Hyper-redundant manipulator dynamics: a continuum approximation

Hyper-redundant, or 'snake-like', 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. Furthermore, these methods 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-or-freedom' (or continuum) problem. The dynamics for this case is developed. The approximate dynamics of actual hyper-redundant manipulators is then reduced to a problem which is O(1) in time, i.e. the algorithm is O(n) is the total number of computations, but these computations can be completely distributed over n parallel processors. This is achieved by 'projecting' the dynamics of the continuum model onto the actual robotic structure. Applications of this method to practical computed torque control schemes for hyper-redundant manipulators is demonstrated with two examples: (i) industrial pick-and-place tasks and (ii) inspection in an environment filled with viscous sludge, such as a hazardous waste dump. The results are compared with a lumped mass model of a particular hyper-redundant manipulator.