High Performance Optical Angular Position Sensing at Low-cost: a Bio-inspired Approach Rapha¨el Juston∗ , St´ephane Viollet∗ , Lubin Kerhuel† and Nicolas Franceschini∗ ∗ Biorobotics,
Institute of Movement Sciences, CNRS & Univ. of the Mediterranean, Marseille, France Email:
[email protected],
[email protected] and
[email protected] † Movea, Grenoble, France Email:
[email protected]
Abstract— Accurate remote contactless angular sensing at high accuracy often requires emissive sensors with high energy consumption, complex processing and high cost. Thanks to active micro-vibrations applied to its elementary retina, our low-cost bio-inspired optical position sensing device is able to measure the angular position of a contrasting edge at low cost with hyperacuity. This sensor is able, for example, to estimate the elevation of a real edge such as the horizontal roof of a distant building with a resolution (0.025o ) at least 160-fold better than the sensors’s static resolution (4o ), despite any changes in the contrast and illuminance. The visual processing algorithm is based on just a few linear filters and arithmetic operations, which require few computational resources. The high performances and low cost of this novel position sensing device make it suitable for applications in the fields of metrology, astronomy, robotics, automotive and aerospace.
I. I NTRODUCTION In many applications, highly accurate contactless position sensing devices (PSDs) are required for measuring angular positions. PSDs react effectively to an emissive point source such as that produced by a laser, but they are expensive and power-consuming. In several recent studies, low-cost non-emissive optical sensors have been developed for locating natural contrasting objects with a high level of accuracy, and even with hyperacuity (i.e., with an accuracy better than the angle between the optical axes of two neighboring photoreceptor sites)[1]. Some sensors of this kind have been based on the overlapping fields of view of neighboring photoreceptors ([2], [3] and [4]), and some others have also used retinal micro-movements in addition ([5], [6], [7] and [8]). Inspired by findings made on the fly compound eye[9], we built artificial visual sensors with retinal micro-scanning ([5], [10], [11] and [8]). These sensors, in which the photoreceptors Gaussian angular sensitivity functions (obtained by defocusing) are combined with retinal micro-scanning movements, show high sensitivity and even hyperacuity. Here we present our novel optical position sensing device (PSD) and the underlying algorithm, with which highly accurate angular position sensing performances can be obtained. The PSD was tested experimentally and found to be able to cope with natural visual environments and natural lighting conditions. To assess its performances, its output signal was recorded as a function of its true angular orientation relative to the horizontal edge formed by the roof of a distant building.
Fig. 1. Picture (top view) and CAD (bottom view) of the angular position sensing device (PSD) after removing its optical shield. A photosensor array (LSC from iC-Haus) mounted at the tip of a piezo bender (PL128.10 from PI) is made to oscillate near the focal plane of a tiny inexpensive lens (extracted from a sparkfun SEN00637). A stepper motor operating in the micro-step mode is used to pitch the whole sensor in 0.025o steps. The red line drawn at the top of the building (located at a distance of 56m) marks the natural contrasting edge to be located. Unlike the configuration shown in the picture, the PSD points toward the roof of the building.
II. D ESCRIPTION OF THE DEVICE Our position sensing device (Fig. 1) consists of an elementary two-pixel-retina which is made to perform translational oscillations close to the focal plane of a tiny lens (f = 2mm). The whole PSD device is rotated micro-stepwise in elevation so that it points in the direction of the roof of a distant building.
Fig. 2. Block diagram of the visual signal processing system used to locate an edge with a high level of accuracy. The piezo bender generates a periodic translation (double arrow) of the two pixels, along with angular micro-scanning movements of the photoreceptor axes, in line with a sinusoidal law (scanning frequency 40Hz, amplitude 1∆ϕ peak to peak with ∆ϕ = 4o and ∆ρ = 4.2o ). The center frequency fp is equal to the scanning frequency. The cut-off frequencies of the first order analog and second order digital low-pass filters are 50Hz and 10Hz, respectively. Gain K = 2.4.
A. A hyperacute position sensing device Hyperacuity was obtained by reproducing two biophysical phenomena discovered in the fly’s visual system. The first phenomena is the Gaussian angular sensitivity function of the photoreceptors, which in insects’ compound eyes results from optical diffraction [12]. In our case, the bell-shaped angular sensitivity function is simply obtained by defocusing the lens placed in front of the photodiodes. The photoreceptor output can therefore be expressed as a convolution of the Gaussian angular sensitivity s and the light intensity of the scene, I as follows:
s(Ψ) · I(Ψ − Ψc ) dΨ
(1)
−∞
where Ψc is the angular position of the visual scene, and: p ln(2) 2 2 π ln(2) − 4∆ρ 2 Ψ e s(Ψ) = π∆ρ
x
2
e−t dt
(5)
0
The second biophysical finding on which our PSD was based is the retinal micro-scanning process found to occur in the fly’s eye[9]. In our PSD, photosensors were glued to the tip of a piezo bender actuator. The latter device generates a periodic 1-D translation of the retina placed behind the lens, which causes the optical axes of the two photoreceptors to scan the environment back and forth. A sinusoidal vibration law was applied to the retina, Ψmod , with a peak-to-peak amplitude 2A, at the frequency fmod :
I(Ψ) =
I1 I2
Ψ
