| For dynamically-interacting systems, such as a robot contacting an environment during an assembly operation or multiple robots collaborating in a manipulation task, issues of stability can be difficult to analyze. One very valuable tool is passivity analysis. If each dynamic subsystem (linear or nonlinear) satisfies the property of passivity with respect to its interaction port(s), then any arbitrarily-complex interaction among these subsystems is guaranteed to be stable. This sweeping implication makes it attractive to design robots (and other dynamically-interacting machines) such that each subsystem satisfies passivity. This approach yields building blocks that can be assembled safely into more sophisticated systems.; For linear plants controlled by sampled-data controllers, the resulting interaction admittance is nonlinear. It is shown that satisfying the linear requirements for passivity is insufficient to guarantee passivity of the nonlinear system. A method for passivity analysis of a class of nonlinear systems, specifically linear time invariant systems under sampled-data control, is described. To analyze such plants, it is shown that if a waveform constituting a counter-example of passivity exists, then a counter-example may also be found within a limited class of functions. By restricting attention to this class of functions, a numerical passivity evaluation is feasible. Examples using the method are presented. |
