Abstract

The most efficient methods for representing dynamics in the literature require serial computations which are proportional to the number of manipulator 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-of-freedom’ (or continuum) 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. This is achieved by ‘projecting’ the dynamics of the continuum model onto the actual robotic structure. The results are compared with a lumped mass model of a particular hyper-redundant manipulator. It is found that the continuum model can be used to generate joint torques to within ten percent of values computed from the lumped mass model.

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