A continuum approach to hyper-redundant manipulator dynamics

Hyper-redundant, or snakelike, manipulators have a very large number of actuatable degrees of freedom. This paper develops an efficient formulation of approximate hyper-redundant manipulator dynamics. The most efficient methods for representing manipulator dynamics in the literature require serial computations proportional to the number of degrees of freedom and are not fully parallelizable. For hyper-redundant manipulators, which may have tens, hundreds, or thousands of actuators, these formulations preclude real time implementation. This paper therefore looks at the mechanics of hyper-redundant manipulators from the point of view of an approximation to an infinite degree-of-freedom problem. The dynamics for this infinite dimensional case is developed. The approximate dynamics of actual hyper-redundant manipulators is then reduced to a problem which is O(1) in the number of serial computations, i.e., the algorithm is O(n) in the total number of computations, but these computations are completely parallelizable. Applications to practical computed torque control schemes are demonstrated.