A compact smoothing-differentiation and projection approach for the kinematic data consistency of biomechanical systems

The estimation of the skeletal motion obtained from marker-based motion capture systems affects the results of the kinematic and dynamic analysis of biomechanical systems. The main source of error is the inaccuracy of velocities and accelerations derived from experimentally measured displacements of markers placed on the skin of joints. This error is mainly due to the amplification of high-frequency low-amplitude noise introduced by the motion capture system when the raw displacement signals are differentiated. Another source of error is the skin motion artifact that produces violations of the kinematic constraint equations of the multibody system. An integrated smoothing-differentiation-projection approach to ensure the kinematic data consistency in the context of the analysis of biomechanical systems is presented. The raw data differentiation problem is solved by applying a single-step smoothing-differentiation technique based on the Newmark integration scheme. A systematic multibody procedure is proposed based on the projection of the positions and its smoothed derivatives into their corresponding constraint manifolds to ensure the kinematic data consistency. Several benchmark kinematic signals that include an acquired nonstationary mono-dimensional motion of biomechanical origin and computer generated data of a four-bar mechanism were processed using the proposed method to study its performance.