Complex Map Robot Navigation Simulation

A complete autonomous robot navigation pipeline implemented in MATLAB, featuring binary occupancy grid mapping, probabilistic path planning (PRM, RRT, RRT*), Pure Pursuit trajectory tracking, and real-time differential drive robot simulation with video output.

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System Pipeline

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Project Overview

This project simulates a mobile robot navigating through a complex maze-like environment with obstacles. It covers the full autonomy stack — from raw map ingestion to real-time simulation and quantitative performance analysis.

Raw Map → Obstacle Inflation → Path Planning → Trajectory Generation → Robot Simulation → Analysis

Stage	Method	MATLAB Tool
Map Creation	Binary Occupancy Grid	binaryOccupancyMap
Obstacle Inflation	Minkowski Sum	inflate()
Path Planning	PRM	mobileRobotPRM
Path Planning	RRT	plannerRRT
Path Planning	RRT*	plannerRRTStar
Motion Control	Pure Pursuit	controllerPurePursuit
Robot Model	Differential Drive	Euler integration
Output	Video + Plots	VideoWriter

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Repository Structure

complex-map-robot-simulation/
│
├── ComplexMapSimulation.mlx        ← MATLAB Live Script (recommended)
├── ComplexMapSimulation.m          ← Plain MATLAB script
│
├── results/
│   ├── assets/
│   │   └── pipeline_diagram.png
│   └── plots/
│       ├── 01_occupancy_grid.png
│       ├── 02_inflated_map.png
│       ├── 03_prm_path.png
│       ├── 04_waypoint_headings.png
│       ├── 05_simulation_final.png
│       ├── 06_position_profile.png
│       ├── 07_heading_profile.png
│       ├── 08_distance_to_goal.png
│       └── 09_rrtstar_path.png
│
├── ALGORITHM_NOTES.md              ← Explanation of PRM, RRT, RRT*
├── RESULTS_ANALYSIS.md             ← Quantitative analysis writeup
├── CHANGELOG.md
├── .gitignore
└── README.md

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Requirements

Requirement	Version
MATLAB	R2020b or later (R2024a recommended)
Robotics System Toolbox	Required
Navigation Toolbox	Required

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How to Run

1. Clone or download this repository
2. Open MATLAB and navigate to the repository folder
3. Open ComplexMapSimulation.mlx (recommended) or ComplexMapSimulation.m
4. Click Run or press F5
5. The simulation will display all intermediate plots, run the robot in real time, and save robot_simulation.avi to your current directory

Open ComplexMapSimulation.mlx for the best experience — outputs render inline alongside the code.

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Demo Video

Running the simulation generates robot_simulation.avi — a real-time recording of the robot navigating from start [2, 2] to goal [24, 18] through the complex map.

Final robot pose: x=24.01, y=17.51, theta=1.59
Result: Robot reached the goal successfully

To view the video, run the script locally and open the generated .avi file in MATLAB or any media player.

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How It Works

Step 1 — Occupancy Grid Map

Loads MATLAB's built-in complexMap and converts it to a binaryOccupancyMap at 2 cells/meter resolution.

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Step 2 — Map Inflation

Inflates obstacles by the robot radius (0.5 m) so that path planning treats the robot as a point, guaranteeing collision-free clearance via Minkowski sum expansion.

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Step 3 — PRM Path Planning

Uses a Probabilistic Roadmap (PRM) with 2000 nodes and a connection distance of 5 m. If no path is found, retries with 5000 nodes and distance 8 m.

• Start: [2, 2] meters
• Goal: [24, 18] meters

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Step 4 — Waypoint Trajectory

Converts the PRM path into a full pose trajectory [x, y, θ] by computing heading angles between consecutive waypoints. Travel time is estimated at 0.5 m/s.

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Step 5 — Robot Simulation and Video

Runs a Pure Pursuit controller on a differential drive robot model:

x(t+dt)  = x(t)  + v · cos(θ) · dt
y(t+dt)  = y(t)  + v · sin(θ) · dt
θ(t+dt)  = θ(t)  + ω · dt

Every frame is captured and written to robot_simulation.avi.

Planned trajectory (blue dashed) vs actual robot path (magenta) overlay on the inflated map.

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Step 6 — Trajectory Analysis

Generates position, heading, and distance-to-goal profiles. A full metrics report is printed at the end of each run.

X / Y Position Profile

Heading Angle Profile

Distance to Goal Convergence

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Bonus — RRT and RRT* Comparison

Runs both RRT and RRT* planners on the same map for side-by-side comparison against PRM.

RRT* result: 33.91 meters, 24 waypoints.

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Results

============ FINAL ANALYSIS ============
Planned path length:    31.75 meters
Actual travel length:   30.25 meters
Total time simulated:   60.60 seconds
Average speed:          0.50 m/s
Path efficiency:        105.0%
Goal position:          [24.0, 18.0]
Final robot position:   [24.01, 17.51]
Position error:         0.49 meters
========================================

The robot successfully reached the goal with a terminal position error of 0.49 m, well within the 0.5 m acceptance radius.

Planner	Path Length	Waypoints
PRM	31.75 m	—
RRT*	33.91 m	24

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Tunable Parameters

Parameter	Location	Default	Effect
robotRadius	Step 2	0.5 m	Inflation clearance
planner.NumNodes	Step 3	2000	PRM coverage
planner.ConnectionDistance	Step 3	5 m	PRM edge length
DesiredLinearVelocity	Step 5	0.5 m/s	Robot speed
MaxAngularVelocity	Step 5	1.0 rad/s	Turn rate limit
LookaheadDistance	Step 5	1.5 m	Pure Pursuit look-ahead
sampleTime	Step 5	0.1 s	Simulation timestep
goalRadius	Step 5	0.5 m	Goal acceptance radius

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Concepts Covered

• Binary occupancy grid mapping
• Configuration space obstacle inflation (Minkowski sum)
• Sampling-based motion planning: PRM, RRT, RRT*
• Pure Pursuit path tracking
• Differential drive kinematics (Euler integration)
• Trajectory analysis and quantitative metrics
• Real-time visualization and video recording in MATLAB

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Author

Ishaan Jha
B.Tech Mechatronics Engineering — IIIT Bhagalpur
Skills: MATLAB · Robotics · Path Planning · Autonomous Navigation

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License

MIT License — see LICENSE for details.