Top 10 Robot Path‑Planning Algorithms That Will Wow You

If you’ve ever watched a self‑driving car glide through traffic or seen a warehouse robot pick up boxes with surgical precision, you’ve witnessed the magic of robotic path planning. Behind those smooth moves lies a rich tapestry of algorithms that decide how a robot gets from point A to point B. In this post we’ll break down the ten most influential algorithms, sprinkle in some humor, and give you a few exercises to test your newfound knowledge. Grab a cup of coffee, roll up your sleeves, and let’s dive in!

1. Breadth‑First Search (BFS)

BFS is the kid on the block that always gets everyone’s attention first. It explores all nodes at a given depth before moving deeper, guaranteeing the shortest path in an unweighted graph.

queue = [start]
while queue not empty:
  node = dequeue(queue)
  if node == goal: return path
  enqueue(all unvisited neighbors of node)

• Pros: Simple, guarantees optimality in unweighted graphs.
• Cons: Memory hungry; not suitable for large continuous spaces.

Exercise 1: BFS in a Maze

Implement BFS to find the shortest path from the top-left corner to the bottom-right corner in a 2D maze represented by a grid of 0s (free) and 1s (walls).

2. Depth‑First Search (DFS)

DFS is the adventurous cousin of BFS that dives deep before backtracking. It’s not optimal for shortest paths but shines in memory‑constrained environments.

stack = [start]
while stack not empty:
  node = pop(stack)
  if node == goal: return path
  push(all unvisited neighbors of node)

• Pros: Low memory usage.
• Cons: Can get stuck in deep branches; no optimality guarantee.

Exercise 2: DFS to Find All Paths

Modify your DFS implementation to list all possible paths from start to goal in a small graph.

3. A* (A Star)

A* is the superhero of path planning: it combines BFS’s systematic search with a heuristic that predicts how close you are to the goal.

g(n) = cost from start to n
h(n) = heuristic estimate from n to goal
f(n) = g(n) + h(n)
use priority queue ordered by f(n)

• Pros: Finds optimal path if heuristic is admissible.
• Cons: Requires a good heuristic; can be computationally heavy.

Exercise 3: Manhattan vs Euclidean Heuristics

Implement A* on a grid with diagonal moves allowed. Compare the performance and path length using Manhattan vs Euclidean heuristics.

4. Dijkstra’s Algorithm

Dijkstra is essentially A* with a zero heuristic. It’s perfect for weighted graphs where all edge costs are non‑negative.

• Pros: Guarantees shortest path; no need for heuristics.
• Cons: Slower than A* when a good heuristic exists.

Exercise 4: Road Network Shortest Path

Given a city map with distances between intersections, use Dijkstra’s algorithm to find the quickest route from your home to the office.

5. Rapidly‑Exploring Random Tree (RRT)

RRT is the wild child of robotics, designed for high‑dimensional spaces. It builds a tree by randomly sampling the configuration space.

while not goal_reached:
  q_rand = random_sample()
  q_near = nearest_node_in_tree(q_rand)
  q_new = extend(q_near, q_rand)
  add_edge(q_near, q_new)

• Pros: Handles complex constraints; scalable to high dimensions.
• Cons: Not guaranteed optimal; can produce jagged paths.

Exercise 5: Simple RRT in 2D

Create a basic RRT implementation that navigates a point robot around circular obstacles.

6. Probabilistic Roadmap (PRM)

PRM is RRT’s sibling that builds a graph of random nodes and connects them if a collision‑free path exists. It’s great for repetitive planning in static environments.

• Pros: Fast query times after construction; works well in static maps.
• Cons: Construction can be expensive; not ideal for dynamic scenes.

Exercise 6: PRM with K‑Nearest Neighbors

Implement a PRM that connects each node to its k nearest neighbors. Test how varying k affects path quality.

7. Visibility Graph

This algorithm treats the environment as a polygonal map and connects all visible vertices. It’s optimal for planar graphs with straight‑line movement.

• Pros: Generates optimal paths in visibility‑friendly maps.
Cons: Computationally heavy for many obstacles; assumes perfect visibility.

Exercise 7: Constructing a Visibility Graph

Create a visibility graph for a simple room with rectangular obstacles and find the shortest path.

8. Potential Field Methods

Think of the robot as a particle attracted to the goal and repelled by obstacles. The resulting vector field guides motion.

F_total = F_attract + sum(F_repulse_i)

• Pros: Simple to implement; works well in smooth environments.
• Cons: Prone to local minima; can get stuck in loops.

Exercise 8: Avoiding Local Minima

Add a random perturbation or use navigation functions to escape local minima in a cluttered space.

9. Dynamic Window Approach (DWA)

DWA is the go‑to algorithm for mobile robots that need to consider velocity constraints and dynamic obstacles.

• Pros: Real‑time performance; accounts for robot dynamics.
• Cons: Requires tuning of velocity windows; may produce suboptimal paths.

Exercise 9: Simulate DWA in a Moving Crowd

Implement DWA for a robot navigating through a crowd of moving pedestrians. Measure success rate and path smoothness.

10. Graph Search with Learning (Reinforcement Learning)

Modern robots are turning to RL to learn policies that implicitly encode path planning. Algorithms like DQN or PPO can be trained on simulated environments.

• Pros: Learns to handle complex dynamics and uncertainties.
• Cons: Requires large training data; hard to guarantee safety.

Exercise 10: Train a Simple RL Agent

Using OpenAI Gym’s “MountainCar” environment, train a policy that learns to reach the goal efficiently. Compare its performance with classical planners.

Memes & Motivation

Let’s lighten the mood with a classic robotics meme. When you finally get your robot to navigate without crashing:

Feel free to embed this video where you see fit; it’ll give your readers a good laugh and a break from the technical grind.

Conclusion

From BFS’s brute‑force search to RL’s learned policies, robotic path planning has evolved into a vibrant field that blends classic graph theory with cutting‑edge machine learning. Each algorithm brings its own strengths and trade‑offs—think of them as different tools in a roboticist’s toolbox. The exercises above should give you hands‑on experience and deepen your understanding of how these algorithms behave in practice.

Now that you’ve met the stars of path planning, go experiment! Build a robot in simulation, tweak these algorithms, and watch your creations glide across obstacles with grace. Happy planning!