Control of nonholonomic free-joint manipulators with one actuator

Manipulators with free joints are second-order nonholonomic systems whose dynamical constraints are nonintegrable. Such systems are known to be under-actuated systems which can be controlled by less actuators than the dimension of the configuration space. Previously proposed methods to control free-joint manipulators have been based on the assumption of perfectly frictionless free joints. In this paper, averaging analysis of 3R manipulators with one actuator clarifies that their frictionless models are Hamiltonian systems with conservation of an energy-like quantity. From experiments and simulations, 3R free-joint manipulators with friction at the free joints show dissipative behaviors converging to an equilibrium point. A convergence control method using the energy-like quantity to stabilize to the equilibrium point is proposed.