Using Diffusion Map for Visual Navigation of a Ground Robot

Oleg Kupervasser, Hennadii Kutomanov, Michael Mushaelov and Roman Yavich
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Oleg Kupervasser: Department of Mathematics, Ariel University, Ariel 4070000, Israel
Hennadii Kutomanov: Department of Mathematics, Ariel University, Ariel 4070000, Israel
Michael Mushaelov: Department of Mathematics, Ariel University, Ariel 4070000, Israel
Roman Yavich: Department of Mathematics, Ariel University, Ariel 4070000, Israel

Mathematics, 2020, vol. 8, issue 12, 1-16

Abstract: This paper presents the visual navigation method for determining the position and orientation of a ground robot using a diffusion map of robot images (obtained from a camera in an upper position—e.g., tower, drone) and for investigating robot stability with respect to desirable paths and control with time delay. The time delay appears because of image processing for visual navigation. We consider a diffusion map as a possible alternative to the currently popular deep learning, comparing the possibilities of these two methods for visual navigation of ground robots. The diffusion map projects an image (described by a point in multidimensional space) to a low-dimensional manifold preserving the mutual relationships between the data. We find the ground robot’s position and orientation as a function of coordinates of the robot image on the low-dimensional manifold obtained from the diffusion map. We compare these coordinates with coordinates obtained from deep learning. The algorithm has higher accuracy and is not sensitive to changes in lighting, the appearance of external moving objects, and other phenomena. However, the diffusion map needs a larger calculation time than deep learning. We consider possible future steps for reducing this calculation time.

Keywords: diffusion map; vision-based navigation; visual navigation; ground robots; tethered platform; airborne control; prototype; vision-based navigation; artificial neural network; deep learning convolution network; autopilot; time delay; stability of differential equations (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
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