Efficient Resolution of Hyper-Redundancy Using Splines

Abstract

Hyper-redundant systems such as snake robots, flexible manipulators, ropes and strings discretized as rigid links connected by joints can be reasonably assumed to length preserving during their motion. The resolution of the redundancy in such systems have been addressed by several researchers using least squares and other techniques in which the computation effort increases rapidly with the number of links and thus are not amenable to real time motion planning. In this chapter, we present a computationally efficient, tractrix based algorithm which appear more ‘natural’ with motion of links ‘dying’ down along the length of the hyper-redundant system. The hyper-redundant system is represented by splines and it is shown that an approximate length preserving motion of the hyper-redundant system can be obtained by employing the tractrix based algorithm on the control polygon which generate the spline. The deviation from the actual length is related to the configuration of the control polygon and it is shown that this approach reduces the dimension of the problem space leading to a very efficient resolution scheme. The approach also has the added advantages of better visualization of the motion due to the higher order continuities and capability of localized shape control available in splines.