EXPERIMENTAL VALIDATION OF CDT-BASED SATELLITE DOCKING SIMULATIONS USING SOSS TESTBED Ou Ma1, George Yang2, and Xiumin Diao1 1
2
New Mexico State University, P.O. Box 30001, MSC 3450, Las Cruces, NM 88003, USA,
[email protected] MDA Space Missions,9445 Airport Rd., Brampton, Ontario, Canada L6S 3J4,
[email protected]
ABSTRACT This paper describes a project which experimentally validates a generic contact-dynamics toolkit in a Simulink based satellite docking simulator. The simulation software was developed by MDA for supporting the design and verification of the ISS robotic systems and several satellite on-orbit servicing systems. The hardware experiment was performed using an air-bearing supported docking testbed specially designed for testing different docking and capture mechanisms. The simulation results compare favourably with the measured experimental data, which demonstrates the validity of the simulation tools and increases the confidence of using the simulation tool for design of various space servicing missions such as the Shuttle-Return-to-Flight, Orbital Express and the potential Hubble Telescope robotic repair missions. 1.
INTRODUCTION
There has been an increasing interest in satellite onorbit autonomous servicing in the space industry recently. JAXA completed a technology demonstration mission ETS-7 [1]. DARPA is developing a more advanced technology demonstration mission to be launched in 2006 through the Orbital Express Program [2-4]. Germany and Canada are also jointly developing a robotics-based satellite rescue mission called TECSAS which has a planned launch four years from now [5-6]. In order to perform on-orbit service, the servicing spacecraft has to first dock to or capture the satellite to be serviced in orbit. As in any space system for which full and representative ground hardware tests are extremely expensive or often even impossible to develop, computer simulations are mandatory for developing a system for satellite docking and servicing. Simulations are also instrumental in concept studies during proposals and early design stages. Finally, simulations are useful during the operational phase of satellite servicing, such as improving the operational procedures, training ground operators, command and control, etc. Therefore the need is strong for highfidelity satellite docking simulations. In order to achieve high simulation fidelity, docking simulators have to go through rigorous validation process. MDA Space Missions (previously MD Robotics), under the support of the Canadian Space Agency, developed a Contact Dynamics Toolkit (CDT) [7] in
support of the design, verification, and operation support of the International Space Station (ISS) robotic systems. Besides the mandatory support roles in the ISS Program, CDT is also playing an increasing role in programs of on-orbit servicing business including the current development of the robotic arm for the Orbital Express and the potential robotic mission for servicing the Hubble Space Telescope [8]. In these new and challenging space-robotics programs, many critical operations are being analyzed and assessed by MDA using dynamics simulations incorporating CDT models. Although CDT has been extensively validated against hardware tests in several different cases, validation against experiment of satellite docking is still new. To this end, MDA initiated an R&D project aiming at further validating CDT along with a Satellite Docking Simulator (SDS) using a special hardware testbed called Satellite on-Orbit Servicing System (SOSS). SDS is a Simulink-based, multibody system dynamics simulator with generic contact dynamics capabilities, which was also developed by MDA in support of design and concept evaluation of satellite docking mechanisms [9]. The SOSS testbed, as shown in Fig.1, was designed for testing special docking and capturing mechanisms. The hardware was designed to be representative of the real operational situations so that the typical dynamic behaviour of the docking mechanisms could be studied.
Fig. 1: SOSS Testbed
This paper describes an R&D project of validating the docking simulations against the SOSS hardware tests. The objectives of the project were: − to demonstrate that contact dynamics simulation is capable of predicting realistic dynamic behaviour of satellite docking operations. − to demonstrate that the existing simulation software tools SDS and CDT have sufficient validity for supporting the development of satellite docking mechanisms.
Proc. of 'The 8th International Symposium on Artifical Intelligence, Robotics and Automation in Space - iSAIRAS’, Munich, Germany. 5-8 September 2005, (ESA SP-603, August 2005)
− to better understand the roles of the key contactdynamics model parameters and explore techniques of identifying these parameters. In the project the dynamic model of the SOSS testbed was implemented on the Simulink-based docking simulator SDS. The contact interfaces were modelled using CDT as part of the SDS simulation model. To help the modelling, several independent hardware tests and analyses were used to identify the model parameters which are not directly available from the design. A large number of operational scenarios were tested and also simulated. The simulation results were compared with the test data. Discrepancies or errors found in the comparison were investigated in order to identify the sources of errors. With such an exercise, we achieved a better understanding of some modeling aspects which otherwise would not have been observed without the hardware tests or proper comparison between the simulation model and the hardware test. The findings from this validation exercise have added significant value to the increasing practice of using contact-dynamics simulations to support the design and verification of docking and capture mechanisms for satellite on-orbit servicing missions.
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Fig.2: Architecture of SDS Docking Simulator Version 2.0
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Simulation Initialization Simulation Job: ASTRO_dock_MicroSat_p5r5x4_v3
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2.
SIMULATION TOOLS
Two simulation software tools are involved in this validation exercise, one is called Contact Dynamics Toolkit (CDT) and the other is Satellite Docking Simulator (SDS). The two software tools have to be integrated together for dynamic simulation of general satellite docking scenarios, as described next.
external force applied on MBS 1, first body
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Post-Simulation Analysis
CDT was developed and validated by MDA for the International Space Station Program over the period of 1992-1999. It is a plug-in solution for the modeling and simulation of low-speed impact and contact dynamics of general mechanical objects with complex geometry. CDT is capable of simulating all dynamic behavior resulting from physical contact such as impact, bouncing, sliding, rolling, spinning, sticking, and jamming. The initial motivation for the development of CDT came from the need for simulation based engineering verification of ISS remote manipulator systems. Applications of the ISS manipulators require execution of complex robotic operations involving constrained/contact dynamics. Examples of such complex robotic operations are the replacement of Orbital Replaceable Units (ORUs) by the Special Purpose Dexterous Manipulator (SPDM) [10] and the assembly of the International Space Station by the Space Station Remote Manipulator System (SSRMS) [11]. CDT has been verified against analyses and various experimental results [7, 12]. It has been incorporated and used in dynamics simulators at CSA and MDA for the SSRMS and SPDM development, operations support, and crew training. It has also been installed in NASA’s SRMS dynamic simulators for SRMS operations support.
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Fig.3: The highest level Simulink block diagram of SDS
SDS is a Simulink-based Satellite Docking Simulator which was developed by MDA during 2000-2002 in support of the development of space robotic systems for satellite on-orbit servicing [9]. The simulator was implemented in the environment of Matlab/Simulink because Simulink provides a rich set of available toolboxes and easy-to-use GUI-based user interfaces. The architecture and major components of the simulator are shown in the diagram of Figs.2&3. Simulink and 3D Studio Max/VIZ are commercial software components. As shown in the diagram, the SDS consists of a main “engine” of multibody dynamics and several external modules including CDT. The responsibility of CDT in the docking simulator is to identify all the contact areas and determine the contact forces between the docking interfaces of the two docking satellites. One can easily plug additional attitude control and robotics modules into the SDS platform, which is necessary for a full study of docking operations. In addition, another already developed complex multibody dynamics engine may also be added to include an additional capability of simulating
robotic servicing operations, thus extending the simulator to an end-to-end satellite servicing simulator.
− one load cell for axial spring load of the compliance mechanism − three strain gauges for nozzle loads in all 3 axes
3.
SOSS EXPERIMENT TESTBED
The SOSS testbed, as shown in Fig.4 and Fig.5, was designed for testing various different docking and capturing mechanisms. It consists of two separate units (also called vehicles), which represent a scaled-down hardware mock-up of a real servicing spacecraft (also called chaser) and its target satellite. Each mock-up unit is supported on three precision air bearings and thus, can smoothly and freely float on the solid floor of a granite table. The mass and inertial distribution of each unit can be adjusted to match those of the real satellite of interest. Both units are equipped with cold gas propulsion systems to provide thrusts as needed. The docking mechanism being tested on this project was designed by MDA for capturing a class of satellites originally not designed for being serviced in orbit. The testbed was designed as close as possible to the real operational case so that representative docking dynamic behaviour can be studied. Trailing electrical cables and air tubes were avoided to prevent drag on each vehicle from affecting the tests. Instead, on-board tanks were used to deliver nitrogen to the air bearings. An onboard wireless device was installed to transfer telemetry from the vehicles to the operator workstation and to transmit commands from the workstation to the two vehicles. The prototyped docking mechanism used in this project consists of a probe, a compliance mechanism and a berthing mechanism. The probe consists of an expendable probe head, a probe boom and an abutment plate. The abutment plate is mounted to a compliance mechanism consisting of a linear guide and spring. The compliance mechanism is mounted to a berthing mechanism consisting of a ball-screw-actuated sliding stage. The berthing mechanism is driven using a motor controller. A full-sized replica of the exhaust nozzle of the Liquid Apogee Motor (LAM) of the tested satellite is used in the testbed and the following flight system dimensions are also maintained: − LAM nozzle to target spacecraft centre of gravity − The distance from the probe tip to the mass center of the chaser The launch vehicle interface ring is scaled down to minimize the overall height of the target and the chaser vehicles. A setup using a lower center of mass requires a smaller footprint on the air bearing tables. Masses and moments of inertia are scaled down based on the results of a dimensionless analysis. The following sensors are installed in the testbed for collecting test data: − three strain gauges for probe loads in all 3 axes
− Overhead cameras and vision system for position and orientation determination.
Fig. 4: Hardware of the SOSS chaser unit
` Fig.5: Hardware of the SOSS target unit
Due to the fact that the comparison of position and orientation is of major interest, the vision sensor accuracy is critical. A number of tests were conducted to calibrate the accuracy of the vision sensors, and the resulting average errors are about ≤2 mm in position and ≤0.19 deg in orientation, within a measurement area of about 1.93×1.52 (72”×60”) meters. The SOSS docking procedure consists of three stages, which mimics the real docking procedure in space. First, the chaser vehicle applies a burst from its thrusters (or a calibrated push) to push itself across the granite table toward the target vehicle while the target vehicle remains stationary. The two vehicles come into contact with each other. Then the docking mechanism latches the two vehicles together but not securely (i.e., soft docking). Secondly, at the “soft-docked” position a motor driven slide is powered to bring the two vehicles firmly together into a “hard docked” position. Finally, an undock procedure is simulated by reversing the operation of the motor driven slide.
4.
SOSS SIMULATION MODEL
The SOSS testbed was modelled on SDS. The major model parameters are shown in Figs.6&7. These model data were either extracted from the design of the hardware or obtained from hardware measurements.
at the point where a spring is to be modelled is measured. All the measurements were done when the vehicles were locked (i.e., in static condition). In this validation project, only linear stiffness parameters were assumed and measured. 1.70 y
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0.22 Chaser Parameters Assembly mass: 201.8 kg Assembly inertia: 96, 96, 96 kg.m2 Docking mechanism mass: 4.58 kg Probe shaft mass: 0.0657 kg Probe head mass: 0.0172 kg Compliance axial stiffness: 118.83 N/m Compliance damping coeff.: 9.45 N.s/m Probe rotational stiffness: 14 Nm/rad Probe rotational damping ratio: 0.5
Contact Parameters Probe Young’s modulus: 7.0e+10 N/m2 Probe damping ratio: 0.0035 Probe Poisson ratio: 0.35 Nozzle Young’s modulus: 7.0e+10 N/m2 Nozzle Poisson ratio: 0.35 Probe finger / nozzle friction coefficient: 0.2 Probe head / nozzle friction coefficient: 0.55 Contact damping ratio: 0.2
Unit: meters (Dimensions are not in right scaling)
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Target Parameters Target assembly mass: 700.8 kg Target assembly inertia: 679, 679, 679 Kg.m2 Nozzle Young’s modulus: 7.e+10 N/m2 Nozzle Poisson ratio: 0.35
Fig. 7 Model parameters of the SOSS target unit
Fig.6 Model parameters of the SOSS chaser unit
The geometry parameters of the contact dynamics model were determined completely from the design of the contact interfaces. Since the algorithms of contact detection and geometric interference employed in CDT require contact surfaces in the model to be either linear (planar) or quadratic (conic), the geometry model of the contact interfaces have to be linearized. Thus, the nozzle of the SOSS target vehicle is approximated as four conic surfaces connected one after another, as shown in Fig.8. The diameters of the two ends of each conic surface exactly match these of the nozzle hardware. Moreover, each conic surface is further approximated by 15 planar slices equally distributed around the surface. More linear pieces used in the linearized geometry model will lead to more accurate contact model. Based on our experience of modelling numerous contact-dynamics application cases, such a degree of approximation for this particular case is considered adequate. Stiffness can be easily measured statically from simple hardware test. The stiffness parameters of the compliance mechanism and probe boom were directly measured using separate hardware tests. In such a test, a known force or torque is applied at a specific location of the tested hardware and then the resulting deflection
Fig. 8: Contact geometry model of the docking interface The compliance mechanism and the probe boom have damping effects, which need to be modeled. It is rather difficult to identify damping parameters because (1) they cannot be measured directly and (2) they have to be identified from a dynamic (transient) response. We performed component level tests for the compliance mechanism and probe boom isolated from the rest of the system. In the test, a known force or initial deflection was applied to the tested component and then the resulting dynamic response was collected. The test data were compared to the simulation of an assumed second-order dynamics model of the tested component. A genetic-algorithm based estimation method was used in the process to identify the damping
parameters. Fig.9 shows a typical comparison of the dynamic responses of the component models and their corresponding component-level hardware tests.
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(b) Fig.10 Absolute position & velocity of the Chaser
Fig. 9 Comparison of the model and the hardware test data for the compliance mechanism (upper figure) and the probe boom (lower figure)
In determination of the friction parameters, we applied the results of another R&D project collaboratively conducted by MDA and the University of Toronto. In that project, variations of friction coefficients with respect to different materials, environment conditions (such as temperature and vacuum levels), motion speeds, normal loads, and contact geometries were experimentally investigated [14]. The values of contact friction coefficients were determined based on the guidelines concluded from that project. 5.
COMPARISON WITH HARDWARE
Many hardware test cases have been set up and tried. They are categorized into five series to cover different docking conditions, as described below: − A series: docking without initial misalignments. − B series: docking with lateral misalignment only. − C series: docking with lateral misalignment and drifting (nonzero initial lateral velocity). − D series: docking with lateral misalignment and both lateral and rotational drifting. − E series: some failure cases were simulated due to slow approaching velocity or a combination of misalignments in higher magnitudes.
Fig.11 Absolute position & velocity of the Target
docking interfaces happened at about 0.15 seconds after the simulation started. The relative velocities between the two vehicles at the first contact were about 5.6 cm/s in the axial direction, 0.7 cm/s in the lateral direction, and 0.13 deg/s about the yaw direction. The initial nonzero off-axial linear and angular velocities in this case were due to the imperfect triggering of the axial motion and the slight asymmetry of the structures of the testbed. As one can see from the plots, the SDS simulation results match the experiment data not only in gross motion trend but also in details. The maximum position errors over the entire operation period are only 5.6cm, 0.25cm, and 0.6° in axial, lateral, and yaw directions, respectively. Comparing these errors to the overall relative motion range between the two vehicles, the maximum relative errors are only about 10%, 5%, and 10% in axial, lateral, and yaw directions, respectively.
Fig. 12 Relative position & velocity between the two
vehicles (expressed in the first vehicle frame) Since initial conditions of simulation can be easily defined, the simulation runs were set up after the corresponding hardware tests were completed and the data collected. In general, there was a close correspondence between the trends observed in the simulation and experimental test results including situations where the docking failed. The only exception was where the docking misalignments or docking speeds were very large. One of the comparison examples is shown in Fig.10 through Fig.12. The positions and velocities shown in the plots are these of the inboard nodes of the vehicles. Inboard node is located at the center of each vehicle, as shown in Fig.6 or Fig.7. The absolute motion is measured with respect to the inertia frame and the relative motion is expressed in the inboard frame of the Chaser vehicle. In this example, the chaser vehicle was pushed axially (in X direction) toward the stationary target unit intending to achieve an axial docking speed of 5 cm/s. The simulation started from the time when the two parts of the docking interfaces in the hardware test were about to make physical contact. At that time (i.e., the initial time of the simulation), the two vehicles had a lateral (along the X axis) misalignment of about 4.7 cm and an angular misalignment (about the Y axis) of 1.7 degrees. The first physical contact between the
A small oscillatory behaviour with a frequency of around 2.4 Hz can be observed in the test data. This phenomenon presented in all the tested cases. In the investigation we found that the phenomenon still presented even when the air-bearing system was turned off and the vehicles were locked to the granite tables. Therefore, it was concluded that this small oscillation was most likely caused by vibration of the support structure of the overhead vision system. Table 1. Comparison results for different test series Max. Yaw Error
Prediction Correctness
0.001
0.006
Yes
0.001
0.002
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A6
Chaser Target
B3
Chaser
0.01; 0.017
0.02
Target
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0.01
B7
Chaser
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0.015
Target
0.005; 0.001
0.002
Chaser
0.03; 0.025
0.023
Target
0.002;0.004
0.0025
D2
Chaser
0.04; 0.01
0.02
Target
0.01; 0.002
0.015
E1
Chaser
0.04; 0.015
0.03
Target
0.015; 0.002
0.01
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E5
Yes
Yes
Yes
Yes
Yes
Yes
In most of the compared cases, the relative errors (relative with respect to the overall motion scale) between the SDS simulation and the hardware test are typically below 10% in all individual directions. The comparison results of some representative cases of different test series are summarized in Table 1. The last
column of the table indicates the qualitative conclusion of the comparison between the simulation and test for the associated case. Comparison of the tip positions and velocities of the docking interfaces of the two vehicles cannot be done because such test data could not be collected with the given measurement system in the experiment. These data could not be derived from the measured vehicle position and velocity data either because the deflections of the compliance mechanism and the flexible probe could not be measured too. It is also difficult to compare contact forces because the strain gauge data (installed near the root of the probe boom) was insufficient to represent the real contact forces between the complex docking interfaces. In order to measure and validate these quantities, much more sophisticated measurement system had to be incorporated into the experiment, which was beyond the scope of this project. 6.
CONCLUSIONS
A ground-based satellite docking testbed and its various test cases have been modeled on a Simulinkbased satellite docking simulator SDS with the portable contact dynamics toolkit CDT. The comparison between the SDS/CDT simulations and hardware tests demonstrated that the simulator can correctly predict not only the gross motion trends but also the detailed dynamic responses of the tested docking operations to the extent of only about 10% relative errors. With such an exercise, we gained a better understanding of some contact-dynamics modeling aspects which otherwise would not be able to learn without the hardware tests and the comparison between the simulation model and the hardware test. This validation exercise has further increased our confidence of using the contact dynamics toolkit CDT to support the design and verification of space robotic systems for future satellite on-orbit servicing missions such as the Shuttle-Return-toFlight, Orbital Express and the potential Hubble Telescope repair missions. REFERENCES [1] Kasai T., Oda M. and Suzuki T., “Results of the ETS-7 Mission – Rendezvous Docking and Space Robotics Experiment”, 5th Int. Symp. on Artificial Intell., Robotics and Auto. in Space, ESTEC/ESA, Nordwijk, The Netherlands, pp.299-306., 1999 [2] Wilson S., “Orbital Express”, Presentation on the Industrial Day, Tactical Technology Office, DARPA, Nov.10, 1999. [3] Whelan D.A., Adler E.A., Wilson S. and Roesler G., “DARPA Orbital Express program: Effecting a revolution in space-based systems”, Proc. of SPIE – The Int. Society for Orbital Engr., Vol.4136, pp.48-56, 2000.
[4] Seth D.P., “Orbital Express: Leading the way to a new space architecture”, Space Core Tech Conf., Colorado Springs, November 19-21, 2002. [5] Hirzinger G., Landzettel K., Brunner B., Fischer M., Preusche C., Reintsema D., Albu-Schäffer A., Schreiber G. and Steinmetz B.M., “DLR's robotics technologies for on-orbit servicing”, Advanced Robotics, Vol.18, No.2, pp.139-174, 2004. [6] Dupris E., Doyon M., Martin E., Allard P., Piedboeuf J.-C., and Ma O., “Autonomous Operations for Space Robots”, Proc. the 55th Int. Astronautical Congress, October 2004, Paper #IAC-04-IAA.U.5.03. [7] Ma O., “CDT – A General Contact Dynamics Toolkit”, Proc. 31st Int. Symp. on Robotics, Montreal, Canada, May 2000, pp.468-473. [8] King D., “Saving the Hubble”, Proc. of the 2004 IAF World Space Congress, Oct.4-8, 2004, Vancouver, Canada, Paper #IAC-04-IAA.4.9.1.05 [9] Ma O., Crabtree D., Jones H., Yang G., Martin E., Carr R., and Piedboeuf J.C., “Development and Applications of A Simulink-Based Satellite Docking Simulator with Generic Contact Dynamics Capabilities”, Proc. 2002 IAF World Space Congress, Oct.10-19, 2002, Houston, USA. [10] Ma O. and Carr R., “Dynamics Modelling and Simulation of SPDM Contact Operations, Part I: Simulation Model and Berthing 6B Avionics Boxes” and “Part II: SPDM Handling the IEA Battery ORUs”, Proc. 1st IAF Space Robotics Workshop, Saint-Hubert, Quebec, October 1998, pp.167-178. [11] Abou-Fayssal, H., Maclean, J., and Podwalski, K., 1998, Simulation of the SSRMS dynamics for payload maneuvering and berthing, The 1st IFAC Workshop on Space Robotics, Montreal, pp.73-77. [12] Van Vliet J., Sharf I. and Ma O., “Experimental Validation of Contact Dynamics Simulation of Constrained Robotic Tasks. The Int. J. of Robotics Research, Vol.19, No.12, pp.1203-1217, 2000. [13] Pohlheim, H., Evolutionary Algorithms - Methods, Operators, Practical Examples. Berlin, Heidelberg, New York: Springer-Verlag, 1999. [14] Sliding Friction and Stiction Data Summary Report for Orbital Replacement Unit’s (ORU) Materials, Tribology Lab, UTIAS, January 2001.
