Identifying critical transitions and instability in haptic systems

• Published in: Nonlinear dynamics Vol. 111; no. 13; pp. 12607 - 12623
• Main Authors: Kerr, Liam, Hutchison, Chantal, Kövecses, József
• Format: Journal Article
• Language: English
• Published: Dordrecht Springer Netherlands 01.07.2023; Springer Nature B.V
• Subjects: Autocorrelation; Automotive Engineering; Bifurcations; Classical Mechanics; Control; Designers; Dynamical Systems; Engineering; Haptic interfaces; Haptics; Inertia; Interface stability; Mechanical Engineering; Methods; Original Paper; Stability analysis; Time series; Velocity; Vibration; Bifurcations; Instability detection; Critical slowing down; Haptic systems
• ISSN: 0924-090X; 1573-269X
• DOI: 10.1007/s11071-023-08457-z

In this paper, we show that oscillations associated with instability in haptic feedback systems can be identified using methods developed to detect impending critical transitions in dynamical systems employing the concept of critical slowing down . We use a state-space stability analysis of a model of a haptic device interfacing with a virtual inertia-spring-damper to show that haptic systems can be subject to secondary Hopf or Niemark-Sacker bifurcations, which often exhibit critical slowing down. We propose the use of indicators of critical slowing down, namely the lag-1 autocorrelation and variance of the haptic device state, to detect the onset of instability in real haptic systems. We present results from experiments with the haptic device interfacing with the virtual inertia-spring-damper, based on which we provide recommendations for the length of rolling window to use when calculating the autocorrelation and variance. We also compare the proposed critical slowing down methods to two common haptic instability detection methods from the literature using a haptic device interfacing with a virtual vehicle model. The critical slowing down method detects instability earlier than the other methods while using about half of the computation time.