  This paper presents a quantitative method to construct voluntary manual
control and sensor-based reactive control in human-robot collaboration based on
Lipschitz conditions. To collaborate with a human, the robot observes the
human's motions and predicts a desired action. This predictor is constructed
from data of human demonstrations observed through the robot's sensors.
Analysis of demonstration data based on Lipschitz quotients evaluates a)
whether the desired action is predictable and b) to what extent the action is
predictable. If the quotients are low for all the input-output pairs of
demonstration data, a predictor can be constructed with a smooth function. In
dealing with human demonstration data, however, the Lipschitz quotients tend to
be very high in some situations due to the discrepancy between the information
that humans use and the one robots can obtain. This paper a) presents a method
for seeking missing information or a new variable that can lower the Lipschitz
quotients by adding the new variable to the input space, and b) constructs a
human-robot shared control system based on the Lipschitz analysis. Those
predictable situations are assigned to the robot's reactive control, while
human voluntary control is assigned to those situations where the Lipschitz
quotients are high even after the new variable is added. The latter situations
are deemed unpredictable and are rendered to the human. This human-robot shared
control method is applied to assist hemiplegic patients in a bimanual eating
task with a Supernumerary Robotic Limb, which works in concert with an
unaffected functional hand.
