Multi Degree-of-Freedom Input-to-State Stable approach for stable haptic interaction

Passivity has been the most often used constraint for the controller design of haptic interfaces. However, the designed controller based on passivity constraint has been suffering from its conservatism, especially when the user wants to increase the maximum achievable impedance. To overcome this problem, our group have proposed Input-to-State Stable (ISS) approach [1], which reduce the design conservatism of the passivity-based controller by allowing bigger output energy from the haptic interface compared with the passivity-based controller while guaranteeing the stability. However, the previous paper was limited to single Degree-of-Freedom (DoF) systems. This paper extends the ISS approach for multi-DoF haptic interaction. For multi-DoF haptic interaction, penetration depth-based rendering method using Virtual Proxy (VP) is adopted, and VP allows us to decouple the interaction into each axis. Although the interaction can be decoupled, previous ISS analysis “cannot” be directly implemented because the decoupled system, unlike to the previous case, has unconstrained end point, that is a moving Virtual Environment (VE). To include the moving VE into the ISS approach, we extend the previous one-port ISS approach to two-port ISS approach, and generalize this into multi-DoF ISS approach by augmenting each two-port analysis. Proposed approach is experimentally verified with Phantom Pre. 1.5, and showed the effectiveness of the proposed multi-DoF ISS approach.