Lyapunov Direct Method and PID Algorithm for Differential Drive Robot Control

This study implements simulations using both Lyapunov's direct method and PID algorithms to control the motion of differential drive wheeled robots. The implementation enables robots to follow predefined straight-line or circular trajectories through programming. In the simulation environment, control parameters can be adjusted to optimize the robot's motion path, achieving more precise and stable control performance. The Lyapunov-based controller typically involves designing a positive definite function and ensuring its derivative is negative definite, while the PID controller implements proportional, integral, and derivative terms for error correction. Additionally, integrating sensors and feedback control mechanisms can significantly enhance the robot's navigation capabilities and dynamic responsiveness. These control approaches, combined with proper motion planning algorithms, enable precise control and trajectory execution for differential drive wheeled robots. The code structure typically includes kinematic models, controller modules, and trajectory generation functions that work together to achieve the desired motion patterns.