NMSU NANOSATELLITE WITH ROBOTICS CAPABILITIES Ou Ma1 and Stephen Horan2 1 Department of Mechanical Eng., New Mexico State University, Las Cruces, NM 88003, USA, Email:
[email protected] Department of Electrical and Computer Eng., Mexico State University, Las Cruces, NM 88003, USA, Email:
[email protected]
2
ABSTRACT This paper introduces a student nanosatellite project which is currently going on at the New Mexico State University under the University Nanosatellite Program sponsored by Air Force Office of Scientific Research in conjunction with NASA and AIAA. This has been the second nanosatellite project run by students at the university. The primary engineering mission objectives are to test a simple dual-arm robotic system and use the robots for satellite-exterior inspection and inertiaproperty estimation. The paper provides an overview of the concept design of the satellite, focusing on the structure, attitude determination and control, and robotics subsystems. It also outlines the methodology of the robotics-based approach for identifying the inertia distribution of the satellite. 1.
INTRODUCTION
The faculty and administration at New Mexico State University (NMSU) have identified research on space science and engineering as one of the strategically emphasized research clusters at the university. One of the key programs of the Space cluster is the nanosatellite program that has been progressing at the university since 1999. This program is seen as a key program for the Space cluster because it will assist both science and engineering research missions of the university as well as being of interest to the commercial development of the space business that is beginning in the state of New Mexico. The primary goal of the nanosatellite program is to educate and train the future work force for satellite design, manufacturing, and operation. Other than the education goal, the long-range engineering emphasis for the NMSU nanosatellite program will concentrate on developing the full capabilities for space robotics for satellite on-orbit servicing. Robotics-based satellite on-orbit servicing has been gaining increasing attention in the international space community in recent years. There are significant advantages to have a robotics mission to service or rescue a satellite in space for economical reasons or emergency purposes. However, the technologies required for autonomous on-orbit servicing have far from being mature. Many research activities are still going on around the world currently. JAXA completed an on-orbit technology demonstration mission ETS-7 in 1999 [1]. In that mission, a small satellite was first deployed from the main satellite in orbit. It then rendezvoused and docked back to the main satellite. A
few robotic operations were tested in the mission but the robotic capture of the smaller satellite was done while the two satellites were still loosely hooked together (for reducing mission risk). DARPA/USAF is currently developing a more advanced technology demonstration mission to be launched in 2006 through the Orbital Express Program [2-3]. In this mission, more aggressive robotic operations will be exercised on orbit, which includes the deployment, capture, ORU replacement, and refueling. Germany and Canada are also jointly developing a robotics-based satellite rescue mission called TECSAS [4-5]. The major challenges of that mission are in two aspects: the rescuing satellite and the rescued satellite will be launched separately (two years in part) and the rescued satellite will have a slight tumbling motion before being captured. US government announced a new vision last year for space science and technology development. That is to implement a sustained and affordable human and robotic program to explore the solar system and beyond. Under this new vision, more innovative technologies and enhanced infrastructure need to be developed to support the future space exploration and other applications benefiting the nation and the peace of the world in an affordable, reliable/safe and effective fashion. The space community realizes that enhancing robotic technologies is essential for achieving this new vision because robotic assistance is essential for both manned and unmanned missions. In responding to this vision, NMSU would like to begin training students who will be able to work in the future space industry. We envision that our students will be able to design, build, test, and operate nanosatellites. Our long-term goal is to have full capabilities of developing space robotics for autonomous on-orbit servicing missions. Such a goal is consistent with the goals of Air Force and NASA for more autonomous approaches for future space exploration missions. Obviously, such a challenging goal cannot be practically done by one student nanosatellite project, which typically lasts for only two years. It has to go step by step through an integrated series of incremental development projects. Each project will be built upon the technology development of its previous one and will advance the program towards the final capabilities. The NMSU nanosatellite program is part of the overall strategy for developing the space science and engineering capabilities of the university. It will continue to enhance the engineering capabilities at NMSU by building up the aerospace engineering component and increasing cross-departmental
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)
collaborations. The program will also serve as an excellent training component for the upcoming aerospace engineering degrees program that NMSU is creating as an effort to address particular industrial needs within the state of New Mexico. The paper provides an overview of the background and long-term goals of the NMSU nanosatellite program in Section 2, which is followed by an outline of the mission objectives of the current nanosatellite project in Section 3. The preliminary concept design of the satellite is presented in Section 4 with focuses on the structure, attitude control, and robotics subsystems. Section 5 describes the methodology of the roboticsbased approach for identifying the inertia properties of the satellite. Section 6 outlines the test and verification approach. The paper is concluded in Section 7. 2.
BACKGROUND AND LONG-TERM PLAN
The 3 Corner Satellite (3CS) design [7], which started in 1999, was the first nanosatellite project involving NMSU. Since then, at least 60 students from several departments across the College of Engineering have participated in 3CS and the subsequent projects. The first nanosatellite built entirely at NMSU, called NMSUSat1, was designed to make measurements of cosmic ray interactions with the earth’s upper atmosphere [6]. This 18-kg satellite had a geometric shape of hexagonal-prism of 18” in diameter and 16” in length. It did not have an attitude control capability. Hence, a large number of sensors were distributed around the satellite body to permit data acquisition in any attitude on the orbit. The satellite was brought to the complete engineering design unit phase and is now searching for a launch as either a free-flying satellite or as an attached payload on a research balloon flight. To continue developing nanosatellite capabilities, the faculty from the College of Engineering and the College of Arts and Sciences of NMSU proposed to develop a second nanosatellite, called NMSUSat2, as part of the AFRL’s University Nanosatellite Program (also called Nanosat Program). This satellite will be developed based on the heritage of the NMSUSat1 design, the preceding 3CS mission, and the existing engineering and science capabilities available on campus. Given the fact that there are growing activities for human and robotics-based space exploration and commercialization in the 21st century, we envision our students will be able to design, build, and operate a nanosatellite to demonstrate on-orbit robotic servicing tasks. This is the driver behind our long-term goal of developing the capabilities to perform autonomous onorbit servicing. Obviously, such a challenging goal cannot be practically achieved within one nanosatellite project under the University Nanosat Program, which typically lasts for two years. It has to go step by step through a series of incremental development projects. With our vision, a ten-year plan of the development is
presented in Table 1. Each step of the plan will build upon the technology development of the previous step and will advance the program towards the final capabilities. Table 1 NMSUSat Development Plan Capabilities
NMSUSat 1
NMSUSat 2
NMSUSat 3
2005-2007
2007-2009
Time frame
2003-2005
Mission Objectives
− Developed satellite bus
− Test 2-axis stabilization
− Test 3-axis stabilization
(Engineering)
− Developed basic nanosat subsystems
− Test robotic arm and joint elements
− Test robotic arm control and sensors
− Selected compact science sensors
− Inspect partial satellite exterior
− Spot-check satellite exterior
− Test roboticbased inertia estimation
− Further test inertia estimation
Satellite Body
− Single unit
− Single unit
− Single unit
ACS
− None
Robotics
− None
Sensors for ACS and Robotic Operations
− N/A
Autonomy
− Scheduled
− 2-axis passive
− 3-axis active
− Gravitygradient
− Momentum exchange
− 2 dependent arms
− 2 dependent arms
− 1-DOF each arm
− 2- DOF each arm
− No hands
− No hands
− Sun & earth sensors
− Sun & earth sensors
− Cameras
− Cameras − IMUs
operations
− Preprogrammed operations
− Preprogrammed operations − Reactive control
Science Mission Capabilities
− General near-space sensing − Limited sensor directionality
Support Capabilities
Ground Operation (for robotics)
− 1200/9600 baud comm.
− Earth imaging − Near Space measurements
− Directional measurements of earth and near space
− 57600 baud communications
− 115200 baud communications
− Supervision
− Supervision
- Internet file transfer capabilities − Supervision
− Emergency handling
From the plan, one can see that our ultimate mission objectives at the end of the next decade are to be able to rendezvous and capture a tumbling satellite and then perform some degree of robotic services in the mission. 3.
NMSUSAT2 MISSION OBJECTIVES
As described in Sections 2, NMSUSat2 mission is not a full demonstration of space robotics mission of satellite
on-orbit servicing. Rather, it is just an early step of the ultimate long-term goal of the NMSUSat program that is to develop full capabilities of space robotics for autonomous on-orbit servicing. Based on the long-term plan described in Table 1, the NMSUSat2 project has the following mission objectives: 1) To enhance student education and outreach and to support the new aerospace engineering degrees program to be created in NMSU. 2) To demonstrate the simplest attitude control capability in LEO orbit. 3) To demonstrate the simplest space robotics capabilities, which includes: − two single-DOF robotic arms. − the ability to use the robotic arms to inspect the exterior of the satellite structure. − the ability to use the robotic arms to estimate the inertia property of the satellite; 4) To provide remote telemetry operations for − cosmic ray studies like those found in the first nanosatellite but with a more efficient sensor array because the pointing is being used, − the development of detectors for scientific studies (cosmic ray, solar and lunar observations, bright star measurements, particulate measurements). 5) To establish an infrastructure and testbed for further technology development in space robotics. The above stated NMSUSat2 mission objectives will meet the programmatic objectives of the University Nanosat Program as described below. a) The Air Force and NASA have identified the space-robotics as a relevant technology area for the University Nanosat Program. The NMSUSat2 mission will have this topic area as its primary mission focus. It is expected that mission success on this satellite will enable NMSU to pursue more advanced concepts along this line. b) The University Nanosat Program is interested in developing sensors and actuators for guidance, navigation, and control. The attitude determination and stabilization techniques to be tested in the NMSUSat2 mission are relevant to these needs. c) On 3 Corner Satellite and the NMSUSat1 projects, NMSU developed standardized radio communications technologies. The basic NMSU design is being used by several of the schools in the University Nanosat Program. In particular, the University of Colorado and NMSU are using the NMSU modifications to the 3 Corner Satellite radio system to achieve higher data rates (9600 bps vs. 1200 bps). With a stabilized platform, the NMSUSat2 mission will be able to achieve higher data rates for space-to-ground communications. The radio design for this will be shared with the wider University Nanosat Community with the goal of making the design useful to other schools.
Table 1 (Cont’d) NMSUSat Development Plan Capabilities Time frame Mission Objectives (Engineering)
NMSUSat 4 2009-2011 − Test 3 axis stabilization with large disturbances − Test 2-arm coordinated control − Test robot hand control − Inspect entire exterior
Satellite
NMSUSat 5 2011-2013
NMSUSat 6 2013-2015
− Test 3 axis ADCS
− Further test 3 axis ADCS
− Deploy a target satellite
− Rendezvous and capture a rotating target satellite
− Rendezvous and capture a cooperative target satellite − Test multi-dof hands
− On-orbit robotic services, e.g., replacing ORUs & refueling
− Single unit
− Two units
− Two units
− 3-axis active
− 3-axis active
− 3-axis active
Body ACS
− Cold gas propulsion − Momentum exchange Robotics
− Independent two arms − 3-DOF each arm − 1-DOF each hand
Sensors for ACS and Robotic Operations
Autonomy
Science Mission Capabilities
− Cold gas propulsion
− Propulsion
− Momentum exchange
− Momentum exchange
− Single arm
− Independent two arms
− 6-DOF robotic arm − 2-DOF hand
− 6-DOF each arm − 3- or moreDOF hands
− Sun & earth sensors
− Sun & earth sensors
− Sun & earth sensors
− IMUs
− IMUs
− IMUs
− Cameras
− Cameras
− Cameras
− Proximity sensors
− Ranger finder
− Ranger finder
− Proximity sensors
− Proximity sensors
− Preprogrammed operations
− Preprogrammed operations
− Preprogrammed operations
− Intelligent controls
− Intelligent controls
− Intelligent controls
− Directional
− Distributed
− Distributed
measurements
measurements
directional
of earth and
measurements
near space Support
− Internal
− Inter-satellite
Capabilities
satellite
communications
networking
networking Ground Operation (for robotics)
4.
− Supervision − Emergency handling
− Intersatellite
− Ground control (using computers)
− Ground control − Human operation
SYSTEM OVERVIEW
The NMSUSat2 project started in spring 2005. The efforts made so far were mainly in the development of mission objectives, mission requirements and success
criteria, system requirements, and preliminary concept design. The current concept of the satellite is illustrated in Fig.1. The satellite consists of the following subsystems: − Structure − Attitude determination and control − Robotics − Electrical power generation and management − Communications − Software, computing and data management − Thermo protection − Ground station
The main structure is made of aluminium and designed to support and encase most of the subsystems. It must meet all structural vibration and strength specifications defined in [8]. The eight faces of the hexagonal-prism structure are covered with solar panels of size 8.5”×11” each. Each solar panel consists of a number of 1.5”×2.5” solar cells. Expected perform of each panel is 8V and 1.2A.
Fig.1 NMSUNanosat2 (The solar cells covering the exterior are not shown) The maximum allowed mass budget and dimension envelope for a university nanosatellite, as specified in [8], are 30 kg and 18.7”×18.7” cylinder. The NMSUSat1 weighs 18 kg and has a dimension of 18” in diameter and 12” in length (not including antennas). Therefore, there are lots of room in both mass and volume available for extending the design to NMSUSat2. The satellite is powered by a set of 5 NiCd batteries charged by solar panels and it is designed for flying on a LEO orbit of 150~250 km altitude.
Fig.2 Structure design of the NMSU Nanosat2 4.2 Attitude Determination and Control
4.1 Satellite Main Body and Structure
Due to the first design of a nanosatellite having attitude control capability plus the strict resource limitations, we decided to use the simplest attitude control technique, namely, the gravity-gradient based passive control technique. A gravity-gradient based ACS consists of a deployable long boom and a mass unit on the tip of the boom. The preliminary concept of our student-designed ACS is shown in Fig.3, where the boom consists of two foldable tapes and the tip mass is basically the housing unit of the ACS assembly. Such a design has advantages of taking up a minimal space of the satellite and making a maximum use of the mass of the hardware assembly. In the ACS hardware, the tapes are pre-folded around the two drums of the housing unit and locked during the launch of the satellite. They will be triggered to unfold when the satellite is in orbit. The reason for using two parallel tapes is to increase the rigidity of the resulting “boom”.
The main body of the satellite has a shape of hexagonal prism, as shown in Fig.2. Since we will reuse the design of NMSUSat1, the dimensions of the main structure remain 18” in outer diameter and 12” in length. On top of that, a 6”-long ACS assembly will be attached. This extends the total length of the satellite to 18”, which meets the maximum length requirement.
There are a variety of different techniques available for attitude determination. Some of them are expensive and require extensive data processing. Since the attitude of NMSUSat2 will not be actively controlled, it is unnecessary to have a high-performance attitude determination system (ADS). For this reason, we try to make best use of the existing inexpensive sensors (as
Students from the Department of Mechanical Engineering (including an upcoming new aerospace engineering program), with assistance of the team members from other departments, are responsible for the design of three subsystems: the satellite structure, the attitude determination and control subsystem, and the robotic subsystem. These three subsystems are the main focuses of this paper.
opposed to introducing new sensors) for the design of the ADS. The current concept is to use three kinds of existing sensors: the earth sensors which are inherited from NMSUSat1, the sun sensors which are nothing but the solar panels, and the two cameras which will be installed at the tips of the robotic arms for inspection. The data from all the three types of sensors will be fused by the ADS software to determine the attitude of the satellite, i.e., the pitch and roll angles of the satellite with respect to the orbital frame (the yaw angle will remain uncontrolled as defined in the mission requirements). In the rest of this section, we will briefly describe these sensors.
handling methods have to be worked out for the singular situations such as surface areas without solar cells or the entire satellite being off the sun light. Sun Sun sensor measurement
NMSUSat2 Orbital frame x x z z Satellite frame
Earth sensor measurement
Camera measurement
Orbit
Earth
ω Deploying direction
Housing (Mass) Tape (boom)
Spring preloaded drums
Fig.4 Sensors used for attitude determination Tape (boom)
Satellite Structure
Fig.3 Concept of the gravity-gradient based ACS In the design of NMSUSat1, each of the eight faces of the hexagonal-prism body has an in-house-built, infrared based earth sensor installed at its center location. These sensors (eight pieces in all) are used to detect which side of the satellite is facing the earth, which can be considered as a very coarse ADS. In the new design, these earth sensors will be installed at the vertices of the satellite body in order to improve the resolution of the earth detection. Moreover, corners of the satellite body will be free of other physical attachments and thus always available for installing the earth sensors. The algorithm for determining the direction of the satellite with respect to the earth can be used almost as is because such a relocation of sensors does not change the fundamental of the methodology. The NMSUSat1 has solar panels covering the entire exterior of the satellite. Because the satellite does not have an attitude control capability, such a design allows the satellite always to have one or more solar panels facing the sun for power supply. This feature will be kept in the design of NMSUSat2, where the solar panels around the satellite body will have a second purpose. That is to measure the position of the sun with respect to the satellite. Since each solar panel has its unique orientation with respect to the satellite frame, the direction of the sun with respect to the satellite frame can be estimated by identifying the specific solar panel or panels which are facing the sun. Of course, the resolution of this method of attitude determination will rely on the total number of solar panels available and how they are distributed around the satellite body, as well as the satellite’s earth orbit. It can determine only two axes of the attitude. Special
NMSUSat2 will have two digital cameras installed at the tips of the robotic arms for taking images of the satellite and the earth background. These two cameras will have a second purpose that is to assist the determination of attitude. This is done by identifying the earth horizon from the digital images acquired by the cameras. The horizon is determined by searching the boundary between dark and light in a digital image. Because the configuration of each robotic arm is fully controlled, the position and orientation of the camera with respect to the satellite frame is precisely known. As a result, the relative orientation of the earth horizon with respect to the satellite frame can be estimated from the horizon positions in the images, from which the attitude of the satellite with respect to the orbit can be determined. This technology has been developed by other universities within the University Nanosat Program [9]. The only difference here is that their original system fixed the cameras to the satellite body while in our design the cameras are manoeuvred by robotic arms. As long as the configurations of the robotic arms are known, the pose of each camera is also known. As a result, the technology and experience described in [9] can be applied. 4.3 Robotic System In order to meet the mission objectives and programmatic constraints as defined in Section 2, the robotic system of NMSUSat2 will be a simple system consisting of two identical arms, as shown in Fig.1. Each arm has only one single-DOF, rotational joint, which articulates the arm with the top surface of the satellite’s main body, as shown in Fig.5. Since NMSUSat2 uses passive ACS technology which has very small stability margin, one of the most critical design criteria of the robotic system is to have minimum disturbance to the ACS when the robot is in
motion. The dual-arm design is for maintaining the center of mass and the symmetry of inertia distribution when the arms are at any configurations. This also requires that the two arms are designed and always kept symmetric with respect to vertical axis of the satellite. This will not be difficult because each arm has only one DOF. For the same token, the speed of the joints will be very slow for having minimal inertial torques to the system when the arms are in motion. Each joint will be driven either by a stepper motor or servo motor, which has not being finalized so far. Angular momentum hC
Angular momentum hC Angular velocity ω1
Angular velocity ω 2
C
Arm configuration 2
Fig.5 Two different arm configurations 5.
h C = (I S + ∆I S1 + I R ,C1 )ω1
ROBOTICS-BASED INERTIA ESTIMATION
Inertia properties (also called mass properties) of a satellite can change in orbit for many reasons such as fuel consumption, hardware reconfiguration, payload deployment, docking with another satellite, or some malfunctions like an unexpected deployment failure. Spacecraft state-estimate and control systems have to adapt to the inertia variations. This usually requires an estimation of the inertia properties which is represented by the components of the inertia tensor expressed in a satellite-fixed frame. Common approaches are based on the rigid-body Euler equation of motion, i.e., & + ω × Iω = Στ + Σ(ρ × f ) Iω
In our mission, a robotics-based method of inertiaproperty estimation (identification) is proposed. The method does not require any external excitations and does not require acceleration data either. All it needs is to perform a series of manoeuvres of an onboard robotic arm (or arms) and measure the resulting new angular velocities in steady-state. The principle of this method is briefly described below. Referring to Fig.5 and ignoring the much smaller angular motion due to orbiting, the angular momentum of the satellite system (including both the satellite and the arms) with respect to its centroid C (i.e., the mass center), when the two arms are at Configuration 1, can be expressed as
C
Arm configuration 1
process but the method still requires known external excitations (such as firing thrusts). Without external excitations, the method works only for a rotating satellite with an assumption that the initial rotational kinetic energy is already known. The work reported in [14] used a similar approach but it also considered the effect of the gravity-gradient torques.
(1)
where I is the 3×3 inertia tensor with respect to the & are the 3×1 angular centroid (mass center); ω and ω velocity and acceleration vectors; Στ and Σρ × f are the 3×1 resultant external torque vector and the moment vector of resultant external force Σf . In order to estimate the components of I, we can convert equation (1) into a regression form and then applies the least-square or other filtering techniques to solve it for the unknown components of I or I −1 or some other related terms [10-12]. Such an approach requires measuring not only angular velocity but also angular acceleration of the satellite. Although acceleration can be computed from the measured velocity data, the process will add additional noise to the data system. Moreover, the approach also requires applying external excitations Στ and/or Σf such as firing thrusts. Tanygin and Williams [13] improved the approach by first eliminating the nonlinear inertia moment ω × Iω & from the and then the angular acceleration ω regression equation. This improves the estimation
(2)
where ω1 is the 3×1 angular velocity vector of the satellite; I S is the 3×3 inertia tensor of the satellite (excluding the arms) with respect to its own centroid CS. Thus, I S represents the inertia properties to be determined. ∆I S1 is the incremental of the satellite’s inertia tensor due to the position change of the system’s centroid caused by the change of the arm configuration. I R ,C1 is the 3×3 inertia tensor of the robotic arms with respect to the system’s centroid C. Since the arm configuration is known, matrix I R ,C1 can be easily computed based on the kinematics and inertial properties of the arms. Now, if the arms are moved to a new configuration such as Configuration 2 in Fig.5, even without firing thrusts, the angular velocity of the satellite will change because of the inertia redistribution. However, the system’s centroid C will remain in the same place with respect to the inertial frame because of no external forces. Also, the angular momentum with respect to the system’s centroid will remain unchanged because of no external angular impulses. Therefore, we have h C = (I S + ∆I S 2 + I R ,C 2 )ω 2
(3)
where I R 2 is the new inertia tensor of the arms at Configuration 2. Continue to move the arms to another two new configurations 3 and 4, we have h C = (I S + ∆I S 3 + I R ,C 3 )ω 3 = (I S + ∆I S 4 + I R ,C 4 )ω 4
(4)
Combining the above equations and eliminating the angular momentum hC, we can obtain I S [(ω 2 − ω1 ) (ω 3 − ω1 ) (ω 4 − ω1 )] = H
(5)
where matrix H is defined as H ≡ [((I R ,C 2 + ∆I S 2 )ω 2 − (I R,C1 + ∆I S1 )ω1 ) ((I R ,C 3 + ∆I S 3 )ω 3 − (I R ,C1 + ∆I S1 )ω1 )
(6)
((I R ,C 4 + ∆I S 4 )ω 4 − (I R ,C1 + ∆I S1 )ω1 )]
From equation (5), we can solve for the unknown I S as follows
I S = H[(ω 2 − ω1 ) (ω 3 − ω1 ) (ω 4 − ω1 )]−1
(7)
In the above solution, angular velocities ω1 , ω 2 , ω 3 and ω 4 can be measured by rate gyros or other sensors. The inertia tensors I R,C1 , I R,C 2 , I R,C 3 and I R,C 4 can be computed based on the known arm inertia properties and arm configurations. Tensor increments ∆I S1 , ∆I S 2 , ∆I S 3 , and ∆I S 4 can also be computed if the mass of the satellite is known (see the Appendix of the paper). In fact, the estimation results can be improved by making more than four arm maneuvers and measurements. In such a case, equation (5) should be replaced by a linear regression equation whose number of scalar equations is more than number of unknowns. Then the least-square or other standard filtering techniques can be used to solve for the unknowns. The above is only a concept of the proposed inertia identification method. It will be verified by both simulation and test in the project. There are also several technical issues that need to be addressed: 1) A guideline needs to be established as how to select optimal arm maneuvers such that not only all the inertia properties can be identified but also the resulting numerical procedure is optimized. The observability of I will depend on the design of the robot and the initial angular velocity of the satellite. Due to the simple robotic arms, we will not have much choice for performance optimization. However, the method is still general. 2) The effect of the gravity-gradient torque on the proposed inertia identification method needs to be studied. The gravity-gradient toque may turn out to be a non-negligible factor in our case because it is the basis for the attitude stabilization of the satellite. If that is the case, the left hand sides of eqs.(2-4) will not be all equal. The variation of angular momentum caused by the gravity-gradient must be considered in the equations. 3) Handling of sensor bias and noise problems has to be addressed. This is a common issue for any experiment system. However, it will likely be more significant in our case because we are using inexpensive and low-performance sensors. 4) An analysis of computational complexity is required. Since an inertia identification method is usually used for online assisting spacecraft control system, it has to be executed at a fast rate and a limited memory usage.
These issues and any others which we may encounter later will be carefully studied by both simulation and experiment in the project. Based on the studies, practical solution measures will be proposed. Since we are still in the concept development (pre-PDR) phase of the project, conclusive analysis and results will have to be reported later on. 6.
VERIFICATION AND TEST
The design of the NMSUSat1 has been highly modular. This philosophy will continue for the NMSUSat2 design. This will allow easier integration and test of individual components. Other than the tests already exercised in the NMSUSat1 program as reported in [67], a second test program is being added in the project. That is to test the boom deployment and basic robotic arm movement. An air-bearing supported 2D testbed will be constructed by students for both functional test and partial performance test of the booms and arms. The main objective of the performance test is to verify the impact of the boom or arm deployment on the stability of the satellite body. Additional test of the boom and arm deployment mechanisms will be needed in a “zero-g” environment. We plan to perform this testing using NASA’s Reduced Gravity Research Program. With the assistance of the New Mexico Space Grant Consortium, the NMSUSat2 team will apply for testing time on the Reduced Gravity Program for the spring 2006 flight opportunities. In addition, we are also planning to test the ADS sensors and algorithms by piggybacking the test to a high-altitude balloon experiment to be conducted by the Physical Science Laboratories of NMSU. Other than physical tests, we are also planned to have computer simulation based analysis and verification of the design. Simulation has a unique value for systemlevel performance studies of attitude control and robotics systems because physical testing of these systems under 0-g condition is difficult even with very expensive test facilities. In order to support the design and verification, we therefore need to analyze the dynamics and control performances of the ACS and robotic system by computer simulations. It will also be an excellence opportunity for students to be trained in modeling and simulation of flight dynamic systems. For simulation work, we will use the commercial simulation software ADAMS and Matlab/Simulink, which are currently available in the university. Since these software tools are not specific for developing flight systems, special plug-in software modules will be developed in the project. 7.
CONCLUSIONS
The paper introduced a student-run nanosatellite project which is currently going on at the New Mexico State University. The primary engineering mission objectives of this nanosatellite are to test a simple dualarm robotic system and use the robot for inspection of
the satellite’s exterior and estimation of the satellite’s inertia properties. The satellite also has its scientific mission objectives for observation of near space environment. The project is the first step toward a long-term goal of developing full space robotics capabilities at the university for future satellite on-orbit servicing missions. It is currently in the concept design phase. The preliminary design concept is presented in the paper along with an introduction of the proposed robotics-based inertia property estimation method.
IEEE Midwest Symp. on Circuits and Systems, Tulsa, OK, pp.334-337, Aug 4-7, 2002. [13] S. Tanygin and T. Williams, “Mass property estimation using coasting maneuvering”, J of Guidance, Control, and Dynamics, Vol.20, No.4, 1997, pp.625-632. [14] M.A. Peck, “Estimation of inertia parameters for gyrostats subject to gravity-gradient torques”, Proc. AAS/AIAA Astrodynamics Conf., Quebec City, Quebec, pp.113-131, Jul 30-Aug 2, 2001.
APPENDIX ACKNOWLEDGEMENTS This material is based on work supported by the Air Force Office of Scientific Research under Award No. FA9550-05-1-0267. REFERENCES [1] T. Kasai, M. Oda and T. Suzuki, “Results of the ETS-7 Mission – Rendezvous Docking and Space Robotics Experiment”, in 5th Int. Symp. on Artificial Intelligence, Robotics and Auto. in Space, ESTEC/ESA, Nordwijk, The Netherlands, pp.299-306., 1999. [2] D.A. Whelan, E.A. Adler, S.B. Wilson and G. Roesler, “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. [3] D.P. Seth, “Orbital Express: Leading the way to a new space architecture”, 2002 Space Core Tech Conf., Colorado Springs, November 19-21, 2002. [4] 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. [5] E. Dupris, M. Doyon, E. Martin, P. Allard, J.C. Piedboeuf, and O. Ma, “Autonomous Operations for Space Robots”, Proc. 55th Int. Asronautical Congress, October 2004, Paper #IAC-04-IAA.U.5.03. [6] S. Horan et al., “The New Mexico State University Satellite (NMSUSat) Mission”, Proc. 17th Annual/USU Conf. on Small Satellites, SSC03-IX-5, Logan, UT, August 2003. [7] S. Horan et al., “The Three Corner Satellite Mission,” Proc. Int. Symp. Formation Flying: Missions & Technologies, Toulouse, FR, October 2002. [8] “Nanosat-4 Uner’s Guide”, University Nanosat-4 Program Office, AFRL, Space Vehicle Directive, Kirtland, NM, UN4-0001, March 2005. [9] D. Meller, P. Sripruetkiat, and K. Makovec, “Digital CMOS cameras for attitude determination”, Proc. 14th AIAA/USU Conf. on Small Satellites, SSC00-VII-1, Logan, UT, August 2000. [10] P. Hughes, Spacecraft Attitude Dynamics, Wiley, 1986. [11] E.V Bergmann, B.K. Walker, and D.R. Levy, “Mass property estimation for control of asymmetrical satellites”, J. of Guidance, Control, and Dynamics, Vol.10, No.5, 1987, pp.483-491. [12] E. Wilson, C. Lages, R. Mah, “On-line, gyro-based, mass-property identification for thruster-controlled spacecraft using recursive least squares”, Proc. of 45th
Let m S and m R be the masses of the robot and the satellite; I S and I R are inertia tensors of the satellite and robot about their own centroids C S and C R , respectively. Then, the inertia tensors of the two bodies with respect to the origin O are I S ,O = I S + ∆I S = I S + m S (c TS c S 1 − c S c TS )
(8)
I R ,O = I R + ∆I R = I R + m R (c TR c R 1 − c R c TR )
where c S and c R are the position vectors of the centroids C S and C R , respectively. The math symbol 1 represents the 3×3 identity matrix. Centroid of robot
Centroid of satellite
System's centroid
CR
C
Robot
z cR
CS
c
Satellite
cS
ω
y
O x
Fig.6 Notation of a system of two rigid bodies
Let C be the centroid of the system of both satellite and robot. Then, the position vector of C should be c = (mS c S + m R c R ) /(mS + m R )
(9)
Assume no external forces exerting on the system, then the position of C will remain unchanged even the robot is moving with respect to the satellite. Without loss of generality, we can define the origin O to be coincident with centroid C. It follows that c = 0 and, hence, c S = −(m R / m S )c R
(10)
Therefore, we have ∆I S = m S (c TS c S 1 − c S c TS ) =
(
)
m R2 c R c TR − c TR c R 1 (11) mS
In the above equation, m S and m R are assumed to be known and c R can be computed from the robot’s inertia parameters (including the centroid position at its home configuration) and current configuration. The robot’s inertia parameters are known prior to the launch. The robot’s configuration must be known during its operation.
