Recursive Averaging With Application to Bio-Inspired 3-D Source Seeking

Practical prescribed-time seeking of a repulsive source by unicycle angular velocity tuning

“…We prove semi-global practical stability properties and confirm our theoretical results with simulations. The need and value of second-order averaging in source seeking was recently revealed in the award-winning conference paper [2] and is affirmed by the present paper.…”

“…For this, we prove that the origin of subsystem (38b) and (38c) is GUAS. Then, we show that (38a) is input-to-state stable (ISS) 2 with respect to z and d. Thus, we can conclude that the origin of ( 38) is GUAS. Inspired by [4] and [12], consider a Lyapunov function for subsystem (38b) and (38c) as…”

“…Using the fact that z⊤ P z ≤ λ min (P ) |z| 2 and similarly z⊤ Gz ≤ ∥G∥ |z| 2 , where λ min (P ) is the smallest eigenvalue of the positive definite matrix P and ∥G∥ is the matrix norm of (42), we can derive an upper bound for (46) as…”

“…Several years prior to the efforts in Newton-based ES, numerous source seeking algorithms began to emerge [1], [3], [6], [15], [16], [23]- [27], [29]- [31], where the primary focus was designing algorithms that ensure convergence to the source using a (kinematically) underactuated, non-holonomic unicycle, with limited attention given to the convergence speed. This issue of convergence speed was somewhat addressed in our work [28], with an algorithm that ensures convergence to the source in prescribed time, despite the influence the unknown Hessian, by introducing time-varying gains.…”

Attitude optimization by extremum seeking for rigid bodies actuated by internal rotors only

“…Nevertheless, many studies on source seeking assume a first-order kinematic vehicle model, which means that the velocities can be controlled directly through the inputs. For instance, first-order kinematic vehicle models have been used to describe the motion of wheeled robots, 8,9 drones, 10,11 underwater vehicles, 12,13 and satellites. 14 For a mechanical system, instantaneous changes of the velocity to a prescribed value cannot be realized with bounded forces because of the system's inertia.…”