Linear Optical Trajectory Research Articles

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

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.

Receivers in American Football Use a Constant Optical Projection Plane Angle to Pursue and Catch Thrown Footballs

In the present work we test how well two interceptive strategies, which have been proposed for catching balls hit high in the air in baseball and cricket, account for receivers in American football catching footballs. This is an important test of the domain generality of these strategies as this is the first study examining a situation where the pursuer's locomotor axis is directed away from the origin of the ball, and because the flight characteristics of an American football are far different from targets studied in prior work. The first strategy is to elicit changes in the ball's lateral optical position that match changes in the vertical optical position so that the optical projection plane angle, psi, remains constant, thus resulting in a linear optical trajectory (LOT). The second is keeping vertical optical ball velocity decreasing while maintaining constant lateral optical velocity (generalized optical acceleration cancellation, or GOAC). We found that the optical projection plane angle was maintained as constant significantly more often than maintaining vertical and lateral optical velocities as GOAC predicted. The present experiment extends previous research by showing that the constancy of psi resulting in an LOT is used by humans pursuing American footballs and demonstrates the domain generality of the LOT heuristic.

Catching fly balls in VR: A test of the OAC, LOT and trajectory prediction strategies

Professional baseball players somehow manage to intercept and catch fly balls successfully. Three perceptual strategies have been proposed to explain the outfielder's ability and to predict the fielder's interception path. (1) TP: The trajectory prediction strategy (Saxberg, 1987) proposes that the fielder perceives the ball's initial conditions, computes its trajectory, and runs directly to the predicted landing point. (2) OAC: The optical acceleration cancellation strategy (Chapman, 1968) proposes that the fielder continuously controls their radial motion (toward the ball) by running to null the vertical optical acceleration of the ball. Transverse motion (lateral) is controlled independently by holding the bearing direction of the ball constant. (3) LOT: The linear optical trajectory strategy proposes that the fielder runs so as to keep the ball's rising optical trajectory straight rather than curved; this maintains a constant ratio between the tangents of the ball's elevation and azimuth angles (tana/tanb = c). These strategies are normally highly correlated, but they can be tested in VR by manipulating the ball's trajectory. Brown University players were tested in an immersive virtual environment (12 x 12 m) while wearing a head-mounted-display (60 x 40 deg, 50–70 ms latency) with trackers on the head and glove. The ball's trajectory was manipulated by increasing or decreasing the gravitational constant (g) at the peak of flight. Trials in which gravity was changed were matched with normal trials in which the ball traveled the same distance on a parabolic arc. Participants made rapid and continuous adjustments to compensate for the change in gravity, inconsistent with TP. Moreover, their radial and transverse velocities varied independently, inconsistent with LOT. Behavior was most consistent with the combination of OAC and constant bearing strategies. We describe a dynamical model that implements this control strategy.

Catching fly balls in virtual reality: A critical test of the outfielder problem

How does a baseball outfielder know where to run to catch a fly ball? The "outfielder problem" remains unresolved, and its solution would provide a window into the visual control of action. It may seem obvious that human action is based on an internal model of the physical world, such that the fielder predicts the landing point based on a mental model of the ball's trajectory (TP). However, two alternative theories, Optical Acceleration Cancellation (OAC) and Linear Optical Trajectory (LOT), propose that fielders are led to the right place at the right time by coupling their movements to visual information in a continuous "online" manner. All three theories predict successful catches and similar running paths. We provide a critical test by using virtual reality to perturb the vertical motion of the ball in mid-flight. The results confirm the predictions of OAC but are at odds with LOT and TP.

Evidence for a generic interceptive strategy

In the present work, we first clarify a more precise definition of instantaneous optical angles in control tasks such as interception. We then test how well two interceptive strategies that have been proposed for catching fly balls account for human Frisbee-catching behavior. The first strategy is to maintain the ball's image along a linear optical trajectory (LOT). The second is to keep vertical optical ball velocity decreasing while maintaining constant lateral optical velocity. We found that an LOT accounted for an average of over 96% of the variance in optical Frisbee movement, while maintenance of vertical and lateral optical velocities was random. This work confirms a common interception strategy used across interceptive tasks, extending to complex target trajectories.

A unified fielder theory for interception of moving objects either above or below the horizon

A unified fielder theory is presented that explains how humans navigate to intercept targets that approach from either above or below the horizon. Despite vastly different physical forces affecting airborne and ground-based moving targets, a common set of invariant perception-action principles appears to guide pursuers. When intercepting airborne projectiles, fielders keep the target image rising at a constant optical speed in a vertical image plane and moving in a constantoptical direction in an image plane that remains perpendicular to gaze direction. We confirm that fielders use the same strategies to intercept grounders. Fielders maintained a cotangent of gaze angle that decreases linearly with time (accounting for 98.7% of variance in ball speed) and a linear optical trajectory along an image plane that remains perpendicular to gaze direction (accounting for 98.2% of variance in ball position). The universality of maintaining optical speed and direction for both airborne and ground-based targets supports the theory that these mechanisms are domain independent.

Optical Trajectories and the Informational Basis of Fly Ball Catching.

D. M. Shaffer and M. K. McBeath (see record 2002-02027-006) plotted the optical trajectories of uncatchable fly balls and concluded that linear optical trajectory is the informational basis of the actions taken to catch these balls. P. McLeod, N. Reed, and Z. Dienes (see record 2002-11140-016) replotted these trajectories in terms of changes in the tangent of optical angle over time and concluded that optical acceleration is the informational basis of fielder actions. Neither of these conclusions is warranted, however, because the optical trajectories of even uncatchable balls confound the information that is the basis of fielder action with the effects of those same actions on these trajectories. To determine the informational basis of fielder action, it is necessary to do the control-theory-based Test for the Controlled Variable, in which the informational basis of catching is found by looking for features of optical trajectories that are protected from experimentally or naturally applied disturbances.

How dogs navigate to catch frisbees.

Using micro-video cameras attached to the heads of 2 dogs, we examined their optical behavior while catching Frisbees. Our findings reveal that dogs use the same viewer-based navigational heuristics previously found with baseball players (i.e., maintaining the target along a linear optical trajectory, LOT, with optical speed constancy). On trials in which the Frisbee dramatically changed direction, the dog maintained an LOT with speed constancy until it apparently could no longer do so and then simply established a new LOT and optical speed until interception. This work demonstrates the use of simple control mechanisms that utilize invariant geometric properties to accomplish interceptive tasks. It confirms a common interception strategy that extends both across species and to complex target trajectories.

A linear optical trajectory informs the fielder where to run to the side to catch fly balls.

P. McLeod, N. Reed, and Z. Dienes (2002) argued that the linear optical trajectory (LOT) strategy incorrectly cues fielders to run forward for balls headed beyond them. The authors of this article explain that the downward optical curvature found for balls landing beyond the fielder's initial position occurs because the balls reorient the direction the fielder is facing during pursuit. Thus, when downward optical curvature begins, the ball is headed to land in front of where the fielder is facing and running. This investigation of open-loop failure conditions has led to new insights such as the reorientation of the fielder, and it supports the use of maintaining matching rates of vertical and lateral optical ball movement consistent with primacy of the LOT control mechanism even when interception is unachievable.

自律移動ロボットを介したヒトのボール捕獲戦略の検討

In this paper, we examine the human ball catching strategy called LOT (linear optical trajectory) that had been proposed in the field of human behavior through an autonomous mobile robot. LOT is a model of the motion strategy that explains the rationality of the running path of outfielder in catching the balls. However, this model does not provide concrete shape about how fielders decide the running direction and velocity according to the ever-changing position of balls. We consider the ball catching task by an autonomous mobile robot and derive a visual feedback control method based on LOT. We also demonstrate that the proposed method enables the mobile robot to catch the balls that fly in three-dimensional space only by using the monocular vision system.

Baseball outfielders maintain a linear optical trajectory when tracking uncatchable fly balls.

The authors investigated whether behavior of fielders pursuing uncatchable fly balls supported either (a) maintenance of a linear optical trajectory (LOT) with monotonic increases in optical ball height or (b) maintenance of optical acceleration cancellation (OAC) with simultaneous lateral alignment with the ball. Past work supports usage of both LOT and OAC strategies in the pursuit of catchable balls headed to the side. When balls are uncatchable, fielders must choose either optical linearity or alignment at the expense of the other. Fielders maintained the LOT strategy more often and for a longer period of time than they did the OAC alignment strategy. Findings support the LOT strategy as primary when pursuing balls headed to the side, whether catchable or not.

Baseball outfielders maintain a linear optical trajectory when tracking uncatchable fly balls.

Baseball outfielders maintain a linear optical trajectory when tracking uncatchable fly balls.

How Baseball Outfielders Determine Where to Run to Catch Fly Balls

Current theory proposes that baseball outfielders catch fly balls by selecting a running path to achieve optical acceleration cancellation of the ball. Yet people appear to lack the ability to discriminate accelerations accurately. This study supports the idea that outfielders convert the temporal problem to a spatial one by selecting a running path that maintains a linear optical trajectory (LOT) for the ball. The LOT model is a strategy of maintaining "control" over the relative direction of optical ball movement in a manner that is similar to simple predator tracking behavior.