Perception of rotation, path, and heading in circular trajectories

Abstract

When in darkness, humans can perceive the direction and magnitude of rotations and of linear translations in the horizontal plane. The current paper addresses the integrated perception of combined translational and rotational motion, as it occurs when moving along a curved trajectory. We questioned whether the perceived motion through the environment follows the predictions of a self-motion perception model (e.g., Merfeld et al. in J Vestib Res 3:141-161, 1993; Newman in A multisensory observer model for human spatial orientation perception, 2009), which assume linear addition of rotational and translational components. For curved motion in darkness, such models predict a non-veridical motion percept, consisting of an underestimation of the perceived rotation, a distortion of the perceived travelled path, and a bias in the perceived heading (i.e., the perceived instantaneous direction of motion with respect to the body). These model predictions were evaluated in two experiments. In Experiment 1, seven participants were moved along a circular trajectory in darkness while facing the motion direction. They indicated perceived yaw rotation using an online tracking task, and perceived travelled path by drawings. In Experiment 2, the heading was systematically varied, and six participants indicated, in a 2-alternative forced-choice task, whether they perceived facing inward or outward of the circular path. Overall, we found no evidence for the heading bias predicted by the model. This suggests that the sum of the perceived rotational and translational components alone cannot adequately explain the overall perceived motion through the environment. Possibly, knowledge about motion dynamics and familiar stimuli combinations may play an important additional role in shaping the percept.

Keywords: Eccentric rotation; Heading; Motion perception; Multisensory integration; Psychophysics; Translation; Vestibular.

Fig. 1

a Example of the “straight-ahead” heading, where one is aligned with the motion direction. b The heading (α) is the angle between the instantaneous linear velocity vector $v$ and the body midline

Fig. 2

Predicted perceived motion for a 360° off-center circular motion in the horizontal plane (radius = 1.93 m) while being upright. a Schematic of the motion profile. b Input signals acting on the body, where ${\mathit{\omega }}_z$ = yaw velocity, $a_{tan}$ = tangential acceleration, equal to ${\mathit{\omega }}_z^2·R$, and $a_{\text{cen}}$ = centripetal acceleration, equal to ${\dot{\mathit{\omega }}}_z·R$. c–f Model predictions. c, e A topview of the actual (gray, open symbols) and perceived traveled path (black, filled symbols) in darkness and light, respectively. The dots represent the head, with the outcoming line indicating the direction of the body midline (“the nose”). d, f Perceived tilt in darkness and light, respectively

Fig. 3

CyberMotion simulator in the configuration for the circular trajectories. During the trial, the cabin was rotated using the main centrifuge axis (a); Only after the trial, the cabin was reoriented using the cabin yaw axis (b)

Fig. 4

Individual pointing responses for all participants (labeled with different symbols) and repetitions (a) together with the physical and predicted perceived rotation. The group mean and SD in the final angle are indicated on the right. b The average response (black solid line), SD (shaded areas), and the predicted rotation (dashed line) versus the physical rotation. The dotted line is the 1:1 line

Fig. 5

Model prediction (a) and examples of individual drawings of the perceived path (b–h)

Fig. 6

Stimulus profile of Experiment 2 (a), where ${\mathit{\omega }}_z$ = yaw velocity, $a_{tan}$ = tangential acceleration, and $a_{\text{cen}}$ = centripetal acceleration. How these linear accelerations were acting on the body was determined by the participants heading ($\mathit{\alpha }$), which was varied between trials (b)

Fig. 7

Example of the staircase results for one participant, starting at a yaw offset from 90° in- or outward, and converging to the threshold level TH_in and TH_out, respectively. From these, the bias and differential threshold (DT) were calculated

Fig. 8

Individual results for heading bias (a) and differential threshold (b). The group average is indicated by the plus sign, and the model-predicted bias is shown by the triangle. Group results are summarized in c. The arrows indicate the average bias, i.e., the physical orientation required for the perceptual straight ahead. The shaded triangles indicate the average differential threshold

Fig. 9

Schematic overview of the motion perception model based on Merfeld et al. (1993) and Newman (2009). The vestibular part is shown in the middle, on the gray background. Sensors are indicated in light gray, feedback gains in dark gray, and other mathematical operations in white

Fig. 10

Predicted yaw orientation w.r.t. the motion path during a circular motion in darkness (positive values indicate a perceived outward orientation). Simulations were performed by changing one parameter value at the time, and keeping all others at their default value and using the motion profile of Experiment 2 with the heading straight ahead