A probabilistic method to estimate gait kinetics in the absence of ground reaction force measurements

Abstract

Human joint torques during gait are usually computed using inverse dynamics. This method requires a skeletal model, kinematics and measured ground reaction forces and moments (GRFM). Measuring GRFM is however only possible in a controlled environment. This paper introduces a probabilistic method based on probabilistic principal component analysis to estimate the joint torques for healthy gait without measured GRFM. A gait dataset of 23 subjects was obtained containing kinematics, measured GRFM and joint torques from inverse dynamics in order to obtain a probabilistic model. This model was then used to estimate the joint torques of other subjects without measured GRFM. Only kinematics, a skeletal model and timing of gait events are needed. Estimation only takes 0.28 ms per time instant. Using cross-validation, the resulting root mean square estimation errors for the lower-limb joint torques are found to be approximately 0.1 Nm/kg, which is 6–18% of the range of the ground truth joint torques. Estimated joint torque and GRFM errors are up to two times smaller than model-based state-of-the-art methods. Model-free artificial neural networks can achieve lower errors than our method, but are less repeatable, do not contain uncertainty information on the estimates and are difficult to use in situations which are not in the learning set. In contrast, our method performs well in a new situation where the walking speed is higher than in the learning dataset. The method can for example be used to estimate the kinetics during overground walking without force plates, during treadmill walking without (separate) force plates and during ambulatory measurements.