Motion Planning and Control for a Class of Partially Differentially Flat Systems

This paper deals with motion planning and control problems for a class of partially differentially flat systems. A Betafunction based motion planning algorithm is first constructed by selecting the base variable to be the 2-nd order derivative of Beta-function weighted by a constant parameter. The proposed algorithm has lower computational cost than the optimal control while it provides similar system performance. Then, a function approximation technique based control algorithm is proposed by restructuring a partially differentially flat system in the form of the combination of an auxiliary linear system and its variation from the original system. The variation term was replaced by its approximation as a chosen basis function weighted by constant parameters to be determined. These unknown plant parameters are estimated at each instant, denoted by the adjustable control parameters using a defined update law.