Autonomous unicycle: modeling, dynamics, and control

This article focuses on modeling and analyzing the dynamics of an autonomous unicycle. The equations of motion of the nonholonomic multibody system are derived using the Appellian approach, which enables the use of a minimum number of state variables and results in a system of low complexity. The final equations of motion consist of 8 first-order kinematic differential equations and 6 first-order dynamic differential equations. The stability of the open-loop dynamics is investigated and a PD-type controller with 3 input torques is proposed that enables the unicycle to stabilize its upright position and travel along a straight path. The performance of the closed-loop system is demonstrated via numerical simulations.