a. Provide the complete problem formulation with PSA design.

b. Provide the PEAS description.

c. All the dimensions of the Task Environment
“A Service Agent is trying collect all the gifts, but it requires help from its family of robots!
At below positions, there are initially k gifts (g;, . . . gj). Additiofally, there are ‘n’ gift
picking robot agents at positions (ag),..., Ag»); initially, every robot agent enters the maze
from the bottom left corner marked by the “star” in the below configuration. Consider a
search problem where all agents can move at once, meaning that they each move into an
adjacent position in each step (North, South, East, or West, no STOP).”
To formulate the problem and provide the PEAS description for the given scenario, let's break it down into the required components:

### a. Complete Problem Formulation with PSA Design

**Problem Statement:**
The goal is to collect all the gifts located at specified positions in a maze using multiple gift-picking robot agents that can move simultaneously. The robots start from a designated position and can move to adjacent cells in the maze.

**State Representation:**
- The state can be represented as a tuple consisting of:
  - The positions of all robots (R1, R2, ..., Rn)
  - The positions of all gifts (G1, G2, ..., Gk)
  - The maze layout (indicating walls, open paths, etc.)

**Initial State:**
- The initial state is defined by:
  - All robots starting from the bottom left corner (the "star" position).
  - The positions of the gifts in the maze.

**Actions:**
- Each robot can move to one of the four adjacent cells (North, South, East, or West), provided the move does not lead to a wall or outside the maze boundaries.

**Transition Model:**
- The transition model defines the new state after a move:
  - If a robot moves to a cell with a gift, the gift is collected (removed from the state).
  - The positions of the robots are updated based on their movements.

**Goal State:**
- The goal state is reached when
Here are the requested formulations:

**a. Complete problem formulation with PSA design:**

**Problem:** Gift Collection Problem

**Performance Measure:** Collect all gifts in the minimum number of steps

**Environment:** Maze with gift positions (g1,..., gj) and robot agent positions (ag1,..., agn)

**Actuators:** Robot agents can move North, South, East, or West into an adjacent position

**Sensors:** Robot agents can perceive their current position and the presence of gifts in adjacent positions

**Actions:** Move North, South, East, or West into an adjacent position

**Goal:** Collect all gifts (g1,..., gj)

**PSA Design:**

* **Problem Space:** The maze with gift positions and robot agent positions
* **Actions:** Move North, South, East, or West into an adjacent position
* **Goal Test:** Check if all gifts have been collected
* **Path Cost:** Number of steps taken to collect all gifts

**b. PEAS description:**

**P** (Performance Measure): Collect all gifts in the minimum number of steps

**E** (Environment): Maze with gift positions (g1,..., gj) and robot agent positions (ag1,..., agn)

**A** (Actuators): Robot agents can move North, South, East, or West into an adjacent position

**S** (Sensors): Robot agents can perceive their current position and the presence of gifts