Robotic systems control – Seminar 2 a.y. 2015/16
SEMINAR 2: Remote control of 1D manipulator using force feedback
I. Goal: Test the effect of the network communication delay on the control quality and possibilities for compensating it.
II. Description:
There are many different processes that require remote control established over communication network. This exercise is about
bilateral control, where feedback from the controlled object (following manipulator, slave) to the object which controls it
(guiding manipulator, master) is performed by force. That way the operator has a better feeling of what is going on the slave
side no matter the distance. Because control and feedback signals travel over communication network, problems with response
quality and system stability occur due to communication delays. Communication delay can be constant time or can vary in time.
Figure 1 shows basic structure of bilateral control with varying delays.
Figure 1. Basic structure of bilateral control
For simplicity, in this exercise master and slave manipulators both have 1 degree of freedom and their dimensions are the same.
Equation of motion of the leading manipulator is given by:
J mθm + bmθm =
τm ,
(3-1)
where Jm is moment of inertia, bm is attenuation factor, km is elasticity, θm is acceleration of the arm, θm is speed of the arm and
τ m is torque. Index m means expression is related to the master manipulator.
Motion equation of the slave manipulator is given by:
J sθs + bsθs =
τs .
(3-2)
Index s means expression is related to the slave manipulator.
In order for the slave manipulator to follow the master manipulator PD regulator is developed:
τ=
K pd (θ m − θ s ) + B pd (θm − θs ) ,
pd
where τ pd is output torque from the regulator, Kpd is gain of the regulator and Bpd is derivation constant of the regulator.
Figure 2 shows block diagram of the basic bilateral control structure, given by equations (3-1, 3-3).
Figure 2. Block diagram of the basic bilateral control structure
(3-3)
Robotic systems control – Seminar 2 a.y. 2015/16
This system is stable only if the network communication delay is less than a border delay. This can best be seen by performing
stability analysis. Transfer function of the open circle is given by:
Gol ( s ) =
( B pd s + K pd )( J s s + bs )
( J m s + bm )( J s s 2 + ( B pd + bs ) s + K pd )
e − sT .
(3-4)
Characteristic equation of the system is given by:
Gol + 1 =
0.
(3-5)
Since this equation has infinite solutions, it is solved using phase condition:
Gˆ ol ( s ) e − sT = 1
∠Gˆ ol ( s ) = ωT + π + 2π k
(3-6)
Figure 3 shows root curve of characteristic system equation (3-5) when delay time T is changed from 0 to 1 second. From the
figure we can see that for some border value of T root curve enters right half of the complex plain s, which means system is
unstable.
Figure 3. Root curve
Described bilateral remote guiding system can be made passive (stable) for arbitrary value of delay time T if communication
between master and slave manipulator is achieved in the space of wave variables. Application of wave variables is described in
the lectures.
In this exercise, for simplicity, we assume that slave and master manipulator are identical and that communication delays are
constant. System parameters are:
J=
J=
2 kg m 2
m
s
bm= b=
1 kg m 2 /s
s
(0.1)
Robotic systems control – Seminar 2 a.y. 2015/16
III. TASKS:
a) Configure a PD controller for the given system for the case without communication delay. You may choose any method you
want. Simulate the system in Matlab/Simulink and display responses of positions (angles), angular velocities and torques of
both slave and master manipulators. Also display differences of position (angle), velocity and torque between master and
slave manipulator. Assume that a user applies a torque of 1Nm on the master manipulator for the duration of 1 second and
that the beginning angular velocity of the master manipulator is 0.3deg/s. Starting velocity of the slave manipulator as well
as starting angles of both master and slave manipulators are 0.
b) Simulate the system from a) with the inserted communication delay of 400ms in the control signal and in the feedback (as
shown on Fig. 2). Record all the responses as in a). What can you conclude about the stability of the system?
c) Using lectures include wave variables in the system. Set communication delay at 400ms and record all the responses from
a). Assume that the user applies a torque of 1Nm on the master manipulator for the duration of 1 second. Parameter b=1. All
starting velocities and starting angles are equal to 0. What can you conclude about stability and response quality of the
system?
d) When using wave variables problem of reflection occurs. In order to reduce reflection introduce compensation members on
master and slave side to the system from c). Example given in lectures contains manipulators that only have mass whereas in
this exercise they also gave attenuation factors. That is why you need to find expression for parameter D for the case when
attenuation exists (parameters bm, bs), that ensures same system behavior as if there is no attenuation. Derivation of the
expression has to be presented in the report. After that, simulate system behavior and record all responses as in a). Choose
parameter b=1 and fracture frequency λs = 10 s-1
Note: Parameter R will be negative in this case.
e) Test the behavior of the system from d) in case of outside disturbance. In this case user applies constant torque of 1Nm to
the master manipulator for the entire duration of the simulation. Let’s assume that while doing so the slave manipulator hits
a rigid wall. This can be modelled in a such way that when the angle of the slave manipulator exceeds some predefined
value the speed of the slave manipulator is instantly reset to zero. In Simulink this can be done by using integrator block
with reset signal input (set parameter external reset of the integrator to level). After that simulate the system and record all
the responses as in a). Does the wave reflection appear in the response of the system? Explain!
f) Reduce wave reflections that occur due to changes in the environment by implementing wave variable filter. Implement
wave variable filter on both slave and manipulator side in the system from e). Simulate and record all the responses as in a).
Are the wave reflections reduced? How does the system behavior depend on the value of filter intersection frequency λ?
Note: Do the exercise report according to Instructions for creating report. Besides the report, it is also required to
submit all developed simulation schemes and related materials (.m files).