Search algorithms play a crucial role in path planning for robotics. Two popular search algorithms are Depth-First Search (DFS) and Breadth-First Search (BFS).

Depth-First Search (DFS) is a graph traversal algorithm that explores as far as possible along each branch before backtracking. It starts at the root (or an arbitrary node) and explores each neighboring node before backtracking.

Breadth-First Search (BFS), on the other hand, explores all the neighboring nodes at the current depth level before moving to the next depth level.

In path planning for robotics, DFS can be used to explore a possibly infinite search space until a goal state is reached. BFS, on the other hand, can be used to find the shortest path from a starting point to a goal point.

Here's an example of implementing the BFS algorithm in Python:

1import numpy as np
2
3# Define the adjacency matrix
4adj_matrix = np.array([[0, 1, 1, 0],
5                      [1, 0, 0, 1],
6                      [1, 0, 0, 0],
7                      [0, 1, 0, 0]])
8
9# Implement the Breadth-First Search (BFS) algorithm
10
11def bfs(adj_matrix, start, end):
12    visited = set()
13    queue = [start]
14
15    while queue:
16        vertex = queue.pop(0)
17        if vertex == end:
18            return True
19        if vertex not in visited:
20            visited.add(vertex)
21            for i in range(len(adj_matrix[vertex])):
22                if adj_matrix[vertex][i] == 1:
23                    queue.append(i)
24    return False

In the code snippet above, we define an adjacency matrix that represents a graph. Then, we implement the BFS algorithm using the adjacency matrix. The algorithm starts at a given start node and checks if the end node is reachable from the start node using BFS.

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import numpy as np

​

# Define the adjacency matrix

adj_matrix = np.array([[0, 1, 1, 0],

                      [1, 0, 0, 1],

                      [1, 0, 0, 0],

                      [0, 1, 0, 0]])

​

# Implement the Breadth-First Search (BFS) algorithm

def bfs(adj_matrix, start, end):

    visited = set()

    queue = [start]

​

    while queue:

        vertex = queue.pop(0)

        if vertex == end:

            return True

        if vertex not in visited:

            visited.add(vertex)

            for i in range(len(adj_matrix[vertex])):

                if adj_matrix[vertex][i] == 1:

                    queue.append(i)

    return False