In bilateral teleoperation, the operator holds a local robot which determines the motion of a remote robot and continuously receives delayed force feedback. Transparency is a measure of teleoperation system fidelity. The ideal teleoperator system is the identity channel, in which there is neither delay nor distortion. During the last decades transparency was widely analyzed using two-port hybrid representation of the system in Laplace domain. Such representations define hybrid matrix that maps between the transmission channel inputs and outputs. However, in measuring transparency one should consider also the human operator, and therefore we propose a multidimensional measure of transparency which takes into account: i) Perceptual transparency: The human operator cannot distinguish when the teleoperation channel is being replaced by an identity channel. ii) Local Motor transparency: The movement of the operator does not change when the teleoperation channel is replaced by an identity channel. iii) Remote transparency: The movement of the remote robot does not change when the teleoperation channel is replaced by an identity channel. We hypothesize that by selecting filters and training protocol it is possible to obtain perceptually transparent teleoperation (i) and remote motor transparency (iii) without local motor transparency (ii), namely, to transparentize the system. We formally define the transparency error, analyze this process in the linear case, and simulate simplified teleoperation system according to typical experimental results in our previous studies about perception of delayed stiffness. We believe that these tools are essential in developing functional teleoperation systems.

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