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Acta Astronautica

Acta Astronautica 81 (2012) 335–347

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Use of industrial robots for hardware-in-the-loop simulationof satellite rendezvous and docking

Ou Ma a,n, Angel Flores-Abad a, Toralf Boge b

a Department of Mechanical and Aerospace Engineering, New Mexico State University, 1040 South Horseshoe, Jett Hall 111, Las Cruces, NM 88003, United Statesb German Space Operations Center (GSOC), German Aerospace Center (DLR) Wessling, 81241, Germany

a r t i c l e i n f o

Article history:

Received 13 October 2011

Received in revised form

4 July 2012

Accepted 5 August 2012Available online 30 August 2012

Keywords:

Rendezvous and docking

Contact dynamics

Hardware-in-the-loop simulation

On-orbit servicing

Robotics

Admittance control

65/$ - see front matter & 2012 Elsevier Ltd. A

x.doi.org/10.1016/j.actaastro.2012.08.003

espondence to: Department of Mechanical an

ring, New Mexico State University, 1040 So

1, Las Cruces, NM 88003, United States. Tel.:

575 646 6111.

ail addresses: oma@nmsu.edu (O. Ma),

@nmsu.edu (A. Flores-Abad), toralf.boge@dlr.

a b s t r a c t

One of the most challenging and risky operations for spacecraft is to perform

rendezvous and docking autonomously in space. To ensure a safe and reliable operation,

such a mission must be carefully designed and thoroughly verified before a real space

mission can be launched. This paper describes the control strategy for achieving high

fidelity contact dynamics simulation of a new, robotics-based, hardware-in-the-loop

(HIL) rendezvous and docking simulation facility that uses two industrial robots to

physically simulate the 6-DOF dynamic maneuvering of two docking satellites.

The facility is capable of physically simulating the final approaching within a 25-

meter range and the entire docking/capturing process for a satellite on-orbit servicing

mission. The key difficulties of using industrial robots for high-fidelity HIL contact

dynamics simulation were found and different solution techniques were investigated in

the presented project. An admittance control method was proposed to achieve the goal

of making the robots in the HIL simulation process match the impedance of the two

docking satellites. Simulation study showed the effectiveness and performance of the

proposed solution method.

& 2012 Elsevier Ltd. All rights reserved.

1. Introduction

With the increasing activities for planetary explorationand satellite on-orbit servicing, space missions requiringphysical contact (including low-speed impact) becomemore common than ever. A critical step for satellite on-orbit servicing is to successfully rendezvous and docking(R&D) to the target satellite (also called client or servicedsatellite) in orbit. Autonomous capture or docking is avery difficult and risky operation. Therefore, the docking/capture system of a servicing spacecraft has to be

ll rights reserved.

d Aerospace

uth Horseshoe, Jett

þ1 575 646 6534;

de (T. Boge).

thoroughly tested and verified before a real space missioncan be launched. Ground-based testing and verification ofthe dynamic responses of a spacecraft for a general 3-Dphysical contact in space environment is very difficult.The conventional microgravity test technologies havedifficulties in testing full 6-DOF contact dynamics of largeand complex space systems. For example, the parabolicflight can only mimic 20–30 s of zero/partial gravity envir-onment inside a very limited cargo space, which is inap-propriate for testing a complete docking process; thecounterweight-balance technology suffers extra inertiaeffects which become significant during a contact motiondue to resulting large accelerations; the air-bearing-basedfloating test floor is only a 2-D or pseudo 3-D system and isalso subject to extra inertial burden due to the neededmassive supporting frame/structure; the water-based neu-tral buoyancy technique alters the dynamics characteristicsof the tested system because of the water drag and it

6-DOF roboticsystem

Satellitesimulator

Dockinghardware

Contact force feedback

R&Dcommand

Dockingoutput

Fig. 1. Three essential parts of an HIL contact dynamics simulator.

O. Ma et al. / Acta Astronautica 81 (2012) 335–347336

cannot be used to test real space hardware containingelectronic hardware due to the water environment. Only arobotics-based active gravity compensation system has nolimits on the complexity of the space system to besimulated or tested while still retaining a full 6-DOF motioncondition. Plus, it can use real physical contact hardware togenerate contact forces and thus it is more accurate thanany mathematical contact dynamics model used incomputer-based simulation. The concept of such a generalrobotics-based contact dynamics simulation facility is illu-strated by the diagram shown in Fig. 1. It consists of threebasic parts:

(1)

A real-time satellite simulator used to predict thedynamic responses of the servicing and target satel-lites based on a multibody dynamics model of thesatellites.

(2)

A physical 6-DOF robotic system, whose end-effectormoves according to the dynamic motion of the satel-lite simulator system.

(3)

A mockup of the actual docking hardware, which willmake physical contact (docking and capturing) in thesimulation to generate the contact force and moment.

In the concept of this HIL simulation system, thedynamics of the satellites including the microgravitycondition is predicted by a mathematical model of thedynamical system, because it is very difficult to physicallyproduce a full 6-DOF on-orbit dynamic motion of asatellite on the ground. It is rather easy to accuratelymodel and simulate such dynamics on a computer. On theother hand, the contact dynamics is represented by thereal hardware contact because the contact action is verydifficult to accurately model and simulate on a computer.Therefore, the HIL simulation concept is a hybrid of bothmath model-based software simulation and hardware-based physical test. The combined simulation process isintended to take advantage of both.

There have been several examples of HIL simulationfacilities for simulating operations of space roboticsystems. With the purpose of simulating satellite rendez-vous operations, two decades ago, the German AerospaceCenter (DLR) developed a simulation facility called EuropeanProximity Operations Simulator (EPOS), a former version ofthe new EPOS facility discussed in this paper [1]. The facilitywas used to support the testing of ATV and HTV rendezvoussensors. NASA/MSF developed a HIL simulator using a6-DOF Stewart platform for simulating the Space Shuttlebeing berthed to the International Space Station (ISS) [2,3].The Canadian Space Agency (CSA) developed an SPDM TaskVerification Facility (STVF) using a giant 6-DOF, customer-

built, hydraulic robot to simulate SPDM performing contacttasks on the ISS [4,5]. Furthermore, CSA recently developeda couple of test beds to simulate the autonomous capture ofa tumbling satellite [6,7]. US Naval Research Lab used two6-DOF robotic arms to simulate satellite rendezvous forHIL testing rendezvous sensors [8]. Japanese Institutionshave also developed hybrid facilities to verify orbital opera-tions [9–11]. China has used a dual-robot based facility tosimulate a space robot performing on-orbit servicing [12].

Driven by ever increasing interest in satellite on-orbitservicing missions, DLR is developing a new and advancedrobotics-based HIL simulation facility called EuropeanProximity Operations Simulator (EPOS 2.0) [13]. Theunique features of this new EPOS facility include the useof two heavy-duty industrial robots which can handlepayloads weighing up to 240 kg and it has hardwarecontact capability for testing full proximity rendezvousand docking. The research presented in this paperaddresses the question of how to control the two indus-trial robots such that the dynamic characteristics of theindustrial robots exhibit during the docking phase matchthose of the two real docking satellites. In other words,the impedance between the two robots during a HILdocking simulation should match that between the twodocking satellites in space. Only when such a condition issatisfied, can the simulated satellite docking behavior berealistic (accurate). Although impedance control has beena well studied topic in the robotics field [14], most of theadvanced control strategies require the involved robots tohave a joint force/torque sensing and control capability.The industrial robots for the EPOS (just like almost all theother industrial robots) do not have a joint torque sensingand control capability. Further, their low-level controlsoftware is inaccessible. Therefore, controlling the robotsto have the same impedance property as the two dockingsatellites is a difficult task if directly applying impedancecontrol strategy. In our approach, this problem is solvedby developing an admittance control strategy as an outerloop on the top of the original control system of theindustrial robots. This admittance control method usesthe measured contact force as its input just as it wasoriginally proposed in [15]. The paper presents a simula-tion based study of this strategy. In the simulation study asimplified robotic system conceptually similar to theEPOS was used. The simulation demonstrates that theproposed admittance control strategy can control theEPOS to have realistic contact dynamics simulation.

2. Overview of the new EPOS facility

DLR and ESA developed an EPOS facility (identified asEPOS 1.0) in the 1990s for the simulation of spacecraft

Fig. 2. Physical simulation part of the EPOS facility.

O. Ma et al. / Acta Astronautica 81 (2012) 335–347 337

maneuvers for the last few critical meters of the finalrendezvous phase (just prior to physical contact). The lastintensive utilization of the facility was the test and verifica-tion of the sensors systems which are used for ATV toapproach to the ISS [13]. Future applications for satelliteon-orbit servicing missions require the facility to be able toprovide 6-DOF relative dynamic motion of two satellites inthe final approaching phase, starting from 25 m away untilthe completion of a docking process [16]. The EPOS 1.0facility could not meet these new requirements and hence,it was replaced by a new EPOS system (identified as EPOS2.0). The design and construction of the new facility beganin 2008. The new facility, as shown in Fig. 2, is aimed atproviding test and verification capabilities for the completeR&D process of an on-orbit servicing mission. It is a HILcontact dynamics simulator using two industrial robots tosimulate R&D dynamic behavior. The facility is currentlyready for rendezvous simulation and docking testing withoutmatching satellite impedance.

The main advantages of the new EPOS are: (1) it usestwo industrial robots which can maneuver a payload up to240 kg and the robots are relatively inexpensive and morereliable in comparison with customer-built robots; (2) itallows one of the robots to move on a 25-meter long railsystem to simulate the final approaching operation; (3) itsimulates space-representative sunlight and visual back-ground; and (4) it has a HIL, zero-gravity, contact dynamicssimulation capabilities allowing high-fidelity docking andcapturing simulation.

A typical setup of the EPOS facility for an R&D simula-tion scenario is shown in Fig. 3. In such an operationalscenario, the R&D sensors and the docking/capture inter-face are mounted on one robot and a mockup of the targetsatellite is mounted on the other robot. The R&D sensorscan measure the relative position and attitude of the targetsatellite. Based on this, the onboard computer calculates thenecessary thrusters or reaction wheels commands. Oneimportant part of the HIL simulation system is the proces-sing of the images coming from the navigation cameras.There are two different approaches being implemented toserve two different distance ranges. First, there are methodsfor tracking the target in close range, providing full 6-DOFinformation. Second, there are also methods for tracking

the target at a longer distance (far range rendezvous).In this case, however, only the direction to the target andits approximate distance are estimated. Details of the EPOSvisual tracking system are reported in [17,18].

3. Contact dynamics simulation strategy

The architecture of the high-level EPOS control system isillustrated in the diagram shown in Fig. 4. The two robotsare controlled to track the relative motion between the twosimulated satellites. When a physical contact happens, thecontact force and moment generated by the docking hard-ware will be fed back to the satellite simulator whichsimulates the dynamic responses of the two satellites.As a result of the input contact force and moment,the simulated satellite motion will be affected althoughthe simulator does not have a contact dynamics model.For such a HIL simulation system to have high simulationfidelity, it is required that the simulated docking behavior(which is measured by the simulated motion stateand measured contact force data) must be the same asthat of the real satellites in space. Such a fundamentalrequirement cannot be met without the following twoconditions:

(1)

The robots used to deliver the simulated satelliterelative motion must be able to respond to the HILcontrol commands very fast.

(2)

When reacting to a physical contact during a dockingsimulation, the robots (at their tips) must dynamicallybehave like the on-orbit satellites being simulated.This is equivalent to an impedance match.

Although the necessity of the above-stated first condi-tion is not difficult to understand, it is not easy to meet forthe EPOS system because the two KUKA robots are indus-trial robots with massive bodies. They were designed forcommon industrial applications, such as working in anautomobile assembly line, and thus, the robots do not havevery fast responding speed. The known responding time ofthe robots is about 8 command cycles and each commandcycle takes 4 ms [19]. In other words, the duration from thetime when the EPOS control system issues a controlcommand to the time when the robot physically reacts tothe command can be up to 8 command cycles or 32 ms.This is a large time delay for controlling a robot to performcontact motion. Moreover, the maximum sampling rate ofthe robots is the same as their commanding rate, 250 Hz.Such a rate has been quite high for a usual industrial robot,but it is not considered high for a robot used for HIL contactdynamics simulation, which is preferred to be sampled at arate of at least 1000 Hz [5]. Since the robots must be usedas is, a special process control will be used to handle thetime delay problem. The Robotics and Mechatronics Insti-tute of DLR is currently developing technology to practicallysolve the problem. Their approach is based on the principleof actively balancing the energy input to and that outputfrom the robotic system. In other words, the method istrying to achieve a passivity behavior of the industrialrobots in the HIL simulation process, so that the possible

Fig. 3. Typical EPOS HIL simulation scenario.

Fig. 4. Control system of the EPOS facility.

O. Ma et al. / Acta Astronautica 81 (2012) 335–347338

simulation instability due to the time delay will nothappen. A description of the approach can be found in[20,21].

The second condition cannot be naturally met by theindustrial robots either because the robots have verydifferent dynamics properties than the satellites or they

O. Ma et al. / Acta Astronautica 81 (2012) 335–347 339

are basically positioning machines with very high impe-dance (or very high stiffness when holding on a position).This point can be better understood from the followingbrief description of the dynamics models of the satellitesand the robots.

When the two satellites are in proximity distance fordocking along the V-bar direction, they are in the sameorbit. We can define an orbital frame which moves alongthe orbit as a free-floating satellite does in the orbit. Sincewe are only interested in the relative dynamics of proxi-mity and contact operations within the final 25 m dis-tance, we ignore the celestial mechanics because its effectis negligible in comparison with those of the nonlinearinertia forces (centrifugal and Coriolis forces), the controlforces, and the contact forces. Therefore, the orbital framecan be assumed to be an inertial frame [27] because theorbital dynamics has been ignored. Such an assumptionhas been commonly used in the research and practice forspace robotics and satellite docking, see, for example,[28–32]. With the assumption, the dynamic motion of theservicing satellite with respect to the orbital frame isgoverned by the following Newton–Euler equations:

ms €xs ¼ fsþfc Is _xsþxs � Isxs ¼ ssþrs � fc ð1Þ

where ms is the mass of the servicing satellite; xsAR3 isthe position of the servicing satellite with respect to theorbital frame; fsAR3 is the resultant external force (exceptthe contact force) applied to the servicing satellite; fcAR3

is the resultant contact force applied to the servicingsatellite by the target satellite; IsAR3�3 is the centroidalinertia matrix of the servicing satellite; xsAR3 is theangular velocity of the servicing satellite; ssAR3 is theresultant external torque (except the contact torque)applied to the servicing satellite; and rsAR3 is the vectorfrom the mass center of the servicing satellite to the pointof the satellite on which the resultant contact force fc

exerts. Moreover, operator�means cross product of two3-D vectors. The attitude of the satellite, which may berepresented by three Euler angles fs or four quaternionses, can be determined by the second equation of (1) insimulation. In an application, the individual terms ofEq. (1) should be expressed either in the orbital frameor in the body fixed frame attached to the servicingsatellite or even in another reference frame as long asthey are consistent within the same equation.

The target satellite is assumed to be in free tumblingbefore docking and thus, its dynamic motion with respectto the orbital frame is governed by

mt €xt ¼�fc It _xtþxt � Itxt ¼�rt � fc ð2Þ

where mt is the mass of the target satellite; xtAR3 is theposition of the target satellite with respect to the orbitalframe; ItAR3�3 is the centroidal inertia matrix of thetarget satellite; xtAR3 is the angular velocity of the targetsatellite with respect to the orbit frame; and rtAR3 is thevector from the mass center of the target satellite to thepoint of the satellite on which the resultant contact forcefc exerts. Again, the attitude of the satellite, which may berepresented by three Euler angles ft or four quaternionses, is determined by the second equation of (2). In anapplication, Eq. (2) can also be expressed either in the

orbital frame or in the body fixed frame attached to thetarget satellite or another reference frame as long as theyare consistent within the equation.

On the other hand, the dynamics equations of the two6-DOF industrial robots of the EPOS system, whenexpressed in the robot’s operational space [22], have thefollowing form:

M1ðx1Þ €x1þC1ðx1, _x1Þ _x1þK1ðx1Þx1 ¼ J�T1 s1þ

fr

r1 � fr

" #

M2ðx2Þ €x2þC2ðx2, _x2Þ _x2þK2ðx2Þx2 ¼ J�T2 s2þ

�fr

�r2 � fr

" #

ð3Þ

where xiAR6 represents the generalized coordinates in theoperational space of the ith robot (i¼1,2); MiAR6�6 is thegeneralized inertia matrix of the ith robot in its opera-tional space; Ci _x i 2 R6 is the generalized centrifugal andCoriolis force; KiAR6�6 is the generalized stiffness matrixof the ith robot; JiAR6�6 is the Jacobian matrix of the ithrobot, which maps the joint rates to the tip linear andangular velocities of the robot; siAR6 represents the jointcontrol torques of the ith robot; frAR3is the resultantcontact force applied to the tip of the first robot and thus,�fr is the generalized resultant contact force applied tothe second robot; and riAR3 is the vector from thereference point of the ith robot’s tip to the point of the ithrobot on which the resultant contact force fr exerts. Thedetails of the Mi, Ci, and Ki matrices depend on kinematicsand dynamics properties of the ith robot as well as the time-dependent configuration of the robot [23].

Comparing Eqs. (1) and (2) to Eq. (3), we can under-stand that, even if we can make the tip relative motion ofthe two robots be exactly the same as that of the twosatellites, the resulting contact forces of the two systemsresulting from a docking operation, namely, fc and fr aswell as their resulting contact moments, will not be thesame because the robots and the satellites have verydifferent dynamics properties (the terms on the left-hand sides of the equations). This difference cannot beeliminated naturally because it is impossible to make thetwo robots have the same structures and other physicalproperties as the two satellites. The only possible way toachieve the same contact forces, namely, fc¼fr for thesame motion state of the two systems, is to implement aspecial robot control system to make the robots dynami-cally behave like the satellites during a docking operation.

Therefore, when a robot’s tip is in physical contactwith an external object during a docking operation, therobot may not comply as a free-floating satellite would.The robot may even encounter instability in a stiff contactcase. Note that whether a contact operation to be simu-lated is stiff or not should solely depend on the satellitesand their docking interfaces rather than the two industrialrobots. Therefore, a control loop outside the industrialrobots needs to be implemented to deal with this problem(since no inner control loops of the industrial robots canbe accessed). An end-effector force control method cannotbe used here because the reference contact force for aproper docking operation can never be known in advance.

O. Ma et al. / Acta Astronautica 81 (2012) 335–347340

An ideal approach would be to apply an impedance controlstrategy [14]. However, impedance control methods requiretorque control capability at the joint level. This is notavailable in the KUKA robots. All we have from the robotsis an end-effector position or rate control capability. Similarly,many other advanced and proven robot control strategies,such as the computed torque control [24], passivity-basedcontrol [25], etc. cannot be implemented either because therobots do not have a joint torque control capability or do nothave an inverse dynamics model (robot manufacturersusually do not provide dynamics models of their products).As a result, an end-effector admittance control strategy isproposed to deal with the problem because such a controlmethod does not need a joint torque control capability anddoes not need a dynamics model of the robot either, but itstill can achieve the required impedance at the tip duringcontact motion. The control strategy is shown in Fig. 5 and isbriefly explained next.

For the design of the admittance control of the EPOSrobots, we need to assume a reference impedance modelof the robotic system in terms of the relative motionbetween the two robots, namely

f ¼MD €xþCD _xþKDx ð4Þ

where fAR6 is the resultant contact force-moment exertedon the approaching robot, DxAR6 is the error between thecurrent relative pose (position and orientation) and thetargeted relative pose between the two sides of thedocking interface (one side of the interface is with theservicing satellite and the other part is with the targetsatellite). The targeted relative pose is assumed to zerowhen the two sides of the docking interface are perfectlyengaged. Therefore, Dx is also considered as the misalign-ment between the two sides of the docking interface oreven the misalignment between the two satellites. Since adocking operation (i.e., physical contact) would not hap-pen until the two satellite have been aligned within a very

Fig. 5. Admittance control stra

Fig. 6. Position feedback controller for tra

small envelope of a few inches in translation and a fewdegrees in rotation [26], the angular part of the relativepose can be approximated as non-coupled. Hence, therelative pose may be simply defined as

Dx¼ ½x2�x1 y2�y1 z2�z1 a2�a1 b2�b1 g2�g1�T ð5Þ

where (x1,y1,z1,a1,b1,g1)are the 3 Cartesian coordinatesand 3 Euler angles of the docking interface of the servicingsatellite and (x2,y2,z2,a2,b2,g2) are those of the targetsatellite. Note that all of these coordinates must beexpressed in the same coordinate frame (either in theorbital frame or anyone of the two satellite body fixedframes) so that the calculation of the docking gap Dx ismeaningful.

Since the robots are controlled to simulate thedynamic behavior of a docking satellite, it is reasonablethat the coefficient matrices of the impedance model (4)the same as those given in the satellite dynamics model(1). In other words, the admittance control is intended tomake the industrial robot’s tip dynamically behave likethe servicing satellite during a docking operation. Thus,the admittance control law is chosen as

DX ¼ ðMs2þCsþKÞ�1F ð6Þ

where DX and F are the Laplace transforms of the relativeposition-orientation and the contact force-momentbetween the two robots, respectively. Contact force fR ismeasured by the force-moment sensor installed behindthe docking interface hardware. For simplification, thecoefficient matrices of the impedance model (4) may beassumed constant. This approximation is valid becausethe docking relative speeds of all the known real spacedocking cases are very low (no more than several cen-timeters per second).

The DX obtained from (6) will be used to adjust thereference trajectory of the industrial robot’s tip positioncontroller. In fact, the robot may not be able to reach thedesired trajectory because of inevitable disturbances and

tegy for the EPOS robot.

jectory tracking of the End-Effector.

O. Ma et al. / Acta Astronautica 81 (2012) 335–347 341

uncertainties. To make sure that the robot can accuratelytrack the desired trajectory, an end-effector position feed-back loop should be added for improving the robot’stracking performance, as shown in Fig. 6. The desiredend-effector trajectory xd, _xd is compared to the actualend-effector motion xR, _xR, and a PD controller compen-sates for any error, then an inverse kinematics model ofthe KUKA robots calculates the reference joint angles andjoint rates qd, _qd. Finally, the internal joint position controlwill compute the necessary torquessto drive the KUKArobots at the required configuration.

Finally, it should be pointed out that the intention ofintroducing the HIL simulation is to take advantages of bothsoftware simulation and hardware test but there exists apossible risk that the resulting system takes disadvantagesof both software simulation and hardware test. We usedtwo measures to prevent or at least mitigate such a risk: (1)make sure that the simulation of satellite dynamics (note:without contact dynamics) is as accurate as possible. Thisshould not be difficult with the current state-of-the-artmodeling and simulation technologies and lots of simula-tion experience from the past missions; (2) avoid the robotcontrol system (which is not the satellite’s control system)reacting to the physical contact arbitrarily by itself. Instead,the robot has to exhibit the contact dynamics property (i.e.,impedance) of the docking satellites. If these two measuresare implemented properly, the said risk will be small ornone. Note that such a risk exists in all the other hardware-in-the-loop simulation systems too. Another obvious draw-back of EPOS is that it is a much more complicated activesystem in comparison to an air-bearing based passivetesting system. We believe that the added complexity willlead to better performance and fidelity as a tradeoff.

4. Simulation study

We use dynamic simulations to investigate if theproposed control strategy can achieve the desired HILsimulation for satellite docking. Without loss of general-ity, we use a planar case to demonstrate the implementa-tion and performance of the EPOS HIL system because a2D case can be easily derived analytically and understood,especially for the contact dynamics modeling.

4.1. Satellites and robots models

As shown in Fig. 7, each satellite is modeled as a tworigid-body system. The first body is the main body of thesatellite and the second body is the docking interface.The two bodies are connected with a spring-damper.The centers of mass of the two satellites are labeled withCOM11 and COM21, respectively. Each satellite has abody fixed frame called ‘‘satellite frame’’ originated atthe satellite’s center of mass while the x–y frame isassumed to be an inertial frame. The center of mass ofthe docking interface is marked with COM12 and COM22,respectively, for the two satellites. The docking interfaceconsists of a conic surface (such as a nozzle of a mainrocket engine) on one satellite and a stick probe on theother satellite. The contact can occur anywhere on theinner surface of the cone. A compliance-based contact

dynamics model was implemented to calculate the localcontact force during docking. In this case, the relativepose of the two satellites is defined as

xS ¼ ½xS2�xS1 yS2�yS1 aS2�aS1�T ð7Þ

The simplified EPOS robotic system is depicted inFig. 8. The first robot (Robot 1) is modeled as a 2-bodysystem in which the first body is a fixed rigid pole becausethe real EPOS Robot 1 is stationary in a normal operation.The second body represents the docking interface hard-ware (the conic part of the docking interfaces). The twobodies are connected by a 3-DOF (2 translational and onerotational) spring. Thus, the docking interface of Robot 1has compliance in all three axes. Robot 2 is modeled as a3-joint planar manipulator. The docking interface isattached to the tip of the manipulator with a spring.Points P1 and P2 represent the tips of Robot 1 and Robot 2,respectively. Robot 1 has the cone attached to its tip as itsdocking interface and Robot 2 has the stick probe as itsdocking interface. When the local contact force is appliedto the equations of motion, it has to be resolved to thereference points P1 and P2 in a proper frame. The gravityforces applied to both robots are included in the robots’simulation model because these two robots operate onthe ground. Therefore the relative pose of the two HILindustrial robots is defined as

xR ¼ ½xR2�xR1 yR2�yR1 aR2�aR1�T ð8Þ

The mathematical model of the robotic system shown inFig. 8 (although only a planar case) is very lengthy and thus,will not be presented in the paper, so that we can focusmore on the discussion of the main topic of the paper.

4.2. Contact force modeling

For relative simplicity in the mathematical develop-ment, we deal with a specific contact scenario, namely, astick probe contacting an inner cone surface as shown inFig. 9. This type of geometry roughly represents severalreal contact interface designs used in space missions.

The modeling is based on the following assumptions:

�

The contact is assumed to be point contact, whichmeans the contact area is just a point so that thecontact force will be a concentrated acting on thecontact point.

�

This contact geometry can be uniquely described bythree parameters: L1, L2 and a, as depicted in Fig. 9.

�

The contact surface (the conic surface in this case) will notbe deflected or change its shape because of the contact, sothat the geometry parameters will not change.

The position and velocity of the probe P are arbitrarilygiven as p¼ x y

� �Tand _p ¼ ½ _x _y�T . The relative position

of the probe with respect to the cone has four cases asshown in Fig. 10. These different cases can be identified bythe following conditions:

(1)

If x�L1 40 ) probe is outside the cone (no contact) (2) elseif x40 and ðx2tan2a�y2Þ40 ) probe is

inside the cone (no contact)

Fig. 7. Dynamics model of two docking satellites.

Fig. 8. 3-DOF robotics system used to represent the EPOS robots.

-fc

fc

Fig. 9. Point-contact-cone contact model.

fc

Fig. 10. Four different contact situations between a cone and probe.

O. Ma et al. / Acta Astronautica 81 (2012) 335–347342

O. Ma et al. / Acta Astronautica 81 (2012) 335–347 343

(3)

Fig.the

elseif x40 and ðx2tan2a�y2Þr0 ) probe touchesthe cone’s inner surface (in contact)

(4)

elseif xo0) probe touches the end of the cone (incontact)

In Cases (2) and (3), there are always two points on thecone surface (namely, Pc and Pcin Fig. 9) which have aminimum distance to the probe tip P. The coordinates ofthe two closest points on the cone surface can be found as

Pc : xc ¼ ðxþytanaÞcos2a, yc ¼ ðxþytanaÞsina cosa

Pc : xc ¼ ðx�ytanaÞcos2a, yc ¼�ðx�ytanaÞsina cosað9Þ

Which of the two points is closer to the given point P

can be easily identified by checking their distances to P asfollows:

d¼ signðx�xcÞ

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiðx�xcÞ

2þðy�ycÞ

2q

ð10Þ

Contact happens when distance d is zero or less thanzero. A negative distance value indicates the amount thatthe probe’s tip penetrates into the cone surface. Of course,a positive distance means no contact. The magnitude ofthe contact force can then be computed based on theHertz model as follows:

f c ¼kc9d9

3=2þbc

_d, if dr0 ðin contactÞ

0, otherwise ðno contactÞ

(ð11Þ

where kc and bc are the contact stiffness and contactdamping coefficient which depend on the material andgeometry of the contacting areas. Since we are dealingwith a 2D contact motion, it is more convenient to expresseverything in vector form. In this way, the position of theclosest point of the conic surface can be expressed in

11. Method to verify the fidelity of the EPOS simulation. (For interpretation

web version of this article.)

terms of the position of the probe tip as follows:

pc ¼xc

yc

" #¼

cos2a sinacosasinacosa sin2a

" #x

y

" #or pc ¼

xc

yc

" #

¼cos2a �sinacosa

�sinacosa sin2a

" #x

y

" #ð12Þ

The contact force vector is then

fc ¼ðkcd3=2

þbc_dÞn, if x�xc r0 ðin contactÞ

0, otherwise ðno contactÞ

(ð13Þ

where n is a unit normal vector of the contacting surfaceat the contact point. In general, the normal vector of apoint (xc, yc) on a surface, which is reduced to a curve inthe 2D space, is defined as

n¼1ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

ðdx=dlÞ2þðdy=dlÞ2q dx=dl

dy=dl

" #x ¼ xc ,y ¼ yc

¼1ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

ðdx=daÞ2þðdy=daÞ2q dx=da

dy=da

" #¼�sin a7cos a

" #ð14Þ

where l is the parameter of the curve, namely, x¼x(l) andy¼y(l). The sign on the second component depends onwhether the normal is of the upper or lower part of thecone surface. The time rate of the penetration can becomputed from the relative velocity as follows:

_d ¼ vTr n¼ ð _p� _pcÞ

T n ð15Þ

where _p and _pc are the velocities of points P and Pc,respectively; and vr is the relative velocity between thetwo closest points.

4.3. Simulation results

In order to verify that the proposed control strategycan render the EPOS robots the same or very close

of the references to colour in this figure legend, the reader is referred to

0 2 4 6 8 100

0.5

1

Tip

rel.

X (m

)

EPOS HIL simulationTrue satellite motion

0 2 4 6 8 10-0.2

0

0.2

Tip

rel.

Y (m

)

0 2 4 6 8 10160

180

200

220

Time (s)

Tip

rel.

angl

e (d

eg)

Fig. 13. Comparison of the relative tip pose between the two systems.

0 2 4 6 8 10-0.1

0

0.1

Tip

rel.

Vx

(m/s

)

EPOS HIL simulationTrue satellite motion

0 2 4 6 8 10-0.2

0

0.2

Tip

rel.

Vy

(m/s

)

0 2 4 6 8 10-10

0

10

20

Time (s)

Tip

rel.

angu

lar

V. (

deg/

s)

Fig. 14. Comparison of relative the tip velocities between the two

systems.

O. Ma et al. / Acta Astronautica 81 (2012) 335–347344

impedance property as that of the two simulated satel-lites during contact motion, we designed a verificationmethod as shown in Fig. 11. The block named ‘‘Indepen-dent Satellite Simulator’’ is a stand-alone simulation ofthe two satellites performing docking in zero gravityconditions. The contact dynamics model was used in thesimulator to compute the contact forces resulting fromdocking. The output of this simulator is considered as the‘‘true docking behavior’’ for evaluating the fidelity of theEPOS HIL simulation. The block named ‘‘Real-time Satel-lite Simulator’’ represents the satellite simulator of theEPOS system which is the software simulation part of theEPOS. The block called ‘‘EPOS Robotic System’’ simulatesthe two EPOS robots, representing the hardware simula-tion part of the EPOS. These two blocks comprise theentire EPOS HIL simulation system (enclosed with reddashed line in the diagram). Since this is a simulationstudy, a contact dynamics model is needed in the ‘‘EPOSRobotic System’’ block to represent the real contact hard-ware. We used the same contact dynamics model as thatused in the ‘‘Independent Satellite Simulator’’ block.Because of this, the resulting docking behavior from the‘‘Independent Satellite Simulator’’ block and that from the‘‘EPOS Robotic System’’ block should be identical if theproposed EPOS control system works perfectly. Therefore,the two outputs are compared for judging the fidelity ofthe EPOS system. The block named ‘‘Comparison plots’’provides the comparison plots presented in Figs. 12–17.

In the presented simulation case, Satellite1 is assumedat rest initially and Satellite2 moves toward Satellite1 atan initial relative speed of 0.05 m/s along the �x direc-tion. Such a relative speed for docking is reasonable inpractice [26]. The two satellites are assumed to have aninitial lateral misalignment of 0.15 m in the y axis. Whensetting up a docking simulation, we have to first assumeinitial motion conditions. From the application’s point ofview, it is logical to first define the initial conditions ofthe two satellites and then calculate the correspondinginitial conditions of the two EPOS robots because theEPOS facility is used to simulate the satellite operations.

0 2 4 6 8 100

0.5

1

Tip

rel.

X (m

) Sat relative tip motionRob relative tip motion

0 2 4 6 8 10-0.2

0

0.2

Tip

rel.

Y (m

)

0 2 4 6 8 10150

200

250

Time (s)

Tip

rel.

angl

e (d

eg)

Fig. 12. Comparison of the ‘‘Satellite Simulator’’ output and the EPOS

Robot 2 tip motion.

0 2 4 6 8 10-300

-200

-100

0

X fo

rce

(N)

EPOS HIL simulationTrue satellite motion

0 2 4 6 8 10

-200

-100

0

100

Y fo

rce

(N)

0 2 4 6 8 10-5

0

5

Time (s)

Mom

ent (

Nm

)

Fig. 15. Comparison of the tip contact force and moment with the action

of the admittance control.

5.5 6 6.5 7 7.5

-200

-100

0

X fo

rce

(N)

EPOS HIL simulationTrue satellite motion

5.5 6 6.5 7 7.5-200

0

200

Y fo

rce

(N)

5.5 6 6.5 7 7.5-5

0

5

Time (s)

Mom

ent (

Nm

)

Fig. 16. Comparison of the tip contact force and moment without the

admittance control.

5.5 6 6.5 7 7.5-300

-200

-100

0

X fo

rce

(N)

EPOS HIL simulationTrue satellite motion

5.5 6 6.5 7 7.5-200

0

200

Y fo

rce

(N)

5.5 6 6.5 7 7.5-5

0

5

Time (s)

Mom

ent (

Nm

)

Fig. 17. Comparison of the tip contact force and moment with the action

of the admittance control.

O. Ma et al. / Acta Astronautica 81 (2012) 335–347 345

This will have a problem because the EPOS is a hardwaresystem and it is nontrivial to set up a given initial tipposition and velocity simultaneously because the robothas to move from rest and not from an arbitrarily desiredvelocity. For this reason, in our simulations, we madeRobot 2 match only the initial relative position of the twosatellites, leaving the initial relative velocity at zero.Simulation tests have showed that the robot’s controlsystem can drive the robot to quickly (within 0.3 s) reachand then follow the reference velocity provided by thesatellite simulator.

In the simulated docking case, Satellite2 passively floatstoward Satellite1 along the x axis with a constant speed of0.05 m/s until the tip of its probe hits the inner surface ofthe docking interface of Satellite1 at about t¼0.8 s for thefirst time. Then the probe tip continues moving forwardwith a few small bounces and slips along the conic surfaceuntil it reaches the end of the conic surface at about t¼5 s.Then the probe tip enters into the hole at the end of the

cone and makes a few bounces around the walls of the holeat the end of the cone. Since there is no capture mechanismimplemented in the simulation model to catch the probeand lock the two satellites together, Satellite2 eventuallybounces back from Satellite1, which causes the probe tostart moving away from the end of the cone at about t¼7 s.The simulation stops at t¼10 s.

Fig. 12 shows the relative pose between the two satellites,as defined in Eq. (7), which was calculated from the‘‘independent satellite simulator’’ as indicated in Fig. 11.The relative pose between the two EPOS robots, as definedin Eq. (8), was calculated by the ‘‘EPOS robotic system’’ blockin Fig. 11. From the plots, one can see that the EPOS Robot 2tracks the output of the ‘‘Real-Time Satellite Simulator’’ blockvery well, since the two plots are overlapped. This indicatesthat the EPOS robots are capable of tracking the satellitesimulator as expected.

The simulated relative tip motion from the ‘‘Indepen-dent Satellite Simulator’’ block and those from the ‘‘EPOSrobotic system’’ block are shown in Figs. 13 and 14. Thetwo plotted curves should be perfectly overlapped if theEPOS HIL simulation was perfectly accurate. As we cansee, EPOS HIL simulation and the independent satellitesimulation perfectly match before the docking and theydo not precisely match after the docking starts. Thismeans that the EPOS HIL simulation does not perfectlysimulate the satellite docking. Since the shown errors inthe plots are not large enough to change the operationconsequence, it should be acceptable in practice [5].

Fig. 15 depicts the simulated contact force-momentdata from the ‘‘Independent Satellite Simulator’’ block andthose from the ‘‘EPOS robotic system’’. The two plottedcurves should be perfectly overlapped if the EPOS HILsimulation was perfectly accurate. As expected, this is notthe case. However, the two velocity profiles grossly match(the motion trends are matching). The poorly matchedtime period (i.e., from 5 to 7 s) is when the probe tip wasbouncing around inside the hole at the end of the conicdocking interface. This is a very chaotic contact situationand very difficult to model and simulate precisely. Again,because the errors shown in the plots are not largeenough to change the operation consequence, they shouldbe acceptable in practice.

In order to show the resulting tip contact forces withand without using admittance control, the tip contactforce and moment from the EPOS HIL simulation and theIndependent Satellite Simulation during the most signifi-cant contact period are plotted in Figs. 16 and 17. It can benoticed that in the absence of admittance control (Fig. 16)the contact force and moment from the EPOS HIL simula-tion is very different from these from the independentsatellite simulation. When the admittance control isactivated (Fig. 17), the differences become much smaller,which indicates that the admittance control does its job asexpected to help the EPOS robots to match the impedanceof the docking satellites during contact operation.

It should be emphasized that the above discussed com-parison results are mainly qualitative as opposed to quanti-tative in terms of the comparison errors. We consider such aqualitative comparison sufficient for its purpose in this paper.In fact, for such a complicated robotics-based HIL simulation

O. Ma et al. / Acta Astronautica 81 (2012) 335–347346

system to simulate satellite docking with nontrivial contactscenario, simulation errors are inevitable. Simply comparingthe magnitude errors shown in the plots at isolated timepoints is inappropriate because errors exist in both themagnitude and phase of any compared quantity. In fact, avery small phase error (phase shift) may cause significantmagnitude error in the plots, especially during drasticimpact–contact times. Therefore, more sophisticated quanti-tative comparison criteria must be developed if one reallywants to do such comparison. Reference [5] has a detaileddiscussion about how to establish criteria for reasonablecomparison in both qualitative and quantitative levels forspace robotics applications.

5. Conclusion

The on-going effort of DLR to develop a high-fidelity,hardware-in-the-loop (HIL) contact dynamics simulationcapability for the new European Proximity OperationsSimulator (EPOS) system was introduced. The facility usestwo 6-DOF industrial robots to deliver the relative motionof the two satellites which perform proximity rendezvousand docking. To meet the special requirements for the HILcontact dynamics simulation, the two robots have to beproperly controlled with advanced robotics control tech-nology. However, it was found that many advancedrobotics control techniques cannot be implementedbecause the industrial robots do not have a joint torquesensing and control capability and their dynamics models(including the key model parameters) are unavailablefrom the manufacturer. Further, the joint control hard-ware and software are not accessible or changeable to theEPOS developer because they are commercial products.To solve the problem, an admittance control strategy wasproposed. The method can be implemented withouttouching the original control system of the industrialrobots at both the joint and arm levels. A simulationstudy with a 3-DOF robotic system showed that theproposed admittance control method can make the indus-trial robots in the current setting of the EPOS facilitybehave like the two docking satellites, in the senseof impedance matching during a docking operation.The findings from this study provides good evidence andexperience to the EPOS development team or other inter-ested people to confidently use industrial robots for high-fidelity HIL contact dynamics simulations.

Acknowledgments

The authors acknowledge many fruitful discussionswith Mr. Klaus Landzettel and Mr. Rainer Krenn of theDLR’s Robotics and Mechatronics Institute for the devel-opment of the HIL contact dynamics capability of EPOS.Dr. Ou Ma acknowledges the support of the GermanAcademic Exchange Service through a DLR-DAAD researchfellowship for working as a senior visiting scientist at DLRwhile he was on a sabbatical leave from the New MexicoState University.

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