Static optimal estimation of joint accelerations for inverse dynamics problem solution

In inverse dynamics computations, the accuracy of the solution strongly depends on the accuracy of the input data. In particular, estimated joint moments are highly sensitive to uncertainties in acceleration data. The aim of the present work was to improve classical inverse dynamics computations by providing an accurate estimation of accelerations. Accelerations are usually calculated from noise-polluted position data using numerical double differentiation, which amplifies measurement noise. The objective of the present paper is to use all available imperfect position and force measurements to extract optimum acceleration estimations. A weighted least-squares optimisation approach is used to provide optimal acceleration distributions most consistent with position and force data, and which account for the propagation of measurement uncertainties. The task chosen for comparing the solution methodology with other classical methods is a typical experimental postural movement, consisting in upper limb swings from an upright stance. The proposed method delivers a set of optimal accelerations well consistent with all available measurements. It also leads to an accurate prediction of ground reactions and it produces no residual moment at the top-most segment.