UDC 531.3 Trajectory Tracking Control of Programmed Motion in Second Order Nonholonomic Systems C. T. Deressa Department of Theoretical Physics and Mechanics Peoples’ Friendship University of Russia 6, Miklukho-Maklaya str., Moscow, 117198, Russia The D’Alembert–Lagrange principle in general stands for all ideal holonomic and nonholonomic constraints of arbitrary order. <...> But in practice the application of the principle is restricted to ideal holonomic and linear first order nonholonomic constraints. <...> In recent years the direct application of this famous principle is made to model dynamic equation of acceleration level constrained systems. <...> This paper uses the dynamic equation developed to establish a theoretical framework for trajectory tracking control of programmed motion with acceleration level constraints. <...> The trajectory tracking control is accomplished by two models called Reference Control Model constructed using both the programmed and natural constraints and a Dynamic Control Model developed by considering the natural constraints only. <...> The Reference control model is used to plan the required trajectory based on a given acceleration or lower level programmed constraint. <...> Finally, to verify the effectiveness of the framework developed in the paper, a practical example is provided and simulation results are depicted. <...> Key words and phrases: programmed constraint, natural constraint, programmed motion, reference control model, dynamic control model, trajectory tracking, stability. 1. <...> Moreover many dynamic equations uses holonomic and first order linear nonholonomic systems with the exception of Appell equation that can be applied to systems with second order constraints [4]. <...> Imposing tasks to be performed by a dynamic system are examples of Programmed constraint [4, 6]. <...> In nonlinear control theory, motion tracking is the same [1] as trajectory tracking. <...> There are two types [1] of models for accomplishment of Trajectory tracking in nonlinear control: a kinematic model in which the control input is velocity of the system and the dynamic model of the system in which the control Received 26th June, 2014. 96 Bulletin of PFUR. <...> Kinematic models highly exploited for trajectory tracking control of programmed constraints of lower levels. <...> Trajectory tracking of first order nonholonomic systems is achieved using dynamic <...>