Bounded-Impedance Absolute Stability of Bilateral Teleoperation Control Systems

Available passivity-based robust stability methods for bilateral teleoperation control systems are generally conservative, as they consider an unbounded range of dynamics for the class of passive operators and environments in the complex plane. In this paper, we introduce a powerful 3D geometrical robust stability analysis method based on the notions of wave variables and scattering parameters. The methodology, which was originally a 2D graphical method used in microwave systems for single-frequency analysis [1], is further developed in this paper for teleoperation and haptic systems. The proposed method provides both mathematical and visual aids to determine bounds or regions on the complex frequency response of the passive environment impedance parameters for which a potentially unstable system connected to any passive operator is stable, and vice-versa. Furthermore, the method allows for the design of bilateral controllers when such bounds are known, or can even be utilized when the environment dynamics are active. The geometrical test can also be replaced by an equivalent mathematical condition, which can easily be checked via a new stability parameter. The proposed method results in less conservative guaranteed stability conditions compared to the Llewellyn's criterion; thus, promising a better compromise between stability and performance. The new method is numerically evaluated for two bilateral control architectures.