• Numerical method for estimation of ground reaction forces. • Unilateral contact model expressed at the center of pressure. • Foot/ground reaction forces modelled by unilateral Lagrange multipliers. • Indeterminacy in the force estimation handled using a least square approach with filtering. The inverse dynamics simulation of the musculoskeletal system is a common method to understand and analyse human motion. The ground reaction forces can be accurately estimated by experimental measurements using force platforms. However, the number of steps is limited by the number of force platforms available in the laboratory. Several numerical methods have been proposed to estimate the ground reaction forces without force platforms, i.e., solely based on kinematic data combined with a model of the foot-ground contact. The purpose of this work is to provide a more efficient method, using a unilaterally constrained model of the foot at the center of pressure to compute the ground reaction forces. The proposed model does not require any data related with the compliance of the foot-ground contact and is kept as simple as possible. The indeterminacy in the force estimation is handled using a least square approach with filtering. The relative root mean square error (rRMSE) between the numerical estimations and experimental measurements are for the vertical component of the ground reaction forces (GRF), for the anterior component and for the ground reaction moment (GRM) in the sagittal plane.
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