# Franco Bernelli-ZazzeraPolitecnico di Milano | Polimi · Department of Aerospace Engineering

Franco Bernelli-Zazzera

PhD in Aerospace engineering

## About

169

Publications

39,151

Reads

**How we measure 'reads'**

A 'read' is counted each time someone views a publication summary (such as the title, abstract, and list of authors), clicks on a figure, or views or downloads the full-text. Learn more

2,331

Citations

Introduction

Additional affiliations

November 1992 - present

## Publications

Publications (169)

The objective of all universities in the Partnership of a European Group of Aeronautics and Space UniversitieS (PEGASUS) network is to offer highly relevant educational and research programmes and thereby attract the best students and scientists. Coordinated developments, exchange of students and staff and innovation are the basis on which these ob...

The paper presents the evolution and trends in the Master’s-level studies in aerospace engineering in Italy, looking at the past 20 years. In the year 2000, a major reform of the higher education in engineering took place in Italy, with the introduction of the so-called ‘Bologna system’ and the clear separation of Bachelor’s and Master’s degree stu...

The need for a safe and efficient integration of space vehicle operations into air traffic system to minimize the risk of impacts of spacecraft and aircraft and to sustain a steady air traffic is evident. This work provides a strategy toward more efficient management of uncontrolled re-entries by combining uncertainty propagation analysis with the...

No general rules exist for constellation design; instead, constellation designers have to consider various cost drivers in a trade-off way. This paper presents a systematic method for the design of continuous global coverage Walker and Street-of-Coverage constellations, by taking seven critical constellation properties (coverage, robustness, self-i...

This paper deals with the planar transfer problems (orbit raising and de-orbiting) for co-planar satellites with low-thrust propulsion, taking the self-induced collision avoidance into consideration at the mission design stage. A Blended Error-Correction steering law, with which the thrust direction changes in a self-adaptive way, is developed by b...

The ReDSHIFT (Revolutionary Design of Spacecraft through Holistic Integration of Future Technologies)
project was concluded on March 31, 2019. The 3-year project involved 13 European partners and was aimed
at studying, implementing and testing novel solutions for space debris mitigation. The focus was on passive
means to reduce the impact of Space...

In this study, a high-order state transition polynomial with time expansion (STP-T) method is developed to propagate an initial orbital state around its reference value to a variable final time based on the differential algebra (DA) technique. STP-T is a high-order Taylor polynomial of the final orbital state expanded around the reference initial s...

In recent years, Brushless DC (BLDC) motors have been gaining popularity as a solution for providing mechanical power, starting from low cost mobility solutions like the electric bikes, to high performance and high reliability aeronautical Electro-Mechanical Actuator (EMA). In this framework, the availability of fault detection tools suited to thes...

Recent developments in machine learning for anomaly detection make it possible to use spacecraft status telemetry to produce sophisticated system health monitoring applications, that can run autonomously on-board. Both archived and simulated data are used to train intelligent algorithms to automatically detect and classify anomalous time series of...

The H2020 ReDSHIFT project aims at finding passive means to mitigate the proliferation of space debris. This goal is pursued by a twofold research activity based on theoretical astrodynamics, computer simulations and the analysis of legal aspects of space debris, coupled with an experimental activity on advanced additive manufacturing (3D printing)...

The paper presents a possible roadmap for the definition of a European quality label for aerospace related higher education degrees. The proposal is the result of a two-years long Horizon 2020 project that has involved a great portion of the European stakeholders in aerospace: Universities, research centres, industries (both small and large) networ...

In this study, the problem of propagating an intial orbital state around its reference value to a variable final time is addressed. Based on the differential algebra (DA) technique, a high-order state transition polynomial with time expansion (STP-T) method is developed. The STP-T is a high-order Taylor approximation of the final orbital state expa...

This paper deals with the planar transfer problem (i.e. orbit raising and de-orbiting phases) for low Earth orbit coplanar satellites constellation. The objectives are to minimize the total time of transfer and to maximize the miss distance during these phases so as to minimize the collision hazard. A Blended Error-Correction (BEC) steering law, co...

A set of linearized relative motion equations of spacecraft flying on unperturbed elliptical orbits are specialized for particular cases, where the leader orbit is circular or equatorial. Based on these extended equations, we are able to analyze the relative motion regulation between a pair of spacecraft flying on arbitrary unperturbed orbits with...

The present work introduces a method to solve constrained nonlinear optimal control problems using statedependent coefficient factorization and Chebyshev polynomials. A recursive approximation technique known as approximating sequence of Riccati equations is used to replace the nonlinear problem by a sequence of linearquadratic and time-varying app...

This paper conducts a general study of the constellation geometries for two classical constellation patterns with circular orbits in the region of continuous global coverage. The significant properties for constellation design are identified and assessed with a parametrical approach. The comparison of two constellation patterns in terms of the seve...

This paper develops an adaptive linear uncertainty rejection control for attitude tracking based on the fusion of an adaptive quaternion feedbackcontrolandalinearextendedstateobserver(LESO).Theproposedmethodestimatesthe uncertainmomentsofinertia,environmentaldisturbancetorquesandRWfrictionandcompensates for them in each sampling period to ensure th...

This work deals with the space systems devoted to drilling and sampling of low-gravity extra-terrestrial soils and, in particular, with the cometary instrument SD2 (Sampler, Drill and Distribution subsystem) onboard the lander Philae of Rosetta mission, which was in charge to drill and sample the comet 67/P Churyumov-Gerasimenko. The behaviour of S...

The paper presents the results of a pilot project aiming at proposing a sector-specic quality system that can complement the existing national or European accreditation systems, providing added value to the internal and/or external quality assurance processes that are in place in most EU Universities. In particular, the proposed system implies a si...

Under dynamic conditions, the centroiding accuracy of the motion-blurred star image decreases and the number of identified stars reduces, which leads to the degradation of the attitude accuracy of the star sensor. To improve the attitude accuracy, a region-confined restoration method, which concentrates on the noise removal and signal to noise rati...

We analyse a concept for the detection of Potentially Hazardous Asteroids (PHAs) from a space-based network of telescopes on retrograde distant periodic orbits. Planar periodic orbits are designed in the Sun-Earth circular restricted three-body problem, starting from initial conditions in the Hill’s problem available from the literature. A family o...

Suboptimal solutions of nonlinear optimal control problems are addressed in the present work. These suboptimal approaches are known as Approximating Sequence of Riccati Equations (ASRE) methods. In the ASRE methods, the nonlinear problem is reduced to a sequence of linear-quadratic and time-varying approximating problems. For this purpose, the nonl...

In this chapter, a method to assess the occurrence of impacts between objects (either spacecraft or space debris) orbiting around the Earth is presented. The method is based on the computation of the minimum distance between two evolving orbits by means of a rigorous global optimizer. Analytical solutions of artificial satellite motion are utilized...

The lander Philae of the Rosetta mission landed on the surface of the comet 67 P/Churyumov–Gerasimenko on November 12, 2014. Among the specific subsystems and instruments carried on Philae, the sampling, drilling and distribution (SD2) subsystem had the role of providing in-situ operations devoted to soil drilling, sample collection, and their dist...

Current approaches to uncertainty propagation in astrodynamics mainly refer to linearized models or Monte Carlo simulations. Naive linear methods fail in nonlinear dynamics, whereas Monte Carlo simulations tend to be computationally intensive. Differential algebra has already proven to be an efficient compromise by replacing thousands of pointwise...

This paper presents a state-dependent method for solving nonlinear, control-affine, finite-time optimal control problems. The problem is set in a state-dependent form and solved as a sequence of time-varying linear-quadratic regulators, for which an approach based on state transition matrices has been developed. The novelty of the method consists o...

A study was conducted to demonstrate low-thrust minimum-fuel optimization in the circular restricted three-body problem. The study solved the problem of geostationary transfer orbit (GTO)-to-halo transfer for the first time. This result was achieved with an indirect approach and constant specific impulse engine. Thrust-to-mass ratios in agreement w...

Three methods for the computation of the probability of collision between two space objects are presented. These methods are based on the high order Taylor expansion of the time of closest approach (TCA) and distance of closest approach (DCA) of the two orbiting objects with respect to their initial conditions. The identification of close approache...

A method to design ballistic capture orbits in the real Solar System model is presented, so extending previous works using the planar restricted three-body problem. In this generalization a number of issues arise, which are treated in the present work. These involve reformulating the notion of stability in three-dimensions, managing a multi-dimensi...

A method to design ballistic capture orbits in the real Solar System model is presented, so extending previous works using the planar restricted three-body problem. In this generalization a number of issues arise, which are treated in the present work. These involve reformulating the notion of stability in three-dimensions, managing a multi-dimensi...

Rosetta is the third cornerstone mission of the European Space Agency scientific program "Horizon 2000". Rosetta will be the first spacecraft to orbit around a comet nucleus. It was launched in March 2004 and will reach the comet 67P/Churymov- Gerasimenko in 2014. A lander (Philae) will be released and land on the comet surface for in-situ investig...

In Rosetta lander Philae, the ability to increase the on-comet power production gives the chance to maintain the system alive, as well as the opportunity to accomplish scientific experiments during the Long Term Science (LTS) phase. This can be accomplished if the lander operates at solar incidence angles that maximize the total power produced by t...

This paper presents the results of a spacecraft
attitude control system based on magnetic actuators designed for
Low Earth Orbits. The control system is designed using a nonlinear
control technique based on the Approximating Sequence
of Riccati Equations (ASRE). The behavior of the satellite is discussed
under perturbations and model uncertainties....

The European Student Moon Orbiter (ESMO) was the first European student mission to the Moon and the fourth mission within ESA (European Space Agency) Education Satellite Programme. The purpose of this mission was to place the spacecraft on a polar orbit around the Moon, return new data by acquiring surface images of the Moon South Pole and test new...

Optimal feedback control is classically based on linear approximations,
whose accuracy drops off rapidly in highly nonlinear dynamics. Several
nonlinear optimal feedback control strategies have appeared in recent
years. Among them, differential algebraic techniques have been used to
tackle nonlinearities by expanding the solution of the optimal con...

Current approaches to uncertainty propagation in astrodynamics mainly refer to linearized models or Monte Carlo simulations. Naive linear methods fail in nonlinear dynamics, whereas Monte Carlo simulations tend to be computationally intensive. Differential algebra has already proven to be an efficient compromise by replacing thousands of pointwise...

The possibility of having collision between a satellite and a space debris or another satellite is becoming frequent. The amount of propellant is directly related to a satellite’s operational lifetime and revenue. Thus, collision avoidance maneuvers should be performed in the most efficient and effective manner possible. In this work the problem is...

A high order optimal control strategy is proposed in this work, based on
the use of differential algebraic techniques. In the frame of orbital
mechanics, differential algebra allows to represent, by high order
Taylor polynomials, the dependency of the spacecraft state on initial
conditions and environmental parameters. The resulting polynomials can...

This article proposes a concept for the detection of Potentially Hazardous Asteroids (PHAs) from a space-based network of telescopes placed on retrograde distant periodic orbits. Planar periodic orbits in the circular restricted threebody problem are designed, starting from initial conditions in the Hill problem available from the literature. Based...

During the last 40 years, the mass of the artificial objects in orbit increased quite steadily at the rate of about 145 metric tons annually, leading to a total tally of approximately 7000 metric tons. Now, most of the cross-sectional area and mass (97% in LEO) is concentrated in about 4600 intact objects, i.e. abandoned spacecraft and rocket bodie...

In this work we discuss issues related to the simulation of low power systems with hardware means. Simulating low power systems is a challenging task as the possible low-intensity, low-temperature environment, together with possible dust deposition and ice condensation, worsen not only the production of power but also make it difficult to predict i...

Planar Circular Restricted Three Body Problem, Hénon , Distant Periodic Orbits

In this chapter, differential algebra is used to globally optimize multi-gravity assist interplanetary trajectories with deep space maneuvers. A search space pruning procedure is adopted, and the trajectory design is decomposed into a sequence of sub-problems. As far as differential algebra is used, the objective function and the constraints are re...

A method to solve nonlinear optimal control problems is proposed in
this work. The method implements an approximating sequence of time-varying linear quadratic regulators that converge to the solution of the
original, nonlinear problem. Each subproblem is solved by manipulating
the state transition matrix of the state-costate dynamics. Hard, soft,...

A high order method to quickly assess the effect that uncertainties produce on orbital conjunctions through a numerical high-fidelity propagator is presented. In particular, the dependency of time and distance of closest approach to initial uncertainties on position and velocity of both objects involved in a conjunction is studied. The approach rel...

Continuous-thrust orbit transfers are designed by solving an optimal control problem that minimizes fuel consumption while satisfying mission constraints. The optimal control problem is usually solved in nominal conditions: at the design stage, the dynamics modeling is supposed to exactly represent the reality. An algorithm to include uncertain par...

In this paper a two-step approach to approximate the invariant manifolds in the circular restricted three-body problem is presented. Given any combination of the two scalars used to parameterize the manifolds, a two-dimensional interpolation is computed, and a successive correction is performed. A two-dimensional cubic convolution interpolation is...

This paper describes an efficient and robust optimal control algorithm for the design of fuel-optimal low-thrust interplanetary transfers. The solution is obtained with an indirect optimization approach, which has been selected to minimize the number of unknowns and to limit the computational effort. The optimization algorithm can deal with differe...

In this paper, a method for low-thrust trajectory optimization in n-body vector fields has been explored. In the context of direct transcription, a collocation method based on Gauss-Lobatto schemes has been implemented. With this method, arbitrary order integrations with variable grid points can be performed by only changing the parameters of a com...

In small-body missions, the determination of the landing site from Earth observations is typically unreliable, mostly due to the poor spatial resolution available with telescopes. The landing site is thus to be selected in the phase of close approach, where accurate information on the target body can be retrieved. In this paper a multidisciplinary...

The feasibility of a nonlinear state-dependent Riccati equation (SDRE) control design for relative position control of satellite formations is demonstrated. The design can include options for collision avoidance. Although there is no formal proof of the asymptotic stability of the closed-loop system, the necessary conditions for stability are verif...

This paper deals with the feasibility study of a mission in which the debris is removed by using a hybrid propulsion module as propulsion unit. Specifically, the engine is transferred from a servicing platform to the debris target by a robotic arm so to perform a controlled disposal. Hybrid rocket technology for de-orbiting applications is consider...

This paper presents two ways to transfer a spacecraft to distant periodic orbits in the Earth–Moon system. These unstable periodic orbits of the restricted three-body problem reveal a rich phase-portrait structure that can be used by space missions. Through the perspective of dynamical system theory, distant periodic orbits' invariant manifolds can...

Two-impulse trajectories as well as mixed invariant-manifold and low-thrust efficient transfers to the Moon are discussed. Exterior trajectories executing ballistic lunar capture are formalized through the definition of special attainable sets. The coupled restricted three-body problems approximation is used to design appropriate first guesses for...

A method for the computation of the probability of collision between two space object is pre- sent.ed. The method is based on the Taylor expansion of the time of close approach (TCA) and distance of close approach (DCA) of the two orbiting objects. These quantities are computed during the conjunction detection phase by means of a global optimizer b...

Optimal feedback control is classically based on linear approximations, whose accuracy drops off rapidly in highly nonlinear dynamics. Several nonlinear optimal feedback control strategies have appeared in recent years. Among them, differential algebraic techniques have already been used to tackle nonlinearities by expanding the solution of the opt...

A method to incorporate low-thrust propulsion into the invariant manifolds technique for space trajectory design is presented in this paper. Low-thrust propulsion is introduced by means of attainable sets that are used in conjunction with invariant manifolds to define first guess solutions in the restricted-three body problem. They are optimized in...

This work analyzes special Earth-Moon transfers that make use of both chemical and solar electric propulsion. A first high-thrust, low-Isp impulse is used to place the spacecraft into an exterior-like low-energy transfer to the Moon, possibly performing a lunar gravity assist. The subsequent use of low-thrust, high-Isp propulsion makes it possible...

Special Earth-Moon transfers that make use of both chemical and solar electric propulsion are investigated in this work. Two different types of launch are considered which inject the spacecraft into a GTO: shared launch with Ariane 5 ECA or dedicated launch with Soyuz 2.1b/Fregat M. Firstly three high-thrust, low-Isp impulses are used to place the...

A method to solve nonlinear optimal control problems is proposed in this work. The method implements an approximating sequence of time-varying linear quadratic regulators that converge to the solution of the original, nonlinear problem. Each sub-problem is solved by manipulating the state transition matrix of the state-costate dynamics. Hard, soft,...

This work introduces a full magnetic control scheme for satellite attitude control. It is particularized for a nadir pointing spacecraft. A new model which includes the satellite attitude dynamics and kinematics considering the magnetic field of the Earth is presented. The model is written in the State-Dependent-Coefficient (SDC) form. In addition,...

A method to incorporate low-thrust propulsion into the invariant manifolds technique is presented in this paper. The low-thrust propulsion is introduced by means of special attainable sets that are used in conjunction with invariant manifolds to define a first-guess solution. This is later optimized in a more refined model where an optimal control...