Singularity and Workspace Analysis for Modular Continuum Robots

Continuum robots offer yet unknown possibilities in the design of modular manipulators with several redundant degrees of freedom. Those designs have various advantages such as an increased dexterity or an implicit fail-safe mechanism. However, established singularity definitions and workspace analysis methods are restricted to non-redundant robots in many cases or become computationally demanding because they scale exponentially with the available degrees of freedom. In this paper, a sufficient condition for forward singularities of redundant, constrained manipulators is given and it is explained why the commonly used rank condition is only a necessary condition. Furthermore, a method to improve efficiency for position workspace analysis is proposed. For an exemplary 6-module manipulator, the required number of samples is reduced by as much as 99.9%.