Koopman Modeling of Human Gait Dynamics for Global Modal Analysis Using Periodic Motion Regularization

This paper presents a data driven global linear model of steady state walking dynamics. Instantaneous whole body angular momentum is a physics informed aggregate quantity used as a marker for dynamic balance during locomotion. Gait dynamics are often modeled as hybrid and nonlinear. We propose using Koopman Operators to model the gait stability dynamics with a global, linear model. This is achieved by augmenting the whole body angular momentum state variables with learned observables, or basis functions, such that the dynamics look linear in the lifted dimension. Considering that the gait dynamics are periodic, a regularization term that encourages the state transition matrix to be orthonormal is added to the loss term when learning the observables. This forces a periodic model to be learned and prevents the likelihood of unstable poles. A low average MSE was obtained over 2 gait cycles for different population types, each with slightly differing gait dynamics. Furthermore, this linear representation enables the use of linear analysis tools that could have clinical implications for assessing the gait of different patient groups.