Adaptive Nonlinear PD Controller of Two-Wheeled Self-Balancing Robot with External Force

This paper proposes an adaptive nonlinear proportional-derivative (ANPD) controller for a two-wheeled selfbalancing robot (TWSB) modeled by the Lagrange equation with external forces. The proposed control scheme is designed based on the combination of a nonlinear proportional-derivative (NPD) controller and a genetic algorithm, in which the proportional-derivative (PD) parameters are updated online based on the tracking error and the preset error threshold. In addition, the genetic algorithm is employed to adaptively select initial controller parameters, contributing to system stability and improved control accuracy. The proposed controller is basic in design yet simple to implement. The ANPD controller has the advantage of being computationally lightweight and providing high robustness against external forces. The stability of the closed-loop system is rigorously analyzed and verified using Lyapunov theory, providing theoretical assurance of its robustness. Simulations and experimental results show that the TWSB robot with the proposed ANPD controller achieves quick balance and tracks target values with very small errors, demonstrating the effectiveness and performance of the proposed controller. The proposed ANPD controller demonstrates significant improvements in balancing and tracking performance for twowheeled self-balancing robots, which has great applicability in the field of robot control systems. This represents a promising solution for applications requiring precise and stable motion control under varying external conditions.