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

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

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

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

The Isoline Tracking in Unknown Scalar Fields with Concentration Feedback

The isoline tracking of this work is concerned with the control design for a sensing vehicle to track a desired isoline of an unknown scalar field. To this end, we propose a simple PI-like controller for a Dubins vehicle in the GPS-denied environments. Our key idea lies in the design of a novel sliding surface based error in the standard PI controller. For the circular field, we show that the P-like controller can globally regulate the vehicle to the desired isoline with the steady-state error that can be arbitrarily reduced by increasing the P gain, and is eliminated by the PI-like controller. For any smoothing field, the P-like controller is able to achieve the local regulation. Then, it is extended to the cases of a single-integrator vehicle and a doubleintegrator vehicle, respectively. Finally, the effectiveness and advantages of our approaches are validated via simulations on the fixed-wing UAV and quadrotor simulators

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

Nonlocal Nonholonomic Source Seeking Despite Local Extrema

In this paper, we investigate the problem of source seeking with a unicycle in the presence of local extrema. Our study is motivated by the fact that most of the existing source seeking methods follow the gradient direction of the signal function and thus only lead to local convergence into a neighborhood of the nearest local extremum. So far, only a few studies present ideas on how to overcome local extrema in order to reach a global extremum. None of them apply to second-order (force- and torque-actuated) nonholonomic vehicles. We consider what is possibly the simplest conceivable algorithm for such vehicles, which employs a constant torque and a translational/surge force in proportion to an approximately differentiated measured signal. We show that the algorithm steers the unicycle through local extrema towards a global extremum. In contrast to the previous extremum-seeking studies, in our analysis we do not approximate the gradient of the objective function but of the objective function's local spatial average. Such a spatially averaged objective function is expected to have fewer critical points than the original objective function. Under suitable assumptions on the averaged objective function and on sufficiently strong translational damping, we show that the control law achieves practical uniform asymptotic stability and robustness to sufficiently weak measurement noise and disturbances to the force and torque inputs

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

Target capture and station keeping of fixed speed vehicles without self-location information

The final publication is available at Elsevier via https://dx.doi.org/10.1016/j.ejcon.2018.06.003 © 2018. This manuscript version is made available under the CC-BY-NC-ND 4.0 license https://creativecommons.org/licenses/by-nc-nd/4.0/Target capture and station keeping problems for an autonomous vehicle agent have been studied in the literature for the cases where the position of the agent can be measured. Station keeping refers to moving the agent to a target whose distances are predefined from a set of beacons that can be stations or other agents. Here we study the target capture and station keeping problems for a nonholonomic vehicle agent that does not know its location and can measure only distances to the target (to the beacons for station keeping). This sensing limitation corresponds to consideration of unavailability of GPS and odometry in practical UAV settings. For each of the target capture and station keeping problems, we propose a control algorithm that uses only agent-target (agent-beacon for station keeping) range and range rate information. We show the stability and convergence properties of our control algorithms. We verified the performance of our control algorithms by simulations and real time experiments on a ground robot. Our algorithms captured the target in finite time in the experiments. Therefore, our algorithms are efficient in scenarios where GPS is unavailable or target identification by vision algorithms is unreliable but continuous agent-target range measurements are available.King Abdullah University of Science and Technolog