Omnidirectional vision sensors based on catadioptric systems with discrete infrared photoreceptors for swarm robotics

TL;DR

This work develops two camera-less omnidirectional catadioptric vision sensors for swarm robotics, each using one infrared LED, eight discrete photodiodes, and a rotationally symmetric mirror. The authors characterize the optical components, design and fabricate two mirror geometries, and measure emission and reception patterns to build a low-complexity mean-response model for the eight photodiodes. They implement a non-derivative inversion to estimate distance and orientation from a single sensor readout and demonstrate that the vertical PD orientation yields better distance precision, while the outward-facing (flower) arrangement improves orientation accuracy, both achieving full 360-degree planar FOV. The results support the viability of inexpensive, scalable camera-less sensors for pairwise interactions in swarm robotics and point to potential hybrids or calibration strategies to enhance performance.

Abstract

In this work, we fabricated and studied two designs for omnidirectional vision sensors for swarm robotics, based on catadioptric systems consisting of a mirror with rotational symmetry, eight discrete infrared photodiodes and a single LED, in order to provide localization and navigation abilities for mobile robotic agents. We considered two arrangements for the photodiodes: one in which they point upward into the mirror, and one in which they point outward, perpendicular to the mirror. To determine which design offers a better field of view on the plane, as well as detection of distance and orientation between two agents, we developed a test rail with three degrees of freedom to experimentally and systematically measure the signal registered by the photodiodes of a given sensor (in a single readout) from the light emitted by another as functions of the distance and orientation. Afterwards, we processed and analyzed the experimental data to develop mathematical models for the mean response of a photodiode in each design. Finally, by numerically inverting the models, we compared the two designs in terms of their accuracy. Our results show that the design with the photodiodes pointing upward resolves better the distance, while the other resolves better the orientation of the emitting agent, both providing an omnidirectional field of view.

Figures (12)

• Figure 1: In (a) and (e), CAD design and test jig for the characterization of the cone of light emitted by the IR LED, respectively. In (b), (c) and (d), photographs taken with an IR sensitive camera using the screen with 0.6 mm thickness at distances of 20, 30 and 40 mm from the base of the LED. In (f), (g) and (h), photographs taken using the screen with 0.8 mm thickness at distances of 20, 30 and 40 mm from the base of the LED.
• Figure 2: Schematic diagram used to determine the angle of the cone $\theta_\mathrm{fp}$, as well as the apparent position $x_\mathrm{fp}$ of the focal point of the light source of the LED, from the diameter $\phi_i$ of the circle covering the illuminated area on the screen (obtained by analyzing the photographs of Fig. \ref{['fig-cones']}) at a distance $x_i$ from the front of the screen to the base of the IR LED (see the text for more details).
• Figure 3: Test stage developed in-house for all the experimental measurements performed in this work. This experimental setup includes a linear bearing that allows us to vary the distance between two bases (one mounted on the carriage of the linear bearing and one mounted on one of the supporting posts of the rail) that can rotate $360^{\circ}$, thus providing us with a total of three degrees of freedom: one longitudinal and two rotational.
• Figure 4: Measured PD reception (a) and LED emission (b) patterns. A readout of the signal was obtained every 1 cm with the increasing distance, and with an angular resolution corresponding to approximately 1 cm of arc, covering $360^{\circ}$ for each case. The black dashed lines depict the corresponding viewing angles according the the datasheets, while the green lines in (b) depict the LED's cone of emission from the angle obtained with the analysis of the photographs of Fig. \ref{['fig-cones']}, using the jig with the moving screen.
• Figure 5: CAD designs for the structure of the discrete components, one LED at the center, pointing upwards to the mirror, and eight PDs arranged at the base in a circular pattern and pointing upwards for the vertical design (a), and horizontally and pointing outwards for the flower design (b). The mirrors are supported by three thin posts on top of the discrete components.