George Vukovich

Global Finite-Time Attitude Tracking via Quaternion Feedback

Abstract This paper addresses the attitude tracking of a rigid body using a quaternion description. Global finite-time attitude controllers are designed with three types of measurements, namely, full states, attitude plus constant-biased angular velocity, and attitude only. In all three scenarios hybrid control techniques are utilized to overcome the well-known topological constraint on the attitude manifold, while coupled nonsmooth feedback inputs are designed via homogeneous theory to achieve finite-time stability. Specially, a finite-time bias observer is derived in the second scenario and a quaternion filter is constructed to provide damping in the absence of velocity feedback. The proposed methods ensure bounded control torques a priori and, in particular, include several existing attitude controllers as special cases.

Finite-time output-feedback position and attitude tracking of a rigid body

The position and attitude tracking of a rigid body without velocity measurements is addressed. Dual quaternions are used to describe the coupled rotational and translational motions of the rigid body, yielding compact forms of the kinematics and dynamics suitable for control law synthesis. An output-feedback pose (position and attitude) tracking controller is then designed by integrating techniques from passivity and homogeneity. More precisely, a passivity-enabling auxiliary system is proposed to provide necessary damping instead of velocity feedback and a homogeneous method is used to ensure finite-time convergence. The proposed controller guarantees uniform almost global finite-time stability of the closed-loop system and produces a well-defined vector field on the attitude configuration manifold, thus avoiding the unwinding phenomenon. Moreover, it can be split to obtain velocity-free controllers with finite-time convergence for the cases of translation-only or rotation-only control. Numerical examples verify the effectiveness of the proposed method.

Adaptive integral sliding mode control for spacecraft attitude tracking with actuator uncertainty

Abstract The attitude tracking of a rigid spacecraft with actuator uncertainties, such as actuator faults, alignment errors, and saturation constraints is examined. In addition, the unknown external disturbances and spacecraft inertia are also taken into consideration. A novel integral-terminal-sliding mode (ITSM), which is singularity free compared to traditional TSM, is designed such that the attitude tracking error converges to zero in finite time on the ITSM. An adaptive technique is then utilized to develop an adaptive ITSM controller (AITSMC), which achieves finite-time attitude tracking in the presence of some or all of the above uncertainties. Numerical examples are presented to demonstrate the effectiveness of the proposed method.

Attitude tracking of a rigid spacecraft using two internal torques

The attitude-tracking control of a rigid spacecraft using only two internal torques is addressed. First, a given reference trajectory is classified as feasible or unfeasible according to the preservation or violation of the momentum conservation law. The dynamics of the attitude-tracking error is then formulated on the attitude manifold SO(3) with the angular momentum of the actuators as inputs. Given the Lie group structure of SO(3), the transverse function approach is utilized to design an attitude-tracking law ensuring asymptotically ultimately bounded tracking error for any reference trajectory. For feasible reference trajectories satisfying certain persistence conditions, asymptotic tracking is achieved by constructing an asymptotically stable zero dynamics for the closed-loop system. To deliver control torques to the actuator command signals, steering laws are designed for two reaction wheels, two single-gimbal control moment gyros mounted in parallel, and one variable-speed control moment gyro, respectively. The resulting control law can be applied to a spacecraft with different kinds of momentum actuators but underactuated for tasks ranging from bounded tracking of a generic trajectory, three-axis earth pointing to line-of-sight pointing, etc. Numerical examples are presented to verify the effectiveness of the proposed method.

Adaptive finite-time control for spacecraft hovering over an asteroid

This paper presents a means of near asteroid hovering of a rigid spacecraft in the asteroid body-fixed frame with parameter variations and external disturbances. An adaptive finite-time control scheme is proposed, where the upper bounds of the parametric uncertainties and disturbances are not required for controller design. The detailed design principles and a rigorous stability analysis are provided. Finally, a body-fixed hovering maneuver is employed in numerical simulation to verify the effectiveness of the proposed strategy.

Robust Adaptive Unscented Kalman Filter for Spacecraft Attitude Estimation Using Quaternion Measurements

AbstractA robust unscented Kalman filter based on a multiplicative quaternion-error approach is proposed for high-precision spacecraft attitude estimation using quaternion measurements under measur...

A novel robust non-fragile control approach for a class of uncertain linear systems with input constraints

This paper addresses the non-fragile control problem for a class of uncertain linear systems subject to model uncertainty, controller perturbations, fault signals and input constraints. The controller to be designed is supposed to have additive gain perturbations. A novel state feedback controller is proposed based on the exact available expectation of a Bernoulli random variable, which is introduced to model the feature of the controller gain perturbation that randomly occurs. By using Lyapunov stability theory, new sufficient conditions are derived to design non-fragile controller for a class of uncertain linear systems considering input constraints. Compared with the existing non-fragile state feedback controller methods, the non-fragile property is fully considered to improve the tolerance of uncertainties in the controller, where the conservativeness can be reduced via the Bernoulli random variable. The effectiveness of the proposed control strategy is illustrated by two numerical examples.

Robust Adaptive Tracking of Rigid-Body Motion With Applications to Asteroid Proximity Operations

This paper addresses the coupled position- and attitude-tracking control of a rigid spacecraft in the proximity of asteroids, where multiple, complicated, unknown perturbations resulting from highly uncertain environment must be dealt with. Dual quaternions are used to formulate the tracking error dynamics in a compact manner for unified translational and rotational control law design. A robust adaptive control scheme is then developed from an originally model-dependent controller by introducing an adaptive algorithm to dynamically adjust the compensation for perturbations due to parametric uncertainties and external disturbances. The proposed method has a simple structure and is computationally efficient, since it requires no information about the unknown perturbations and involves only two adaptive variables. Numerical simulations for asteroid landing and hovering control are presented to verify the effectiveness of the proposed methods.

Comments on Finite-time consensus and collision avoidance control algorithms for multiple AUVs Automatica 49 (2013) 3359-3367

This correspondence points out an error in the proofs of Theorems 2 and 4 of Li and Wang (2013). Fortunately, this error does not affect the correctness of the main results.