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This paper presents a quantitative method to construct voluntary manualcontrol and sensor-based reactive control in human-robot collaboration based onLipschitz conditions. To collaborate with a human, the robot observes thehuman's motions and predicts a desired action. This predictor is constructedfrom 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 ispredictable. If the quotients are low for all the input-output pairs ofdemonstration data, a predictor can be constructed with a smooth function. Indealing with human demonstration data, however, the Lipschitz quotients tend tobe very high in some situations due to the discrepancy between the informationthat humans use and the one robots can obtain. This paper a) presents a methodfor seeking missing information or a new variable that can lower the Lipschitzquotients by adding the new variable to the input space, and b) constructs ahuman-robot shared control system based on the Lipschitz analysis. Thosepredictable situations are assigned to the robot's reactive control, whilehuman voluntary control is assigned to those situations where the Lipschitzquotients are high even after the new variable is added. The latter situationsare deemed unpredictable and are rendered to the human. This human-robot sharedcontrol method is applied to assist hemiplegic patients in a bimanual eatingtask with a Supernumerary Robotic Limb, which works in concert with anunaffected functional hand.

Shared Control Based on Extended Lipschitz Analysis With Application to Human-Superlimb Collaboration