optimal control and mu-synthesis techniques, is given for the design of a
controller to achieve a pre-specified time-delay stability margin subject to a
general set of performance specifications. This procedure amounts to modeling the
communication time delay as a perturbation, in the
sense, to the nominal system in a non-conservative manner. Design using mu-synthesis techniques ensures robust performance and robust stability to all such
perturbations. A control architecture is presented which allows for performance
specifications to be satisfied in both contact and noncontact tasks. Computer
simulations are used to verify system stability for up to the pre-specified time
delay. Performance of the system is quite good and degrades as the time delay
increases.
The practical implementation of nonlinear control of a bilateral teleoperator is treated. Two cases are considered. The first is nonlinear control in joint space, where it is assumed that the master and slave manipulators are kinematically equivalent. The second is the more general case of nonlinear control in task space. In both cases, the teleoperator is approximately linearized by a feedback linearizing torque, computed from estimated manipulator dynamic models. Sufficient conditions for the L_infinity input/output stability of the system are given. This result requires the computation of certain norm bounds on the dynamic elements of the teleoperator and their estimates. In addition, computation of the spectral radius of a real matrix (two-by-two for joint space, and three-by-three for task space) is also required. Explicit formulae for all necessary computations are given. All theoretical results are verified by numerical simulations with SIMNON. The results of the simulations indicate that the conditions for stability are quite conservative; however, while the system may remain stable when these conditions are violated, the system performance can be quite poor.