The Main Sequence of Saccades Optimizes Speed-accuracy Trade-off

Abstract

In primates, it is well known that there is a consistent relationship between the duration, peak velocity and amplitude of saccadic eye movements, known as the 'main sequence'. The reason why such a stereotyped relationship evolved is unknown. We propose that a fundamental constraint on the deployment of foveal vision lies in the motor system that is perturbed by signaldependent noise on the motor command. This noise imposes a compromise between the speed and accuracy of an eye movement. We propose that saccade trajectories have evolved to optimize a trade-off between the accuracy and duration of the movement. Taking a semi-analytical approach we use Pontryagin's minimum principle to show that there is an optimal trajectory for a given amplitude and duration; and that there is an optimal duration for a given amplitude. It follows that the peak velocity is also fixed for a given amplitude. These predictions are in good agreement with observed saccade trajectories and the main sequence. Moreover, this model predicts a small saccadic dead-zone in which it is better to stay eccentric of target than make a saccade onto target. We conclude that the main sequence has evolved as a strategy to optimize the trade-off between accuracy and speed.

Adaptive Control of Saccades via Internal Feedback

“…Finally, the term ␣ is simply a cost per unit time. This parameter penalizes movement duration, encouraging movements to terminate as soon as possible (Harris and Wolpert, 2006). Therefore, the term ␣ reflects the value (or importance) that we assign to completing the task.…”

“…Given a visual target and the internal value that the controller assigns to that target, the controller generates the initial motor commands based on the current state of the eye. These motor commands minimize a specific cost (Harris and Wolpert, 2006) that balances the need to arrive at the target as soon as possible (specified by the value of the target) with the need to minimize variability (specified by the signal-dependent noise in the motor commands). While the commands are taking effect, the forward model uses a copy of the commands to estimate the moment-by-moment sensory state of the eye, which in turn is used by the controller to generate the subsequent motor commands.…”

Conservation law for self-paced movements

“…Drive conservation provides a new perspective for understanding movement regularities. In the optimal control framework, modeling the global regularities requires auxiliary motor tasks that motivate faster movements, such as maximizing the reward rate (8,10) or minimizing the time cost with an accuracy constraint (11,12) or a total-cost constraint (13), or without any constraint (14,15). Despite their pertinence for externally motivated movements, such as lever pressing (8) and fast reaching movements (25), however, these models are not applicable to most spontaneous movements that are produced in the absence of reward or time pressure, such as comfortably paced reaching movements (26) and curved hand movements (18).…”

“…In addition to minimizing the cost of making a movement, however, optimal control models must also restrict the duration of the movement (2-7), or introduce motor tasks that encourage faster movements (8)(9)(10)(11)(12)(13)(14)(15); otherwise, the minimum cost could be achieved by simply decreasing the overall movement speed. Consequently, this approach neglects biological movements that are generated in a self-paced manner (i.e., in the absence of external task contingencies that can affect the pace of movements).…”

Gaze-Assisted Pointing for Wall-Sized Displays

“…These are typically followed by small corrective saccades (see Fig. 2 right) which fall below our adopted threshold of 120 px [6]. In turn, these could have led to conflicts between the users' expectations and the displayed position of the pointer.…”