Per Hagander

Controllability issues of robots in singular configurations

Examples are given that modify some oversimplified statements usually made about the motion of robots in singular configurations. A robot may be controlled in an arbitrary direction from a singular configuration if the velocity profiles are shaped in a proper way. The observations on possible motions open a number of questions, since a wider class of motions is possible that at first sight. Hence, the results are of relevance to path programming, to path following, and to controller design.<<ETX>>

On the notion of strong stabilizability

A system is called strongly stabilizable (SS) if it can be stabilized using a stable controller. Observer state feedback can be used to design a controller of the same order as the system, but the designs may lead to unstable controllers. The implementation of an unstable controller should be done with care and with a well-designed safety net. One implementation could use a stable observer fed with actual input in addition to the measured output. Several examples are discussed, and how unstable controllers might be required for good closed-loop performance, even if they are not required for stability is shown. >

A stochastic differential games approach to mixed H 2 H ∞ -control

Standard H_∞-control can be applied to disturbaace attenuation design, but it has then fundamental practical limitations.

A simple but rich test example for H ∞ -optimal control

A simple second order feed-forward disturbance attenuation problem is analyzed. The problem has one free parameter, the control weight ρ in the loss function. It is found that controller structure and uniqueness for H∞-control, in the optimal case, changes when ρ is varied. Sensitivity to initial conditions is also drastically changed. The example is simple enough to allow a solution by formula manipulation, but is rich enough to give physically reasonable controllers and insight into the behavior of both state-space and polynomial H∞-methods at optimality. Details can be found in [6].