Giacomo Curzi

Some of the most common metrics for collision risk assessment are the probability of collision, miss distance in Mahalanobis space, and confidence intervals. Sometimes they are used in combination; for example, the miss distance is used as a prescreening method to identify potentially hazardous conjunctions; other times they are used as alternative means; that is, covariance ellipse overlapping checks are employed instead of computing the probability of collision. In this work, we show that the three risk indexes are intimately connected once a suitable distance is defined. We argue that Mahalanobis miss distance is a proper metric only when the sigma-normalized hard-body size is negligible; we thus investigate the minimum Mahalanobis distance between the hard-body circle and the combined position covariance as an alternative. Its computation is fully analytic, as the most complex operation is finding the roots of a quartic polynomial. When multiplied by the sigma-normalized hard-body radius, such distance provides an upper bound to the collision probability. When used to scale the covariance matrix, it provides the largest confidence interval supporting a noncollision event. Finally, when adopted as an actionable threshold, analytical bounds on the probability of miss detection and of false alarms can be computed.

Constellations of satellites are being proposed in large numbers; most of them are expected to be in orbit within the next decade. They will provide communication to unserved and underserved communities, enable global monitoring of Earth and enhance space observation. Mostly enabled by technology miniaturization, satellite constellations require a coordinated effort to face the technological limits in spacecraft operations and space traffic. At the moment in fact, no cost-effective infrastructure is available to withstand coordinated flight of large fleets of satellites. In order for large constellations to be sustainable, there is the need to efficiently integrate and use them in the current space framework. This review paper provides an overview of the available experience in constellation operations and statistical trends about upcoming constellations at the moment of writing. It highlights also the tools most often proposed in the analyzed works to overcome constellation management issues, such as applications of machine learning/artificial intelligence and resource/infrastructure sharing. As such, it is intended to be a useful resource for both identifying emerging trends in satellite constellations, and enabling technologies still requiring substantial development efforts.

To enable a reliable verification of attitude determination and control systems for nanosatellites, the environment of low Earth orbits with almost disturbance-free rotational dynamics must be simulated. This work describes the design solutions adopted for developing a dynamic nanosatellite attitude simulator testbed at the University of Bologna. The facility integrates several subsystems, including: (i) an air-bearing three degree of freedom platform, with automatic balancing system, (ii) a Helmholtz cage for geomagnetic field simulation, (iii) a Sun simulator, and (iv) a metrology vision system for ground-truth attitude generation. Apart from the commercial off-the-shelf Helmholtz cage, the other subsystems required substantial development efforts. The main purpose of this manuscript is to offer some cost-effective solutions for their in-house development, and to show through experimental verification that adequate performances can be achieved. The proposed approach may thus be preferred to the procurement of turn-key solutions, when required by budget constraints. The main outcome of the commissioning phase of the facility are: a residual disturbance torque affecting the air bearing platform of less than 5 × 10⁻⁵ Nm, an attitude determination rms accuracy of the vision system of 10 arcmin, and divergence of the Sun simulator light beam of less than 0.5° in a 35 cm diameter area.