Cost-Effective Numerical Procedure for Quantifying Positional Error and Uncertainty in Large Volume Optical Motion Capture Systems

Optical motion capture (OMC) is a relatively new experimental tool used in many branches of science and engineering. Despite OMC’s widespread use, literature and practical procedures on the quantification of error and uncertainty in OMC systems for rigid bodies are currently underdeveloped. However, in most studies involving error and uncertainty quantification, the OMC volumes are relatively small (maximum length of 2m in any dimension) and involve expensive experimental apparatuses. Therefore, a cost-effective procedure to quantify the positional errors and uncertainties present in a large volume OMC system is presented. The procedure utilizes the kinematics of a wooden block traveling through air to predict errors and uncertainties in the OMC system by only collecting trajectory data. The procedure performs this task by utilizing statistical and numerical methods coupled with an ordinary differential equation (ODE) solver to predict a numerical projectile flight from the experimental data for which to compare and get the error in the OMC system. The positional uncertainty is calculated in two components and added in quadrature. The first component of uncertainty is calculated from 95% mean confidence interval values of the initial conditions propagated through the same ODE solver and compared to the numerical trajectory. The second component quantifies the uncertainty of the numerical path from drag due to the orientation of the block. Computational fluid dynamics (CFD) is used to find the coefficient of drag for the uncertainty case, which is then used to compute another numerical trajectory to compare to the original numerical path to quantify uncertainty. The OMC system consisted of 30 VICON Vantage V5 cameras with a test volume of 19.2 x 8.5 x 5.8 m³. The results of the study suggest that the procedure is valid and produces reasonably small mean errors and uncertainty between the range of 10 to 20mm.