A Study on Design and Implementation of Two-Wheel Double Inverted Pendulum Robot

The two-wheeled inverted pendulum serves as a representative testbed for various technological elements, including robot dynamics, sensor operation, signal processing, and the use of optimal control theories such as LQR. This study presents the design and implementation of an advanced version of a two-wheeled double-inverted pendulum robot, including a fully functional prototype. We propose a physical model for this robot and derive the corresponding Lagrangian equations of motion. According to these equations, an LQR controller with full-state feedback was designed. In addition, we used a commercial IMU sensor and implemented Kalman filtering to sensor fusion. The system was implemented using a microprocessor, and its performance was evaluated through experiments aimed at balancing the behavior and driving characteristics on a two-dimensional plane. The state-space equations that describe the robot’s motion combine reference variables for wheel rotation speeds and directional angular velocityof the body, resulting in a 10-dimensional state vector and a system matrix. Voltage vectors and matrices govern the left- and right-wheel motors, and thesedefine the control inputs. The controller uses state feedback gains derived from the LQR method, and simulations of the robot’s dynamics are conducted using tools such as Excelrather than specialized mathematical software tools.