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Liebermann, D. G., Ben-David, J., Schweitzer, N., Apter, Y., & Parush, A. (1995). A field study of braking reactions during driving I: Triggering and modulation. Ergonomics, 38(9), 1894–1902.
Abstract: The present experiment was carried out to explore the response of driving subjects to emergency braking. The field trial consisted of driving behind a leading vehicle while the following drivers' responses were recorded by telemetry. A group of 51 individuals performed a series of trials at two driving speeds (60 and 80km/h), two following distances (6 and 12 m), and two braking conditions (real and dummy braking). Not all of these subjects completed all conditions or the minimum number of trials. The dependent variables were the total braking time (TBT) and its subcomponents: braking reaction time (BRT), and accelerator-to-brake movement time (MT). These data were analysed in three separate three-way ANOVAs with repeated measures on all factors. The results showed that when subjects were not aware of the forthcoming braking, the distance and braking conditions had major effects on all dependent variables. At the shorter following distance drivers reacted and moved faster. Similarly, when the brakes were real compared with dummy (i.e. brake lights only) drivers reacted faster. In addition, drivers reacted to onset of brake lights in 83% of the cases when dummy braking was applied, compared with 97% when real brakes were applied. Speed of driving did not show any significant effects and did not appear to influence the cognitive or attentional set to anticipate an emergency manoeuvre. These findings suggest that changes in angular velocity during optic expansion of the leading vehicle may be used as a cue to modulate braking movement, while onset of brake lights alone may be enough to trigger a ‘ballistic’ preventive response.
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Biess, A., Liebermann, D. G., & Flash, T. (2007). A computational model for redundant human three-dimensional pointing movements: integration of independent spatial and temporal motor plans simplifies movement dynamics. J Neurosci, 27(48), 13045–13064.
Abstract: Few computational models have addressed the spatiotemporal features of unconstrained three-dimensional (3D) arm motion. Empirical observations made on hand paths, speed profiles, and arm postures during point-to-point movements led to the assumption that hand path and arm posture are independent of movement speed, suggesting that the geometric and temporal properties of movements are decoupled. In this study, we present a computational model of 3D movements for an arm with four degrees of freedom based on the assumption that optimization principles are separately applied at the geometric and temporal levels of control. Geometric properties (path and posture) are defined in terms of geodesic paths with respect to the kinetic energy metric in the Riemannian configuration space. Accordingly, a geodesic path can be generated with less muscular effort than on any other, nongeodesic path, because the sum of all configuration-speed-dependent torques vanishes. The temporal properties of the movement (speed) are determined in task space by minimizing the squared jerk along the selected end-effector path. The integration of both planning levels into a single spatiotemporal representation simplifies the control of arm dynamics along geodesic paths and results in movements with near minimal torque change and minimal peak value of kinetic energy. Thus, the application of Riemannian geometry allows for a reconciliation of computational models previously proposed for the description of arm movements. We suggest that geodesics are an emergent property of the motor system through the exploration of dynamical space. Our data validated the predictions for joint trajectories, hand paths, final postures, speed profiles, and driving torques.
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