Neural Comput - Movement duration, Fitts's law, and an infinite-horizon optimal feedback control model for biological motor systems.


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Optimization models explain many aspects of biological goal-directed movements. However, most such models use a finite-horizon formulation, which requires a prefixed movement duration to define a cost function and solve the optimization problem. To predict movement duration, these models have to be run multiple times with different prefixed durations until an appropriate duration is found by trial and error. The constrained minimum time model directly predicts movement duration; however, it does not consider sensory feedback and is thus applicable only to open-loop movements. To address these problems, we analyzed and simulated an infinite-horizon optimal feedback control model, with linear plants, that contains both control-dependent and control-independent noise and optimizes steady-state accuracy and energetic costs per unit time. The model applies the steady-state estimator and controller continuously to guide an effector to, and keep it at, target position. As such, it integrates movement control and posture maintenance without artificially dividing them with a precise, prefixed time boundary. Movement pace is determined by the model parameters, and the duration is an emergent property with trial-to-trial variability. By considering the mean duration, we derived both the log and power forms of Fitts's law as different approximations of the model. Moreover, the model reproduces typically observed velocity profiles and occasional transient overshoots. For unbiased sensory feedback, the effector reaches the target without bias, in contrast to finite-horizon models that systematically undershoot target when energetic cost is considered. Finally, the model does not involve backward and forward sweeps in time, its stability is easily checked, and the same solution applies to movements of different initial conditions and distances. We argue that biological systems could use steady-state solutions as default control mechanisms and might seek additional optimization of transient costs when justified or demanded by task or context.

Resumo Limpo

optim model explain mani aspect biolog goaldirect movement howev model use finitehorizon formul requir prefix movement durat defin cost function solv optim problem predict movement durat model run multipl time differ prefix durat appropri durat found trial error constrain minimum time model direct predict movement durat howev consid sensori feedback thus applic openloop movement address problem analyz simul infinitehorizon optim feedback control model linear plant contain controldepend controlindepend nois optim steadyst accuraci energet cost per unit time model appli steadyst estim control continu guid effector keep target posit integr movement control postur mainten without artifici divid precis prefix time boundari movement pace determin model paramet durat emerg properti trialtotri variabl consid mean durat deriv log power form fittss law differ approxim model moreov model reproduc typic observ veloc profil occasion transient overshoot unbias sensori feedback effector reach target without bias contrast finitehorizon model systemat undershoot target energet cost consid final model involv backward forward sweep time stabil easili check solut appli movement differ initi condit distanc argu biolog system use steadyst solut default control mechan might seek addit optim transient cost justifi demand task context

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