Model-based control of a third-order nonholonomic system

This paper addresses dynamics modelling and control of mechanical systems subjected to constraints due to the tasks they are to perform. The researched problem refers to the control of a manipulator end-effector motion subjected to a constraint on an acceleration change, that is, jerk. In the presented approach, the acceleration and jerk constraints are incorporated into a system constrained dynamics and then passed to its control dynamics using a unified approach, which is based on an advanced dynamics modelling method, that is, on the generalized programmed motion equations method. This enables one to derive motion equations for systems subjected to high-order constraints. The novelty of this approach consists of the formulation of a unified representation of constraints by differential equations, merging them into system constrained dynamics and then using nonlinear control theory techniques to design controllers for tracking motions along the pre-specified constraints.