9: Logical Planning

Logical planning enables agents to reason about actions, their effects, and constraints to create sequences of steps that lead to achieving their objectives. This chapter explores the representation,

9.1 Planning Problem Definition

A planning problem is defined by:

1. Initial State: The starting condition of the environment. Example: "The robot is in room A, and room B is dirty."

2. Goal State: The desired condition the agent aims to achieve. Example: "All rooms are clean."

3. Actions: A set of operations the agent can perform. Example: "Move(room A, room B)" or "Clean(room B)."

4. Action Effects: The changes an action produces in the environment. Example: "Cleaning room B removes dirt from room B."

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9.2 Representing Actions and States

Planning relies on formal representations of actions and states. A common approach is STRIPS (Stanford Research Institute Problem Solver) notation.

9.2.1 STRIPS Representation

An action is defined by:

• Preconditions: Conditions that must hold for the action to be executed.

• Add List: Facts added to the state after the action is performed.

• Delete List: Facts removed from the state after the action.

Example: Cleaning Action

• Action: Clean(room X)

• Preconditions: Room X is dirty.

• Add List: Room X is clean.

• Delete List: Room X is dirty.

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9.3 Planning Algorithms

9.3.1 Forward State-Space Search

Explores the state space by simulating the effects of actions starting from the initial state.

Steps:

1. Apply applicable actions to the current state.

2. Generate successor states.

3. Repeat until the goal state is reached.

Advantages:

• Simple and intuitive.

Limitations:

• Can become computationally expensive for large state spaces.

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9.3.2 Backward State-Space Search

Starts from the goal state and works backward to find a sequence of actions leading to the initial state.

Steps:

1. Identify actions that achieve the goal state.

2. Determine their preconditions.

3. Continue until reaching the initial state.

Advantages:

• Focuses on relevant actions directly tied to the goal.

Limitations:

• Requires careful tracking of preconditions.

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9.3.3 Partial-Order Planning

Instead of fully specifying the order of actions, it creates a flexible plan where actions are only partially ordered.

Steps:

1. Identify steps needed to achieve the goal.

2. Add constraints to ensure actions are performed in the correct order.

3. Resolve conflicts between actions.

Advantages:

• More efficient for problems where the order of some actions does not matter.

Example:

• In preparing a meal, "boiling water" and "cutting vegetables" can occur in any order, but both must precede "cooking soup."

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9.4 Planning with Constraints

9.4.1 Temporal Planning

Considers time constraints, such as actions that require specific durations or cannot overlap.

Example: A factory scheduling system ensures that machines operate in the correct sequence without exceeding time limits.

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9.4.2 Resource-Constrained Planning

Accounts for limited resources, such as energy, personnel, or equipment.

Example: A robot vacuum plans its cleaning route while ensuring it has enough battery to return to its charging station.

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9.5 Heuristics in Planning

Heuristics guide planning algorithms to improve efficiency by estimating the cost of reaching the goal from a given state.

Examples of Heuristics:

1. Relaxed Problem Heuristic: Simplifies the problem by ignoring certain constraints.

2. Goal Distance Heuristic: Estimates the number of steps required to reach the goal.

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9.6 Applications of Logical Planning

9.6.1 Robotics

Robots use planning to navigate environments and perform tasks. Example: A robot arm plans a sequence of moves to assemble parts in a factory.

9.6.2 Logistics

AI systems optimize delivery schedules and routes for maximum efficiency. Example: Planning the delivery of packages to minimize travel time and fuel consumption.

9.6.3 Game AI

Planning algorithms help characters in video games execute complex strategies. Example: An AI-controlled opponent plans moves in a strategy game like StarCraft.

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9.7 Planning Example

Problem: Warehouse Robot

• Initial State: Robot is in room A, and room B is dirty.

• Goal State: All rooms are clean, and the robot is back in its charging station.

• Actions:

  • Move(room X, room Y): Preconditions: Robot is in room X.

  • Clean(room X): Preconditions: Room X is dirty.

Plan:

1. Move(room A, room B).

2. Clean(room B).

3. Move(room B, charging station).

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9.8 Summary

In this chapter, we explored:

1. The definition of planning problems and their components.

2. Representation of actions and states using STRIPS notation.

3. Planning algorithms, including forward and backward search and partial-order planning.

4. Applications in robotics, logistics, and gaming.