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Extremum seeking for mobile robots

Abstract

The work in this thesis describes theoretical and experimental results of extremum seeking applied to vehicle(s) with the objective of localizing the source of an unknown, nonlinear, signal field. For environments where position information is unavailable, the extremum seeking method is applied to autonomous vehicles as a means of navigating to find the source of some signal which the vehicles can measure locally. The signal is at maximum intensity at the source and decreases with distance away from the source. Although we only assume that the signal field has a maximum in experiments, to prove theoretical stability we use quadratic form a local approximation of the signal field. We explore the idea of dealing with a very slow or drifting sensor and provide stability results for several distinct variations of an extremum seeking scheme for 1D optimization and 2D source localization with point-mass vehicle dynamics. Detailed convergence analysis and simulations for steering-based source seeking with forward velocity regulation applied to nonholonomic vehicles are provided. We develop a deterministic algorithm in a continuum to deploy a group of autonomous vehicles (agents) capable of measuring relative position to neighbors, in a line formation, which has a higher density of agents near the source of a measurable signal and a lower density away from the source in 1D. We also consider stochastic swarming algorithms in 2D that force the net of agents to spread, maintain a formation, and seek a source without position information, whereby each agent is given a local measurement of signal field and the relative distance from neighbors. Experimental results of extremum seeking applied to mobile vehicles to perform localization, tracking, and level-set tracing of a light source are shown. We perform experiments with multiple vehicles using extremum seeking not only to localize the light source but also to avoid objects and each other. Finally, we discuss details of setting up a testbed to produce a characterized smoke plume and the results of plume source seeking experiments

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