Dynamic Balancing of Mechanisms and Synthesizing of Parallel Robots by Dan Zhang & Bin Wei

Author:Dan Zhang & Bin Wei
Language: eng
Format: epub
Publisher: Springer International Publishing, Cham

Definition 10.6 (Temporal Constraint).

A temporal constraint is a tuple , where e 1 and e 2 are events, and l and u represent lower and upper bounds on the time between these events. Thus, , and , such that . In the QSP of Fig. 10.12, the temporal constraint restricts the time between the start and finish events. Events are used to represent start and finish times of an activity.

10.4.3 Plan Execution: The Problem Solved by the Model-Based Executive

Having formally defined a Plant and a QSP, we are now in a position to define the problem solved by the Model-based Executive in terms of a successful execution of a QSP. Successful execution can be expressed in terms of satisfaction of the individual activities in the QSP, and a consistent schedule, which combined, define satisfaction of a QSP.

Definition 10.7 (Schedule and Consistent Schedule).

Given a QSP, Q, a Schedule, T, is an assignment of a specific time to each Event in Q. T is consistent with Q if it satisfies all Temporal Constraints in Q, that is, for each Temporal Constraint, , then a schedule assigns , such that , where are the elements of c from Definition 10.8.

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