Absolute Stability Of Multilateral Haptic Teleoperation Systems

Multilateral systems involving haptic information sharing between several users have recently found interesting applications in cooperative haptic teleoperation and haptic-assisted training. It is intuitively understood that some tasks are performed more effectively with two hands or through collaboration than one hand or individual operation. By using multiple user interfaces(“masters”) and one remote robot(“slave”) or more, multilateral tele-cooperation systems enable haptic information sharing and collaboration in performing a task in a remote environment between multiple users. Despite the aforementioned benefits, research in this area is still in its initial stage. In fact, the only multilateral system that has been thoroughly investigated is the most basic one: the bilateral teleoperation system involving teleoperation between one master and one slave.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, absolute stability or passivity 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 tassumption: the teleoperator’s terminations are passive.As with bilateral teleoperation system, stability of multilateral haptic teleoperation systems is of paramount importance. Study of stability of such systems must consider the fact that the human users are part of the closed-loop system and thus affect the stability. However, to model the human operator is practically impossible, imposing great difficulties in the system’s stability analysis. This dissertation studies the stability of multilateral teleoperation systems based on absolute stability. The main contributions of this thesis are as follows:(1)Trilateral haptic systems can be modeled as three-port networks. In Chapter 2, we present a criterion for absolute stability of a general class of three-port networks. Traditionally, existing(i.e., Llewellyn’s) criteria have facilitated the stability analysis of bilateral haptic systems modeled as two-port networks. If the same criteria were to be used for stability analysis of a three-port network, its third port termination would need to be assumed known for it to reduce to a two-port network. This is restrictive because, for absolute stability, all three terminations of the three-port network must be allowed to be arbitrary(while passive). Extending Llewellyn’s criterion, we present closed-form necessary and sufficient conditions for absolute stability of a general class of three-port networks. We first find a symmetrization condition under which a general asymmetric impedance(or admittance) matrix Z has a symmetric equivalent eqZ from a network stability perspective. Then, via the equivalence of passivity and absolute stability for reciprocal networks, an absolute stability condition for the original nonreciprocal network is derived.(2)Analysis of coupled stability of a three-port network can be accomplished in either the passivity or the absolute stability frameworks assuming all three ports are connected to passive but otherwise unknown terminations. In Chapter 3, we first introduces passivity criterion for general three-port networks. Next, we show that the absolute stability criterion is less conservative than the passivity criterion.( 3) Multi-degree-of-freedom(DOF) multi-lateral haptic systems involve teleoperation of several robots in physical environments by several human operators or collaborative interaction of several human operators in a virtual environment. An m-DOF n-lateral haptic system can be modeled as an n-port network where each port(terminal) connects to a termination defined by m inputs and m outputs. The stability analysis of such systems is not trivial due to dynamic coupling across the different DOFs of the robots, the human operators, and the physical/virtual environments, and unknown dynamics of the human operators and the environments exacerbate the problem. The absolute stability of a general m-DOF bilateral haptic system where m?1 cannot be obtained from m applications of Llewellyn’s criterion to each DOF of the bilateral system. Also, if we were to use Llewellyn’s criterion for absolute stability analysis of a general 1-DOF n-lateral haptic system where n?2, we would need to couple n?2 terminations of the n-port network to(an infinite number of) known impedances in order to reduce it to an equivalent two-port network; this is a cumbersome process that involves an infinite number of applications of Llewellyn’s criterion. In Chapter 4, we present a straightforward and convenient criterion for absolute stability analysis of a class of m-DOF n-lateral haptic systems for any m?1 and n?2.(4)In bilateral teleoperation of a dexterous task, to take full advantage of the human’s intelligence, experience, and sensory inputs, a possibility is to engage multiple human arms through multiple masters(haptic devices) in controlling a single slave robot with high degrees-of-freedom(DOF); the total DOFs of the masters will be equal to the DOFs of the slave. A multi-master/single-slave cooperative haptic teleoperation system with w DOFs can be modeled as a two-port network where each port(terminal) connects to a termination defined by w inputs and w outputs. The stability analysis of such a system is not trivial due to dynamic coupling across the different DOFs of the robots, the human operators, and the physical or virtual environments. The unknown dynamics of the users and the environments exacerbate the problem. In Chapter 5, we present a novel, straightforward and convenient frequency-domain method for stability analysis of this system.