Immersion-and Invariance-Based Adaptive Control of Asteroid-Orbiting and - Hovering Spacecraft

• Published in: The Journal of the astronautical sciences Vol. 66; no. 4; pp. 537 - 553
• Main Authors: Lee, Keum W., Singh, Sahjendra N.
• Format: Journal Article
• Language: English
• Published: New York Springer US 01.12.2019; Springer Nature B.V
• Subjects: Adaptive control; Aerospace Technology and Astronautics; Angular velocity; Asteroids; Control systems; Control systems design; Control theory; Engineering; Equivalence; EROS asteroid; Feedback control; Hovering; Invariance; Mathematical Applications in the Physical Sciences; Modular structures; Modular systems; Moments of inertia; Orbital mechanics; Parameter estimation; Parameter identification; Rotating bodies; Space Exploration and Astronautics; Space Sciences (including Extraterrestrial Physics; Spacecraft orbits; State variable; Steering; Submerging; Tracking errors; Design via immersion and invariance asteroid; Nonlinear adaptive control; Adaptive spacecraft control; Asteroid orbiting spacecraft; Noncertainty equivalence adaptive control; Hovering spacecraft control
• ISSN: 0021-9142; 2195-0571
• DOI: 10.1007/s40295-019-00163-6

The development of an immersion-and invariance-based adaptive state variable feedback control law for the closed orbit and hovering control of spacecraft in the vicinity of asteroids is the subject of this paper. The celestial body is assumed to be rotating with constant angular velocity about a fixed axis. Also, it is assumed that the mass and moments of inertia matrix of the asteroid, and the mass of the spacecraft are not known. The objective is to control the orbit of the spacecraft despite uncertainties in the system parameters. Based on the immersion and invariance theory, a noncertainty-equivalence adaptive control system is designed for steering the spacecraft along prescribe closed orbits or to fixed points for hovering control. The control system has a modular structure - consisting of an stabilizing control module and an parameter identifier. The control law is synthesized using filtered signals so as to circumvent the complexity of the immersion and immersion methodology. Unlike certainty-equivalence systems, the parameter estimates include judiciously selected nonlinear state-dependent algebraic functions and partial estimates derived from an integral update law. By the Lyapunov analysis, it is shown that the trajectory tracking error asymptotically converges to zero and all the signals in the closed-loop system are bounded. For illustration, numerical results are presented for control around 433 Eros and Ida asteroids. These results show that, despite uncertainties in the relative spacecraft dynamics, the adaptive law accomplishes closed orbit as well as hovering control.