3-D Velocity Regulation for Nonholonomic Source Seeking Without Position Measurement

We consider a three-dimensional problem of steering a nonholonomic vehicle to seek an unknown source of a spatially distributed signal field without any position measurement. In the literature, there exists an extremum seeking-based strategy under a constant forward velocity and tunable pitch and yaw velocities. Obviously, the vehicle with a constant forward velocity may exhibit certain overshoots in the seeking process and can not slow down even it approaches the source. To resolve this undesired behavior, this paper proposes a regulation strategy for the forward velocity along with the pitch and yaw velocities. Under such a strategy, the vehicle slows down near the source and stays within a small area as if it comes to a full stop, and controllers for angular velocities become succinct. We prove the local exponential convergence via the averaging technique. Finally, the theoretical results are illustrated with simulations.Comment: submitted to IEEE TCST;12 pages, 10 figure

Newton Nonholonomic Source Seeking for Distance-Dependent Maps

The topics of source seeking and Newton-based extremum seeking have flourished, independently, but never combined. We present the first Newton-based source seeking algorithm. The algorithm employs forward velocity tuning, as in the very first source seeker for the unicycle, and incorporates an additional Riccati filter for inverting the Hessian inverse and feeding it into the demodulation signal. Using second-order Lie bracket averaging, we prove convergence to the source at a rate that is independent of the unknown Hessian of the map. The result is semiglobal and practical, for a map that is quadratic in the distance from the source. The paper presents a theory and simulations, which show advantage of the Newton-based over the gradient-based source seeking

Prescribed-Time Seeking of a Repulsive Source by Unicycle Angular Velocity Tuning

All the existing source seeking algorithms for unicycle models in GPS-denied settings guarantee at best an exponential rate of convergence over an infinite interval. Using the recently introduced time-varying feedback tools for prescribed-time stabilization, we achieve source seeking in prescribed time, i.e., the convergence to the source, without the measurements of the position and velocity of the unicycle, in as short a time as the user desires, starting from an arbitrary distance from the source. The convergence is established using a singularly perturbed version of the Lie bracket averaging method, combined with time dilation and time contraction operations. The algorithm is robust, provably, even to an arbitrarily strong gradient-dependent repulsive velocity drift emanating from the source

Particle Swarm Optimization Based Source Seeking

Signal source seeking using autonomous vehicles is a complex problem. The complexity increases manifold when signal intensities captured by physical sensors onboard are noisy and unreliable. Added to the fact that signal strength decays with distance, noisy environments make it extremely difficult to describe and model a decay function. This paper addresses our work with seeking maximum signal strength in a continuous electromagnetic signal source with mobile robots, using Particle Swarm Optimization (PSO). A one to one correspondence with swarm members in a PSO and physical Mobile robots is established and the positions of the robots are iteratively updated as the PSO algorithm proceeds forward. Since physical robots are responsive to swarm position updates, modifications were required to implement the interaction between real robots and the PSO algorithm. The development of modifications necessary to implement PSO on mobile robots, and strategies to adapt to real life environments such as obstacles and collision objects are presented in this paper. Our findings are also validated using experimental testbeds.Comment: 13 pages, 12 figure

A survey on fractional order control techniques for unmanned aerial and ground vehicles

In recent years, numerous applications of science and engineering for modeling and control of unmanned aerial vehicles (UAVs) and unmanned ground vehicles (UGVs) systems based on fractional calculus have been realized. The extra fractional order derivative terms allow to optimizing the performance of the systems. The review presented in this paper focuses on the control problems of the UAVs and UGVs that have been addressed by the fractional order techniques over the last decade

Planar Cooperative Extremum Seeking with Guaranteed Convergence Using A Three-Robot Formation

In this paper, a combined formation acquisition and cooperative extremum seeking control scheme is proposed for a team of three robots moving on a plane. The extremum seeking task is to find the maximizer of an unknown two-dimensional function on the plane. The function represents the signal strength field due to a source located at maximizer, and is assumed to be locally concave around maximizer and monotonically decreasing in distance to the source location. Taylor expansions of the field function at the location of a particular lead robot and the maximizer are used together with a gradient estimator based on signal strength measurements of the robots to design and analyze the proposed control scheme. The proposed scheme is proven to exponentially and simultaneously (i) acquire the specified geometric formation and (ii) drive the lead robot to a specified neighborhood disk around maximizer, whose radius depends on the specified desired formation size as well as the norm bounds of the Hessian of the field function. The performance of the proposed control scheme is evaluated using a set of simulation experiments.Comment: Presented at the 2018 IEEE Conference on Decision and Control (CDC), Miami Beach, FL, US

Source Seeking Control of Unicycle Robots with 3-D-Printed Flexible Piezoresistive Sensors

We present the design and experimental validation of source seeking control algorithms for a unicycle mobile robot that is equipped with novel 3D-printed flexible graphene-based piezoresistive airflow sensors. Based solely on a local gradient measurement from the airflow sensors, we propose and analyze a projected gradient ascent algorithm to solve the source seeking problem. In the case of partial sensor failure, we propose a combination of Extremum-Seeking Control with our projected gradient ascent algorithm. For both control laws, we prove the asymptotic convergence of the robot to the source. Numerical simulations were performed to validate the algorithms and experimental validations are presented to demonstrate the efficacy of the proposed methods