Relative Position
Localizing System

Each mobile robot in the distributed robotic system is equipped with a rotating laser beacon that projects a vertical slit laser beam. Below the beacon, photodiodes are installed in a circular array to detect a laser beam from any direction around the robot. Distance is measured from the linear velocity of the vertical slit beam as it sweeps across the array. Direction is found from the area on the array where the beam is projected and from the center of that area.

The sensor produces a Swept Laser Projection Matrix (SLPM). Its omnidirectional sensing capability allows beams from multiple robots to sweep the same sensor array, creating overlapping SLPM patterns. This paper presents a simple, real-time algorithm that can separate these patterns while handling error and noise.

Coordination among autonomous mobile robots often requires each robot to know the relative positions of nearby robots. Centralized localization is unsuitable for a fully distributed system, while passive methods such as stereo vision demand considerable processing and cost. The proposed alternative uses an active rotating laser beacon with a known, constant angular speed.

Photodiodes arranged as a circular sensor belt detect the linear speed of a vertical slit laser beam sweeping past them. Combining this measured speed with the beacon’s known angular speed yields distance; the photodiode position indicates direction. Every robot carries both a beacon and a sensor array, so each beacon periodically projects onto neighboring robots without the heavy processing normally required by vision systems.

The circular sensor array is sampled repeatedly to form a Swept Laser Projection Matrix. When a neighboring beacon is within range, detections form an almost straight line called an SLPM pattern. The line’s slope represents distance, while the location of the photodiode at its center represents direction.

All robots emit independently rotating slit beams. Two or more beams can therefore reach one sensor array at the same time, causing SLPM patterns to overlap. A detector that merely finds the beginning and end of one pattern then produces an erroneous reading. Separating multiple patterns is essential for a multi-robot system.

The algorithm is deliberately simple because the sensor must sample continuously and process data in real time. After the interface circuit latches all photodiode outputs, data is transferred to memory and each horizontal line of the matrix is scanned.

A photodiode with no valid laser detection is a “0-pixel”; a detected laser is a “1-pixel”. A new 1-pixel is either attached to an existing SLPM pattern or treated as the start of a new one. The program compares an actual 1-pixel with a predicted 1-pixel calculated from the previous line and the current slope. If the positional error is within a predefined limit, tracking continues. A sudden change in slope terminates that track and signals an overlap.

Because the circular array makes the beam speed vary slightly, a real SLPM pattern resembles a gently curved letter S rather than a perfectly straight line. A bias factor places the temporary last 1-pixel between the actual and predicted positions, allowing the tracker to follow gentle curvature without following abrupt, incorrect changes.

An actual 1-pixel uses an exact sensor coordinate, while the predicted 1-pixel may use a sub-pixel coordinate. This improves slope resolution. The bias factor controls the relative influence of the actual and predicted positions on the temporary endpoint.

If a 1-pixel does not fit any existing pattern within the allowed positional error, it begins a new SLPM pattern. The tolerance adjusts automatically: a steep pattern receives a smaller positional error limit, and a shallow pattern a larger one. The same tracking strategy also rejects isolated errors and noisy inputs.

The detection program was first tested with data from an SLPM simulator whose parameters were chosen to force overlaps. Results label detected patterns A, B, C and so on. If one 1-pixel belongs to more than one line, the display uses an integer formed by adding the weights assigned to those lines; 0-pixels are omitted for clarity.

The illustrated test contains three overlapping patterns. The detector separates them into lines A, B and C and reports each line’s start, endpoint and slope, demonstrating that the line-tracking method can recover individual patterns from a shared region.

A prototype sensor was developed for the PICO-BOT mobile robot. It could detect the distance and direction of a single neighboring robot. To test overlap detection with real measurements, separately recorded SLPM pattern files were merged and fed to the program off-line.

The prototype used a circular sensor array with a radius of 0.13 meter, 90 photodiodes, a beacon frequency of 0.08 hertz and a sampling period of 13.5 milliseconds. The program successfully separated two patterns synthesized from the measured sensor data.

A single SLPM pattern can be found with a simple beginning-and-end detector, but locating multiple robots requires the individual lines in overlapping patterns to be extracted. The experiments verify both the sensing strategy and the real-time algorithm.

The proposed active relative-position sensor offers omnidirectional sensing, needs no complicated lens system, has only one moving part—the beacon—uses a simple algorithm, and is low-cost.

The integrated system of rotating beacons and circular photodiode arrays locates other robots in the same vicinity. Distance comes from the observed linear velocity of a vertical slit beam generated by a beacon rotating at constant speed; the circular array acts as an omnidirectional detector.

Repeated readings form the SLPM. A complete pattern is a near-straight collection of 1-pixels against a background of 0-pixels. Although an isolated pattern is easy to find, overlapping patterns are not. The proposed algorithm extracts individual lines using slope, predicted pixels, actual pixels and a bias factor that preserves gently curved tracks.