Trajectory Tracking Control of Programmed Motion in Second Order Nonholonomic Systems

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 concept of dividing constraints based on their sources into natural and programmed constraints is employed. 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. The Dynamic Control Model is utilized to control and stabilize the trajectory tracking process. Finally, to verify the effectiveness of the framework developed in the paper, a practical example is provided and simulation results are depicted.

programmed constraint, natural constraint, programmed motion, reference control model, dynamic control model, trajectory tracking, stability