The Input-to-State Stable (ISS) Approach for Stabilizing Haptic Interaction With Virtual Environments

Passivity has been a major criterion for designing a stable haptic interface due to its numerous advantages. However, passivity-based controllers have suffered from the design conservatism of the passivity criterion, particularly when users want to increase the maximum apparent impedance. Based on the input-to-state stable (ISS) criterion and an analogy between haptic interfaces and systems with hysteresis, this paper proposes a control framework that is less conservative than passivity-based controllers. The proposed ISS approach allows a non-predetermined finite amount of output energy to be extracted from the system. Therefore, the proposed method can increase the maximum apparent impedance compared with passivity-based approaches. The focus of this paper is on how the proposed approach is designed to satisfy the input-to-state stability criterion in real time without prior knowledge of the system. This paper also extends the primary single-port ISS approach to a two-port ISS approach for multiple-degree-of-freedom generalization. The experimental and numerical results demonstrate that the proposed ISS approach is able to stabilize a higher impedance range than the time-domain passivity approach. The experimental results also confirm that the proposed approach provides higher actual apparent impedance to the operator compared with the energy-bounding and force-bounding approaches.