Attitude estimation using moment invariants

The problem of estimating the three-dimensional rotational parameters of a rigid body from its monocular image data has been considered using the method of moment invariants. Second- and third-order moment invariants are used to construct the feature vector for the scale and orientation independent identification of the camera view axis direction in the body-fixed reference frame. The camera rotation angle about the view axis is derived from second-order central moments. The relative attitude of the rigid body is then expressed in terms of quaternion parameters to model the outputs of a video sensor in attitude control simulations. Experimental results and simulation outputs are presented using the mathematical model of a spacecraft.

A Jacobian-Based Algorithm for Planning Attitude Maneuvers Using Forward and Reverse Rotations

Algorithms for planning quasistatic attitude maneuvers based on the Jacobian of the forward kinematic mapping of fully-reversed (FR) sequences of rotations are proposed in this paper. An FR sequence of rotations is a series of finite rotations that consists of initial rotations about the axes of a body-fixed coordinate frame and subsequent rotations that undo these initial rotations. Unlike the Jacobian of conventional systems such as a robot manipulator, the Jacobian of the system manipulated through FR rotations is a null matrix at the identity, which leads to a total breakdown of the traditional Jacobian formulation. Therefore, the Jacobian algorithm is reformulated and implemented so as to synthesize an FR sequence for a desired rotational displacement. The Jacobian-based algorithm presented in this paper identifies particular six-rotation FR sequences that synthesize desired orientations. We developed the single-step and the multiple-step Jacobian methods to accomplish a given task using six-rotation FR sequences. The single-step Jacobian method identifies a specific FR sequence for a given desired orientation and the multiple-step Jacobian algorithm synthesizes physically feasible FR rotations on an optimal path. A comparison with existing algorithms verifies the fast convergence ability of the Jacobian-based algorithm. Unlike closed-form solutions to the inverse kinematics problem, the Jacobian-based algorithm determines the most efficient FR sequence that yields a desired rotational displacement through a simple and inexpensive numerical calculation. The procedure presented here is useful for those motion planning problems wherein the Jacobian is singular or null.

Structured model-following neuro-adaptive design for attitude maneuver of rigid bodies

A new structured model-following adaptive approach is presented in this paper to achieve large attitude maneuvers of rigid bodies. First, a nominal controller is designed using the dynamic inversion philosophy. Next, a neuro- adaptive design is proposed to augment the nominal design in order to assure robust performance in the presence of parameter inaccuracies as well as unknown constant external disturbances. The structured approach proposed in this paper (where kinematic and dynamic equations are handled separately), reduces the complexity of the controller structure. From simulation studies, this adaptive controller is found to be very effective in assuring robust performance.

Generalised quaternion methods in conformal geometry

A new approach to Penrose's twistor algebra is given. It is based on the use of a generalised quaternion algebra for the translation of statements in projective five-space into equivalent statements in twistor (conformal spinor) space. The formalism leads toSO(4, 2)-covariant formulations of the Pauli-Kofink and Fierz relations among Dirac bilinears, and generalisations of these relations.

Star Camera Calibration Combined with Independent Spacecraft Attitude Determination

A methodology for determining spacecraft attitude and autonomously calibrating star camera, both independent of each other, is presented in this paper. Unlike most of the attitude determination algorithms where attitude of the satellite depend on the camera calibrating parameters (like principal point offset, focal length etc.), the proposed method has the advantage of computing spacecraft attitude independently of camera calibrating parameters except lens distortion. In the proposed method both attitude estimation and star camera calibration is done together independent of each other by directly utilizing the star coordinate in image plane and corresponding star vector in inertial coordinate frame. Satellite attitude, camera principal point offset, focal length (in pixel), lens distortion coefficient are found by a simple two step method. In the first step, all parameters (except lens distortion) are estimated using a closed-form solution based on a distortion free camera model. In the second step lens distortion coefficient is estimated by linear least squares method using the solution of the first step to be used in the camera model that incorporates distortion. These steps are applied in an iterative manner to refine the estimated parameters. The whole procedure is faster enough for onboard implementation.

Consistent quaternion interpolation for objective finite element approximation of geometrically exact beam

We explore an isoparametric interpolation of total quaternion for geometrically consistent, strain-objective and path-independent finite element solutions of the geometrically exact beam. This interpolation is a variant of the broader class known as slerp. The equivalence between the proposed interpolation and that of relative rotation is shown without any recourse to local bijection between quaternions and rotations. We show that, for a two-noded beam element, the use of relative rotation is not mandatory for attaining consistency cum objectivity and an appropriate interpolation of total rotation variables is sufficient. The interpolation of total quaternion, which is computationally more efficient than the one based on local rotations, converts nodal rotation vectors to quaternions and interpolates them in a manner consistent with the character of the rotation manifold. This interpolation, unlike the additive interpolation of total rotation, corresponds to a geodesic on the rotation manifold. For beam elements with more than two nodes, however, a consistent extension of the proposed quaternion interpolation is difficult. Alternatively, a quaternion-based procedure involving interpolation of relative rotations is proposed for such higher order elements. We also briefly discuss a strategy for the removal of possible singularity in the interpolation of quaternions, proposed in [I. Romero, The interpolation of rotations and its application to finite element models of geometrically exact rods, Comput. Mech. 34 (2004) 121–133]. The strain-objectivity and path-independence of solutions are justified theoretically and then demonstrated through numerical experiments. This study, being focused only on the interpolation of rotations, uses a standard finite element discretization, as adopted by Simo and Vu-Quoc [J.C. Simo, L. Vu-Quoc, A three-dimensional finite rod model part II: computational aspects, Comput. Methods Appl. Mech. Engrg. 58 (1986) 79–116]. The rotation update is achieved via quaternion multiplication followed by the extraction of the rotation vector. Nodal rotations are stored in terms of rotation vectors and no secondary storages are required.

A smart approach to precision attitude maneuvers of spacecrafts

A nonlinear adaptive approach is presented to achieve rest-to-rest attitude maneuvers for spacecrafts in the presence of parameter uncertainties and unknown disturbances. A nonlinear controller, designed on the principle of dynamic inversion achieves the goals for the nominal model but suffers performance degradation in the presence of off-nominal parameter values and unwanted inputs. To address this issue, a model-following neuro-adaptive control design is carried out by taking the help of neural networks. Due to the structured approach followed here, the adaptation is restricted to the momentum level equations.The adaptive technique presented is computationally nonintensive and hence can be implemented in real-time. Because of these features, this new approach is named as structured model-following adaptive real-time technique (SMART). From simulation studies, this SMART approach is found to be very effective in achieving precision attitude maneuvers in the presence of parameter uncertainties and unknown disturbances.

Simultaneous attitude control and trajectory tracking of a micro quadrotor: a SNAC aided nonlinear dynamic inversion approach

This paper presents an advanced single network adaptive critic (SNAC) aided nonlinear dynamic inversion (NDI) approach for simultaneous attitude control and trajectory tracking of a micro-quadrotor. Control of micro-quadrotors is a challenging problem due to its small size, strong coupling in pitch-yaw-roll and aerodynamic effects that often need to be ignored in the control design process to avoid mathematical complexities. In the proposed SNAC aided NDI approach, the gains of the dynamic inversion design are selected in such a way that the resulting controller behaves closely to a pre-synthesized SNAC controller for the output regulation problem. However, since SNAC is based on optimal control theory, it makes the dynamic inversion controller to operate near optimal and enhances its robustness property as well. More important, it retains two major benefits of dynamic inversion: (i) closed form expression of the controller and (ii) easy scalability to command tracking application even without any apriori knowledge of the reference command. Effectiveness of the proposed controller is demonstrated from six degree-of-freedom simulation studies of a micro-quadrotor. It has also been observed that the proposed SNAC aided NDI approach is more robust to modeling inaccuracies, as compared to the NDI controller designed independently from time domain specifications.

Autonomous Star Camera Calibration and Spacecraft Attitude Determination

This paper presents two methods of star camera calibration to determine camera calibrating parameters (like principal point, focal length etc) along with lens distortions (radial and decentering). First method works autonomously utilizing star coordinates in three consecutive image frames thus independent of star identification or biased attitude information. The parameters obtained in autonomous self-calibration technique helps to identify the imaged stars with the cataloged stars. Least Square based second method utilizes inertial star coordinates to determine satellite attitude and star camera parameters with lens radial distortion, both independent of each other. Camera parameters determined by the second method are more accurate than the first method of camera self calibration. Moreover, unlike most of the attitude determination algorithms where attitude of the satellite depend on the camera calibrating parameters, the second method has the advantage of computing spacecraft attitude independent of camera calibrating parameters except lens distortions (radial). Finally Kalman filter based sequential estimation scheme is employed to filter out the noise of the LS based estimation.

Stability of large flexible damped spacecraft modeled as elastic continua

Vibrational stability of a large flexible, structurally damped spacecraft subject to large rigid body rotations is analysed modelling the system as an elastic continuum. Using solution of rigid body attitude motion under torque free conditions and modal analysis, the vibrational equations are reduced to ordinary differential equations with time-varying coefficients. Stability analysis is carried out using Floquet theory and Sonin-Polya theorem. The cases of spinning and non-spinning spacecraft idealized as a flexible beam plate undergoing simple structural vibration are analysed in detail. The critical damping required for stabilization is shown to be a function of the spacecraft's inertia ratio and the level of disturbance.

Effects of solar radiation pressure and Aerodynamic forces on satelliteattitude Dynamics and their utilization for Control: a survey

The environmcnl exerts an important inJuence on the pefirmance of space systems. A brief rel'iew of mo.s/ of the studies, pre.~ented over the past eightem years, relating to the influence ar7d the possible utilization of thc solar radiation pressure &d aero&namic forces, with particular reference to attitude dynamics and control qf satellites is presented here. The semi-passive stabilizers employing rhese forces show p~qmise of long life, low power and economic sjsfems, which though slower in response, compare we1I wit11 the octiw coi~trollers. It is felt that mud more attention is necessary to the actual implema~tution of these ideas and devices: some of which me quite ingenious und unique.

Hall thruster sequencer using Intel-8051 microcontroller for ion thrust measurement

Hall thrusters, such as Stationary Plasma Thruster (SPT), have been widely used on board modern satellites placed in geo-synchronows orbits for reasons such as orbit maintenance, repositioning and attitude control. In order to study the performance of the stationary plasma thruster, the thrust produced by it has been measured, using a thrust balance with strain gauge sensors under vacuum conditions, by activating the thruster. This activation of thruster has been carried out by switching ON and switching OFF of the necessary power supplies and control of other feed system such as the propellant flow in a particular sequence. Hitherto, these operations were done manually in the required sequence. This paper reports the attempt made to automate the sequential operation of the power supplies and the necessary control valves of the feed system using Intel 8051 microcontroller. This automation has made thrust measurements easier and more sophisticated.

On the L2 stability of linear multidimensional time varying systems

This paper analyzes the L2 stability of solutions of systems with time-varying coefficients of the form [A + C(t)]x′ = [B + D(t)]x + u, where A, B, C, D are matrices. Following proof of a lemma, the main result is derived, according to which the system is L2 stable if the eigenvalues of the coefficient matrices are related in a simple way. A corollary of the theorem dealing with small periodic perturbations of constant coefficient systems is then proved. The paper concludes with two illustrative examples, both of which deal with the attitude dynamics of a rigid, axisymmetric, spinning satellite in an eccentric orbit, subject to gravity gradient torques.