Stability of Bilateral Teleoperation Systems: Effect of Sampled-data Control and Non-passivity or Strict-Passivity of Terminations

A bilateral teleoperation system comprises a human operator, a teleoperator, and an environment. The teleoperator consists of a master robot, a slave robot, their controllers, and a communication channel between the master and the slave. Since the exact models of the teleoperator’s terminations, namely the human operator and the environment, are typically unknown and/or time-varying, passivity or absolute stability of the two-port network teleoperator is considered in order to ensure the stability of the coupled teleoperation system. This stability analysis conventionally relies on two important assumptions: (a) all teleoperation system components operate in continuous-time, and (b) the teleoperator’s terminations are passive. This dissertation studies the stability implications of violation of either assumption. The stability of a bilateral teleoperation system may be jeopardized by controller discretization due to energy-distilling effects of a zero-order-hold. In this dissertation, a tool is developed to analyze the passivity of the sampled-data teleoperator. In the passivity framework, the teleoperation system is guaranteed to be passive and, therefore, stable for any passive and otherwise arbitrary terminations. Sufficient conditions for teleoperator passivity are derived for when position error based controllers are implemented in discrete-time and the rest of the system is in continuous-time. This new analysis is necessary because discretization does not necessarily preserve the passivity of a system. The proposed criterion for sampled-data teleoperator passivity imposes lower bounds on the teleoperator’s robots dampings, an upper bound on the sampling time, and bounds on the control gains. The proposed criterion is verified through simulations and experiments. This constitutes Chapter 3 of this dissertation. Teleoperator passivity is sufficient for the stability of the coupled teleoperation system including the terminations. A less conservative approach to guaranteeing the coupled system’s stability is teleoperator’s absolute stability. In the absolute stability framework, the teleoperation system is guaranteed to be stable for any passive and otherwise arbitrary terminations. This dissertation proposes a novel approach to analyzing the absolute stability of a sampled-data bilateral teleoperation system consisting of discrete-time controllers and continuous-time master, slave, operator, and environment. The proposed stability criterion permits scaling and delay in the master and the slave positions and forces. The absolute stability conditions impose bounds on the gains of the discrete-time controller, the damping terms of the master and the slave, and the sampling time. The resulting absolute stability condition has been verified via experiments with two Phantom Omni robots. This comprises Chapter 4 of this dissertation. A design-related application of the above results is in proper selection of various control parameters and the sampling rate for stable teleoperation under discretetime control. To explore the trade-off between the control gains and the sampling time, it is studied how large sampling times, which necessitate low control gains for maintaining stability, can lead to unacceptable teleoperation transparency and human task performance in a teleoperated switching task. This shows that the effect of sampling time must be taken into account because neglecting it undermines both the stability and transparency of teleoperation. In the passivity and absolute stability analyses for investigating the coupled stability of a teleoperation system, the exact models for the teleoperator’s terminations (the human operator and the environment) are not available. To make the stability analysis independent of the termination models, it is typically assumed that they are passive but otherwise arbitrary. However, the assumption of passivity of the terminations is less than accurate and may be violated in practice. Using Mobius transformations, in this dissertation we develop a new stability analysis tool for investigating the stability of a two-port network when coupled to an input strictly-passive, an output strictly-passive, an input non-passive, or a disc-like non-passive termination. While this new stability criterion is applicable to any two-port network, we apply it to bilateral teleoperation systems with position-error-based and direct-force-reflection controllers. Simulations and experiments are reported for a pair of Phantom haptic robots. This problem is presented in Chapter 5 of this dissertation. Finally, Chapter 6 has concluding remarks and outlines possible future directions for this research. Specifically, it is suggested that in continuation of this research, other controllers are checked for sampled-data stability in bilateral teleoperation systems, non-passivity and strict-passivity of both of the terminations are considered in the absolute stability analysis, the previous analyses are extended to multi-lateral teleoperation systems and finally, the integral quadratic constraints formulation is used to analyze the teleoperation system stability.