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Songthumjitti et al. Intell Robot 2023;3(3):306-36 I http://dx.doi.org/10.20517/ir.2023.20 Page 3 of 31

Figure1. Block diagram of an admittance control robot, where represents the admittance model, and represents the robot characteristic
transfer function.

pand the stability region by a significant amount. However, the stability region of a feed-forward compensated
system will easily decrease if the structure characteristic of the actual system is not the same as the measure-
ment. Therefore, we designed a feedback compensated system to overcome this limitation. With feedback
compensation, the system can maintain the stability region even if the structure characteristics change from
our measurement.

Experiments are carried out to test the improvement of the compensated systems. The results show that both
systems can stably operate with a higher admittance characteristic, indicated by a lower mass parameter, com-
pared to the uncompensated system. And also, feedback compensation can operate at a lower mass parameter
in the admittance model compared to feed-forward compensation, which means feedback compensation is
more robust and preferable in practical application.

2. ADMITTANCE CONTROL OF THE HUMAN-INTERACTIVE ROBOT
2.1. Admittance control
The admittance control is a way to control robots with human interaction; control input to the system will
come from the applied force of human operators, and the robot will move according to the admittance model
tothedesiredposition. Admittanceistheinverseofimpedance, andanimpedancemodelisatransferfunction
thatreceivespositioninformationandcalculatesforceoutput; therefore,anadmittancemodelwillreceiveforce
input information, ℎ, and calculate position information, . In combination with a position-controlled robot,
as shown in Figure 1, where represents the admittance model, and represents the robot characteristic
transfer function. The calculated position reference, , can be directly fed into the system, and the robot
position, , will move to the desired position.

We consider the mass spring damper system as an admittance model. However, in our study, it does not need
to return to the origin after the operator breaks the contact, so the stiffness parameter can be neglected. The
transfer function of the admittance model, , will be represented as Equation (1). Lowering the coefficient
results in a lighter workload for the operator and less stability in the system. On the other hand, a higher
coefficient increases the workload for the human operator in exchange for greater system stability.

1
= (1)
+
2
2.2. Human-machine system
The robot requires instructions to move according to the needs of the human operator. The admittance con-
trol method is used when control is input via human-robot interaction. As shown in Figure 2, a robot that
makes contact with the operator forms a single-couple system, and human interaction creates a closed-loop
[5]
system . The impedance of the human operator, , will create force, ℎ, according to errors that come from
the displacement of the robot, , subtracted from the intended position of the operator, . The force that
a human operator needs to apply to the system is highly dependent on the admittance characteristics of the