Holonomy-based motion planning of a second-order chained form system by using sinusoidal functions

In motion planning of a symmetric affine system under kinematic non-holonomic constraints, a control method using holonomy is known. The holonomy is a state displacement caused by periodic control inputs. A class of kinematic non-holonomic systems can be expressed by the first-order chained form; a class of dynamic non-holonomic systems can be represented by the second-order chained form. To my best knowledge, there is no previous works in which holonomy is explicitly used for a control method of a second-order chained form system. This paper discusses holonomy extraction for such a system. An example of motion planning based on holonomy is also presented.