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Probability Navigation Function for Stochastic Static Environments

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  • Robot and Applications
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Abstract

The navigation function (NF) is widely used for motion planning of autonomous vehicles. Such a function is bounded, analytic, and guarantees convergence due to its Morse nature, while having a single minimum value at the target point. This results in a safe path to the target. Originally, the NF was developed for deterministic scenarios where the positions of the robot and the obstacles are known. Here we extend the concept of NF for static stochastic scenarios. We assume the robot, the obstacles and the workspace geometries are known, while their positions are random variables. We define a new Probability NF that we call PNF by introducing an additional permitted collision probability, which limits the risks (to a set value) during the robot’s motion. The Minkowski sum is generalized for the geometries of the robot and the obstacles with their respective Probability Density Functions (PDF), that represent their locations’ uncertainties. The probability for a collision is therefore the convolution of the robot’s geometry, the obstacles’ geometries and the PDFs of their locations The novelty of the proposed algorithm is in its ability to provide a converging trajectory in stochastic environment without inflating the ambient space dimension. We demonstrate our algorithm performances using a simulator, and compare its results with the conventional NF algorithm and with a version of the well known RRT* and Voronoi Uncertainty Fields methods for uncertain scenarios. Finally, we show simulation results of the PNF in disc-shaped world, as well as in star-shaped world.

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Authors and Affiliations

  1. School of Engineering, Ariel University, Ariel, Israel

    Shlomi Hacohen, Shraga Shoval & Nir Shvalb

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  1. Shlomi Hacohen
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  2. Shraga Shoval
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  3. Nir Shvalb
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Correspondence to Nir Shvalb.

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Recommended by Associate Editor Ning Sun under the direction of Editor Myo Taeg Lim.

Shlomi Hacohen is a Lecturer at Engineering Faculty at Ariel University, Israel. He is the Head of robotics and Kinematics Laboratory. His main interests concern uncertain dynamic environments. He graduated both his M.Sc. degree in Electrical Engineering and his M.B.A. in Economics and Business Management at Ariel university. His main interests are nonlinear estimation and robot motion planning.

Shraga Shoval is an associate professor at Engineering Faculty at Ariel University, Israel. He is the Head of the center for robotics research and applications. Most of his research activities revolve around autonomous mobile robots. He earned both his M.Sc. and Ph.D. degrees in Mechanical Engineering from the Technion, Israel (1994, 1987). He is currently a research fellow at the School of Engineering and Information Technology at the University of New South Wales, Australia.

Nir Shvalb is a Senior Lecturer at Engineering Faculty at Ariel University, Israel. He is the Head of Robotics and Kinematics Laboratory together. His main interests are edical robotics, global path planning and theoretical foundations of robotics. He earned his Ph.D. in Mechanical Engineering from the Technion, Israel (2006). He received his MSc in Mathematics at the University of Haifa. He graduated at the Technion in both mechanical engineering and physics departments.

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Hacohen, S., Shoval, S. & Shvalb, N. Probability Navigation Function for Stochastic Static Environments. Int. J. Control Autom. Syst. 17, 2097–2113 (2019). https://doi.org/10.1007/s12555-018-0563-2

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  • DOI: https://doi.org/10.1007/s12555-018-0563-2

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