SSC07-XI-4 Autonomous Proximity Operations of Small Satellites with Minimum Numbers of Actuators

A novel testbed is introduced to examine the problem of multiple spacecraft interacting in close proximity in a laboratory setting. This testbed enables validation of guidance, navigation and control (GNC) algorithms by combining six-degrees of freedom (DoF) computer simulation and three-degrees of freedom hardware-in-the-loop experimentation. The 3-DOF spacecraft simulator enables real-time hardware-in-the-loop testing of GNC algorithms by employing the principle of air-flotation along a flat floor to duplicate the frictionless and weightlessness inherent to orbital flight. This 3-DoF spacecraft simulator fuses sensor data from pseudo-GPS and a fiber-optic gyroscope in order to provide precise state estimation while employing a novel single gimbaled miniature control moment gyroscope and rotating thruster actuator for attitude and translational control. With its inherent high torque to required power ratio, the miniature CMG enables a high slew-rate capability for the spacecraft simulator which is a key measure of performance in spacecraft proximity operations. Furthermore, the rotating thruster design enables simultaneous translation and attitude control, allowing for efficient CMG desaturation when required. This paper presents the basic components and key parameters of the robotic vehicle with specific focus on the small time local controllability of this uniquely actuated system. The small time local controllability and input-output linearizability of the nonlinear Multi-Input Multi-Output system are demonstrated through both analytical means using Lie algebra methods as well as numerical simulations. Utilization of the designed input-output linearization controller with a standard Linear Quadratic Regulator for computation of the requisite linear gains provides a promising control system for a minimally actuated small spacecraft during autonomous proximity operations. INTRODUCTION The current space acquisition process, with the enormous monetary cost and lengthy production schedule required for a successful launch of a traditional, single-purpose, tailored design, spacecraft system, demands reconsideration. One potential option requires a paradigm shift from the monolithic spacecraft system to one involving multiple interacting spacecraft that can autonomously assemble and reconfigure. This group of spacecraft constitutes a flying system fractionated in either heterogeneous or homogenous agents. This option has numerous benefits ranging from a removal of significant intra-modular reliance which provides for parallel design, fabrication, assembly and validation processes to the inherent smaller nature of fractionated systems which allows for each module to be placed into orbit separately on more affordable launch platforms. 1 With respect specifically to the validation process, the significantly reduced dimensions and mass of fractionated spacecraft with respect to the traditional monolithic spacecraft allows for not only component but even full-scale on-the-ground hardware-in-the-loop experimentation. This type of hardware-in-the-loop experimentation complements analytical methods and numerical simulations by providing a low-risk, relatively low-cost and potentially high-return method for validating spacecraft systems technology, navigation techniques and control approaches. Several approaches exist for the actual hardware-in-the-loop testing in a laboratory environment with respect to spacecraft guidance, navigation and control. One such method involves reproduction of the kinematics and vehicle dynamics for 3-DoF (two horizontal translational degrees and one rotational degree about the vertical axis) through the use of robotic spacecraft simulators that float via linear air bearings on a flat Hall 1 21 Annual AIAA/USU Conference on Small Satellites horizontal floor. This particular method is currently being employed by several research institutions and is the validation method of choice for our research into GNC algorithms for proximity operations at the Naval Postgraduate School. With respect to spacecraft involved in proximity operations, the inplane and cross-track dynamics are decoupled, as modeled by the Hill-Clohessy-Wiltshire (HCW) equations, thus the reduction to 3-DoF does not appear to be a critical limiter. One consideration involves the reduction of the vehicle dynamics to one of a double integrator. However, the orbital dynamics can be considered to be a disturbance during the proximity navigation and assembly phase of multiple fractionated systems that need to be compensated for by the spacecraft navigation and control system. Thus the flat floor test bed can be used to capture many of the critical aspects of an actual autonomous proximity maneuver that can then be used for validation of numerical simulations. This paper introduces a new and unique hardware-inthe-loop small spacecraft simulator that can be used to experimentally demonstrate GNC methods for small spacecraft proximity operations. It will be shown through Lie algebra analytical methods as well as numerical simulation, that the minimum set of actuators required for a spacecraft system reduced to 3-DoF consists of two vectorable thrusters on opposite faces. The advantages of a vectorable thruster configuration include the ability to decrease propellant use through optimized thrust vectors, free up of surface area for other critical components and possible reduction in the propulsion subsystem mass due to piping and valves. The recently developed robotic joint, invented by Dr. Steven Canfield, is capable of providing just such capabilities in a hemispherical vector space and is being considered by NASA for the Crew Exploration Vehicle. These important benefits provide the motivation to determine both the impact that a hemispherical actuator (reduced to semicircular for 3DoF dynamics) has on the overall system controllability with an emphasis on determination of the minimum thruster configuration as well as fuel-efficient GNC algorithms. This paper is organized as follows: Section two describes the hardware architecture of the spacecraft simulator. Section three develops the spacecraft simulator equations of motion and discusses the notions of controllability. Section four focuses on the controllability of the spacecraft simulator. Section five analytically presents the input-output linearizable nature of the system and presents a controller based on this theory. Finally, Section six demonstrates the Small Time Local Controllability (STLC) of the input-output linearizable system combined with a Linear Quadratic Regulator for computation of the requisite linear feedback gains. AMPHIS TESTBED ARCHITECTURE Figure 1: The Robotic Spacecraft Simulator at the NPS Spacecraft Robotics Laboratory The AMPHIS (Autonomous Multi-Agent Physically Interacting Spacecraft) testbed provides a relatively low-cost and easily acquired and assembled system that can be used for hardware-in-the-loop testing of multiple spacecraft assembly and reconfiguration concepts. Currently, the testbed consists of one 3-DOF prototype spacecraft simulator and a 6-DOF simulator consisting of four stand-alone computers. Figure 1 depicts the prototype spacecraft simulator in the Proximity Operations Simulator Facility at the Naval Postgraduate School with key components identified. The vehicle is modularly constructed with three easily assembled sections dedicated to each primary subsystem. Prefabricated 6105-T5 Aluminum fractional t-slotted extrusions form the cage of the vehicle while one square foot, .25 inch thick static dissipative rigid plastic sheets provide the upper and lower decks of each module. The use of these materials for the basic structural requirements provides a high strength to Hall 2 21 Annual AIAA/USU Conference on Small Satellites Hall 3 21 Annual AIAA/USU Conference on Small Satellites weight ratio and enable rapid assembly and reconfiguration. Propulsion and Floatation Subsystems The vehicle is maintained in a frictionless state by a 10 micron air gap between four linear air bearings and the flat epoxy floor of the POSF. This air gap is maintained by dual 4500 PSI (31.03 MPa) carbon-fiber spun air cylinders providing air flow at 50 PSI (.35 MPa). Each cylinder has a 68 cubic inch air capacity, enabling nearly 75 minutes of continuous friction-free experimentation time. Similar to the floatation system, the propulsion system is fed by a second set of air cylinders and is regulated to 100 PSI (.70 MPa). Electronic and Power Distribution Subsystems The power distribution subsystem is composed of triple lithium-ion batteries wired in parallel to provide 28 volts for up to 12 Amp-Hours. A four port DC-DC converter distributes the requisite power for the system at either 5 volts or 24 volts DC. An attached cold plate provides sufficient and unobtrusive heat transfer from the array to the power system mounting deck. The current power requirements include dual PC-104 CPU stacks, a wireless router, three motor controllers, two separate normally-closed solenoid valves for thruster actuation, a fiber optic gyro and a wireless server for transmission of the vehicle’s position via a pseudo-GPS system. Translation and Attitude Control System Actuators The AMPHIS simulator includes actuators to provide both translational control and attitude control. A full development of the controllability for this unique configuration of dual rotating thrusters and one-axis Miniature-Single Gimbaled Control Moment Gyro (MSGCMG) will be demonstrated in subsequent sections of this paper. The translation control is provided by two cold-gas on-off convergent nozzle thrusters in a dual vectorable configuration as pictured in Figure 2. Each thruster is capable of providing .28 N of vectorable thrust limited in a region , 2 2 π π ⎡− ⎢⎣ ⎦ ⎤ ⎥ with respect to the face normal. The MSGCMG is capable of providing .668 Nm of torque with a maximum angular momentum of .098 Nms. The key parameters of the AMPHIS simulator are summarized in Table 1 and are used for development of the simulated control system with feedback linearization presented in the last section of the paper. Table 1: Key Parameters of the AMPHIS Spacecraft Simulator Subsystem Characteristic Parameter Length and Width .30 [m] Height .69 [m] Mass 37 [kg] Structure MOI z J .75 [kg-m ] Propellant Air Equiv Storage Cap .002 [m] @ 31.03 [MPa] Operating Pressure .70 [MPa] Propulsion Thrust (x2) .28 [N] Max Torque .668 [Nm] Attitude Control Momentum Storage .098 [Nms] Battery Type Lithium-Ion Storage Cap 12 [Ah] @ 28 [V] Electrical & Electronic Computers 2 PC-104 PIII Fiber Optic Gyro ±20o/hr bias LIDAR SICK 360 o iGPS Sensor <.050 [mm] accuracy Sensors Accelerometer ±8.5x10 [g] bias Propellant Air Equiv Storage Cap .002 [m] @ 31.03 [MPa] Operating Pressure .35 [MPa] Floatation Linear Air Bearing 32 [mm] diam (x4) DEVELOPMENT OF EQUATIONS OF MOTION FOR THE AMPHIS 3-DOF SIMULATOR Given two rotating thrusters and a momentum exchange device such as the MSCCMG, Figure 2 depicts the reference frames used in defining the necessary parameters to describe the AMPHIS vehicle’s orientation and the effect of the individual actuators. The vehicle’s two degrees of translational freedom are described in an inertial coordinate system (IJK) by the vector ( ) , G X Y r . Likewise, the vehicle’s rotational freedom is described by an angle of rotation θ between the inertial coordinate system and the body coordinate system (ijk) where the body k-axis is aligned with the inertial K-axis.