Differential Drive Sim

This project simulates the forward kinematics and position control using PID of a differential drive robot. The goal was to implement the kinematics from scratch to better understand differential drive mechanics and control systems.

Features

• Visualization of robot movement and orientation
• Visual representation of wheel rotations and robot orientation
• Speed control with acceleration and deceleration

Robot Kinematics

Forward Kinematics

The forward kinematics for a differential drive robot are described by the following equations:

dx/dt = v * cos(θ)
dy/dt = v * sin(θ)
dθ/dt = ω

where:
v = (v_right + v_left) / 2
ω = (v_right - v_left) / L

v_right, v_left: velocities of the right and left wheels
L: distance between the wheels (wheel base)
θ: robot's orientation 

It takes the initial state of the robot, the wheel velocities and the time step as input to provide the updated robot state as the output.

Position Controller

There are two controllers implemented here, one for linear velocity and one for angular velocity. Both use the basic form of a proportional controller:

v = Kp * distance_error
ω = Kp_angular * angular_error

where:
Kp, Kp_angular: proportional gains for linear and angular velocity
distance_error: Euclidean distance to the goal position
angular_error: difference between current orientation and desired orientation

Files

main.py : Main simulation loop and visualization

robot_model.py : Robot kinematics and state update functions

scenarios.py : Predefined movement scenarios

Getting Started

1. Ensure you have Python and Pygame installed.
2. Clone this repository.
3. Run main.py to start the simulation.