ABSTRACT
In this chapter, we study the reliability of reactive plan executions, in terms of execution times and success probabilities. To clarify what we mean by these concepts, we consider the following minimalistic example: a robot is searching for an object, and can choose between the two sub-tasks searching on the table, and opening/searching the drawer. One possible plan is depicted as a FSM in Figure 9.1 and as a BT in Figure 9.2. Here, the robot first searches the table and then, if the object was not found on the table, opens the drawer and searches it. In the figure, each task has an execution time and a success probability. For example, searching the table has a success probability of 0.1 and an execution time of 5s. Given a plan like this, it is fairly straightforward to compute the reliability of the entire plan, in terms of execution time distribution and success probability. In this chapter, we show how to compute such performance metrics for arbitrary complex plans encoded using BTs. In particular, we will define Stochastic BTs in Section 9.1, transform them into discrete time Markov chains (DTMCs) in Section 9.2, compute reliabilities in Section 9.3 and describe examples Section 9.4. Some of the results of this chapter were previously published in the paper [11].
