Results and Verification of Spacecraft Docking Emulation using Hardware-in-the-Loop Simulation

Transcription

1 Results and Verification of Spacecraft Docking Emulation using Hardware-in-the-Loop Simulation S6bastien Laurier Chapleau t*, l~ric Martin t* and Luc Baron* t Canadian Space Agency, St-Hubert (QC), Canada, Eric.Martin@space.gc.ca * ]~cole Polytechnique, Montr6al (QC), Canada, Sebastien.Laurier-Chapleau@polymtl.ca Luc.Baron@polymtl.ca Abstract. The interest in new demonstration missions of space servicing is decidedly rising in this beginning of the twenty-first century, as attested by several well-known projects like the Orbital Express, TECSAS, CX-OLEV and others. Such missions require a thorough knowledge of the mechanical behaviour of spacecrafts during docking or berthing. In order to adequately study the dynamics involved, a number of docking emulation test-beds have been elaborated worldwide and tested for their efficiency in providing realistic results, thereby preventing an eventual failure of the docking process. The Canadian Space Agency is developing such a test-bed for spacecraft docking emulation by using hardware-in-the-loop simulation. This paper describes this test-bed and presents the verification procedure used to verify the functionality of this type of simulation. 1 Introduction As attested by such demonstration missions as the Orbital Express (Potter, 22), TEC- SAS (Martin, Dupuis et al., 25) and CX-OLEV ( there is a worldwide interest in space servicing. These missions involve the docking or berthing of spacecrafts and necessitate the anticipation of their mechanical behaviour during impact before performing those operations in space. To this end, analyses can be done on ground by three different docking system emulations: numerical simulation, hardware test-bed and hybrid test-bed (Yokota et al., 1998). For numerical simulations, mathematical models are used to simulate the behaviour of the spacecrafts during contact. One such model is the Contact Dynamics Toolkit (CDT) developed by MDA (Ma, 2). This toolkit can perform different types of contact simulation such as bouncing, sliding, rolling, spinning, sticking, and jamming. It is a useful model for the modelling and simulation of intermittent contact/constrained dynamics of mechanical bodies (Martin, Parsa et al., 25). The Canadian Space Agency (CSA) is also developing a contact module to accurately model complex contact behaviours (Gonthier et al., 24). The major disadvantage of numerical simulations is that they are very sensitive to the variation of mechanical properties such as the geometry and the *Applications for permission to use, reproduce or translate all or part of this paper should be made to the Canadian Space Agency (~) Canadian Space Agency

2 398 S.Laurier Chapleau, E.Martin, L.Baron surface properties of the model, for example the friction coefficient. Consequently, these properties have to be defined with precision, and they can be difficult to evaluate. One alternative is the use of a hardware test-bed with free-floating physical mockups to emulate the dynamic movements and determine the contact forces during the docking of spacecrafts. Examples of such models are the Air-Bearing Mobility Simulators (ABMS) of the George C. Mashall Space Flight Centre (MSFC) (Hays et al., 23), the Experimental Free-Floating Robot Satellite Simulator (EFFORTS) of the Tokyo Institute of Technology (TIT) (Yoshida, 23) and the MDA Space Missions capture test-bed. When the effect of earth gravity and friction with the exterior is eliminated effectively, this kind of test-bed provides more realistic data than numerical simulations, but is less effective for the validation of a large range of spacecraft configurations and cannot be used with all real spacecraft prototypes (Uchiyama et al., 23). Hybrid test-beds use mockups to measure the contact forces, and numerical simulations to compute the trajectory of one or both spacecrafts. Example of such test-beds is the Rendezvous and Docking Operation Test System (RDOTS) of the Japan Aerospace exploration Agency (JAXA) consisting of a nine-dof system obtained by a six-dof parallel platform and a rail-mounted chaser base with two additional degrees of freedom. Several hybrid test-beds using rail and air-table do not permit all DOF motion, and the precision of the results are often affected by friction and inconstant inertia of mockups. To bypass these problems, the CSA is developing a test-bed for spacecraft docking emulation by using Hardware-in-the-Loop Simulation (HLS) to provide a technology that facilitates the study of satellite docking capabilities. This test-bed, which is described in detail in Section 3, uses an existing test-bed, namely the Special Purpose Dextrous Manipulator (SPDM) Task Verification Facility (STVF) presented in Section 2. Section 4 describes the experimental results that were obtained and the verification processes used. 2 STVF approach As a partner in the International Space Station (ISS), Canada is responsible for the verification of all tasks involving the SPDM. One component of the verification process is performed using the STVF, which is located at the John H. Chapman space centre. The STVF Manipulator Test-bed (SMT) shown in Fig. 1 is used to refine the analysis of the contact portion of the SPDM tasks before they are conducted in space. Aside from the rigid robot SMT and its controller, the HLS test-bed consists of a simulation of the Space Station Remote Manipulator System (SSRMS) and the SPDM dynamics, as well as a visualisation engine. The motion of the SPDM is controlled by an operator through a simulation engine that generates the endpoint trajectory of the SPDM, which is used as a setpoint for the SMT Robot controller Figure 1. SMT Robot with the MDA end-effector.

3 Results and Verification of Spacecraft Docking to command the SMT end-effector's position. To allow the dynamics simulation to react to external contact forces, these forces are measured using a force/moment sensor and fed back to the dynamics simulation model. This approach can be used for different types of space robots and can effectively emulate such phenomenons as the vibrations of the space-robot base. The controlled ground robot must be transparent in the frequency band of contact tests, and is made to behave like the simulated space robot by forcing it to track the Cartesian acceleration of the latter. In addition, in order to correct positioning errors, Cartesian position and velocity feedback are used. In the bandwidth of interest for the SPDM, experimentations give good performance and stability (Martin, Doyon et al., 25). 3 Docking emulation approach To further develop the HLS approach, the CSA projected to implement this type of simulation to emulate the docking phase of spacecrafts floating in a zero-gravity environment by using STVF as a test environment. This project requires the implementation of a spacecraft simulator in the STVF environment. The major functionalities of the STVF test-bed were kept intact and only the dynamic simulation part was changed. The SPDM simulation was modified to simulate the relative motion of the chaser and target spacecrafts. The contact forces occurring between the chaser's end-effector installed on the SMT Robot, and the target's grapple fixture positioned on the fixed force/moment sensor are measured and applied as external forces on both spacecraft models in the simulator. As shown in Fig. 1, the MDA end-effector is mounted on the SMT Robot as an experimental prototype of docking mechanism. The dynamics of the chaser and target spacecrafts are modelled with SYMOFROS (L'Archev~que et al., 2) in the Docking Simulator, within the MATLAB/SIMULINK environment. Contrary to the target model, which is a rigid body, the chaser model has the particularity of having a 6-DOF spring and damper compliant mechanism between its body and its end-effector. This mechanism allows for the docking of two spacecrafts even if the chaser has some misalignment approach. It could also represent the compliance of an uncontrolled robot arm. The simulator also includes the necessary functions to determine the relative trajectory of the chaser frame with respect to the target frame required to perform HLS. The Docking Simulator has the capabilities of running not only in HLS mode but also with a contact dynamics model based on the CDT of MDA (introduced in Section 1). The operator can use both methods by toggling a switch in the command console. More detailed information is given in Martin, Doyon et al. (25). 4 Experimental tests and verifications This section presents the Docking Simulator verification procedures and the results obtained. Subsection 4.1 presents the results obtained with contact dynamics simulation as the active mode and Subsection 4.2 describes the verification procedures and results obtained in HLS mode.

4 4 S.Laurier Chapleau, F,.Martin, L.Baron (a).6 ~,, i O: (b) Time (s) Figure 2. Simulation results using CDT: (a) Relative normal velocity; (b) Normal contact force; under conditions of Table 1.! Table Fig Simulation parameters for Parameter Value Approach vel. 5 cm/s Target mass 2 kg Chaser mass 5 kg End-effecteor mass 6 kg Compliance fn 1,6 Hz Compl. damp. ratio (~) 1, 4.1 Pure simulation mode In order to verify the Docking Simulator using the contact dynamics mode, the contact parameters and the geometry of the end-effectors shown in Fig. 1 were provided to CSA by MDA Space Missions. When no contact occurs between the chaser and the target spacecrafts, the verification is performed by using analytic results as a reference. When contact does occur during a simulation, the analytic results are virtually incalculable and there is no experimental data from an actual docking of spacecrafts available for comparison. Therefore, the accuracy of the simulator cannot be precisely assessed. Based on engineering judgment, however, it is possible to evaluate the validity of the results. For example, Fig. 2 shows the results obtained with the Docking Simulator using the CDT. The parameters used for this simulation are presented in Table 1. As shown in Fig. 2 (a), the relative velocity of the spacecrafts is null after the docking phase. More results will be presented in Subsection 4.2 together with the results obtained in HLS mode. 4.2 HLS mode This section presents the verification procedure used for the testing of the HLS mode of the Docking Simulator presented in Section 3. After the Docking Simulator was incorporated in the STVF model, tests in HLS mode with the MDA end-effector mounted on the SMT Robot (see Fig. 1) showed instability when contact occurred. To determine the source of this instability, tests were performed under direct central impact on the sensor force, using a round peg as an end-effector, which has the advantage of having both a more robust structure and less complex geometry. This new configuration served to demonstrate that the system shows more signs of instability with certain inertial properties and approach speed configurations, particularly in the case of small spacecrafts. Fig. 3 shows the time history of the force for the simulation (a) and experimental (b) tests with the properties shown in Table 2. After calculation of the

5 Results and Verification of Spacecraft Docking (a) o i...!-"-,,,... i... i... I ol1 i i ""... ~..., ,6 (b) g 4...!... ~..: i!il i~... i Time (s) Figure 3. Measured normal contact force: (a) Pure simulation mode; (b) HLS mode; under conditions of Table 2. Table 2. Spacecrafts configurations for Figs. 3 and 5. Parameter Value Approach vel..2 cm/s Target mass 9.7 kg Chaser mass 25 kg End-effector mass 6 kg Compliance fn 1.5 Hz Compl. damp. ratio (~) 1. areas under the graphs, which are related to the momentum of each body, it is apparent that, for the experimental test, the linear momentum of each spacecraft had a bigger variation. It is important to note that the force applied to the spacecrafts is different from the measured force because of the fact that a first-order filter is used to eliminate undesired frequency bandwidth, as shown in Fig. 4. In this segment of the verification tests, the cut-off frequency is kept identical to the one used in the STVF model, i.e. 4 Hz. The conservation of the kinetic energy of the system was a condition used for the verification of the experimental data. The kinetic energy at time t ~, K(t~), for a one dimensional movement is calculated as 1 1 K(t')- ~Mtarget Vtarget(t' 2 ) + ~MchaserVchaser(t 2,). (4.1) where M and V(t t) are respectively the mass and the velocity of the target and the chaser spacecrafts at time t ~. Using Eq. (4.1), Fig. 5 shows the kinetic energy of the system using the parameters of Table 2. The solid (blue) line represents the experimental kinetic energy and the dashed (red) line, the simulation. The velocities used for the calculation of the kinetic energy in Fig. 5 are calculated in function of the end-effectors' velocities. Since the chaser is constituted by two rigid bodies, we cannot use the transient part as the real kinetic energy of the system. However after stabilization of the chaser's compliant mechanism at approximately 6 seconds, the velocities of both the end-effector and the spacecraft are the same. As shown in Fig. 5, the final kinetic energy in the experimental test is higher than the initial kinetic energy, which is impossible according to the first law of thermodynamics. The kinetic energy reduction in the simulation test is mainly due to the damping mechanism of the chaser and the restitution coefficient during the impact of the end-effectors. As the analytic calculation of the real energy loss resulting of the damping mechanism of the chaser is very complex, experimental tests were performed for a direct central impact (without the spring/damper mechanism of the chaser) of the peg probe on the force/moment sensor. Fig. 6 (a) shows the kinetic energy ratio of the system after impact by varying the mass of the spacecrafts for different approach velocities on this series of

6 42 S.Laurier Chapleau, E.Martin, L.Baron [ First.order [ Measured Contact Force [ / Filter I! Ground Robot ;" ~'";.-"" ~ Tip A~eteration i i, ~ocrdng l,. ~ :......, :. Simulator ~,.~,,,,... / I!... " 111 Tip'S'J I, /, [ Modol~ Moaol,,l Ro~ ~ : ~o~ ~.~... Oiound Ill... ~_L~ar ~'~' 'artesidn ~ Robot ~ x qo "3 ~'-1 spacecrafls, i~ ~,,o Ground Robot Joint,,.- I --I oroun I Angles and Rates ~lxtip, G L.~ Robot [~... --]~ematic.s] Figure 4. First-order filter impact on measured forces. Time (s) Figure 5. Kinetic energy with the vel. of the end-effectors under conditions of Table 2. tests. Fig. 6 (b) shows the kinetic energy ratio of the system by varying the spacecraft masses for different cut-off frequencies of the first-order filter, with an approach velocity of 5 mm/s. It is to be noted that an equal mass was used for the two spacecrafts in this series of tests. The fact that these tests were conducted under very small impact velocity and with high rigidity surfaces allows us to assume that in reality, almost no kinetic energy should be lost during collision. This is equivalent to having a kinetic energy ratio of one. The kinetic energy ratio higher than one as shown in Fig. 6 illustrates that the emulation made with the docking test-bed does not provide conclusive results. One possible reason for this inconsistent data is that the test-bed that was used is made up of a closed-loop emulation (the SMT Robot is fixed to the ground, as is the forces/moments sensor), contrary to free-floating spacecrafts that consist of an open-loop system (no parts retain the two spacecraffs together). Consequently, the STVF configuration has some unknown internal forces resulting from contact that create disturbance in the forces to be applied on spacecrafts. This makes the impedance of the test-bed used different from the impedance of the free-floating spacecraft system to be emulated' The impedance matching of the emulating robot to the free-floating spacecraft system is required to obtain a good level of fidelity (Aghili and Namvar, 24). However, this process is relatively complex and is limited by the bandwidth of the robot under consideration. As shown in Fig. 6 (a), when a small mass is used for the spacecrafts the energy ratio is higher than one. One of the reasons for this is the fact that the first force peak obtained in HLS mode, as shown in Fig. 3 (b) between time.1s and.15s, remains the same, regardless of the inertial configurations and approach velocity. However, as shown in Fig. 3 (a), the expected force is much lower than the applied force of 6N. Applying this non-representative force on the two spacecrafts adds energy to the system, which explains that the energy ratio is higher than one. Under that assumption, increasing the mass of the spacecrafts should improve the performance so that the non-representative force has less impact. A different sequence of tests done with higher masses demonstrates that once again, an energy ratio higher than one is observed. The explanation in this case is that, due to errors in the controller (wrong impedance), the integrator is building up during contact and needs to discharge

7 Results and Verification of Spacecraft Docking C> (a) (b) = ~3.2 ~2 : =1 o c o 1' 2 3~ Spacecrafts mass (kg) Spa~fts 1~ mass (kg) 2~ Figure 6. Kinetic energy ratio after impact in function of the mass of spacecrafts: (a) for various approach velocities; (b) for various cut-off frequencies of the first-order filter; Mchaser -- Mtarget. x 1 ~ (a) (9 C g e- x 1 "4 (b),., Feedback' ~on ~~,/ I ~,... i y... \ Feedback ~on i i /... j ~o,: i ;/' I ~ ",, Set-point position I... i",,::... -""... I : Time (s) N c- O -15 :i Set-~int psition / :i \ :i \ i i... :..\ :~i... :i \... Ii ,8 Time (s) Figure 7. Positioning delay due to the integrator with spacecrafts mass of: (a) 4kg; (b) 8kg; with an approach velocity of 5 mm/s. after the separation of the spacecrafts. For this reason the robot continues to apply a force although it should have separated from the force/moment sensor, as shown in Fig. 7 (b), and this results in an accumulation of energy in the systems. As shown in Fig. 6 (b), the kinetic energy ratio can be considerably reduced by decreasing the cut-off frequency of the first-order filter. By this verification process, it is apparent that the SMT Robot is not precise enough for the emulation of spacecraft docking; perhaps a parallel platform with a higher bandwidth could provide better results. 5 Conclusion Several space missions involving contacts between chaser and target spacecrafts are currently in development. Ground-based validation of the procedures for such demonstrations and the physical properties of the spacecrafts used are important to the success of these missions. Therefore, the CSA developed a Docking Simulator to study the phases of contact during the docking, berthing or capture phases. This simulator can be used in pure simulation mode as well as in HLS mode. The HLS test-bed borrowed the concept of the STVF, the verification facility developed by the CSA to verify the contact portion of

8 44 S.Laurier Chapleau, E.Martin, L.Baron the SPDM robot's tasks on the ISS. The simulation mode of the Docking Simulator does provide promising results. However, when tests are performed in HLS mode, inconsistent data show that the simulator cannot be used with the SMT Robot, as the impedance matching is not sufficiently accurate. A faster and more precise robot, such as a parallel platform with higher bandwidth, could enhance results. Bibliography F. Aghili and M. Namvar, A robust impedance matching scheme for emulation of robots, In Proceedings of 24 IEE/RSJ, vol.3, pages , Sept R. L'Archev@que, M. Doyon, J.-C. Piedboeuf and Y. Gonthier, SYMOFROS: Software architecture and real time issues, In DASIA 2 - Data systems in Aerospace, vol. SP-457, Montreal, Canada: ESA, pages 41-46, May Y. Gonthier, J. McPhee, C. Lange and J.-C. Piedboeuf, A regularized contact model with asymetric damping and dwell-time dependent friction, In Multibody System Dynamics, 11(3), pages , April 24. A. B. Hays, P. Tchoryk, Jr., J. C. Pavlich, and G. Wassick, Dynamic simulation and validation of a satellite docking system, In Proceedings of SPIE - Space Systems Technology and Operations, vol.588, pages 77-88, Aug. 23. O. Ma, CDT - a general contact dynamics toolkit, In Proceedings of the 31st International Symposium on Robotics: ISR 2, Montreal, Canada, pages , May 2. E. Martin, M. Doyon, Y. Gonthier and C. Lange, Validation process of the STVF Hardware-in-the-Loop Simulation facility, In Proc. of the 8th International Symposium on Artificial Intelligence and Robotics & Automation in Space: i-sairas 25, Munich, Germany, Sept E. Martin, E. Dupuis, J.-C. Piedboeuf and M. Doyon, The TECSAS mission from a Canadian perspective, In Proc. of the 8th International Symposium on Artificial Intelligence and Robotics & Automation in Space: i-sairas 25, Munich, Germany, Sept E. Martin, K. Parsa, S. Laurier Chapleau and L. Baron, Towards spacecraft docking emulation using Hardware-in-the-Loop Simulation, In Proc. of the 8th International Symposium on Artificial Intelligence and Robotics & Automation in Space: i-sairas 25, Munich, Germany, Sept S.D. Potter, Orbital Express: Leading the way to a new space architecture, In 22 Space Core Tech Conf., pages , Nov. 22. M. Uchiyama, S. Tarao and H. Kawabe, A New Class of Hybrid Motion Simulation Using a Very Fast Parallel Robot, In Springer Tracts in Advanced Robotics, Robotics Research: The Tenth International Symposium, vol.6, pages , 23. K. Yokota, K. Yamanaka, S. Shirasaka, H. Koyama, M. Inoue, T. Shima, K. Yamada, Evaluation of contact dynamics simulation fidelity of RDOTS (Rendezvous and Docking Operation Test System), In Proceedings of the twenty-first International symposium on Space Technology and Science, vol.1, pages , Omiya, Japan, K. Yoshida, Engineering Test Satellite VII Flight Experiments for Space Robot Dynamics and Control: Theories on Laboratory Test Beds Ten Years Ago, Now in Orbit, In The International Journal of Robotics Research, vol.22, no.5, pages , 23.