DYNAMICS OF SPACE ROBOTIC ARM DURING INTERACTIONS WITH NON COOPERATIVE OBJECTS

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1 DYNAMICS OF SPACE ROBOTIC ARM DURING INTERACTIONS WITH NON COOPERATIVE OBJECTS Karol Seweryn 1, Marek Banaszkiewicz 1, Bernd Maediger 2, Tomasz Rybus 1, Josef Sommer 2 1 Space Research Centre of the Polish Academy of Sciences 2 ASTRIUM Space Transportation GmbH 11th Symposium on Advanced Space Technologies in Robotics and Automation ASTRA April, ESA/ESTEC, Noordwijk

2 , M q q C q q q G q 6x 1 3x 1 6x1 6x6 6x 12 { Q } q QGNC Q fix 6x6 K q 6x1 dist

3 Framework 1. Theoretical study of the nonholonomic systems conducted in SRC during the last couple of years. 2. Over 3 years of experience in high level mechanical systems development. 3. Cooperation with Astrium Bremen in the frame of the Inveritas project. SPACE MECHATRONICS AND ROBOTICS LABORATORY

4 Outline 1. Satellite servicing. 2. Considered scenario of orbital rendezvous maneuver. 3. System dynamics. 4. Simulation tool. 5. Capture of tumbling target satellite. 6. Folding of the manipulator with attached target satellite. 7. Results of simulations. 8. Possible methods to verify the simulations. 9. Conclusions. SPACE MECHATRONICS AND ROBOTICS LABORATORY

5 Satellite servicing Lifetime of a considerable number of satellites is significantly shortened by malfunctions occurring during pre operational and operational period. Especially common are: failures of deployment mechanisms for communication antennas and solar arrays, failures of attitude control systems, premature depletion of fuel or cooling agent, rocket failures: payload not delivered to the required orbit (e.g. ARTEMIS case). Various studies show that servicing might prove economically justified.

6 Satellite servicing

7 Space manipulators Space manipulators manipulators mounted on the orbiting satellites. In the Earth case, manipulator s arm is usually fixed, in orbiting satellite manipulator s arm is not fixed. Motion of the manipulator cause reaction of the satellite such system is nonholonomic. System has 6 DoF of the manipulator + 6 DoF of the satellite. During maneuvers an interaction between two satellite subsystems appear, i.e. satellite GNC subsystem and manipulator arm subsystem, which can be a source of disturbances.

8 Considered scenario Scenario based on the INVERITAS project (joint project between EADS Astrium, Jena Optronik and the RICDFKI Bremen, supported by the DLR). Considered system consists of: client (target) satellite (mass = 34 kg), servicer (chaser) satellite (mass = 75 kg), 6 DoF manipulator mounted on the chaser satellite (L = 3 m, moving mass = 35 kg). Servicer satellite is equipped with GNC, which exploits thrusters for attitude control. Joint controller based on Linear quadratic regulation (LQR) is used.

9 System dynamics Generalized equations of motion for a system consisting of a freefloating satellite on the Earth s orbit equipped with 6 DOF robotic arm. Inverse dynamics: State vector: M61 x Mq q Cq, q q Gq T qr,, { Q fix} T q r,, Mass matrix Coriolis matrix Potential forces For this study we have assumed that inverse dynamics is reduced to fixed case Generalized moments M q r,, Mass matrix: A B C T B E F T T C F N T

10 Path planning State vector: q q q r,, r,, r,, T T T Polozenie, Predkosc, Przyspieszenie (nie w skali) v ee (t ) r ee (t ) Polozenie r ee (t) Predkosc v ee (t) Przyspieszenie a ee (t) r ee (t k ) v ee (t k ) Czas [s]

11 Straight forward dynamics System dynamics M q q C q, q q Gq 6x1 { Q } fix 6x6 6x6 6x12 K 6x1 q q 3x1 Q Q GNC 6x1 dist Disturb. Generalized moments calculated for fixed base LQR controller GNC controller Mass matrix: M A B C T B E F T T C F N State vector: T qr,, q q r,, r,, T T

12 Approach to simulations Two types of software were used: Simmechanics (Mathworks) to simulate bechaviour of the satellites in orbit (forword dynamics). Own software for path planning (inverse dynamics).

13 Simulation tool

14 Capture of tumbling target During the final part of the manoeuvre both satellites are close and there is no relative translation motion between them. The target satellite is tumbling. EE is moved to a point, from which the final approach to the docking port is conducted. The straight line (in the docking port CS) trajectory was selected.

15 Capture of tumbling target Trajectory planning is constrained by the final state (i.e. position, orientation, angular and linear velocity and acceleration) of the EE which should be the same as the state of the docking port at the moment of capture. At the beginning of the final approach EE is.5m away from the docking port. Approach was planned for 2 seconds, with 8 seconds of acceleration and 8 seconds of breaking (in the docking port CS). Initial State vector: {ψ,θ,φ}={ π/6, π/7,3 π/2} [rad] {ω}={1.5,2, 1} [deg/s] Orientation [deg] Time [s] Target satellite orientation (Euler angles in convention)

16 Position [m] P x P y P z EE position in inertial reference frame located in target satellite CG Results of simulations Distance between EE and Target DP [m] time Velocity between EE and Target DP [m/s] time Position and velocity of the EE in the grasping point CS Joint position [rad] Joint 1 Joint 2 Joint time Positions of the first three manipulator s joints -.2 Torques at the joints [N*m].4.2 Torque at joint 1 Torque at joint 2 Torque at joint time Torques applied at first three manipulator s joints

17 Results of simulations Reaction torque [N*m] Torque X Torque Y Torque Z time Reaction torques induced by the motions of the manipulator in respect to chaser satellite CG Reaction torques acting on the chaser satellite are extremely important in development of the GNC.

18 Folding of the manipulator with attached target After capture and de tumbling, target satellite must be positioned for docking with the chaser satellite. Mass of the target satellite attached to the EE of the manipulator is significant in comparison to the mass of the servicer satellite. This manoeuvre can be performed with very low velocity, but the resulting reaction torques may be large.

19 Results of simulations Reaction torque [N*m] Reaction torque [N*m] GNC off GNC on fixed base Time [s] -.1 X axis reaction torques in respect to chaser satellite CG.2.1 GNC off GNC on fixed base Time [s] Z axis reaction torques in respect to chaser satellite CG (1) Manoeuvre without attitude control of servicer. (2) Manoeuvre with attitude control. (3) Manoeuvre for fixed base manipulator as a reference which corresponds to the ideal attitude and position keeping. LQR joint controller (operation in quasi coordinates mode) was used in cases (1) and (2) to assure appropriate trajectory following of quasi coordinates.

20 Chaser orientation Orientation [deg] Time [s]

21 Results of simulations summary When GNC is active, attitude control torques are counteracting the reaction torques and satellite is keeping constant orientation. In such case, because of limited freedom of satellite, torques applied at the joints must be higher and, as a result, reaction torques induced by the manipulator are also higher. When the manoeuvre is performed without attitude control and the servicer satellite is allowed to rotate freely, the joint controller assures proper relative motion of the target satellite, while resulting reaction torques are very small. The difference between case (2) and (3) is due to the linear motion of servicer CG. The performance of GNC can be enhanced by using predicted reaction torques as a feed forward.

22 Possible methods to verify simulations Technology demonstration space missions: expensive, complicated. Some aspects of simulations and specific technologies can be verified in test bed systems: hardware in the loop simulators of orbital rendezvous and docking manoeuvres based on industrial robots, experiments in underwater environment, system based on air bearings, experiments performed during parabolic flights, experiments on board space station.

23 Planar air bearing test bed Three link manipulator (with rotational joints) connected to a model of chaser satellite. Satellite manipulator system moving on air bearings supplied with compressed air from gas cylinders. Flat round air bearings based on porous media technology. Data obtained during experiment from special vision system and encoders will be compared with values derived from simulations performed by our Simulink tool.

24 Experiment on board ISS Experiment inside the Columbus module of the International Space Station (ISS). Proposal submitted for Call fo Ideas ISS for exploration. Small model of the chaser satellite (equipped with attitude control air based thrusters) with three link manipulator. Rendezvous manoeuvre with fixed docking port. Micro gravity environment with almost no external disturbances (accelerations no higher than 1µg). Low cost (in comparison with dedicated technology demonstration satellite missions). Verification of numerical simulations of different aspects of possible on orbit servicing mission, experimental investigations of a non holonomic system.

25

26 Thank you for your attention!

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