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- Danil Ivanov

# Danil IvanovRussian Academy of Sciences | RAS · Attitude and Motion Control

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Introduction

Area of professional interest comprises spaceflight dynamics, attitude motion, attitude determination, satellite formation flying control algorithms, computer and laboratory methods of simulation of attitude dynamics and formation flying motion.

Research Experience

Jun 2010

Education

Sep 2004 - Jun 2010

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Research Items (43)

The paper is devoted to the problem of nanosatellites swarm deployment immediately after their separation from the launcher. Some error in the ejection velocity during the launch is inevitable. It leads to a slightly different orbital period of the satellites, so they gradually move apart along the orbit, and the relative trajectories become unlimited. The decentralized differential drag-based control is applied to the problem of the swarm forming. It is assumed that each satellite is provided with information about the relative motion of the other satellites within a certain communication area. The purpose of the developed control algorithm is to eliminate the relative drift between neighbouring satellites. The separation effect which occurs when the swarm is divided into several independent groups is studied. This effect depends on size of the communication area, on the number of the communicating satellites and the initial conditions. The boundary values of these parameters for twenty, as an example, 3U CubeSats in the swarm are investigated. The influence of the J 2 harmonic and uncertainties in the atmosphere density is studied.

The paper considers a problem of satellites formation flying construction immediately after their launch. During the separation from the launcher some error in the ejection velocity is inevitable. It results in a slightly different orbital period of the satellites, so they will gradually move apart along the orbit and the relative trajectories become unbounded. The differential drag-based control is considered. The attitude control of the satellite is implemented by magnetorquers.

The flight results of the Technological NanoSatellite TNS-0 #2 is presented in the paper. The main feature of the TNS-0 nanosatellite series is to use the GlobalStar communication system. The details on the communication sessions are given in the paper. The main purpose of the nanosatellite TNS-0 № 2 is to obtain the flight qualification of the instruments and sensors installed onboard. The results of the attitude motion determination using magnetometer and sun sensors data during the mission are presented in the paper. Using the measurements of GPS/GLONASS receiver the TNS-0 #2 orbit degradation in the dense layers of the atmosphere is tracked.

Satellite formation flying promises a breakthrough in space exploration and scintific experiments. It is necessary to control the relative motion of the satellites flying at short relative distances. Due to the wide distribution of nano and microsatellites in the formation flying missions the control approaches without fuel consumtion are of special interest. Electromagnetic, aerodynamic forces, momentum exchange concept etc. can be utilized for formation flying construction and maintenance. The talk covers the description of the well-known and new-developed control algorithms. The implementation problems of different control concepts is disscussed. The features of the satellite swarm decentralized control is considered.

The flight results of the Technological NanoSatellite TNS-0 #2 is presented in the paper. The main feature of the TNS-0 nanosatellite series is to use the Globalstar communication system. The details on the communication sessions are given in the paper. The main purpose of the nanosatellite TNS-0 № 2 is to obtain the flight qualification of the instruments and sensors installed onboard. The results of the attitude motion determination using magnetometer and sun sensors data during the mission are presented in the paper. Using the measurements of GPS/GLONASS receiver the TNS-0 #2 orbit degradation in the dense layers of the atmosphere is tracked.

The paper is devoted to the study of decentralized control using differential lift and drag for the construction and maintenance of the tetrahedral configuration. The most popular in the class of nanosatellites 3U CubeSats are considered. They have a suitable form-factor which let the cross-sectional area of satellites relative to the incoming airflow vary by a factor 3 depending on the attitude. The satellites are assumed to be subsequently deployed from the launcher. Each satellite is equipped with a reaction wheel-based attitude control system which allows to provide the required angular motion. Each satellite has also information about the relative state vector of all neighboring satellites provided by the inter-satellite communication or sensors of relative motion determination system. In this paper a decentralized control algorithm is developed which ensures the tracking of the relative reference trajectory. Due to this reference trajectory the satellites moves at the vertices of the tetrahedron. The possibility of constructing a tetrahedral configuration after deployment of the satellites depending on the initial conditions is studied.

This work utilizes magnetorquers as the sole attitude control system unit used both for control and determination. An algorithm of the three-axis attitude determination is proposed. It utilizes only measurements of the electromotive force induced in magnetorquers. The extended Kalman filter is applied. The paper studies the accuracy of the developed algorithm, its dependence on the angular motion of the satellite and the measurement noise. Three axis attitude is achieved with the same magnetorquers using the Lyapunov control approach.

The paper proposes a two stage algorithm for autonomous relative motion determination of noncooperative and unknown object flying in space. The algorithm is based on image processing and can be applied to motion determination of space debris with unknown geometry and dynamical characteristics. The first stage of the algorithm is aimed to form a database of possible reference points of the object during continuous observation. Tensor of inertia, initial velocity and angular velocity of the object are also estimated. Then these parameters are used in the second stage of the algorithm to determine the relative motion in real-time. The algorithm is studied numerically and tested using the video of the Chibis-M microsatellite separation.

An algorithm of satellite formation flying control in the Low-Earth Orbit using the aerody-namic force is considered. A simple model of the aerodynamic force that takes into account the lift component of the force is proposed. It allows us to calculate the satellite attitude relative to the incoming flow that provides the required aerodynamic force. For the given model parameters the acceptable control region is obtained. The relative motion control algorithm based on the Lin-ear-Quadratic Regulator is considered. The technique for the algorithm parameters determination is suggested. Numerical study of the controlled motion is carried out. The simulation takes into account the second harmonic of the Earth gravitational field and the inaccuracy of the atmospheric density model.

CubeSats are often designed and manufactured in a very tight time schedule. However, no one expects to have only one month for the preparation of a mission long before abandoned by another team. This contribution focuses on the rapid attitude control decisions necessary to ensure the CubeSat satellite communication via Iridium constellation. Having magnetorquers, magnetometer and very limited power budget, the only available addition to the system becomes a constant magnet. This forces the satellite to track the geomagnetic induction vector. The satellite acquires promising Iridium orbits visibility while easing burden on the magnetorquers in an energy saving endeavor. Some relevant analysis spotlights, experiments and reasoning are provided.

A motion control algorithm for microsatellite mock-up with flexible rods docking with noncooperative target on the air table is proposed in the paper. A linear motion model of the mock-up with flexible rods is developed. The state vector of the mock-up body and flexible rod is estimated by the extended Kalman Filter using the visual-based navigation system measurements. The results of the experimental study of the developed algorithms are presented.

- Jan 2018

A description of a COSMOS laboratory facility for the controlled motion simulation of microsatellites created in Keldysh Institute of Applied Mathematics of the Russian Academy of Sciences and the results of its application to the simulation of the control algorithms are presented. The laboratory facility consists of an aerodynamic table and microsatellite mock-ups. Due to the air cushion between the table surface and the disks on which the mock-ups are installed, free motion with three degrees of freedom becomes possible: two translational and one rotational. A review of the simulator’s international analogues has revealed its advantages and disadvantages. A motion determination algorithm based on video processing is described and its accuracy is studied. The results of the investigation of perturbations acting on the mock-ups on the aerodynamic table are presented. The performance of the control algorithms is demonstrated.

In this paper the facility for the simulation of satellite motion based on planar air-bearing deweighting is considered. The air bearing provides almost frictionless horizontal motion of the small satellite mock-ups. Due to the presence of gravitational and air flow disturbances the motion is far from rectilinear and uniform. This paper is devoted to the determination of these disturbances.

- Sep 2017
- Proceedings of the International Astronautical Congress, IAC

The paper considers a problem of 3U CubeSats swarm construction right after their separation from the bus launcher. During the separation of the satellites, some error in the ejection velocity is inevitable. It results in a slightly different orbital period of the satellites, so they will gradually fly apart along the orbit and the relative trajectories will be unbounded. Aerodynamic force acting on the satellite depends on its attitude. Therefore, it is possible to control relative motion without spending any propellant. Each satellite has information about relative motion of satellites inside certain communication area. Purpose of the control is to eliminate the relative drift between neighbour satellites. The paper develops such decentralized control algorithm. Effect of clustering-when the swarm is divided into several groups-is studied. This effect depends on size of the communication area, initial conditions and control parameters. Boundary values of these parameters in case of ten 3U CubeSats are investigated.

- Aug 2017
- 3rd IAA Conference on Dynamics and Control of Space Systems, Moscow, 30 May - 1st June 2017

The paper proposes an algorithm of three-axis attitude determination using measurements of electromotive force (EMF) induced in magnetic torquers. The extended Kalman filter is applied. The paper studies the accuracy of the developed algorithm, its dependence on angular motion of the satellite and measurement noise.

- Aug 2017
- 9th International Workshop on Satellite Constellations and Formation Flying, University of Colorado Boulder June 19-21, 2017

A motion control algorithm for mock-up with flexible booms docking with noncooperative target on the air table is proposed in the paper. The state vector of the mock-up body and flexible boom is estimated by the extended Kalman Filter using the visual-based navigation system measurements. The results of the experimental study of the developed algorithms are presented.

Methods for dynamic parameters identification and vibrations estimation of large spacecraft with flexible structures are reviewed. Different approaches to the structural deviation determination and to the vibration frequency identification by processing measurements from the onboard sensors are compared. Measuring devices and sensors for the motion estimation of large nonrigid structures are reviewed.

Attitude motion of a satellite equipped with magnetic control system is considered. System comprises of three magnetorquers and one three-axis magnetometer. Satellite is stabilized in orbital reference frame using PD controller and extended Kalman filter. Three-axis attitude is analyzed numerically with advanced assumptions: inertia tensor uncertainty, disturbances of unknown nature, magnetometer errors are taken into account. Stabilization and determination accuracy dependence on orbit inclination is studied.

В книге рассматриваются магнитные системы ориентации, в первую очередь – для малых спутников. Приводится результаты исследования динамики спутников, оснащенных постоянным магнитом, гистерезисными стержнями, сферическим магнитным демпфером, магнитными катушками и дополнительными исполнительными элементами – тангажным маховиком, гравитационной штангой. Аналитические исследования, проведенные с помощью асимптотических методов, теории устойчивости, теории Флоке дополняются численными расчетами, результатами лабораторных и летных испытаний.

Three-axis magnetic control in orbital reference frame is considered. Magnetorquers are the only actuators and gravitational torque is the only disturbance source. Full attitude knowledge is assumed. Control is constructed on the basis of PD-controller. Stability is analyzed using Floquet theory. Optimal in terms of degree of stability control parameters are found using this approach. These parameters may be further adjusted using numerical simulation. Results for three typical satellites are provided. Numerical example with Kalman filter implementation and additional disturbance sources is provided.

An analytical approach to study of attitude determination algorithms is considered. The approach is applicable for quasi-stationary motion determination. It is based on filter post-convergence computation of the Kalman filter covariance matrix and allows one to estimate the influence of unaccounted perturbations on motion determination accuracy. The dependence of attitude determination accuracy on filter parameters and perturbations is obtained. The proposed method of improving the Kalman filter performance is applied on board a microsatellite of the TabletSat series.

Novel approach for formation flying relative motion control is proposed and studied. It is based on a mass exchange between satellites. A certain mass is separated from one satellite in a given direction with a given velocity. It impacts absolutely inelastically another satellite to impart a pulse. The mass exchange causes desired change in a relative motion trajectory of both satellites. The feasibility of such a control approach is shown in the paper. The Hill-Clohessy-Wiltshire equations are used for relative motion representation. The resulting trajectory equations after mass exchange are analytically derived. The control approach is applied to formation reconfiguration, drift-stop and also to relative motion trajectory maintenance under perturbation effect J2. The mass exchange approach is verified by numerical simulations.

Kalman filter accuracy study method is proposed. Application of the method is demonstrated by a satellite attitude determination algorithm which uses sun-sensor and magnetometer measurements. The algorithm was implemented onboard of a microsatellite Chibis-M. The attitude determination algorithm study method validated using in-flight measurements.

- May 2014

The attitude control system of the Chibis-M microsatellite is described. Results of flight experiments on damping the initial angular velocity (made using magnetorquers) are considered, as well as stabilization in the orbital referece frame, and orientation of solar arrays toward the Sun using reaction wheels. The operation of algorithms of satellite attitude determination on sunlit and shadow segments of the orbit is also under study. The general logic of operation of the attitude control system in automatic mode is presented and discussed.

Design, analytical investigation, laboratory and in-flight testing of
the attitude determination and control system (ADCS) of a
microsatellites are considered. The system consists of three pairs of
reaction wheels, three magnetorquers, a set of Sun sensors, a three-axis
magnetometer and a control unit. The ADCS is designed for a small 10-50
kg LEO satellite. System development is accomplished in several steps:
satellite dynamics preliminary study using asymptotical and numerical
techniques, hardware and software design, laboratory testing of each
actuator and sensor and the whole ADCS. Laboratory verification is
carried out on the specially designed test-bench. In-flight ADCS
exploitation results onboard the Russian microsatellite "Chibis-M" are
presented. The satellite was developed, designed and manufactured by the
Institute of Space Research of RAS. "Chibis-M" was launched by the
"Progress-13M" cargo vehicle on January 25, 2012 after undocking from
the International Space Station (ISS). This paper assess both the
satellite and the ADCS mock-up dynamics. Analytical, numerical and
laboratory study results are in good correspondence with in-flight data.

The paper discusses the problem of formation flying relative motion control by new approach which based on a mass exchange between satellites. One satellite initially carries a supplementary mass which separates from the satellite and collides inelastically with the other one. Both satellites get additional impulses applied to their centers of mass according to the momentum conservation law. The relative trajectories are described by Clohessy-Wiltshire equations. The resulting relative trajectory after the mass transfer changes and it may be used for relative motion control. Described method is fuelless and the supplementary mass can be used repeatedly. This approach can be applied for a wide range formation flying reconfigurations. It was shown that one can obtain a closed relative trajectory and alter the size of it by a single mass exchange. The paper explores some of the optimization problems of the approach. The solutions of these optimization problems are demonstrated on the particular examples. The paper also studies the influence of the separation point and velocity defining errors on relative motion. Copyright ©2014 by the International Astronautical Federation. All rights reserved.

Results of the experimental determination of the parameters of hysteresis rods made of soft magnetic materials used in passive attitude control systems to damp the perturbed motion of satellites relative to their center of mass are described. Based on the classical solution of the linear magnetization problem and an approximate solution of the problem of nonlinear magnetization in a variable magnetic field, it is shown that the considerable distortion in the experimental determination of the parameters is explained by eddy currents induced in the rods. To mitigate the effect of those currents, it is shown that the measurements must be performed when the frequency of the magnetic fields variation is not higher than 0.1–0.2 Hz. Using nonlinear magnetization theory, a procedure for the experimental determination of the parameters of hysteresis rods is developed. This procedure is augmented by the corresponding computer processing of weak valid signals. The procedure can be used for the choice of the parameters of damping devices included in satellite passive attitude control systems.

A laboratory facility developed at the Engineering Technological Center “Scan Ex” for testing algorithms for determination of attitude and stabilization of the attitude system of the satellite “Chibis-M” is described. The results of experiments on damping initial angular rotation, using magnetorquers, stabilization of the mock-up using flywheels, and flywheel unloading are analyzed. The operation of the algorithm for determination of the mock-up attitude is studied; the main characteristics of this algorithm are the accuracy of the state vector estimation and the time of convergence.

The key-problems of design, examination, laboratory' and flight testing of the attitude determination and control system (ADCS) dedicated for a microsatellite arc considered. The system consists of three pairs of the reaction wheels, three magnetorquers, set of Sun sensors, three-axis magnetometer and a control unit. ADCS, on one hand, is subjected to the high accuracy and reliability requirements, and, on the other hand, power consumption, total mass and volume limitations. It is meant for the LEO satellite with mass between 10 and 50 kg. The problems are solved within several steps, i.e. preliminary study of the satellite dynamics using asymptotical and numerical techniques, hardware and software design, testing of each actuator and sensor and the whole ACS on the test-bench dedicated specially for such a laboratory simulation. Finally flight testing has been carried out to validate ADCS functioning. In this paper both dynamics of the microsatellite with ADCS and mock-up of ADCS operation are studied. Reaction wheels control law parameters are chosen to provide the maximum degree of stability. The evolution of the reaction wheels angular momentum is also studied and the problem of the desaturation with use of the magnetorquers is solved. Attitude accuracy is estimated in terms of closed-form formulae. Some aspects of in-flight ADCS exploitation onboard the Russian microsatellite "Chibis-M" developed, designed and fabricated by the Institute of Space Research of RAS and orbited from SC "Progress" on 25th of January, 2012 are presented. Flight showed a good correspondence between analytical, numerical and laboratory' study with in-flight testing.

- Feb 2011

Axial motion of a balloon payload with respect to the center of mass under action of ventilator engines is studied. An implementation
of a control algorithm is suggested. The possibility of using ventilator engines for trajectory tracking is examined. A technique
for determining engine parameters and results of laboratory tests of a system mock-up are presented.

- Nov 2010

Once been orbited, the technological nanosatellite TNS-0 no. 1 is supposed to be used in one of the next missions for the demonstration of orbital maneuvering capability to eliminate a secular relative motion of two satellites due to the J2 harmonic of the Earth gravitational field. It is assumed that the longitudinal axis of the satellite is stabilized along the induction vector of the geomagnetic field and a thruster engine is installed along this axis. Continuous and impulsive thruster control algorithms eliminating the secular relative motion have been developed.Special equipment was developed in ZARM for demonstration and laboratory testing of the satellite motion identification and control algorithms. The facility consists of a horizontal smooth table and mobile mock-up that enables to glide over the table surface due to compressed air stored in on-board pressure tanks. Compressed air is used to control the translation and attitude motion of the mock-up equipped with a number of pulse thrusters. In this work a dynamic model for mock-up controlled motion over the table is developed. This allows us to simulate a relative motion of a pair of TNS-0 type nanosatellites in the plane of the orbit.

The laboratory facility named LuVeX is developed for motion control algorithms verification of the formation flying purposed
for the Earth remote sensing. The mock-up description, the parameter determination of its individual elements, description
of the realized algorithms for its thruster engine control are given in the chapter. The mathematical simulation results of
a mock-up motion controlled with the algorithms which provide the required mock-up formation motion in given trajectories
are presented. Several configurations of the formation and formation’s elements coupling methods are shown. Required motion
precision and its dependence on formation parameters are examined.

The paper presents a combined approach to teaching of Spaceflight Dynamics, Theoretical Mechanics and Control Theory. In addition to a standard lecture course, this approach provides hands-on training at the laboratory, offering to the student a possibility to develop, design, assemble and test his/her own project of a nanosatellite attitude control system. We describe the software for mathematical modeling, the facilities for laboratory simulation of controlled system dynamics and student training based on these facilities.

- Oct 2009

A laboratory facility LuVeX consisting of a smooth horizontal table and models moving on its surface was developed at ZARM
for adjustment of control algorithms for group motion of satellites. This paper describes the facility and implemented control
algorithms for air-breathing pulsed jet engines mounted on moving models to provide their translational and rotational motion.
The facility performance is proved by the results of numerical simulation of the control algorithm for the motion of a group
of models along a given trajectory.