The Relationship between Curvature and Velocity in Two-Dimensional Smooth Pursuit Eye Movements

de'Sperati, Claudio; Viviani, Paolo

doi:10.1523/jneurosci.17-10-03932.1997

Cited by 128 publications

(82 citation statements)

References 57 publications

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“…The other not perfect result, i.e., the 2/3rd power law, can be related with the nature of trajectories, which are not oscillatory (circles, ellipses, Lissajous figures, etc.) as in the papers, which observed first the phenomenon (de'Sperati and Viviani, 1997). The boundary effects (also related to initial and final speed and curvature) can have indeed a strong influence on the results, which indeed do not depend on the human likeness of the trajectories.…”

Section: Discussionsupporting

confidence: 69%

A Neural Network-Based Approach for Trajectory Planning in Robot–Human Handover Tasks

et al. 2016

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Service robots and even industrial robots recently started sharing human workspace for creating new working settings where humans and robots work even hand by hand. On the one hand, this new scenario raises problems of safety, which are being solved by adding suitable sensor batteries to robot control systems, and on the other hand, it entails dealing with psychophysical aspects as well. Motion intention understanding and prediction comes more natural and effective if the controlled movement is biologically inspired. In order to generate biologically inspired movements in a robotic-assisted surgery scenario, where a robotic assistant shares the execution of tasks with, or hands over tools to a surgeon, we designed a trajectory planning system based on an artificial neural network architecture trained on human actions. After the design and training of the neural controller for motion planning, we checked the objective characteristics of the achieved biologically inspired motion as functional minimization (minimum jerk), two-third power law and bell-shaped velocity. The controller was also experimentally implemented by using a redundant serial robotic arm (LWR4+, Kuka, Germany), and it was actually perceived as "human-like" in the majority of cases by naive subjects. The implemented neural-based control strategy provided to be an effective scheme for human-robot interaction control, also by qualitative assessment.

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Section: Discussionsupporting

confidence: 69%

A Neural Network-Based Approach for Trajectory Planning in Robot–Human Handover Tasks

et al. 2016

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“…The same dimensionless representation may also be useful in analyzing other scale-invariant features and reveal spectrum of power laws in other motor contexts. Power laws have indeed been observed in many types of movements, including 3D hand movements (16), smooth pursuit eye movements (17), speech (18), and walking (19), and also appear in visual motion perception (20).…”

Section: Discussionmentioning

confidence: 92%

Spectrum of power laws for curved hand movements

Huh

Sejnowski

2015

Proc. Natl. Acad. Sci. U.S.A.

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In a planar free-hand drawing of an ellipse, the speed of movement is proportional to the −1/3 power of the local curvature, which is widely thought to hold for general curved shapes. We investigated this phenomenon for general curved hand movements by analyzing an optimal control model that maximizes a smoothness cost and exhibits the −1/3 power for ellipses. For the analysis, we introduced a new representation for curved movements based on a moving reference frame and a dimensionless angle coordinate that revealed scale-invariant features of curved movements. The analysis confirmed the power law for drawing ellipses but also predicted a spectrum of power laws with exponents ranging between 0 and −2/3 for simple movements that can be characterized by a single angular frequency. Moreover, it predicted mixtures of power laws for more complex, multifrequency movements that were confirmed with human drawing experiments. The speed profiles of arbitrary doodling movements that exhibit broadband curvature profiles were accurately predicted as well. These findings have implications for motor planning and predict that movements only depend on one radian of angle coordinate in the past and only need to be planned one radian ahead.optimal control | motor system | free-hand drawing | power law N atural body movements have surprising regularities despite the complexity of the movements and the many degrees of freedom that are involved. These regularities provide insights into principles underlying the mechanisms that generate the movements. We investigate here conditions when a known regularity fails to adequately describe motor behavior, which adds new insights into how movements are generated by the nervous system.One of the best-studied movement regularities is the inverse relationship between the speed and curvature of 2D hand movements observed when subjects are instructed to freely draw curved shapes such as ellipses, which follow a remarkably simple power law (1):This empirical relationship is called the one-third power law between speed and curvature, or equivalently, the two-thirds power law between angular speed and curvature. On a log curvature vs. log speed plot of hand movement, the power law appears as a single straight line with a slope of −1=3 (Fig. 1A). However, deviations from Eq. 1 have been observed for some movement trajectories. One class of deviation occurs when the curvature changes sign: The power law predicts the speed should diverge to infinity as the curvature approaches zero, which is physically implausible, whereas actual movements exhibit smooth, finite speed profiles at such inflection points. Deviations have also been observed for movements without inflection points (1-4). These noninflectional deviations occur in complex movements and are characterized by fragmentation of the log speed vs. log curvature plot into multiple line segments (Fig. 1B). These observations led to the segmented control hypothesis that complex movements could be generated by concatenating smaller and simpler movement...

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“…Since the original demonstration, it has been reported that the law also applies to different types of motion, such as tongue movements during speech (Tasko and Westbury 2002;Perrier and Fuchs 2008), locomotive trajectories (Vieilledent et al 2001;Ivanenko et al 2002;Hicheur et al 2005;Pham et al 2007), and smooth eye movements (de'Sperati and Viviani 1997). It was also found that the Abstract Several types of continuous human movements comply with the so-called Two-Thirds Power Law (2/3-PL) stating that velocity (V) is a power function of the radius of curvature (R) of the endpoint trajectory.…”

Section: Showed That V(t) Is Approximately Proportional To the Cubic mentioning

confidence: 99%

Drawing ellipses in water: evidence for dynamic constraints in the relation between velocity and path curvature

et al. 2016

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Several types of continuous human movements comply with the so-called Two-Thirds Power Law (2/3-PL) stating that velocity (V) is a power function of the radius of curvature (R) of the endpoint trajectory. The origin of the 2/3-PL has been the object of much debate. An experiment investigated further this issue by comparing two-dimensional drawing movements performed in air and water. In both conditions, participants traced continuously quasi-elliptic trajectories (period T = 1.5 s). Other experimental factors were the movement plane (horizontal/vertical), and whether the movement was performed free-hand, or by following the edge of a template. In all cases a power function provided a good approximation to the V-R relation. The main result was that the exponent of the power function in water was significantly smaller than in air. This appears incompatible with the idea that the power relationship depends only on kinematic constraints and suggests a significant contribution of dynamic factors. We argue that a satisfactory explanation of the observed behavior must take into account the interplay between the properties of the central motor commands and the visco-elastic nature of the mechanical plant that implements the commands

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The Relationship between Curvature and Velocity in Two-Dimensional Smooth Pursuit Eye Movements

Cited by 128 publications

References 57 publications

A Neural Network-Based Approach for Trajectory Planning in Robot–Human Handover Tasks

A Neural Network-Based Approach for Trajectory Planning in Robot–Human Handover Tasks

Spectrum of power laws for curved hand movements

Drawing ellipses in water: evidence for dynamic constraints in the relation between velocity and path curvature

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