Lyapunov Observer/Controller for Stable Haptic Interaction

Passivity has been the most common tool to achieve stability in haptic and teleoperation systems; however passivity-based approaches suffer from the conservativism of passivity criteria. Therefore, it is essential to have an approach which is less conservative than conventional approaches, enabling the user to have an immersive experience when interacting with the virtual or remote environment. This paper proposes a Lyapunov observed and controller (LOLC) which has an improved transparency as it uses the Lyapunov boundedness theorem that is less conservative than passivity theorem. The proposed approach also gives the user the freedom to define a relaxed Lyapunov candidate regarding state stability to be chosen. Moreover, the application of the proposed control architecture is not limited to haptic interfaces, and the proposed control methodology could be used to stabilize any control systems. The advantages of the proposed approach to the passivity observer and controller are highlighted via numerical evaluations.