Recursive Formalism With a Minimal Dynamic Parameterization for the Identification and Simulation of Multibody Systems

This paper proposes a recursive formalism to obtain the equations of motion of multibody systems, using a minimal dynamic parameterization. The use of a minimum set of parameters allows its identification, and the recursivity allows to deal with MBS of any size. A semi-explicit form of the equations for subsequent simulation of the MBS is also introduced. Firstly, a symbolic recursive Newton-Euler formalism in barycentric parameters for open tree-like structures is established. It can be shown that the barycentric parameters appear linearly in these equations which can thus be easily derived with respect to the parameters, leading to the corresponding identification matrix. However, in the general case, the barycentric parameters do not form a minimal set of parameters for the MBS. As a consequence, the identification matrix can never be made full rank, whatever the excitation trajectory, preventing us from correctly identifying the parameters. Therefore, a minimal set of parameters is obtained using recursive rules that can be applied systematically to any open MBS. These new parameters are then fed into the Newton-Euler equations which conserve their linearity with respect to them. Finally, a semi-explicit form of the equations of motion is established, using the minimal parameter set, allowing subsequent simulation of the identified MBS. As regards the applications, the initial motivation of these developments is lying in the field of biomechanics, where knowledge of the dynamic parameters of the human body is of great importance. Based on motion data and reaction force/torques data, a minimal set of parameters for the human body can be identified. Simulation results will be shown during the oral presentation.