Trajectory tracking control of two degrees-of-freedom helicopter based on Udwadia–Kalaba theory

Abstract

In this article, by using Lagrange energy method, we establish the dynamical model of a two degrees-of-freedom helicopter, which is subject to holonomic constraints. A control method based on Udwadia–Kalaba theory is proposed to achieve the trajectory tracking control of the 2-degrees-of-freedom helicopter. Different from traditional methods, this method could solve the constraint force of the mechanical system without adding additional parameters such as Lagrange multipliers. When initial conditions are compatible, we can use the nominal control which is based on Udwadia–Kalaba equation to control 2-degrees-of-freedom helicopter in real time. But when initial conditions have incompatibility, the simulation result could produce divergence phenomenon. To solve the trajectory tracking control problem of 2-degrees-of-freedom helicopter under incompatible initial conditions, a modified controller is proposed. We also make simulation contrast by different control methods to validate the effectiveness and superiority of the modified controller. Simulation results show that the modified controller can drive the 2-degrees-of-freedom helicopter to perfectly track the desired trajectory with less control cost and high control accuracy.