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Aaron Fath, Brian Marks, Geoffrey Bingham; Response to perturbation in constant tau-dot versus constant proportional rate models of visually guided braking. Journal of Vision 2013;13(9):747. doi: https://doi.org/10.1167/13.9.747.
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Introduction. We performed simulations to evaluate two models of visually guided braking, in which the deceleration was capped, as might happen when a car brake fails. The two monocular tau models were (1) constant tau-dot control (e.g. Yilmaz & Warren (1997)), and (2) constant proportional rate control (e.g. Anderson & Bingham (2011)). Methods. For each model, we evaluated a system of ordinary differential equations, in which the respective control strategies were to hold either tau-dot or tau-dot/tau constant. However, when a deceleration cap was imposed, these could not be held strictly constant. The models were adjusted to allow change in these visual control variables using an abstract mass-spring model whose equilibrium position was the desired value of the control variable. Our simulations were carried out in Matlab. In the simulations, the initial distance from the target was 350 cm and the initial velocity was ͨ2;100 cm/s, so that the initial time-to-contact was 3.5 s. Results. We show color plots of the final velocity at target acquisition for the two models, for values of the control variable on the x-axis, and the deceleration cap on the y-axis. Each plot shows 100 x 100 = 10,000 total simulation runs. The range of values shown for the control variables was consistent with experimental data in previous studies. A velocity value close to 0 is desirable for soft contact, and higher values indicate a collision. The proportional rate strategy showed a large region of parameter space over which contact was achieved with low or zero velocity, while the constant tau-dot strategy did not recover well from an imposed cap on the deceleration. Conclusion. The proportional rate control model exhibited better stability than did the constant tau-dot model. We also show that these results are the same when disparity tau (Anderson & Bingham, 2011) is used.
Meeting abstract presented at VSS 2013
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