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Developing the Observer

In order to know the current state of the manipulation process we need to observe the sequence of events occurring in the system and make decisions regarding the state of the automaton, state ambiguities are allowed to occur, however, they are required to be resolvable after a bounded interval of events. An observer, have to be constructed according to the visual system for which we developed a DEDS model. The goal will be to make the system a stabilizable one and/or construct an observer to satisfy specific task-oriented visual requirements that the user may specify depending on the nature of the process. It should be noticed that events can be asserted with a specific probability as will be described in the sections to come and thus state transitions can be made according to pre-specified thresholds that compliments each state definition. In the case of developing ambiguities in determining current and future states, the history of evolution of past event probabilities can be used to navigate backwards in the observer automaton till a strong match is perceived, a fail state is reached or the initial ambiguity is asserted.

As an example, for the model of the grasping task, an observer can be formed for the system as shown in Figure 7. It can be easily seen that the system can be made stable with respect to the set (The system always returns to that set).

At the beginning, the state of the system is totally ambiguous, however, the observer can be ``guided'' to the set consisting of all the subsets of the good states as defined on the visual system model. It can be seen that by enabling the tracking event from the state (5, 6) to the state (1, 2), all the system can be made stable with respect to . The singleton states represent the instances in time where the observer will be able to determine without ambiguity the current state of the system.

In the next section we shall elaborate on defining the different events in the visual manipulation system and discuss different techniques for event and state identification. We shall also introduce a framework for computing the uncertainty in determining the observable visual events in the system and a method by which the uncertainty distribution in the system can be used to efficiently keep track of the different observer states and to navigate in the observer automaton.

Next: Examples Up: State Modeling and Previous: Building the Model
Tue Nov 22 21:30:54 MST 1994