Working of Planning Graph

What is a Planning Graph?

A Planning Graph is a data structure primarily used in automated planning and artificial intelligence to find solutions to planning problems. It represents a planning problem’s progression through a series of levels that describe states of the world and the actions that can be taken. Here’s a breakdown of its main components and how it functions:...

Levels in Planning Graphs

Level S0: It is the initial state of the planning graph that consists of nodes each representing the state or conditions that can be true. Level A0: Level A0 consists of nodes that are responsible for taking all specific actions in terms of the initial condition described in the S0. Si: It represents the state or condition which could hold at a time i, it may be both P and ¬P. Ai: It contains the actions that could have their preconditions satisfied at i....

Working of Planning Graph

The planning graph has a single proposition level that contains all the initial conditions. The planning graph runs in stages, each stage and its key workings are described below:...

Mutual Exclusion in Planning Graph

Mutual exclusion in graph planning refers to the principle that certain actions or propositions cannot coexist or occur simultaneously due to inherent constraints or dependencies within the planning problem. Mutex relations can hold between actions and literals under various conditions....

Planning a Graph for a CAKE Problem

To understand the concept of planning a graph, let’s use the CAKE example. This illustration demonstrates various states and actions to achieve the goal of successfully eating the cake. By examining these states, we can see how actions transition from one state to another to reach the desired outcome....

Steps in the Graph Plan Algorithm

Expand the Planning Graph: The graph is expanded level by level until it reaches level n where all the goals are present and non-mutex. Check for Plan Existence: If the planning graph levels off before all goals are present and non-mutex, the algorithm fails. Search for Valid Plan: The algorithm performs a back search from the last level to the initial state to find a sequence of actions leading to the goals without violating mutex constraints. Expand if No Valid Plan Found: If no valid plan is found, another level is added and the search is repeated until a plan is found or the graph levels off....

Properties of Graph Plan

The elements in the planning graph are described as increasing or decreasing monotonically:...

Conclusion

The graph plan algorithm leverages planning graphs to systematically explore and resolve planning problems. By incorporating mutual exclusion principles, it ensures consistency and feasibility. Through the CAKE example, we have demonstrated how planning graphs efficiently handle complex scenarios....