propositional-logic
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Introduction

In artificial intelligence, a knowledge-based agent is a system that utilizes a knowledge base to make informed decisions. The agent reasons about the world and acts upon it, based on what it knows and what it perceives. In this blog, we will explore how to design a knowledge-based agent to solve a robot navigation problem using logical inference.

Problem Statement: The Robot Navigation Challenge

Consider a simple grid-based environment where a robot must navigate from a start position to a goal position. The grid contains obstacles that the robot must avoid. The robot is equipped with sensors that provide information about its surroundings, such as the presence of obstacles in adjacent cells.

The goal is to build a knowledge-based agent that can successfully navigate the grid from the start to the goal, avoiding obstacles, by reasoning about the environment based on its sensory inputs.

PEAS Description of the problem statement :

The PEAS framework (Performance measure, Environment, Actuators, Sensors) is a common way to define the characteristics and requirements of an intelligent agent in AI. Applying the PEAS framework to the robot navigation problem in your blog post would look like this:

1. Performance Measure

  • Objective: Successfully navigate from the start position to the goal position on the grid.
  • Criteria:
    • Success Rate: The percentage of trials where the robot reaches the goal without colliding with obstacles.
    • Efficiency: The number of steps taken to reach the goal. Fewer steps are better, indicating more efficient navigation.
    • Path Optimality: How close the robot’s chosen path is to the shortest possible path. Optimal paths are preferred.
    • Safety: The robot must avoid obstacles and not get stuck.
 

2. Environment

  • Grid-Based Environment: A discrete, grid-like environment where each cell can be empty, contain an obstacle, or be occupied by the robot.
  • Obstacles: Fixed objects on the grid that the robot must avoid. Their positions are known after the robot’s sensors perceive them.
  • Start and Goal Positions: The start position is where the robot begins, and the goal position is where it needs to navigate to.
  • Dynamicity: The environment is static, meaning that once the robot has perceived the obstacles, their positions do not change.
 

3. Actuators

  • Movement Mechanism: The robot can move up, down, left, or right to adjacent cells on the grid. These movements are discrete steps from one cell to another.
  • Actions: The robot’s actions include moving in the direction of an adjacent cell if it is safe to do so.
 

4. Sensors

  • Proximity Sensors: The robot is equipped with sensors that detect the presence of obstacles in adjacent cells (up, down, left, right).
  • Perception: These sensors provide the robot with information about which adjacent cells are free and which are blocked by obstacles.
peas_desc

Knowledge Representation

To represent the knowledge, we will use propositional logic. Each cell in the grid is denoted as \(C_{i,j}\), where i and j are the row and column indices, respectively. The robot perceives the environment through its sensors, which can detect if adjacent cells are free (no obstacle) or blocked (obstacle present).

We can represent the knowledge as:

  • \(F_{i,j}\): Cell \(C_{i,j}\) is free.
  • \(B_{i,j}\): Cell \(C_{i,j}\) is blocked.
 

The robot’s knowledge base (KB) includes the following rules:

  • If a cell \(C_{i,j}\) is blocked, then the robot cannot move into that cell: \(Bi,j→¬Fi,j\).
  • If the robot perceives no obstacles in adjacent cells, it can safely move forward.
agent_env

Logical Inference for Navigation

The robot will use logical inference to decide its next move. For example, if the robot is at  \(C_{2,2}\) and perceives that \(F_{2,3}\) and \(F_{3,2}\) are true, it infers that moving to \(C_{2,3}\) or \(C_{3,2}\) is safe.

Here’s how the agent can infer its actions:

  1. Perception: The robot perceives the status of adjacent cells.
  2. Inference: Using the rules in its KB, the robot infers which cells are safe to move into.
  3. Action: The robot moves to a safe cell.
 

Example and Implementation

Let’s consider a 3×3 grid where the robot starts at \(C_{1,1}\) and the goal is at \(C_{3,3}\). Obstacles are present at \(C_{1,2}\) and \(C_{2,3}\).

  1. Initial Perception:
    • \(C_{1,2}\) is blocked: \(B_{1,2}\) is true.
    • \(C_{2,1}\) is free: \(F_{2,1}\) is true.
  2. Inference:
    • Since \(B_{1,2}\) is true, \(¬ F_{1,2}\) is also true.
    • \(F_{2,1}\) is true, so the robot can move to  \(C_{2,1}\).
  3. Action:
    • The robot moves to \(C_{2,1}\).

This process continues until the robot reaches the goal or determines that no safe path exists.



class Robot:


   def __init__(self, grid):


        self.grid = grid # 2D grid where 0 is free and 1 is an obstacle
        self.kb = {}


    def perceive(self, x, y):


        """Perceive the surrounding cells and update the KB."""


        self.kb[(x, y)] = 'Free' if self.grid[x][y] == 0 else 'Blocked'
        return self.kb[(x, y)]
    def infer_and_move(self, x, y):  """Infer the next move based on the KB."""
        moves = [(x+1, y), (x-1, y), (x, y+1), (x, y-1)]


        for move in moves:
            nx, ny = move
            if 0 <= nx < len(self.grid) and 0 <= ny < len(self.grid[0]):


                status = self.perceive(nx, ny)
                if status == 'Free':
                    print(f"Moving to {nx, ny}")
                    return nx, ny
         print("No safe move available!")
         return None, None


 # Example Grid (3x3)


# 0 = Free, 1 = Obstacle
grid = [
      [0, 1, 0],
      [0, 0, 1],
      [0, 0, 0]
]


 robot = Robot(grid)


x, y = 0, 0 # Start position




while (x, y) != (2, 2):
    x, y = robot.infer_and_move(x, y)
    if (x, y) is None:
break

Performance Analysis

To thoroughly evaluate the performance of the knowledge-based agent in navigating a grid-based environment, we conducted simulations on various grid configurations. The analysis focuses on key metrics such as success rate, average steps taken, computation time, and path optimality. 

 

Experimental Setup

The agent was tested on a range of grid sizes, primarily focusing on 3×3, 5×5, and 7×7 grids. Each grid contained obstacles placed randomly with varying densities. For each configuration, the agent was tasked with navigating from a fixed start position to a goal position while avoiding obstacles. The performance was evaluated across multiple trials for each grid configuration.

Metrics Considered

  • Success Rate: The percentage of successful trials where the agent reached the goal without getting stuck.
  • Average Steps: The mean number of steps the agent took to reach the goal across all successful trials.
  • Computation Time: The average time taken by the agent to compute each move.
  • Path Optimality: A measure of how close the agent’s path is to the shortest possible path.
 
Grid Size
Obstacle Density
Success Rate
Average Steps
Computation Time (s)
Path Optimality
3x3
10%
100%
3 Steps
0.0012s
Optimal
3x3
30%
95%
4 steps
0.0014s
Near-optimal
3x3
50%
85%
5 steps
0.0016s
Sub-optimal
5x5
10%
100%
6 steps
0.002s
Optimal
5x5
30%
90%
8 steps
0.003s
Near-optimal
5x5
50%
80%
10 steps
0.004s
Sub-optimal
7x7
10%
100%
9 steps
0.003s
Optimal
7x7
30%
85%
12 steps
0.005s
Near-optimal
7x7
50%
75%
15 steps
0.007s
Sub-optimal

Explanation:

  • Grid Size:  The dimensions of the grid (e.g., 3×3, 5×5, 7×7).
  • Obstacle Density:  The percentage of cells in the grid that contain obstacles.
  • Success Rate:  Indicates how often the agent successfully navigated to the goal.
  • Average Steps:  Reflects the efficiency of the agent’s navigation in terms of the number of steps taken.
  • Computation Time:  Measures the time required for the agent to make decisions.
  • Path Optimality:  Assesses whether the agent’s path was the shortest or if detours were taken.

Analysis and Insights

  1. Smaller Grids (3×3): The agent consistently performs well, with high success rates and low computation times, even with moderate obstacle density. Path optimality remains high, indicating efficient navigation.
  2. Medium Grids (5×5): As grid size and obstacle density increase, the agent begins to experience a slight decline in success rate and path optimality. The computation time also increases, reflecting the added complexity of reasoning in larger environments.
  3. Larger Grids (7×7): The challenges become more pronounced, with noticeable declines in success rate and path optimality, particularly at higher obstacle densities. The agent takes more steps on average and requires more time to compute each move.

Visualization of Performance

This chart illustrates how the success rate diminishes as both grid size and obstacle density increase. It also highlights the agent’s robustness in simpler environments and its adaptability as the complexity of the navigation task grows. 

 

Summary

The performance analysis demonstrates that the knowledge-based agent is highly effective in navigating simpler and moderately complex environments. However, as the grid size and obstacle density increase, the agent’s success rate and path optimality decrease, and the computation time rises. These results provide valuable insights into the agent’s strengths and limitations, offering a clear direction for future improvements in complex scenarios.

chart

Conclusion

Knowledge-based agents are powerful tools in AI for making decisions based on logical reasoning. By applying logical inference to a well-structured knowledge base, such agents can solve complex problems like robot navigation efficiently. The key lies in accurately modeling the environment and deriving rules that the agent can use to infer safe actions.

  • AI, AI Agent Architectures, Algorithm Design, Autonomous Systems, How-To Guides, Intelligent Systems, Knowledge Representation, Machine Learning, Programming, Python, Robotics
  • September 4, 2024
Vaishakhi Panchmatia

As Tech Co-Founder at Yugensys, I’m passionate about fostering innovation and propelling technological progress. By harnessing the power of cutting-edge solutions, I lead our team in delivering transformative IT services and Outsourced Product Development. My expertise lies in leveraging technology to empower businesses and ensure their success within the dynamic digital landscape.

Looking to augment your software engineering team with a team dedicated to impactful solutions and continuous advancement, feel free to connect with me. Yugensys can be your trusted partner in navigating the ever-evolving technological landscape.

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