Estimation of external contact loads using an inverse dynamics and optimization approach: general method and application to sit-to-stand maneuvers

Abstract

This paper presents a general method to estimate unmeasured external contact loads (ECLs) acting on a system whose kinematics and inertial properties are known. This method is dedicated to underdetermined problems, e.g. when the system has two or more unmeasured external contact wrenches. It is based on inverse dynamics and a quadratic optimization, and is therefore relatively simple, computationally cost effective and robust. Net joint loads (NJLs) are included as variables of the problem, and thus could be estimated in the same procedure as the ECL and be used within the cost function. The proposed method is tested on human sit-to-stand maneuvers performed holding a handle with one hand, i.e. asymmetrical movements with multiples external contacts. Three sets of measured and unmeasured contact load components and three cost functions are considered and simulated results are compared to experimental data. For the population and movement studied, better results are obtained for a least-square sharing between actuated degrees-of-freedom of the relative motor torques (motor torques normalized by the maximal torque production capacity). Moreover, the number of unknown ECL components does not significantly influence the results. In particular, measuring only the vertical force under the seat lead to a relatively correct estimation of the ECL and NJT: not only the values of R% were small (about 10% for the feet ECL and 20% for the NJT), but the influence of an experimental parameters (the Seat Height) was also correctly predicted.

Keywords: External contact loads; Inverse dynamics; Joint loads; Optimization; Sit-to-stand; Underdetermined problem.