## 11.1.2 Defining the History Information Space

This section defines the most basic and natural I-space. Many others will be derived from it, which is the topic of Section 11.2. Suppose that , , and have been defined as in Formulation 10.1, and the notion of stages has been defined as in Formulation 2.2. This yields a state sequence , , , and an action sequence , , , during the execution of a plan. However, in the current setting, the state sequence is not known. Instead, at every stage, an observation, , is obtained. The process depicted in Figure 11.2.

In previous formulations, the action space, , was generally allowed to depend on . Since is unknown in the current setting, it would seem strange to allow the actions to depend on . This would mean that inferences could be made regarding the state by simply noticing which actions are available.11.1Instead, it will be assumed by default that is fixed for all . In some special contexts, however, may be allowed to vary.

Subsections
Steven M LaValle 2020-08-14