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Soft robot are celebrated for their propensity to enable compliant andcomplex robot-environment interactions. Soft robotic manipulators, or slendercontinuum structure robots have the potential to exploit these interactions toenable new exploration and manipulation capabilities and safe human-robotinteractions. However, the interactions, or perturbations by external forcescause the soft structure to deform in an infinite degree of freedom (DOF)space. To control such system, reduced order models are needed; typicallymodels consider piecewise sections of constant curvature although externalforces often deform the structure out of the constant curvature hypothesis. Inthis work we perform an analysis of the trade-off between computationaltreatability and modelling accuracy. We then propose a new kinematic model, thePiecewise Affine Curvature (PAC) which we validate theoretically andexperimentally showing that this higher-order model better captures theconfiguration of a soft continuum body robot when perturbed by the externalforces. In comparison to the current state of the art Piecewise ConstantCurvature (PCC) model we demonstrate up to 30\% reduction in error for the endposition of a soft continuum body robot.

Piecewise Affine Curvature model: a reduced-order model for soft robot-environment interaction beyond PCC