Guiding locomotion in complex, dynamic environments

Abstract

Locomotion in complex, dynamic environments is an integral part of many daily activities, including walking in crowded spaces, driving on busy roadways, and playing sports. Many of the tasks that humans perform in such environments involve interactions with moving objects-that is, they require people to coordinate their own movement with the movements of other objects. A widely adopted framework for research on the detection, avoidance, and interception of moving objects is the bearing angle model, according to which observers move so as to keep the bearing angle of the object constant for interception and varying for obstacle avoidance. The bearing angle model offers a simple, parsimonious account of visual control but has several significant limitations and does not easily scale up to more complex tasks. In this paper, I introduce an alternative account of how humans choose actions and guide locomotion in the presence of moving objects. I show how the new approach addresses the limitations of the bearing angle model and accounts for a variety of behaviors involving moving objects, including (1) choosing whether to pass in front of or behind a moving obstacle, (2) perceiving whether a gap between a pair of moving obstacles is passable, (3) avoiding a collision while passing through single or multiple lanes of traffic, (4) coordinating speed and direction of locomotion during interception, (5) simultaneously intercepting a moving target while avoiding a stationary or moving obstacle, and (6) knowing whether to abandon the chase of a moving target. I also summarize data from recent studies that support the new approach.

Keywords: affordance perception; locomotion; object motion perception; obstacle avoidance; optic flow.

Figure 1

The bearing angle model of interception and obstacle avoidance. The bearing angle is the angle between the object and reference direction that remains fixed in exocentric coordinates (dashed line). By keeping the bearing angle constant, the observer will eventually intercept the moving target.

Figure 2

(A) Top-down view of observer (body width, W) moving straight ahead and an object (black circle) moving from left to right. z and x correspond to the positions of the observer (subscript o) and moving object (subscript m), respectively. t corresponds to the current time and t^* corresponds to the time at which the leading edge of the obstacle reaches the left side of the locomotor path. (B) Illustration of optical angles used in Equations 1–8.

Figure 3

Optically specified distance (A), time remaining (B), and speed (C,D) to pass in front (red line) and behind (blue line) for a stationary observer and a moving obstacle, similar to the situation depicted in Figure 2A. (A–C) Are for a small obstacle, and (D) is for a larger obstacle. Values were calculated using optical variables in Equations 7 and 8. E is the observer's eyeheight, s is seconds, and V_max is the observer's maximum locomotor speed. Gray area in (C) and (D) indicate range of speeds that would result in a collision.

Figure 4

(A) Optic flow field generated by combined motion of observer and object (black dot). (B) The component of optic flow due to self-motion independent of object motion. (C) The component of optic flow due to object motion independent of self-motion. The optic flow field (A) is the vector sum of the self-motion (B) and object-motion (C) components.

Figure 5

Moving observer and moving target. The black lines emanating from observer represent the optically specified speed required to intercept the moving target by moving in the corresponding direction. The light gray circular sector corresponds to the observer's maximum speed and the dark gray sector corresponds to directions for which interception is not possible because required speed exceeds maximum speed.

Figure 6

(A) Observer passing through a lane of obstacles on course to cross the observer's future path. (B) Optically specified range of speeds that would result in a collision with each obstacle as a function of time.

Figure 7

(A) Observer passing through two lanes of obstacles moving at different speeds. (B) Optically specified range of speeds that would result in a collision with each obstacle in the near (light gray) and far (dark gray) lanes as a function of time.

Figure 8

Simultaneous interception of a moving target and avoidance of a stationary obstacle. Black lines emanating from observer indicate speed required to intercept moving target in each direction. Directions that would result in a collision with the obstacle are removed.

Figure 9

Observer attempting to intercept a moving target before it reaches a safe zone (gray region on right side). The observer is capable of intercepting the target in (A) but not in (B).