Analyzing Finger-Movement Trajectories with Stochastic Differential Equations (SDEs)

Fingertip positions can be conceptualized as Brownian particles within a force field. Using stochastic differential equations (SDEs) the force field and its associated potential function can be formally related to observed fingertip positions. Using observed fingertip positions the force field can then be “solved.” This provides a means of describing, comparing, and simulating finger-movement trajectories without formulating the kinematics of the hand. Through discretization of SDEs, the resulting mathematical forms are merely regression equations, which can be solved using familiar mathematical tools such as ordinary least squares and maximum likelihood estimation. Experimental “effects” are specified in the force-field part of the regression, and the Brownian perturbances as the random error of the regression. Using SDEs to specify potential functions can support haptic scientists performing exploratory data analysis, wishing to summarize finger-movement trajectories, compare and test differences in finger-movement trajectories between participants, groups of participants, or experimental conditions, and simulate/predict finger-movement trajectories.