Satellite formation flying control approaches and algorithms

Transcription

1 Remote Sensing Satellite Technology Workshop 2017 December 5, 2017, National Space Organization, Taiwan Satellite formation flying control approaches and algorithms Dr. Danil Ivanov Senior Researcher, Associate Professor Keldysh Institute for Applied Mathematics, Moscow, Russia

2 Content o Formation flying features o Overview of control approaches o Fuelless satellite formation flying control concepts o Mission examples o Laboratory simulations o Conclusion RSSTW /38

3 What is satellite formation flying? o It is space distributed system consisting of multiple elements flying in a short relative distances in orbit that can communicate, coordinate and interact in order to achieve a common goal o Its main advantages: Concurrency between the satellites Tolerance for failure of individual systems Scalability and flexibility in design and deployment of system RSSTW /38

4 What is formation flying needed for? oearth remote sensing using interferometric measurements ogravitational waves measurements obuilding of the space stations in orbit osolar activity precise measuremets ospace debris removal oand so on LISA mission TanDEM-X mission Grabbing the debris RSSTW /38

5 Definitions for distributed space systems Constellation: similar trajectories without control for relative position; coordination from a control center Formation: closed-loop control on-board in order to preserve topology in the group and to control relative distances Swarm: a group of similar vehicles cooperating to achieve a joint goal without fixed positions; Each member determines and controls relative positions in relations to others RSSTW /38

6 Main parameters of distributed SS A number of satellites A degree of autonomy Communication links between satellites Relative trajectory types Distributed space system type Swarm Formation flying Constellation On-ground control In-orbit centralized control Autonomy In-orbit decentralized control Autonomy in relative control RSSTW /38

7 Communication between satellites The communication is information exchange or just measuring of relative pose There could be directed or mutual communication Each satellite has limited communication area If det(a) 0, the formation is decentralized If det(a)=0, the formation is of leader-follower type, communication is cycled A Centralized Decentralized RSSTW /38

8 Natural formation motions School of fishes Flock of birds Swarm of bees Herd of animals RSSTW /38

9 Satellite formation flying features A small number of satellites Centralized control: o Mother-daughter relationship: mother knows the best for her children and command them o Leader-follower relationship: leader moves everywhere it wants, the followers pursue it Communication with all of the group members Motion along predefined trajectories RSSTW /38

10 Equations of relative motion: linear model, near circular orbit On the first stage of control algorithms investigation Clohessy- Wiltshire model is used: x 2 z 0 2 y y 0 z x z Solution is : x 3C t 2C cos t 2C sin t C y C5sin t C6cos t z 2C 1 C2 sin t C3 cos t C t 1 - Relative drift Earth Scheme of motion The relative drift RSSTW /38

11 Formation flying specific relative trajectories Train formation Relative circular orbit Projected circular orbit Docking trajectories And so on KIKU-7 mission A-train formation flying CanSat4&5 mission RSSTW /38

12 Formation flying control actuations On-board propulsion system Cold gas thrusters Plasma thruster Fuelless alternative control concepts Aerodynamic drag Electromagnetic interaction Solar pressure PRISMA mission Tango propulsion system RSSTW /38

13 An example: tetrahedron formation maintenance Problem statement: Given four satellites on closed, possibly elliptical, orbits Need to obtain a reference orbit in order that the corresponding tetrahedron maintains over time Also provide a control algorithm using propulsion system for several satellites to neglect perturbations image from NASA, MMS mission RSSTW /32

14 Reference orbit for circular orbits For reference orbit search we use linearized HCW model, closed orbits estimation x ny n x , y 2nx 0, z 2 n z 0 x A sin( nt ), i i i Introduce the quality of the tetrahedron y C 2A cos( nt ), i i i i z B sin( nt ) i i i (3 V ) (3 V ) Q r r r r r r L /3 2/3 Volume conservation is the conservation of the size Quality conservation is the conservation of the shape RSSTW /38

15 Satellite swarm features A large number of satellites Decentralized control Communication with limited number of group member Motion along occasional trajectories: Random but bounded relative trajectories Launch of 88 3U CubeSats developed by PlanetLabs Example of relative trajectories RSSTW /38

16 Artificial potential control approach Collision avoidance U C e rep ij rep d R ij rep Equations of motion mr U( r ) d i i i i i Alignment Attraction U dij Ral i Cal ij ij e ij j, j i d v r r at ij C e at d R ij at M. Sabatini, G. B. Palmerini and P. Gasbarri. Control Laws for Defective Swarming Systems// RSSTW-2017 Advances in the Astronautical Sciences, Second 16/38 IAA DyCoss'2014, V p

17 Swarm consensus control Convergence to a common orbital plane The error function: n T i aij nn i j j 1 (1 ) Attitude synchronization Non-linear control law: Thakur D., Hernandez S., Akella M.R. Spacecraft swarm finite-thrust cooperative control for common orbit convergence // J. Guid. Control. Dyn Vol. 38, 3. P Zhou J., Hu Q., Friswell M.I. Decentralized Finite Time Attitude Synchronization Control of Satellite Formation Flying // J. Guid. Control. Dyn Vol. 36, 1. P RSSTW /38

18 Virtual structure control approach Imitation the satellite system by a solid structure model Control law Point masses connected by a springdamper mesh Chen Q. et al. Virtual Spring- Damper Mesh-Based Formation Control for Spacecraft Swarms in Potential Fields // J. Guid. Control. Dyn Vol. 38, 3. P /38

19 Fuelless FF Control Concepts Tethered systems Aerodynamic drag Electro-magnetic interaction Solar pressure Momentum exchange RSSTW /38

20 Aerodynamic drug based control o Features: Low Earth Orbit Satellites with variable cross section area o Shortcomings: Short lifetime Reaction wheel saturation during attitude control JC2Sat Mission RSSTW /38

21 LQR-based control algorithm o Aerodynamic force * fi V S{(1 )( ev, ni ) ev 2 ( ev, ni ) ni (1 ) ( ev, ni ) ni}, m V n (cos cos ;sin ;sin cos ). o Linear-quadratic regulator x = A x + bu, Minimising cost function T T J = ( e Q e + u R u ) dt, Feedback control is u b e e x x 1 T R P, where d, matrix P is the solution of Riccati equation Relative trajectories during the maneuver Required trajectory Initial orbit Maneuver 1 T T Q PBR B P PA A P RSSTW /38

22 Electro-magnetic interaction based control Magnetic interaction Youngquist R.C., Nurge M.A., Starr S.O. Alternating magnetic field forces for satellite formation flying // Acta Astronaut. Elsevier, Vol. 84. P Lorenz force of charged satellite Peck M.A. et al. Spacecrat Formation Flying Using Lorentz Forces // J. Br. Interplanet. Soc Vol. 60. P Coulomb force interaction Schaub H. et al. Challenges and Prospects of Coulomb Spacecraft Formation Control of the Astronautical Sciences // J. Astronaut. Sci Vol. 52. P RSSTW /38

23 Force, N Coulomb force based control algorithm o Features: The charging device is required Small relative distances Charges are eliminating by plasma Coulomb force under λ d =140 m Coulomb force under λ d =1400 m J2 perturbation Solar pressure Plasma environment λ d min, m λ d max, m LEO GEO Free space r, m 23/38

24 Solar radiation pressure based control Solar sail with fixed orientation Smirnov G.V., Ovchinnikov M.Y., Guerman A.D. Use of solar radiation pressure to maintain a spatial satellite formation // Acta Astronaut Vol. 61, 7-8. P Solar sail with variable reflection Mori O. et al. First Solar Power Sail Demonstration by IKAROS // Trans. Japan Soc. Aeronaut. Sp. Sci. Aerosp. Technol. Japan Vol. 8, ists27. P. To_4_25 To_4_ RSSTW /38

25 Solar radiation pressure based control We consider: Spherical satellites Variable reflection on pixel surface Nearcircular orbits J2 perturbation e-perturbation Solar pressure 2F liquid-crystal thin (transparent state) Mirror foil liquid-crystal thin (opage stage) F Mirror foil RSSTW /38

26 Numerical example of the SPR control Desired trajectory Without control Desired traj. Controlled traj. Relative trajectories without control Relative trajectories with control RSSTW /38

27 The momentum exchange-based control The momentum from lasers for repulsive force Y. K. Bae. A contamination-free ultrahigh precision formation flying method for micro-, nano-, and pico-satellites with nanometer accuracy. In Space Technology and Applications International Forum- Staif 2006, volume 813, pages , Continuous stream of mass travelling between the satellites S. G. Tragesser. Static formations using momentum exchange between satellites. Journal of guidance, control, and dynamics, 32(4): , Liquid droplet streams exchange T. Joslyn and A. Ketsdever. Constant momentum exchange between microspacecraft using liquid droplet thrusters. In 46th joint Propulsion Conference, volume 6966, pages 25 28, RSSTW /38

28 Laboratory facilities for formation flying control algorithms testing Test facility in the Technion Univercity The Formation Control Testbed at the JPL SPHERES mock-up on board the ISS RSSTW /38

29 Planar Air Bearing Test-Bench in KIAM Air intake tube Camera Mark for motion determination Industrial fun Flexible booms Air table Docking system Flexible booms Control system elements Thrusters imitation Mock-ups Test Bench COSMOS (COmplex for Satellites MOtion Simulation) The magnitude of linear acceleration RSSTW /38

30 Conclusion The formation flying of the satellites is a new paradigm in space systems The fuelless control approaches are fitting small satellite restrictions, they are smart but challenging We should allow for the distributed system to be autonomous and self-organizing And may the fourth be with us RSSTW /38

31 Thank you for your attention! Our research team in KIAM Our web-site: RSSTW /33