An analysis of the kinematics and dynamics of underactuated manipulators

The dynamics and kinematics of manipulators that have fewer actuators than degrees of freedom are studied. These underactuated manipulators arise in a number of important applications such as free-flying space robots, hyperredundant manipulators, manipulators with structural flexibility, etc. In the analysis such underactuated manipulators are decomposed into component active and passive arms. This decomposition allows techniques previously developed for regular (fully actuated) manipulators to be applied to underactuated systems. Spatial operator identities are used to develop closed-form expressions for the generalized accelerations for the system. These expressions form the basis for a recursive O(N) dynamics algorithm. The structure of this algorithm is a hybrid of known forward and inverse dynamics algorithms for regular manipulators. Expressions and computational algorithms are also developed for the generalized and disturbance Jacobians for underactuated manipulators. The application of the results in the paper to space manipulators is also described