The auxiliary wheels in WMR frequently don’t work, so they were removed and the system became the nonholonomic two-wheeled inverted pendulum robot. For this robot, the equations of motion were derived after the design and fabrication along with constructing fundamental control system like the motor controller.
The equations of motion were found by Lagrange’s equations and Kane’s dynamical equations, and both approaches provided the same results. Thus, the derived equations of motion can be said to be reliable. However, the derived results in this thesis are different from that presented by the results of the previous studies.
Based on the derived equations of motion, the controller was selected as LQR which is an optimal controller. Using the LQR, the state-feedback gain matrix was found, and it was applied to the simulation of upright balancing. The robot was controllable with small rising time and overshoot.
The designed optimal controller was applied to the control of the robot, and the upright balancing, rectilinear motion, and spinning motion were realized. There is satisfactory agreement between the experiment and simulation.