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.

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.