APPLICATION OF INSTANTANEOUS INVARIANTS TO THE PATH TRACKING CONTROL PROBLEM OF PLANAR 2 DEGREE-OF-FREEDOM SYSTEMS - A SINGULARITY-FREE MAPPING OF TRAJECTORY GEOMETRY

This paper presents a generalized form of planar two degree-of-freedom Curvature Theory, and applies the results to the synthesis of planar two degree-of-freedom motions. In specific, the kinematic control problem of planar path tracking systems is addressed. The theory yields a new mapping of first-and second-order differential geometric properties from the system's two-dimensional output-space (work-space) to the system's two-dimesional control-space (i.e. joint-space). This mapping is shown to be free from any kinematic singularities.