A constrained extended Kalman filter for the optimal estimate of kinematics and kinetics of a sagittal symmetric exercise

Abstract

This paper presents a method for real-time estimation of the kinematics and kinetics of a human body performing a sagittal symmetric motor task, which would minimize the impact of the stereophotogrammetric soft tissue artefacts (STA). The method is based on a bi-dimensional mechanical model of the locomotor apparatus the state variables of which (joint angles, velocities and accelerations, and the segments lengths and inertial parameters) are estimated by a constrained extended Kalman filter (CEKF) that fuses input information made of both stereophotogrammetric and dynamometric measurement data. Filter gains are made to saturate in order to obtain plausible state variables and the measurement covariance matrix of the filter accounts for the expected STA maximal amplitudes. We hypothesised that the ensemble of constraints and input redundant information would allow the method to attenuate the STA propagation to the end results. The method was evaluated in ten human subjects performing a squat exercise. The CEKF estimated and measured skin marker trajectories exhibited a RMS difference lower than 4mm, thus in the range of STAs. The RMS differences between the measured ground reaction force and moment and those estimated using the proposed method (9N and 10Nm) were much lower than obtained using a classical inverse dynamics approach (22N and 30Nm). From the latter results it may be inferred that the presented method allows for a significant improvement of the accuracy with which kinematic variables and relevant time derivatives, model parameters and, therefore, intersegmental moments are estimated.

Accuracy and kinematics consistency of marker-based scaling approaches on a lower limb model: a comparative study with imagery data

“…It indicates that the optimisation of the marker local coordinates resulted in a similar effect on the joint angles computation for both methods, whereas MB l:a:m: led to different results. Low kinematic errors of MB a:m à : and EB a:m à : does not necessarily mean that joint angles were accurate or that STA were fully compensated (Bonnet et al 2017). Kinematic accuracy can only really be assessed with intra-cortical pins (Andersen et al 2010a) or biplanar fluoroscopic data (Gasparutto et al 2015;Richard et al 2017).…”

A Simple Algorithm for Assimilating Marker-Based Motion Capture Data During Periodic Human Movement Into Models of Multi-Rigid-Body Systems

“…Since the proposed algorithm estimate kinematics of multi-rigid-body model using the joint constraints for the whole body, the proposed algorithm can be considered as a kind of the “global optimization”(Leardini et al, 2005 ) including multi-body kinematics optimization (Duprey et al, 2010 ; Richard et al, 2017 ) and kinematics estimation based on Kalman filter (Cerveri et al, 2003 , 2005 ; Bonnet et al, 2017a ). Here, let us clarify the novel aspect of the proposed algorithm complementary to the existing global optimization methods.…”

Stiffness of a wobbling mass models analysed by a smooth orthogonal decomposition of the skin movement relative to the underlying bone

“…For a better insight, the analysis of the relative movement between the skin and the bone should be completed by the analysis of the ground reaction forces (not known in the present study). The recent studies which simultaneously track skin markers trajectories and external forces to estimate joint kinematics and segment masses (Bonnet et al, 2017;Jackson et al, 2015) may be adapted to thoroughly identify the parameters of the wobbling mass models. Additionally, the deformable modelling of the lower limb segments (Clark and Hawkins, 2010;Halloran et al, 2010;Stelletta et al, 2017) may help in understanding the dynamics effects of the soft tissue deformation (e.g.…”