Verified Analysis of a Model for Stance Stabilization

The stabilization of stance is a subject of continuing research in biology, biomechanics and robotics. It plays an important role in many clinical applications as well as in forward dynamical gait simulation. In this paper, we propose a new model relying on a two cylinder foot contact scheme. This contact model has the advantage of simple and smooth dynamic behavior which in turn results in better efficiency in comparison with other contact models. However, a number of parameters in this model, such as position or mass of the pelvis, are known only with some uncertainty. To deal with the situation, we analyze the model using verifiedmethods, which includes propagating the uncertainty through the system and computing the sensitivities of the equations of motion in the first time interval. To perform verified simulations of the whole model, a verified initial value problem solver for a hybrid system is required, which can switch from one system of the equations of motion to the other depending on a certain switching function. While research in this direction remains a topic of high complexity, a simplified kinetostatic version of the model allows one to analyze the sensitivity of the model to parameter variations, as presented in this paper.