Christian Bruccoleri

The Flower Constellations visualization and analysis tool

The Flower Constellations is a methodology to design satellite constellations characterized by compatible orbits with respect to an assigned given rotating reference frame. In this rotating reference frame all the satellites follow the same close-loop relative trajectory (repeated space tracks). A Flower Constellation is obtained by means of a suitable phasing mechanism that initially distributes the satellites in a subset of admissible positions. The interplay of the design parameters generates beautiful and intriguing axial-symmetric periodic dynamics. These dynamics allow us to explore a wide range of potential applications which include: telecommunications, deep space observation, global positioning systems, and allows us to quickly come up with highly complex satellite formations that no one even knew existed and, consequently, to propose new kind of space missions. These constellation schemes are dramatically innovative and could be hardly imagined, designed or explained without the aid of ad hoc visualization software. In this paper, we describe the software we developed to design the Flower Constellations with its current features and future improvements

MRAD: Modified rodrigues vector attitude determination

This paper presents a novel single-point optimal attitude determination algorithm in terms of the Modified Rodrigues Vector. The proposed technique has been derived from the Second Estimator of the Optimal Quaternion algorithm replacing the quaternion with the Modified Rodrigues Vector. Simulation results illustrate that the proposed attitude determination algorithm can be an efficient alternative over the quaternion-based algorithms in terms of computational efficiency for optimal attitude representation since the Modified Rodrigues Vector is a minimal attitude representation. The use of the Modified Rodrigues Vector has proven useful in the development of Extended Kalman Filters for attitude estimation, because it reduces the length of the state vector and there is no need to enforce the unit length constraint as for the quaternion.

Attitude and orbit error in n -dimensional spaces

This paper focuses on the theoretical aspects associated with the definition of error for Special Orthogonal and General Linear transformations, in any dimensional space, real or complex, including both Euclidean and Riemannian spaces. In particular, we show that the orbit error can be described by a complex number with phase representing the orbit orientation error and modulus describing the orbit shape error. We also show that the angle between two quaternions has a specific geometrical meaning. More specifically, the QR decomposition allows us to see a General Linear transformation as a combination of two subsequent effects: a dilation and a rigid rotation. This decomposition is also applied to the Lorentz transformations, highlighting the relativity effects of length change and coordinate axes bending.