Attitude and Phase Synchronization of Formation Flying Spacecraft: Lagrangian Approach

This article presents a unified synchronization framework with application to precision formation flying spacecraft. Central to the proposed innovation, in applying synchroniza- tion to both translational and rotational dynamics in the Lagrangian form, is the use of the distributed stability and performance analysis tool, called contraction analysis that yields exact nonlinear stability proofs. The proposed decentralized tracking control law synchronizes the attitude of an arbitrary number of spacecraft into a common time-varying trajectory with global exponential convergence. Moreover, a decentralized translational tracking control law based on phase synchronization is presented, thus enabling coupled translational and rotational maneuvers. While the translational dynamics can be adequately controlled by linear control laws, the proposed method permits highly nonlinear systems with nonlinearly coupled inertia matrices such as the attitude dynamics of space-craft whose large and rapid slew maneuvers justify the nonlinear control approach. The proposed method integrates both the trajectory tracking and synchronization problems in a single control framework

Particle Filtering for Sequential Spacecraft Attitude Estimation

A new spacecraft attitude estimation approach using particle filtering is derived. Based on sequential Monte Carlo simulation, the particle filter approximately represents the prob-ability distribution of the state vector with random samples. The filter formulation is based on the star camera measurements using a gyro-based or attitude dynamics-based model for attitude propagation. Modified Rodrigues parameters are used for attitude parametriza-tion when the sample mean and covariance of the attitude are computed. The ambiguity problem associated with the modified Rodrigues parameters in the mean and covariance computation is addressed as well. By using the uniform attitude probability distribution as the initial attitude distribution and using a gradually decreasing measurement variance in the computation of the importance weights, the particle filter based attitude estimator possesses global convergence properties. Simulation results indicate that the particular particle filter, known as bootstrap filter, with as many as 2000 particles is able to converge from arbitrary initial attitude error and initial gyro bias errors as large as 4500 degrees per hour per axis. I

Exact Analytic Solution for the Rotation of a Rigid Body having Spherical Ellipsoid of Inertia and Subjected to a Constant Torque

The exact analytic solution is introduced for the rotational motion of a rigid body having three equal principal moments of inertia and subjected to an external torque vector which is constant for an observer fixed with the body, and to arbitrary initial angular velocity. In the paper a parametrization of the rotation by three complex numbers is used. In particular, the rows of the rotation matrix are seen as elements of the unit sphere and projected, by stereographic projection, onto points on the complex plane. In this representation, the kinematic differential equation reduces to an equation of Riccati type, which is solved through appropriate choices of substitutions, thereby yielding an analytic solution in terms of confluent hypergeometric functions. The rotation matrix is recovered from the three complex rotation variables by inverse stereographic map. The results of a numerical experiment confirming the exactness of the analytic solution are reported. The newly found analytic solution is valid for any motion time length and rotation amplitude. The present paper adds a further element to the small set of special cases for which an exact solution of the rotational motion of a rigid body exists.Comment: "Errata Corridge Postprint" In particular: typos present in Eq. 28 of the Journal version are HERE correcte

ExoMars 2016 Schiaparelli Module Trajectory and Atmospheric Profiles Reconstruction: Analysis of the On-board Inertial and Radar Measurements

On 19th October 2016 Schiaparelli module of the ExoMars 2016 mission flew through the Mars atmosphere. After successful entry and descent under parachute, the module failed the last part of the descent and crashed on the Mars surface. Nevertheless the data transmitted in real time by Schiaparelli during the entry and descent, together with the entry state vector as initial condition, have been used to reconstruct both the trajectory and the profiles of atmospheric density, pressure and temperature along the traversed path. The available data-set is only a small sub-set of the whole data acquired by Schiaparelli, with a limited data rate (8 kbps) and a large gap during the entry because of the plasma blackout on the communications. This paper presents the work done by the AMELIA (Atmospheric Mars Entry and Landing Investigations and Analysis) team in the exploitation of the available inertial and radar data. First a reference trajectory is derived by direct integration of the inertial measurements and a strategy to overcome the entry data gap is proposed. First-order covariance analysis is used to estimate the uncertainties on all the derived parameters. Then a refined trajectory is computed incorporating the measurements provided by the on-board radar altimeter. The derived trajectory is consistent with the events reported in the telemetry and also with the impact point identified on the high-resolution images of the landing site. Finally, atmospheric profiles are computed tacking into account the aerodynamic properties of the module. Derived profiles result in good agreement with both atmospheric models and available remote sensing observations