Blind parameter identification of implicit differential equations using the collocation discretization and homotopy optimization methods

In this paper, our objectives are to estimate the moments of inertia and reconstruct the inputs of a two-link pendulum that models a human arm. A blind parameter identification routine to determine the inertia properties of human limbs without input data based on a combination of collocation discretization and homotopy optimization is suggested. Without the input data, inertia parameters are structurally unidentifiable. Complementary equations in terms of the ratio of inertia parameters in the cost function and the rate of change of the inputs in the constraints are introduced to make the problem structurally identifiable. Numerous simulations are performed to validate our approach. Experiments to record human upper arm and forearm oscillatory movements were also performed, and moment of inertia terms were evaluated. The significance of the proposed method is that the method can be used to evaluate the moments of inertia of human body segments only from the experimental kinematic data. The advantages of the method are: numerical integration of dynamic and sensitivity equations is avoided and the record of the inputs to the system is not needed.