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Application of the Udwadia-Kalaba Approach to Trajectory Tracking Control of Two Degrees-of-Freedom

In this paper, by Lagrange energy method, we establish the dynamical model of two degrees-of-freedom (2DOF) helicopter, which may be subject to holonomic or nonholonomic constraints. Then a control method is proposed to achieve trajectory tracking control of the 2DOF helicopter. Different from other traditional methods, this method with Udwadia-Kalaba theory and could solve the constraint force of the mechanical system without adding additional parameters such as Lagrange multipliers. Then we can verify the correctness of the dynamical model and control method of 2DOF helicopter by theoretical analysis and numerical simulation. When initial conditions are compatible, we can use the traditional Udwadia-Kalaba equation to control 2DOF helicopter in real time during its flight. But when initial conditions have incompatibility, the simulation result could produce divergence phenomenon. Then we propose a modified controller to solve the trajectory tracking control problem of 2DOF helicopter under incompatible initial conditions. Control torques which are generated by the modified controller can control the trajectory of 2DOF helicopter to perfectly track the desired trajectory with high accuracy.