loop systems is a well-known fact. Control researchers have proposed several kinds of approaches to overcome the problems. The rest of the chapter is composed as follows. In Section 2, a characterization of the computer network from the view point of transmission delay is discussed. In Section 3, control systems of force sensorless bilateral tele-operation system and the problems caused by transmission delay are examined with a brief historical review. Section 4 presents a procedure how to design a robust control system over the uncertain time-delay network. In section 5 a simulation result is introduced, and some discussions are presented. In section 6 experimental results over the real broadband computer network are introduced. And the results of experiments and investigation are explained in detail. Section 6 concludes the article. 17

Since the practically implemented algorithm is almost trying and error type, the data buffer sometimes overflowed and fails data(packet loss). In order to ensure the reproducibility of the data several kinds of data processing algorithms are implemented according to transmission protocols. TCP/IP(Transmission Control Protocol/Internet Protocol) provides confirming of receiving data (acknowledge), control of window size, and data retransmission and so on. Because of the complexity of the mechanism and sharing of the resource of the network the time-delay is greater than the circuit channel type communications. And the jitter, variation of the time delay occurs frequently. Fig.1 shows an example of time delay during a day between two campuses(Kumamoto and Fukuoka) in 1998. The left graph (a) indicates the time series from midnight to midnight, and the right(b) is the histogram of the number of packets with respect to transmission delay. It is too difficult to construct the prediction model of time-delay because of the randomness and chaos. Here we adopt a statistical model as a rectangular distribution as follows. 0 < L ≤ L max (1) In practice it is possible to set L max such that 95% of packets are travels in the time interval [0, L max ].

Master slave system
Suppose the situation in which an operator manipulates (push/ pull/ lift/ put on and so on) some object through the communication network. Such a kind of system is called a master slave system or tele-operation system. Usually the terminals for the operator and the object are called the master and the slave equipment each other. Operators motion is converted to the motion data by the master mechanism, transmitted to the slave side and realized as a motion of the slave equipment. If the system can transmit the force information caused in the slave side to the master side it called bilateral tele-operation systems. Several kind of mechanisms are proposed for the control of bilateral tele-operation systems.  It means that the system is a combination of two position feedback control systems. When the master and the slave equipments have the same characteristics the structure of the system is completely symmetric. In FR(Force reflection) type, master equipment transmits the position data and receives the force data from the slave equipment. On the other hand FRP(Force reflection with passivity) type exchanges the velocity data and the force data respectively.

Delay and instability
It is well-known that the time delay in the loop deteriorates the stability, performance and robustness of the feedback systems. Fig.2(b) shows a demonstration of the tarde-off of gain K and time-delay L.I f(L, K) is chosen in the range of stable region the closed loop system depicted in Fig. 2(a) becomes stable, and vice versa. This trade-off curve is identical to the contour of the H ∞ norm of the transfer function with γ = 1. It is easy to calculate that the transfer function matches to one at the cutting point a in Fig.2. This plot says the following facts.
(1) If L = 0 then the gain margin is infinite.
(2) The gain margin decreases rapidly as the time-delay grows, that is, the robustness to time-delay deteriorate as the time-delay grows.
According to the considerations the necessity of careful investigation to time-delay is required.

Scattering and wave variable method
Anderson and Spong (6) introduced a new communication architecture for tele-operation over the network with time-delay. Their method is based on the passivity and scattering representation of the network. Thus the strictly passivity of master and slave systems and stationary time-delay are assumed, which are strong constraints for design. Moreover Niemeyer and Slotine (7) extended their method by using wave variables. Since it is a generalization of Anderson-Spong method, it has the same constraints and difficulties in practice. On the other hand Leung, Francis and Apkarian (8) proposed a controller designed via μ−Synthesis. The proposed method based on robust control theory can deal fluctuation of time-delay and has strong practicability. But all the above methods have the same configuration in which the master and slave system exchanges the velocity and the force variables (v, f ) through the network. This means that the position, integral of velocity v, of the master and the slave systems are depend on the initial conditions, and the stability is ensured not in the sense of position but velocity. Moreover the necessity of force sensors makes the systems configuration sophisticated. The more simple architecture is prefer for the practical application.

Paradigm of robust control
There are several kind of strategies to overcome the problem of time delay. Assuming the rectangular (uniform) distribution of time delay H ∞ control theory can be applied as follows. Fig.4 shows the correspondence between time-delay and multiplicative uncertainty. Now let define a 1-st order high-pass filter W D (s; L) as where A = 2.102904074495... It is easy to verify that the norm of (e −Ls − 1) holds the following inequality for any frequency(on the imaginary axis) and any time delay where L max is the upper bound of the estimated time-delay. This means that the uncertainty caused by the variation of time-delay between [0, L max ] can be covered by the weighting function W D (s; L max ) as a high-pass filter with cut-off frequency 1/L max [rad/sec]

PE type bilateral tele-operation system
Here we introduce a simple PE type bilateral tele-operation system designed with robust control technique. Two joystick mechanisms, corresponds to master and slave, are considered. Each joystick has a DC-servo motor for torque generation and a position sensor for measurement of the angle of the joy-stick. Force sensors attached to the joysticks are not for use of the control but for the performance evaluation of force communications. They are controlled by computers which are connected to the computer network (see Fig.5). These joysticks are assumed to be modeled as where When the master and the slave controllers exchange the information through the network, as stated in the previous section, the time-delay must be considered. Let us assume that the time-delay L > 0 exists between master and slave controllers symmetrically. The evaluated deviations (9)(10) at each controller might be computed as follows.
In the rest of the chapter e m0 , e s0 (e mL , e sL ) are called as errors in ideal ( computed ) deviation. The Laplace transform of computed deviation e mL (11) is written as In the same way the Laplace transform of e sL can be written as This means that the minimization of computed deviations (E mL (s), E sL (s)) is acomplished by the simultaneous minimization of E m0 (s)(= −E s0 (s)), (1 − e −Ls )X s (s) and (1 − e −Ls )X m (s) from the inequality as |E sL (jω)|≤|E s0 (jω)| + |W D (jω; L max )X m (jω)|.
As mensioned in previous section the time delay L includes uncertainty. But if the upper bound of L is obtained as L max according to 4and 5 the minimization problem can be acomplished by the minimization of E m0 (s),W D (s; L max )X s (s) and W D (s; L max )X m (s). H ∞ theory gives a design method to obtain an appropriate feedback gain to keep stability and robustness against the type of model uncertainty.
Let us consider the two joystick mechanisms as a system with two inputs and two outputs plant where, , P s (s)= K s s(J s s + D s ) .
The purpose is the design of a controller which satisfies the requirements specified as follows. The schematic diagram is depicted in Fig.6 (a) (b) The closed loop system is a kind of regulator which makes the deviation e = X m − X s → 0as time goes. For the robust control systems design the deviation e is generalized to a criteria for tracking performance as In general W 11 has to be chosen as high gain at low frequency and low gain at high frequency.

stability augmentation
More over in order to obtain a adequate local feedback gain which improves the stability and robustness of closed loop system, the criteria for stability is formulated as properness of controller In order to ensure the properness of the controller C(s) in (19) the input variables for the plant are added to the criteria for design as where w 1 , w 2 are exogenous inputs or exerted external forces(torques) as in Fig.7.

robust stability against time-delay
As mentioned in the previous section the robustness corresponds to the minimization of W D (s; L max )X s (s) and W D (s; L max )X m (s). Thus we introduce new two output variables with two more variables w 3 , w 4 which come from the uncertainty (6) as Let's define the exogenous input w and evaluated output z as Moreover defining the following vectors the generalized plant is obtained as follows ( see Fig.7).
By applying the controller (19) to the above system a transfer function matrix from w to z can be obtained. By using the design procedure based on the H ∞ control theory a controller is obtained such that where γ is a design parameter chosen as small as possible (5).

An Application of Robust Control for Force Communication Systems over Inferior Quality Network
www.intechopen.com  Table 2 shows simulation results for analysis of stability and tracking performance. The values in the left column indicate actual time-delay L act in simulation. When the actual time-delay is not greater than the assumed maximum one, that is L act ≤ L max , the stability and tracking performance are kept well. On the other hand if the time-delay exceeds estimated value , L act > L max , the performance of the system becomes worse. It points that the importance of the estimate of maximum time delay L max .   Fig. 9 shows bode diagrams of controller C(s). It can be observed that roughly seeing of the controller is a kind of integrator, but it works constant gain in the middle range 1 ∼ 10 3 [rad/sec].

Analysis via hybrid matrix
In order to investigate the force communication ability and transperency of master-slave system hybrid matrix is defined as (37) Table 10 shows the bode daigram of hybrid matrix. h 12 = F s /F m and h 21 = X m /X s indicate that the tracking ability of position and force communication are expected to work in the range from DC upto 1 rad/sec.

Experiments over the network with time-delay
In order to demonstrate the robustness of the proposed control systems a networked control system is constructed as in Figure 11. Master and slave mechanisms and their local controllers (C m , C s ) are located on the same cite (at Kumamoto city), and another computer (C T ) is located beyond the network (at Kitakyushu city, 150km far from Kumamoto city). These three computers are connected to the network JGN , which was Japanese broadband network as an experimental testbed administrated by TAO 1 . The controllers C m and C s can communicate each other by way of relay computer C T , but not admitted to communicate directly. The transmission capacity of the network is about 100Mbps. The control period at C m and C s is 5[msec] and that of communication period between C m and C s is 10[msec]. The communication protocol UDP/IP is adopted. Weighting functions in generalized plant (29) are specified as W 11 = 0.3s + 20 × 10 7 3.9 × 10 6 s + 10 5 , The controllers are implemented in personal computers. The algorithms are coded by C-language with RT-Linux formats and embedded as a kernel modules of Linux system. The control period is set at 5 [msec] and data exchange rate is set at 10 [msec]. Thus the data processing sequences must be synchronized. Fig.12 shows a sequence diagram. The time goes from left to right and the datagram travels from master side(top ) to slave side(bottom ) through the network(middle). Because of the control period is a half of the communication period a copied value of the oposit side is used once every two control calculation. The right half part of the diagram assumes the case of long time-delay. In this case copied value is used over and over again until the new datagram reaches again. and ǫ = 6.6 × 10 −3 Here the ǫ > 0 is selected to reduce the effects of integrator.

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Challenges and Paradigms in Applied Robust Control experimental result Fig. 13 indicates an experimental result for evaluation of tracking performance. In the first half master( solid line ) leads to the slave(dashed line). And last half slave leads to the master. This means that the master-slave tele-operation system works symmetricaly well.

Summary
In this chapter we discussed on an application of robust control for force communication systems over inferior quality network. According to the investigation of the experiments the effectiveness of bilateral tele-operation system for force communication is confirmed. Especially the most important problem of the robustness w.r.t. time-delay is improved by H ∞ control systems theory.