Immersion and Invariance Based Adaptive Backstepping Control for Body-Fixed Hovering Over an Asteroid

Abstract

An adaptive control law is proposed in this paper for body-fixed hovering over an asteroid with an unknown gravity field and an unknown rotation rate. The unknown parameters and irregular shape of an asteroid make the hovering problem challenging. To facilitate the controller design, first, it is assumed that the required parameters are attainable, and then a body-fixed hovering controller is designed using the backstepping approach. Based on the immersion and invariance theory, an adaptive law is devised to estimate the unknown parameters in conjunction with the backstepping controller. To overcome the integrability obstacle arising in the adaptive law design, the regressor matrix is decomposed to two matrices: a Jacobian matrix and a non-Jacobian matrix, and an auxiliary matrix is introduced into the latter to form a Jacobian matrix. Then, a bounded function is employed to dynamically scale the estimate errors and its dynamics is elaborately constructed to stabilize the system. A Lyaponuv function is constructed for the entire closed-loop system to achieve the stabilization conditions by LaSalle's theorem, and the bounded scaling function much simplifies the analysis. Finally, numerical simulations demonstrate the effectiveness of the proposed control scheme. INDEX TERMS Adaptive backstepping, asteroid, hovering control, immersion and invariance.

WITHDRAWN: Composite Immersion and Invariance Based Adaptive Attitude Control of Asteroid-Orbiting Spacecraft in Elliptic Orbit

“…Recently, the immersion and invariance (I&I)-based methodology [26,27] was applied for position trajectory (orbit) control [28,29] and attitude control [30,31] of asteroid-orbiting spacecraft. The control laws of [26][27][28][29][30][31] belong to the class of noncertainty-equivalence adaptive (NCEA) control systems. The NCEA attitude control laws of [30] and [31] are for the control of Euler angles and quaternions, respectively.…”

Velocity-Free Saturated Control for Hovering Over an Asteroid With Disturbance Rejection

“…In this paper, the termd not only contains the uncertainty of asteroid's gravity, but also comprises other disturbances. Therefore,d is more helpful to the controller than the estimates of the gravity model parameters [7], [11], [18].…”

“…To assess the influence of the measurement noise of r on the ESO, the true position vector is corrupted with Gaussian noise with 0 m mean and 0.1 m standard deviation. The uncertainties and the disturbances [15], [18] are mimicked by…”

“…In [1], a controller with both control input saturation and its change rate saturation considered was developed for asteroid hovering by full use of the sliding mode theory. Zhang and Cai [18] developed an adaptive controller for the spacecraft hovering over an asteroid with unknown parameters. The control scheme deals with unknown parameters well, but it is hard to estimate uncertainties and disturbances in the design.…”

Adaptive interconnection and damping assignment passivity‐based control for linearly parameterized discrete‐time port controlled Hamiltonian systems via I&I approach

“…Recently in the literature, a new tool for designing asymptotically stabilizing and adaptive control laws for nonlinear systems called the Immersion and Invariance control method “I&I" has been proposed 19 . Indeed, in several papers, the I&I approach is used to design stabilizing controllers, 20‐22 while in some other works it is used to design adaptive controllers through establishing I&I parameter estimators 19,23‐36 . Nevertheless, there is not any adaptive I&I control study applied to the Hamiltonian systems.…”