Estimating joint kinematics of a whole body chain model with closed-loop constraints

Computer simulation and optimal control requiring actual joint kinematics and based on the definition of a chain model become more used in biomechanics for studying the musculo-skeletal coordination or optimizing the performance. For this purpose, numerical optimization methods using a chain model have been developed and showed promising results to estimate joint kinematics for open-loop movements. The aim of this study was to exhaustively compare the type of method and closed-loop constraint with four criteria: (i) reconstruction quality, (ii) loop closure respect, (iii) regularity of joint kinematics, and (iv) computational time. Five algorithms were tested to estimate the whole body joint kinematics of 10 elite athletes paddling an ergometer: global optimization (GO) without closed-loop constraints, with soft closed-loop constraints and with strict closed-loop constraints, and Kalman filter (KF) without closed-loop constraints and with soft closed-loop constraints. Each athlete was modelled using a personalized 17-segment 42-degree of freedom chain model. Input data were measured by a 10-camera motion capture system sampled at 250 Hz. ANOVAs were performed on the four criteria to identify differences between the five algorithms. Marker residuals were slightly increased by about 2–3 mm using GO under strict constraints and KF with soft constraints. Closed-loop errors were five times reduced when introducing constraints (10 to 2 mm). KF algorithms gave significantly smoother joint kinematics than the three GO algorithms. Computational time was largely increased by introducing closed-loop constraints in GO algorithm (from 21 to 200 ms per frame) while it remained unchanged in KF algorithm (about 60 ms per frame). To conclude, KF with soft constraints represents the best compromise between the four criteria.