Fuzzy forward dynamics of distinct gait phases with a prosthetic foot

Abstract

This work considers epistemic uncertainty in the form of fuzzy parameters in a multibody forward dynamics simulation of the human leg with a prosthetic foot. The thigh and shank are modelled as rigid bodies while the prosthetic foot, modelled after a carbon spring prosthesis, is represented by a predeformed geometrically exact beam model. A variational integrator is used to solve the equations of motion in the forward dynamics simulation and the Graph Follower algorithm is used to include epistemic uncertainty. Two cases are considered. Large movements are examined using a pendulum swing, similar to the swing phase during human gait. To validate the deformation of the prosthesis, a second case is examined, where the prosthesis is fixed in space and deforms under the weight of the body segments. Both cases consider a fuzzy Young’s modulus and determine the envelopes of the resulting uncertain target output. The Graph Follower algorithm was modified to substantially increase computational efficiency, enabling the propagation of fuzzy uncertainty through the complex multibody model with rigid and flexible bodies.