A Mathematician Catches a Baseball

Aboufadel, Edward

doi:10.1080/00029890.1996.12004831

Cited by 12 publications

(14 citation statements)

References 2 publications

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“…The LOT strategy specifies that fielders continuously maintain proportional monotonically ascending vertical and lateral optical angles for fly balls (Aboufadel, 1996;Marken, 2001Marken, , 2014McBeath et al, 1995a;Shaffer et al, 2008;Shaffer, Kruchunas, Eddy, & McBeath, 2004;Shaffer & McBeath, 2002), whereas they continuously maintain proportional monotonically descending vertical and lateral optical angles for ground balls (Sugar, McBeath, Suluh, & Mundhra, 2006;Sugar, McBeath, & Wang, 2006; Figure 4). In the case of ground-based targets, if the optical ball trajectory curves inward, the fielder is headed too far to the side.…”

Section: Linear Optical Trajectorymentioning

confidence: 99%

“…He noted that in cases in which fielders are stationary or run directly forward or backward while heading toward the ball destination, the tangent of the vertical optical angle, tana, increases at a constant rate. As shown in Figure 1a, the optical ball trajectory can be compared to that of an imaginary elevator rising from the home plate at a constant velocity and tilted by the amount that fielders run forward or backward (Babler & Dannemiller, 1993;McLeod & Dienes, 1993, 1996McLeod, Reed, & Dienes, 2003, 2006Michaels & Oudejans, 1992). Although some work examining acceleration discrimination has questioned OAC (Brouwer, Brenner, & Smeets, 2002;Zaal, Bongers, Pepping, & Bootsma, 2012), other Citation: Wang, W., McBeath, M. K., & Sugar, T. G. (2015).…”

Section: Introductionmentioning

confidence: 99%

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Optical angular constancy is maintained as a navigational control strategy when pursuing robots moving along complex pathways

2015

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The optical navigational control strategy used to intercept moving targets was explored using a real-world object that travels along complex, evasive pathways. Fielders ran across a gymnasium attempting to catch a moving robot that varied in speed and direction, while ongoing position was measured using an infrared motion-capture system. Fielder running paths were compared with the predictions of three lateral control models, each based on maintaining a particular optical angle relative to the robotic target: (a) constant alignment angle (CAA), (b) constant eccentricity angle (CEA), and (c) linear optical trajectory (LOT). Findings reveal that running pathways were most consistent with maintenance of LOT and least consistent with CEA. This supports that fielders use the same optical control strategy of maintaining angular constancy using a LOT when navigating toward targets moving along complex pathways as when intercepting simple ballistic trajectories. In those cases in which a target dramatically deviates from its optical path, fielders appear to simply reset LOT parameters using a new constant angle value. Maintenance of such optical angular constancy has now been shown to work well with ballistic, complex, and evasive moving targets, confirming the LOT strategy as a robust, general-purpose optical control mechanism for navigating to intercept catchable targets, both airborne and ground based.

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Section: Linear Optical Trajectorymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Optical angular constancy is maintained as a navigational control strategy when pursuing robots moving along complex pathways

2015

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“…Catching a ball gives a simple example. By moving sideways, out of the plane of the trajectory of the ball, it may be easier to estimate future positions of the ball, and hence enhance the catchers's ability (Aboufadel 1996). This "control for observation" issue is pertinent in many applications, e.g., robotics (Suluh et al 2001;Freda and Oriolo 2007) and natural systems (Ghose et al 2006).…”

Section: Dual Controlmentioning

confidence: 99%

Pseudo-continuous multi-dimensional multi-mode systems

Verriest

2011

Discrete Event Dyn Syst

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The dynamics of multi-mode multi-dimensional (M 3 D) hybrid systems is described. Such systems have modes of different dimensions, for which the state space is defined as a fibre bundle. The implications of the behavior at the mode transitions is investigated in detail, for which pseudo-continuity is introduced. An M 3 D system is pseudo-continuous if instantaneous switching via higher dimensional modes does not have any effect. Canonical forms and parameterizations are derived for pseudo-continuous M 3 D systems. The system may be actively controlled (exo-M 3 D), or passively switched via a fixed switching surface (auto-M 3 D). M 3 D systems are of interest in the approximate and reduced order modeling for nonlinear systems and the remote control over one-way communication channels. The optimal timing (switching) control for such M 3 D systems is solved in the general case. Necessary conditions for a stationary solution are derived and shown to extend those of the equal dimension case (Egerstedt et al. 2003). We also give a specific solution for the linear quadratic problem, involving a generalization of the Riccati equation. This problem is of interest in deriving neighboring extremal solutions for the control under small perturbations of s nominal solution. Some suggestions towards determining the optimal mode sequence are given. We illustrate the problem with the optimal control for a spring assisted high jump (aka man on a trampoline).

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“…Perceptual models that specify how to navigate to catch fly balls are formulated around coordinate systems that are either viewer-based or world-based (McLeod and Dienes, 1993;McBeath et al, 1995;Aboufadel, 1996). Models with viewer-based coordinate systems utilize a geometry that is relative to the vantage of the moving viewer, and only allow information that is perceptually available from that perspective.…”

Section: Introductionmentioning

confidence: 99%

“…This model focuses on objects hit directly at the fielder. Thus, in order to catch the ball, a fielder simply needs to select a running path that maintains the change in tanα equal to a constant, (d/dt(tan α) = c) (Chapman, 1968;McLeod and Dienes, 1993;1996;Oudejans et al, 1996).…”

Section: Introductionmentioning

confidence: 99%

Mobile robot interception using human navigational principles: Comparison of active versus passive tracking algorithms

et al. 2006

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We examined human navigational principles for intercepting a projected object and tested their application in the design of navigational algorithms for mobile robots. These perceptual principles utilize a viewer-based geometry that allows the robot to approach the target without need of time-consuming calculations to determine the world coordinates of either itself or the target. Human research supports the use of an Optical Acceleration Cancellation (OAC) strategy to achieve interception. Here, the fielder selects a running path that nulls out the acceleration of the retinal image of an approaching ball, and maintains an image that rises at a constant rate throughout the task. We compare two robotic control algorithms for implementing the OAC strategy in cases in which the target remains in the sagittal plane headed directly toward the robot (which only moves forward or backward). In the "passive" algorithm, the robot keeps the orientation of the camera constant, and the image of the ball rises at a constant rate. In the "active" algorithm, the robot maintains a camera fixation that is centered on the image of the ball and keeps the tangent of the camera angle rising at a constant rate. Performance was superior with the active algorithm in both computer simulations and trials with actual mobile robots. The performance advantage is principally due to the higher gain and effectively wider viewing angle when the camera remains centered on the ball image. The findings confirm the viability and robustness of human perceptual principles in the design of mobile robot algorithms for tasks like interception.

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A Mathematician Catches a Baseball

Cited by 12 publications

References 2 publications

Optical angular constancy is maintained as a navigational control strategy when pursuing robots moving along complex pathways

Optical angular constancy is maintained as a navigational control strategy when pursuing robots moving along complex pathways

Pseudo-continuous multi-dimensional multi-mode systems

Mobile robot interception using human navigational principles: Comparison of active versus passive tracking algorithms

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