Zinong Li^1,2,3 (), Fangfang Hong⁴, Alex H. Williams^5,6, Robert Volcic^1,7,8, Michael S. Landy^2,3,5; ¹New York University Abu Dhabi, ²New York University, ³Department of Psychology, New York University, ⁴Department of Psychology, University of Pennsylvania, ⁵Center for Neural Science, New York University, ⁶Center for Computational Neuroscience, Flatiron Institute, ⁷Center for Artificial Intelligence and Robotics, New York University Abu Dhabi, ⁸Center for Brain and Health, New York University Abu Dhabi

Visually guided reaching shows systematic differences in endpoint bias and variability across the workspace. We introduce an efficient approach based on a Wishart-Process model to measure such endpoint distributions. It provides estimates of endpoint distributions at tested and untested locations in the workspace. Nine participants performed unseen-hand, center-out reaches (3 amplitudes × 24 directions × 20 trials, 2 hours/participant) using a stylus on a tablet. Participants were encouraged to take 600 ms to complete the reach (ready-set-go procedure). Trials with durations deviating by more than 30% were excluded and re-run. Endpoint distributions were modeled as bivariate Gaussians, with both the bias (the difference between the mean and the target location) and covariance matrix treated as free parameters. These parameters were assumed to vary smoothly across target locations. Each was estimated by maximum likelihood using 10 Zernike-polynomial basis functions, with this number selected by cross-validation to avoid overfitting. Reach-distance bias exhibited a regression to the mean target distance. Reach covariance showed Weber-like growth with increasing target distance and idiosyncratic patterns of bias and covariance across reach space and across participants. To evaluate the potential for increased trial efficiency, we simulated the experiment while varying the number of trials per target location. As a measure of fit accuracy, we used a target-distance-normalized Bures-Wasserstein distance between the ground-truth and fitted covariance matrices. Results showed fit accuracy nearly leveled off at 15 trials/location with half the number of target locations, indicating that 540 trials and less than 1 hour of data collection would be sufficient. Our approach provides an efficient way to profile individual motor variability across a 2D workspace from a relatively modest number of trials. Results can be interpolated to untested target locations. The model can be extended to higher-dimensional problems: 3D reaches, varying duration, final grasp pose, etc.

Acknowledgements: NIH EY08266 (to MSL), NYUAD Center for Brain and Health, funded by Tamkeen under NYU Abu Dhabi Research Institute award CG012 (to MSL and RV), NYUAD Center for Artificial Intelligence and Robotics, funded by Tamkeen under NYU Abu Dhabi Research Institute award CG010 (to RV).