Analysis of exclusively kinetic two-link underactuated mechanical systems

Analysis of exclusively-kinetic two-link underactuated mechanical systems is undertaken in this paper. It is first shown that such systems are not full-state feedback linearizable around any equilibirium point. Also, the equilibrium points for which the system is small-time locally controllable (STLC) is at most a one dimensional submanifold. A concept less restrictive than STLC, termed the small-time local output controllability (STLOC) is introduced, the satisfaction of which guarantees that a chosen configuration output can be controlled at its desired value. It is shown that the class of systems considered are STLOC, if the inertial coupling between the input and output is non-zero. Also, in such a case, the system is nonminimum phase (NMP). An example section illustrates all results presented.