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.

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.

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.

Origin of magnetism and trend in T-c in Cr-based double perovskites: Interplay of two driving mechanisms

Hamiltonian constructed in a first principles manner, we explored the origin of magnetism and the T-c trend in Cr-based double perovskite series, Sr2CrB'O-6 (B' = W/Re/Os). Our study shows that the apparently puzzling T-c trend in Sr2CrB'O-6 (B' = W/Re/Os) series can be understood in terms of the interplay of the hybridization driven mechanism and the superexchange mechanism.

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.

Construction of equivalent circuit of a transformer winding from driving-point impedance function - analytical approach

Analytical solution is presented to convert a given driving-point impedance function (in s-domain) into a physically realisable ladder network with inductive coupling between any two sections and losses considered. The number of sections in the ladder network can vary, but its topology is assumed fixed. A study of the coefficients of the numerator and denominator polynomials of the driving-point impedance function of the ladder network, for increasing number of sections, led to the identification of certain coefficients, which exhibit very special properties. Generalised expressions for these specific coefficients have also been derived. Exploiting their properties, it is demonstrated that the synthesis method essentially turns out to be an exercise of solving a set of linear, simultaneous, algebraic equations, whose solution directly yields the ladder network elements. The proposed solution is novel, simple and guarantees a unique network. Presently, the formulation can synthesise a unique ladder network up to six sections.

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.

Dynamical localization in a chain of hard core bosons under periodic driving

We study the dynamics of a one-dimensional lattice model of hard core bosons which is initially in a superfluid phase with a current being induced by applying a twist at the boundary. Subsequently, the twist is removed, and the system is subjected to periodic delta-function kicks in the staggered on-site potential. We present analytical expressions for the current and work done in the limit of an infinite number of kicks. Using these, we show that the current (work done) exhibits a number of dips (peaks) as a function of the driving frequency and eventually saturates to zero (a finite value) in the limit of large frequency. The vanishing of the current (and the saturation of the work done) can be attributed to a dynamic localization of the hard core bosons occurring as a consequence of the periodic driving. Remarkably, we show that for some specific values of the driving amplitude, the localization occurs for any value of the driving frequency. Moreover, starting from a half-filled lattice of hard core bosons with the particles localized in the central region, we show that the spreading of the particles occurs in a light-cone-like region with a group velocity that vanishes when the system is dynamically localized.

Driving force of water entry into hydrophobic channels of carbon nanotubes: entropy or energy?

Spontaneous entry of water molecules inside single-wall carbon nanotubes (SWCNTs) has been confirmed by both simulations and experiments. Using molecular dynamics simulations, we have studied the thermodynamics of filling of a (6,6) carbon nanotube in a temperature range from 273 to 353K and with different strengths of the nanotube-water interaction. From explicit energy and entropy calculations using the two-phase thermodynamics method, we have presented a thermodynamic understanding of the filling behaviour of a nanotube. We show that both the energy and the entropy of transfer decrease with increasing temperature. On the other hand, scaling down the attractive part of the carbon-oxygen interaction results in increased energy of transfer while the entropy of transfer increases slowly with decreasing the interaction strength. Our results indicate that both energy and entropy favour water entry into (6,6) SWCNTs. Our results are compared with those of several recent studies of water entry into carbon nanotubes.

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.