Nonholonomic Source Seeking With Tuning of Angular Velocity

• Published in: IEEE transactions on automatic control Vol. 54; no. 4; pp. 717 - 731
• Main Authors: Cochran, J., Krstic, M.
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01-04-2009; Institute of Electrical and Electronics Engineers; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Aerospace engineering; Aircraft; Analytical models; Angular velocity; Angular velocity control; Applied sciences; Autonomous; Computer science; control theory; systems; Control system synthesis; Control theory. Systems; Convergence; Detection; Exact sciences and technology; Marine vehicles; Mathematical models; Mobile robots; Motion control; Nonholonomic unicycle; Remotely operated vehicles; Robotics; Scalars; Strategy; Studies; Tuning; Vehicles; Autonomous system; Averaging method; Extreme search; Nonholonomic unicycle; Orbit; Moving robot; Local theory; Control synthesis; Non holonomic system; Attractor; Modeling; Unmanned aerial vehicle; Position measurement; Angular velocity; Numerical convergence; Non local theory
• ISSN: 0018-9286; 1558-2523
• DOI: 10.1109/TAC.2009.2014927

We consider the problem of seeking the source of a scalar signal using an autonomous vehicle modeled as the nonholonomic unicycle. The vehicle does not have the capability of sensing its position or the position of the source but is capable of sensing the scalar signal originating from the source. The signal field is assumed to decay away from the position of the source but the vehicle does not have the knowledge of the functional form of the field. We employ extremum seeking to steer the vehicle to the source. Our control strategy keeps the forward velocity constant and tunes the angular velocity, a setting suitable for most autonomous vehicles, including aerial ones. Because of the constant forward velocity constraint, after it has converged near the source, the vehicle exhibits extremely interesting and complex motions. Using averaging theory, we prove local exponential convergence to an ldquoorbit-likerdquo attractor around the source. We also present a thorough analysis of non-local behaviors and attractors that the vehicle can exhibit near the source. The richness and complexity of behaviors makes only some of them amenable to analysis, whereas others are illustrated through a carefully laid out simulation study.