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eISSN
2444-8656
First Published
01 Jan 2016
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2 times per year
Languages
English
access type Open Access

Research on Stability of Time-delay Force Feedback Teleoperation System Based on Scattering Matrix

Published Online: 15 Jul 2022
Volume & Issue: AHEAD OF PRINT
Page range: -
Received: 26 Jan 2022
Accepted: 14 Mar 2022
Journal Details
License
Format
Journal
eISSN
2444-8656
First Published
01 Jan 2016
Publication timeframe
2 times per year
Languages
English
Abstract

The successful implementation of the robot teleoperation system has greatly improved the ability of remote robots. The force feedback technology is applied to the teleoperation system. On the one hand, the main operator manipulates the operator's related movement information to the target robot; on the other hand, the main hand feeds back the force situation of the target robot in the remote control to the operator. From the robot under the control of the system can more accurately complete the task, with a higher work efficiency. Teleoperation system with force feedback function generally adopts bilateral control, the master and slave end of the system have a certain delay in the transmission process, it makes the stability of the system destroyed. This paper uses a two-port network to simulate the communications link of the teleoperation system as a lossless transmission line, solves the stability problem of teleoperation systems with force feedback in the presence of time delay effectively. Experimental simulation results show that this method can guarantee a higher stability of the system..

Keywords

MSC 2010

Introduction

Teleoperation system enables local operators to manipulate smart devices such as remote robots, Complete designated tasks in hazardous, human-inaccessible, or human-unfriendly environments. But communication delays when the system operator and the remote robot are far apart. Experiments have shown that if there is a delay of 0.25s, it may cause instability in the teleoperation system which affects work efficiency and safety seriously [1].

Description of Time-delay Teleoperation System

Teleoperation system adopts master-slave control mode, the operator interacts with the master, feels the force generated by slave robot and environment. The operator's instructions are sent to the slave robot by signal transmission, makes it follow the instructions of the operator, at the same time, the feedback information is returned to the master through a signal transmission process and fed back to the operator. Treating teleoperational transmission modules as two-port networks, the system structure is shown in Figure 1. There is a correspondence between the force F of the teleoperation system and the speed v and the voltage V and current I in the circuit, which is F->v, V->I. [2].

Figure 1

Teleoperation System Control Diagram

Figure 2

Two-port network

Stability Analysis

In the theory of electric networks, passivity reflects the energy dissipation characteristics of the system during movement. Stability is the basic structural characteristic of a dynamic system, shows the boundedness of system output.

The two-port network shown in Figure 3, it can be described with different parameters. When v2 takes the direction of v1, it can be expressed as: [f1v2]=[h11h12h21h22][v1f2]=H[v1f2] \left[{\matrix{{{f_1}}\cr{- {v_2}}\cr}} \right] = \left[{\matrix{{{h_{11}}} & {{h_{12}}}\cr{{h_{21}}} & {{h_{22}}}\cr}} \right]\left[{\matrix{{{v_1}}\cr{{f_2}}\cr}} \right] = H\left[{\matrix{{{v_1}}\cr{{f_2}}\cr}} \right] the input volume is v1, f2 and the output volume is f2v2[3].

Figure 3

Time-delayed communications

fi(s), vi(s)(i = 1,2) is the Laplace transform of fi(t), vi(t)(i = 1,2), and H is called the mixing matrix. H=[0110] H = \left[{\matrix{0 & 1\cr{- 1} & 0\cr}} \right]

The master and slave dynamic equations of the teleoperation system with force feedback after neglecting the influence of gravity are as follows: {Mm(xm)x¨m+Cm(xm,x¨m)x˙m=fhfmMs(xs)x¨s+Cs(xs,x˙s)x˙s=fsfe \left\{{\matrix{{{M_m}({x_m}){{\ddot x}_m} + {C_m}({x_m},{{\ddot x}_m}){{\dot x}_m} = {f_h} - {f_m}} \hfill\cr{{M_s}({x_s}){{\ddot x}_s} + {C_s}({x_s},{{\dot x}_s}){{\dot x}_s} = {f_s} - {f_e}} \hfill\cr}} \right.

Constructing the following energy storage function based on the definition of passivity: V=12[x˙mx˙s][Mm00Ms][x˙mx˙s]=12x˙mTMmx˙m+12x˙sTMsx˙s V = {1 \over 2}\left[{\matrix{{{{\dot x}_m}}\cr{{{\dot x}_s}}\cr}} \right]\left[{\matrix{{{M_m}} & 0\cr0 & {{M_s}}\cr}} \right]\left[{\matrix{{{{\dot x}_m}}\cr{{{\dot x}_s}}\cr}} \right] = {1 \over 2}\dot x_m^T{M_m}{\dot x_m} + {1 \over 2}\dot x_s^T{M_s}{\dot x_s}

As shown in Figure 3, when there is a delay of T in the communication link of the teleoperation system, the relationship between the input and output of the system is as follows: fmd(t)=fs(tT)vsd(t)=vm(tT) \matrix{{{f_{md}}(t) = {f_s}(t - T)} \hfill\cr{{v_{sd}}(t) = {v_m}(t - T)} \hfill\cr}

vm, fs is the input volume and vsd, fmd is the output volume. The frequency domain is as follows: fmd(t)=esTfs(s)vsd(t)=estvm(s) \matrix{{{f_{md}}(t) = {e^{- sT}}{f_s}(s)} \hfill\cr{{v_{sd}}(t) = {e^{- st}}{v_m}(s)} \hfill\cr} (fmdvsd)=(esTfsesTvm)=(0esTesT0)(vmfs) \left({\matrix{{{f_{md}}}\cr{- {v_{sd}}}\cr}} \right) = \left({\matrix{{{e^{- sT}}} & {{f_s}}\cr{- {e^{- sT}}} & {{v_m}}\cr}} \right) = \left({\matrix{0 & {{e^{- sT}}}\cr{- {e^{- sT}}} & 0\cr}} \right)\left({\matrix{{{v_m}}\cr{{f_s}}\cr}} \right)

So the mixing matrix is: H(s)=(0esTesT0) H(s) = \left({\matrix{0 & {{e^{- sT}}}\cr{- {e^{- sT}}} & 0\cr}} \right)

Passive control strategy based on transmission line theory

The transmission line shown in Figure 4 is a lossless transmission line[4]. When vm, fs is input vsd, fmd is output, the port equation is: fmd(s)=btanh(sT)vm(s)+sech(sT)fs(s) {f_{md}}(s) = b\,\tanh (sT){v_m}(s) + \sec \,h(sT){f_s}(s) vsd(s)=sech(sT)vm(s)+1btanh(sT)fs(s) - {v_{sd}}(s) =- \,\sec h(sT){v_m}(s) + {1 \over b}\tanh (sT){f_s}(s)

Figure 4

Transmission line

b=LC b = \sqrt {{L \over C}} is the characteristic impedance, T=lv0=lLC T = {l \over {{v_0}}} = l\sqrt {LC} , where l is the length of the transmission line, v0 is phase velocity. [5]

According to the theorem of the scattering matrix: S=supωλ12[S*(jω)S(jω)]=supωλ12(0ejωTejωT0)(0esTesT0)=1 \matrix{{\left\| S \right\| = \mathop {\sup}\limits_\omega{\lambda ^{{1 \over 2}}}[S*(j\omega)S(j\omega)]} \hfill\cr{= \mathop {\sup}\limits_\omega{\lambda ^{{1 \over 2}}}\left({\matrix{0 & {{e^{j\omega T}}}\cr{{e^{j\omega T}}} & 0\cr}} \right)\left({\matrix{0 & {{e^{- sT}}}\cr{{e^{- sT}}} & 0\cr}} \right)} \hfill\cr{= 1} \hfill\cr}

According to the definition of the scattering matrix, when the lossless transmission line is used to simulate the communication link, the time delay communication link is passive, so that the entire teleoperation system is passive, that is, the system is stable. The passive control algorithm for the communication link is: fmd(t)=fs(tT)+b[vm(t)vsd(tT)]vsd(t)=vm(tT)+1b[fmd(tT)fs(t)] \matrix{{{f_{md}}(t) = {f_s}(t - T) + b[{v_m}(t) - {v_{sd}}(t - T)]} \hfill\cr{{v_{sd}}(t) = {v_m}(t - T) + {1 \over b}[{f_{md}}(t - T) - {f_s}(t)]} \hfill\cr}

The above formula is a control algorithm for the communication link, so that the communication link remains passive. [6] When the communication link of the teleoperation system with force feedback has a time delay of T=0.5 seconds, the position, velocity and force variation curves of the system master and slave ends are shown in Figure 5 to Figure 7. It can be seen that the system is convergent when it is in an autonomous state, that is, the system is stable. [7]

Figure 5

Position curve of master and slave

Figure 6

Speed curve of master and slave

Figure 7

Force curve of master and slave

Conclusions

According to the structure of the teleoperation system, the influence of time delay on the stability of the system is pointed out, and the connection between the passiveness and the stability is analyzed. Through the analysis of the stability of the time-delay force feedback teleoperation system, it is pointed out that the transmission line theory based on the two-port network is an effective means to solve the poor stability of the teleoperation system due to the delay in the communication link.

Figure 1

Teleoperation System Control Diagram
Teleoperation System Control Diagram

Figure 2

Two-port network
Two-port network

Figure 3

Time-delayed communications
Time-delayed communications

Figure 4

Transmission line
Transmission line

Figure 5

Position curve of master and slave
Position curve of master and slave

Figure 6

Speed curve of master and slave
Speed curve of master and slave

Figure 7

Force curve of master and slave
Force curve of master and slave

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