A network approach to force control in robotics and teleoperation

Abstract

This thesis studies the application of network theory to problems in robot and teleoperator control. Network models, referred to as Hilbert networks, are developed which extend the definition of standard electrical circuit elements, operating over $\IR$, to higher dimensional spaces. First, Hilbert networks are used to represent manipulators. Kinematic, dynamic, Jacobian, and other relationships are found by applying Kirchoff's laws to these models, leading to considerable simplification over conventional approaches, especially in the case of closed chain systems. Hilbert networks are next used to derive realistic models for the environment, including effects of contact/noncontact, coulomb friction, and nonlinear springs. It is shown that the Hilbert network can model distributed parameter systems such as transmission lines and flexible beams as well. Using the Hilbert network approach, passive and nonpassive controller architectures are studied in detail. It is shown that the standard computed torque approach, as well as some hybrid position/force controllers, are nonpassive and can lead to instability. Passive implementations of these controllers are introduced which have desirable stability behavior and transient responses. An entirely new class of critically damped controllers with variable bandwidths is introduced which not only guarantee stability but also maintain constant contact stiffness and fully utilize actuators. The application of Hilbert networks to teleoperators results in the solution of a 20-year-old problem, namely the time-delay instability problem in bilateral teleoperation. By mimicking the behavior of a passive transmission line, a control law is derived which globally stabilizes a teleoperator with force reflection, independent of the time delay in transmission of contact forces between the master and the slave. This result is proved theoretically, and verified experimentally.