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45th International Conference on Environmental Systems ICES-2015-285 12-16 July 2015, Bellevue, Washington
Actuator Sizing and Utility Assessment of Control Moment
Gyroscopes for an Astronaut EVA Jetpack
Todd F. Sheerin1 and Jeffrey A. Hoffman2
Massachusetts Institute of Technology, Cambridge, MA 02139
Michele D. Carpenter3
The Charles Stark Draper Laboratory, Inc. Cambridge, MA 02139
A broad range of human space exploration missions could benefit from an astronaut
mobility unit capable of providing six-degree-of-freedom control during extravehicular
activities (EVAs). Currently, NASA is developing a Jetpack unit based on the Simplified Aid
for EVA Rescue (SAFER) emergency self-rescue unit that provides translation and attitude
control with fixed thrusters. The addition of small control moment gyroscopes (CMGs) to the
Jetpack’s attitude control system could improve the stability of the EVA platform, conserve
onboard fuel and extend the length of EVA missions. In particular, a Mobility-Augmenting
Jetpack with Integrated CMGs (MAJIC) system might provide the most benefit to astronauts
participating in EVA scenarios including surface sample collection, equipment deployment,
satellite servicing, crewmember rescue, and contingency EVA missions at objects lacking
built-in handholds or foot restraints. In order to properly assess the utility of the proposed
MAJIC system, appropriately sized actuators have been identified with simulation. Monte
Carlo analyses constrained to reflect realistic CMG size, mass, power and flywheel motor
limitations have resulted in the identification of a design point for MAJIC system CMGs, and
a performance and utility analysis indicates that the MAJIC system may outperform jetpacks
without CMGs.
Nomenclature
H = angular momentum
𝐼 = mass moment of inertia tensor
J = Jacobian matrix for proposed CMG configuration
𝛼 = angular acceleration
𝛿 = CMG gimbal angles
𝜆 = scaling factor for CMG steering
𝜏 = torque
𝜔 = angular velocity
I. Introduction
T the moment, NASA’s plans for long-term human exploration are uncertain, but several facts have become
clear: on-going development of the Space Launch System (SLS) heavy-lift launch vehicle and the Orion Crew
Exploration Vehicle (CEV) promise a near-future capability to transport astronauts to far away destinations like the
Moon, low gravity objects including asteroids, and ultimately Mars. Currently, astronauts conducting extravehicular
activities (EVAs) rely on the International Space Station’s (ISS’s) robotic arm or handholds and tethers to maneuver.
In the case of an emergency, astronauts have the option of using the Simplified Aid for EVA Rescue (SAFER) unit
for self-rescue, a backpack-mounted thruster mobility unit that is worn over the Extravehicular Mobility Unit (EMU)
1 Graduate Student, Department of Aeronautics and Astronautics, 77 Massachusetts Avenue 37-352, Cambridge, MA
02139. 2 Professor of the Practice, Department of Aeronautics and Astronautics, 77 Massachusetts Avenue 33-312,
Cambridge, MA 02139 3 Technical Staff, Cambridge, MA 02139
A
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space suit [1]. SAFER is based on the previously flown Manned Maneuvering Unit (MMU) [2] that had been used in
the early 1980s to aid satellite capture operations in low-Earth orbit, but is useful only as an emergency option. If no
advances are made to astronaut mobility options before the first deep space human missions with the Orion CEV,
astronauts will have limited capability to perform tasks in the vicinity of the Orion vehicle. The reason is that unlike
the previously-proposed deep space Multi-
Mission Space Exploration Vehicle
(MMSEV), which is a pressurized crew
vehicle designed for low gravity exploration
of near Earth asteroids, the Orion CEV does
not have plans for including a robotic arm
now or in the future. This means that EVAs
near the Orion vehicle are to be restricted to
the mobility afforded by the few handholds
on the vehicle’s external surface. That is,
unless a more flexible technology solution is
developed now.
An operational Jetpack (as opposed to an
emergency-only SAFER unit) would at the
very least afford astronauts more freedom
when conducting inspection and repair
operations on spacecraft including the ISS,
and it would improve the efficiency of EVAs
by reducing astronaut time manipulating
tethers and traversing along limited pathways
on the exterior of vehicles. A more capable Jetpack would enable astronauts to perform functions that would otherwise
only be possible with a mobile exploration spacecraft with robotic arms or robotic features to probe, sample or interact
with low-gravity objects. As part of NASA’s on-going design exploration of a Jetpack, the concept of integrating
control moment gyroscopes (CMGs) in the system design is being explored. The Mobility Augmenting Jetpack with
Integrated CMGs (MAJIC) [3] pictured in Figure 1 promises added stability and improved fuel economy for the
Jetpack, enhancing the potential value of EVAs. This paper describes the process by which CMG actuators are sized
for the Jetpack application and by which the MAJIC system’s utility as an astronaut mobility unit is compared to the
utility of a Jetpack system that does not use CMGs.
II. Jetpack Attitude Control
Attitude control of a Jetpack is analogous to attitude control for a spacecraft in the sense that torques must be
delivered to the system in order to achieve desired pointing or slewing. The magnitude and direction of required torque
𝝉 depends on the mass moment of inertia of the system I and the desired angular acceleration magnitude and direction
𝜶 by the familiar equation 𝝉𝐵/𝑁 = 𝑰𝐵𝜶𝐵/𝑁. In this equation, the moment of inertia tensor is referenced to axes defined
by the spacecraft's body frame B with an origin at the spacecraft's center of mass. The angular acceleration and
resulting torque on the spacecraft body frame is expressed with respect to the inertial frame N using the superscript
B/N. Usually, pointing requirements are driven by payload, power (in the case of solar powered spacecraft) and
thermal subsystem requirements. For example, a geostationary communication satellite (GEO comsat) must point its
antennas to the Earth, its solar arrays to the sun and its radiators to deep space. In the case of GEO comsats and most
other spacecraft, pointing and slewing tasks are well defined by angular rates stipulated by payload specifications and
the spacecraft’s orbit. Torque requirements of the attitude control system (ACS) are readily derived with accurate
knowledge of the spacecraft’s mass properties and expected disturbance torques induced by solar radiation pressure,
gravity, atmospheric drag or Earth’s magnetic field.
A Jetpack differs from the usual spacecraft in two important ways that affect ACS design. First, the center of mass
and mass moment of inertia of the system to be controlled vary throughout a mission beyond the usual mass decrease
associated with fuel consumption. Second, the disturbance torques acting on the Jetpack system are significant and
highly variable. Both the variability in the system’s mass properties and the large range and magnitude of disturbance
torques to be rejected are the result of the astronaut user’s limb articulation, use of tools, or interaction with low gravity
Figure 1 Manned Maneuvering Unit and MAJIC Jetpack
Concept. Left: US astronaut Bruce McCandless and the MMU,
1984, courtesy of NASA. Right: Suited astronaut concept with the
Mobility Augmenting Jetpack with Integrated CMGs (MAJIC)
system.
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objects during an EVA. With this situation, passive attitude
control is not an option, and low torque actuators such as
magnetorquers are not feasible.
The most straightforward solution to the problem of
Jetpack attitude control is to use thrusters for attitude
control, since they are already necessary for position
control. This was the solution implemented in NASA’s
Manned Maneuvering Unit and SAFER astronaut mobility
unit. Thrusters in the MMU, SAFER and a proposed Jetpack
are discrete on-off actuators with attitude control defined by
a phase plane controller like the one in Figure 2. With phase
plane control, propellant use is traded with pointing
accuracy as thruster firings occur more often to maintain a
tighter deadband. Two drawbacks of using thrusters for
Jetpack attitude control are the inherent limit to stability of
a deadband and also the potential for contamination of
samples or optical instruments that an astronaut might be
handling when using the Jetpack.
A principle drawback of using a thruster attitude control
system for a Jetpack for low gravity astronaut EVAs is the
inherent limit to stability of a phase plane controller for on-
off thrusters. The deadband of the controller allows for drift
that precludes platform stiffness. Narrowing the deadband
would increase the system’s stability, but at the expense of
increased fuel consumption.
A second major drawback of using thrusters for reaction
control of a Jetpack is the potential for contamination of
scientific samples or instruments with plume particules
during an EVA. In an asteroid sampling mission, for
instance, a priority of the EVA would be to limit the sources
of contamination on recovered samples. If reaction control
with thrusters were used to maintain astronaut stability during proximity sampling activities, then there would be a
large probability that thruster plumes would be introduced to the asteroid sample population. Likewise, if an astronaut
conduncting and EVA must inspect or repair an optical instrument, then it might be difficult to avoid depositing plume
particles on the optics with the use of a traditional Jetpack.
Control moment gyroscopes provide an attractive alternative to thrusters for attitude control. CMGs are continuous
actuators that are not restricted by a deadband and can thus provide greater stability than thrusters. In addition, their
use as attitude actuators saves thrusters for translation tasks only, decreasing the total amount of fuel required for a
given mission. Interestingly enough, the concept of using CMGs in an astronaut mobility unit to achieve these
promised gains over a thruster-only system is not entirely new. In the initial design studies for the MMU, a unit that
included CMGs was built and flown inside the Skylab orbiting facility as part of the M509 Experiment in 1973 [4].
At the time, CMGs were large and power-hungry and so they were ultimately left out of the final MMU system despite
their success in achieving greater stability.
While there are multiple different types of CMGs including those with multiple gimbals or variable speed
flywheels, single-gimbal CMGs with fixed flywheel rates apply most readily to the Jetpack application since they
feature high torque-to-power ratios [5]. For this reason, any further mention of CMGs in this paper refers to fixed-rate
single-gimbal CMGs. Torques are produced by one CMG unit by gimbaling a fixed-rate flywheel according to the
relation:
𝝉𝑐𝑚𝑔 = �̇��̂� × 𝒉𝑐𝑚𝑔
(1)
where 𝒉𝑐𝑚𝑔 is the instantaneous angular momentum of the CMG assembly, �̇� is the gimbal rate about the gimbal axis
described by the unit vector �̂�. 𝝉𝑐𝑚𝑔 is the CMG torque generated from changing the direction of the angular
momentum vector. Because each single-gimbal CMG provides torques that are constrained to a plane, at least three
CMGs are required to provide full three-axis control. Usually, a fourth actuator is included for redundancy and also
Figure 2. Phase plane controller for attitude control
with thrusters. Allowable bounds for errors in attitude,
𝜽𝒆𝒓𝒓, and angular rate, 𝝎𝒆𝒓𝒓, are selected and thruster
firings only occur should the deadband defined by these
bounds is exceeded. For a controller with proportional
gain 𝑲𝜽 and differential gain 𝑲𝝎, no controller output
is commanded along the dotted line. The existence of a
deadband makes phase plane control inherently limited
with respect to stability, a drawback that attitude
control with CMGs does not have.
International Conference on Environmental Systems
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to ensure singularity avoidance depending on the specific array implementation. The total angular momentum of the
system 𝑯𝑠𝑦𝑠 in the inertial frame N is equal to the sum of the collective angular momentum of n CMGs 𝑯𝐶𝑀𝐺 and the
MAJIC structure 𝑯𝑏𝑜𝑑𝑦:
𝑯𝑠𝑦𝑠 = 𝑯𝐶𝑀𝐺 + 𝑯𝑏𝑜𝑑𝑦 = ∑ 𝒉𝑐𝑚𝑔,𝑖
𝑛
𝑖=1
+ 𝑰𝑏𝑜𝑑𝑦 ∙ 𝝎𝐵 𝑁⁄
(2)
In the equation above, 𝑰𝑏𝑜𝑑𝑦 is the mass moment of inertia of the MAJIC structure with respect to the center of mass
of the system and 𝝎𝐵 𝑁⁄ is the angular rate of the MAJIC structure body frame B with respect to the inertial frame N.
It should be noted that for a more precise description of system angular momentum, the angular momentum of the
gimbal structure should also be included. Extra terms related to this small component of angular momentum are
excluded in this description for clarity. Taking the time derivative of Equation 2 yields the total torque on the system:
𝝉𝑠𝑦𝑠 = −𝝉𝐶𝑀𝐺 + 𝝉𝑏𝑜𝑑𝑦 = 𝑰𝑏𝑜𝑑𝑦 ∙ 𝑑
𝑑𝑡𝝎𝐵 𝑁⁄ +
𝑑
𝑑𝑡𝑯𝐶𝑀𝐺 + 𝝎𝐵 𝑁⁄ × (𝑰𝑏𝑜𝑑𝑦 ∙ 𝝎𝐵 𝑁⁄ + 𝑯𝐶𝑀𝐺)
(3)
The negative sign in front of 𝝉𝐶𝑀𝐺 in Equation 3 represents the fact that torques produced by CMGs generate a reaction
torque in the system that is equal in magnitude but opposite in direction to the CMG torque. The time deriviatives in
the equation are taken with respect to the body frame. Producing a desired torque with the CMG array depends on the
instantaneous gimbal angle of each CMG as well as the relative orientation of the individual units by the following
relation:
𝝉𝐶𝑀𝐺 = ∑ 𝝉𝑐𝑚𝑔,𝑖
𝑛
𝑖=1
=𝜕(𝑯𝐶𝑀𝐺 )
𝜕𝑡
𝜕𝜹
𝜕𝑡= 𝐽(𝜹)�̇�
(4)
In this equation, the gimbal angle vector 𝜹 is 𝑛 × 1, containing the instantaneous gimbal angles for the array. Steering
laws for arrays with n CMGs are designed to solve Equation 4 for gimbal rates �̇� with knowledge of the 3 × 𝑛 Jacobian
matrix 𝐽(𝜹). The CMG array investigated for MAJIC system is a pyramid configuration of 𝑛 = 4 CMGs with skew
angle 𝛽 = 54.7 degrees. The Jacobian for this array can be expressed as:
𝐽(𝜹) = 𝒉𝐶𝑀𝐺 [
−𝑐𝑜𝑠𝛽 𝑐𝑜𝑠𝛿1 𝑠𝑖𝑛𝛿2
−𝑠𝑖𝑛𝛿1 −𝑐𝑜𝑠𝛽 𝑐𝑜𝑠𝛿2
𝑠𝑖𝑛𝛽 𝑐𝑜𝑠𝛿1 𝑠𝑖𝑛𝛽 𝑐𝑜𝑠𝛿2
𝑐𝑜𝑠𝛽 𝑐𝑜𝑠𝛿3 −𝑠𝑖𝑛𝛿4
𝑠𝑖𝑛𝛿3 𝑐𝑜𝑠𝛽 𝑐𝑜𝑠𝛿4
𝑠𝑖𝑛𝛽 𝑐𝑜𝑠𝛿3 𝑠𝑖𝑛𝛽 𝑐𝑜𝑠𝛿4
]
(5)
Subscripts on the gimbal angles in Equation 5 refer to the CMG number within the array. Since a 3 × 4 matrix can’t
be inverted, a pseudoinverse steering law is required to solve for gimbal rates required to achieve a given torque. A
singularity-robust implementation [6,7] takes the form
�̇� = 𝐽𝑇(𝐽 𝐽𝑇 + 𝜆𝐼3) 𝝉𝐶𝑀𝐺 (6)
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In Equation 6, 𝐼3 is the 3 × 3 identity matrix and 𝜆 is a scaling factor determined by the proximity of the CMG array
to a singular configuration, or a state of the CMG array in which torques can no longer be generated in any direction.
In order to exit a singular state, an external torque such as that which can be provided by a thruster pair is required for
desaturation. Figure 3 depicts a representative four-CMG pyramid configuration array with an associated momentum
envelope. A momentum envelope depicts the collective angular momentum states achievable by the array. External
singularities, or saturations, orccur if the collective CMG momentum 𝑯𝐶𝑀𝐺 reaches the edge of the momentum
envelope. The steering law described by Equation 6 avoids these internal singular surfaces with scaling factor 𝜆. When
the CMG array reaches close to saturation, thrusters must maintain attitude while CMG array momentum can be
returned once more to the interior of the usable control volume inside the momentum envelope. While outside the
scope of this work, the topic of avoiding singularities is the subject of on-going steering law design research for CMGs.
For a comprehensive survey of theory and steering law design for single-gimbal CMGs, see Reference [8].
III. Simulation Environment
A system simulation in MATLAB and Simulink is used to test control algorithms for MAJIC. The environment
builds off a Draper-developed simulation for the MMSEV, which was originally designed to include a pyramid
configuration of four CMGs for added stability during robotic arm asteroid sampling maneuvers. Detailed models of
control system actuators and logic are included. Thruster number and placement correspond to the SAFER system and
thruster specific impulse and thrust are defined according to a selection of fuel. As mentioned in the previous section,
a pyramid configuration of CMGs is modeled with a pseudoinverse steering law. In addition to models of the control
system and actuators, there are modules for guidance and navigation that provide the user with the capacity to simulate
a variety of mission profiles. Finally, a six-degree of freedom (6-DoF) human dynamics model is also included for
three astronaut types: a 100 pound, 58.5 inch female, a 180 pound, 72 inch male, and a 210 pound, 76 inch male.
Forces and torques induced on the MAJIC system from human motions including hammer swings, arm extensions
and hip flexions analyzed in [3] are also included in the simulation to reflect realistic disturbance inputs that the
Jetpack will have to counteract. These models utilize human body paramters from the Generator of Body Data
(GEBOD) program [9] and have been built with the use of the astronaut dynamics model developed in [10].
For a Jetpack, control requirements are not dominated by slew rate profiles and desired pointing accuracy but
instead by the nature of disturbance torques that must be rejected. A strategy to address this problem is to model
representative types of disturbance torques that might be expected for a range of missions and then perform a statistical
analysis of the performance of potential CMG designs for these representative missions. This can be done either with
Figure 3. Pyramid configuration and associated momentum envelope. Left: A four CMG pyramid configuration
with pyramid angle 𝜷 = 𝟓𝟒. 𝟕; Right: The pyramid array’s nearly spherically symmetric momentum envelope, with
singular surfaces pictured; image credit [12]. When the CMG array’s momentum reaches the edge of this envelope,
saturation occurs and an external torque provided by thrusters is required to return the CMG array to a fully
controllable state.
International Conference on Environmental Systems
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a series of isolated mission action simulations that could together make up a range of mission types, or with full
mission simulations that include a specific combination of the isolated mission actions.
For actuator sizing described in detail in the following section, full mission simulations were used in order to
provide longer times over which differences in various CMG designs might become more pronounced and also to
challenge the ACS of MAJIC with a range of tasks corresponding to specific concepts of operation (CONOPS). For
utility assessment following a selection of a winning CMG point design, isolated mission actions that could represent
any number of CONOPS were simulated with a MAJIC system with the winning CMGs and without CMGs in order
to make a top-level comparison between the performance differences and mass-to-orbit requirements of both types of
Jetpack systems.
Three basic mission types were considered for the full-length mission simulations for the sizing study and as
inspiration for the isolated mission action simulations for the utility analysis: solar array inspection at the International
Space Station, sampling activities at a low gravity near-Earth asteroid, and emergency crew member rescue of an
incapacitated crew member during an EVA. The three types of
missions are pictured in Figure 4. The solar array inspection
mission has the least aggressive control system requirements
since expected variation in mass properties and disturbance
torques of the controlled system are small. The asteroid sampling
mission depicted in Figure 5 has a mission profile that
corresponds to orbit plane change near the asteroid Itokawa,
followed by an approach and sample collection at the asteroid’s
surface. Throughout the asteroid sampling mission, disturbance
torques corresponding to astronaut limb motions with and
without tools is included from [3], and repeated hammer blows
and reaches to the hip are also modeled to represent the sampling
process. Finally, crew member rescue has been simulated with a
change in the center of mass of the MAJIC system such that the
new center of mass is placed outside the thruster spatial envelope
defined by the placement of thrusters in the proposed MAJIC
system.
The change in mass properties simulated for crew-member
rescue has not been optimized for efficiency in transport. Instead,
the selection of a center of mass off-set of 1m in all three axes as
well as corresponding changes to the Jetpack’s moment of inertia
tensor have been selected to represent a sub-optimal emergency
crew-rescue scenario that might rigorously test the ACS
implementation.
Figure 4. Missions considered for MAJIC simulation. Left: Solar array inspection; photograph of current robotic
arm inspection operations at the ISS, photo courtesy of NASA. Middle: Asteroid sampling mission at Itokawa. Right:
Crew member rescue mission to recover an incapacitated crew member during an EVA.
Figure 5. Asteroid sampling mission profile.
Axes are labeled in kilometers in the asteroid
centered inertial (ACI) frame. An initial approach
followed by orbit plane change, inspection and
approach is followed by sampling activites
conducted at the asteroid’s surface. Human
dynamics models for astronaut motions are
included throughout the mission profile.
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IV. Control Moment Gyroscope Actuator Sizing
Utility assessment of CMGs as attitude actuators for a low-gravity astronaut EVA Jetpack begins with a sizing
study to find optimal CMGs using simulations for MAJIC operations. But what is optimal for the MAJIC system?
Traditionally, optimality in attitude control systems refers to accomplishing a given control task with minimized
requirements for system mass, volume, power, or some combination thereof. But as mentioned in earlier sections,
there are few well-defined tasks for an astronaut Jetpack mainly because there are few well-defined missions or
campaigns that will constitute the next generation of human space exploration. Because of this, analytically deriving
CMG properties is not straightforward.
A previous sizing study and human operator evaluation for MAJIC [11] sought to identify a CMG design that
effectively paid for its weight over the course of a single EVA mission. The idea was that a low-mass CMG ACS
might provide improved stability and control authority of the Jetpack without incurring a mass penalty at any point
during operations. After finding a candidate CMG design with this constraint, though, operator evaluations using
NASA's VR Lab at the Johnson Space Center revealed that such a small CMG did not have the capability to improve
performance beyond the control authority of a thruster ACS.
This section begins with a discussion of the updated constraints placed a new sizing study for MAJIC CMG
actuators. Instead of limiting CMGs to have low enough mass to pay for their weight in one mission, CMGs in this
study are only constrained by the geometry of a Jetpack and the desire to minimize mass and power use while
maintaining precise pointing and high stability during operations. Three options for placement of the CMG array and
control electronics in a notional Jetpack design is pictured in Figure 6.
Figure 6. Proposed Location for CMGs in MAJIC. CMG size is constrained in this sizing study to fit within the
structure proposed for a Jetpack. The compartment considered was previously designed as a fuel tank holding cell,
and so the idea pursued here is to replace half of the fuel tank space with a CMG array. Jetpack body-fixed coordinate
frame is indicated for each view.
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Other CMG sizing studies for small spacecraft [12]-[16] begin with well-defined satellite mission operations
concepts and associated design requirements for slew rates. These studies also usually assume static spacecraft mass
properties throughout a mission, with little emphasis on disturbance torques. With these assumptions, standard
optimization practices can be used to find an appropriate CMG design that minimizes mass, volume and power
requirements while meeting the minimum torque requirements.
This general formulation is useful, but cannot be directly applied to MAJIC since torque requirements are not
known a priori. In this case, control requirements are not dominated by slew rate profiles and desired pointing
accuracy but instead by the nature of disturbance torques that must be rejected. A strategy to address this problem is
to model representative types of disturbance torques that might be expected for a range of missions and then perform
a statistical analysis of the performance of potential CMG designs for these representative missions. Of the three
missions described in the last section, the asteroid sampling mission depicted in Figure 5 involves variability in mass
properties and disturbance torques that lies somewhere between the extremes of the solar array mission (on the low
end of variability) and crew member rescue (at the high end of variability). For this reason, the results of a Monte
Carlo statistical analysis of CMG performance during an asteroid sampling mission is considered in more depth and
is used as a basis from which a point design for the MAJIC CMG actuators is formulated.
Performance drivers for a CMG design are the angular momentum, 𝒉𝑐𝑚𝑔 and torque (Equation 1) achievable with
a single unit. With this in mind, parameters of interest for the Monte Carlo study are the flywheel mass moment of
inertia 𝑰𝑐𝑚𝑔, the fixed flywheel rate 𝜔𝑓𝑙𝑦, and the maximum gimbal rate allowable �̇�𝑚𝑎𝑥. Because the mass and size
of the CMG units is also important, the material density of the CMG flywheel rotors is also varied. Table 1 depicts
the constraints imposed in this sizing study.
After consulting with professional miniature CMG providers including Honeybee Robotics, the provider of CMGs
for a Draper-MIT hardware demonstration of the combined control concept for MAJIC operation [17] a maximum
𝜔𝑓𝑙𝑦 of 30 krpm was identified as the upper limit for standard flywheel motor technology. Because the size of the
CMG array angular momentum is critical to the control authority of the array, all trials in the Monte Carlo analysis
used 𝜔𝑓𝑙𝑦 = 30 krpm. The moment of inertia of the flywheel assumes a simple disk and is constrained to remain
under 4 kg able to fit in a space that would otherwise house fuel for a Jetpack (see Figure 6). The mass constraint of
4 kg was selected in order to ensure that the entire CMG subsystem does not exceed more than 20 kg in total mass to
remain practical for the Jetpack application. Finally, gimbal rates were constrained to a range according to the overall
torque that the CMG unit might provide given the angular momentum of a given design. For the bounds indicated in
Table 1, a uniform distribution is assumed.
Table 1. Monte Carlo Sizing Variables and Constraints
Parameter Initial Bound
Selection
Passing Criterion Constraint
Origin
𝐼𝑓𝑙𝑦 ≤ 4 kg mass
≤ 5 cm radius
0.5 Nms ≤ 𝐻𝐶𝑀𝐺 ≤ 2 Nms Geometric and mass
constraints
𝜔𝑓𝑙𝑦 = 30 krpm 𝜔𝑓𝑙𝑦 = 30 krpm Motor, bearing and
estimation limitations
�̇�𝑚𝑎𝑥 ≤ 40 rpm 0.5 Nm ≤ 𝜏𝐶𝑀𝐺 ≤ 5 Nm Human factors [3]
𝜌𝑓𝑙𝑦 Aluminum, Steel, Brass
or Tungsten
None None
For each trial conducted in the Monte Carlo analysis, seven metrics were used to assess relative performance of
different CMG designs. They include root-mean squared (RMS) attitude error, total fuel consumed, peak power
required, total energy consumed, , total time spent desaturating CMGs that have reached a singularity state, CMG
flywheel radius and CMG flywheel mass. Collectively, these seven metrics represent the constraints of the
optimization problem of the sizing study as defined by the system goals of achieving high performance (small attitude
error, little time spent in desaturation) with minimal overall system mass, volume and power requirements (little fuel
consumed, low peak power and energy capacity required, and small CMG flywheel radius and mass). By using a cost
function with equal weighting for each performance metric, an overall performance score is found for 1000 trials.
International Conference on Environmental Systems
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Table 2 depicts the top three performers from the 1000 trials conducted for the Monte Carlo simulation of MAJIC
performance during the asteroid sampling mission described above.
Table 2. Top Performers of Monte Carlo Simulation
Rank Material Mass (kg) Radius (cm) 𝒉𝒄𝒎𝒈 (Nms) 𝝉𝒄𝒎𝒈 (Nm)
1 Brass 2.35 3.89 1.86 1.55
2 Steel 2.29 3.96 1.88 1.82
3 Steel 2.19 3.90 1.74 0.93
As can be seen from Table 2, all three top performers have similar mass, volume and angular momentum, though
the torques achievable by each varies between roughly 1-2 Nm. This variation reflects the fact that there is a trade
between increasing torque and improving control responsiveness and decreasing torque to lower the probability of
entering into a saturated or internally singular state. Faster gimbal rates (and hence, larger torques) increase the
probability of saturation since the momentum envelope is traversed quicker and so these designs tend to saturate more
often leading to larger mean attitude errors. For CMG designs with low torques, there is less time spent desaturating
which ranks well, but average attitude accuracy decreases given the system’s reduced ability to respond to large input
torques.
The top performing CMGs indicated in Table 2 successfully accommodate for human motions and resulting
disturbance torques in order to maintain a stiff work platform for astronauts in the asteroid sampling mission as well
as the other missions simulated. As a comparison, the small CMGs sized in [11] for the purposes of maintaining
overall system mass had the following attributes: material = brass; mass = 0.98 kg; radius = 2.05 cm; ℎ𝑐𝑚𝑔= 0.35
Nms; 𝜏𝑐𝑚𝑔= 1.80 Nm. This previous design did not meet the performance requirments of the Jetpack in human
operator trials specifically because of the tendency of these CMGs to saturate often. From a comparison of the
properties of this previous design’s CMG to the CMGs sized for this study, it’s clear that the old design has much
lower angular momentum capacity, but roughly equivalent torque. Since torque is the product of a CMG’s angular
momentum and gimbal rate, this means that the previous CMG design had very high gimbal rates (49 rpm). The
combination of low angular momentum and high gimbal rates led directly to the tendency of these small CMGs to
saturate. The latest designs indicated in Table 2 do not share this weakness and instead have relatively higher angular
momentum capacity and low gimbal rates.
V. Combined-Control Utility Assessment
Assessing the relative utility of attitude control system (ACS) options for the MAJIC system requires a
comparative analysis of ACS performance and cost. Because thrusters are a simple solution, the best argument for
CMGs to be included in the Jetpack is one that focuses on the performance gains of the CMGs as well as any cost
benefits that might be expected from the increased fuel economy of a MAJIC system as opposed to a Jetpack without
CMGs.
A. Performance Assessment
In order to assess relative performance of a Jetpack with the top performer CMGs and a Jetpack without CMGs,
two representative mission actions were simulated: first, a simple translation with a center of mass offset; and second,
an attitude hold with periodic astronaut motions. The first mission action represents the situation that might occur
should an astronaut need to transport a large or heavy object such as an experimental payload, a haul of samples, or
an incapacitated crew member. The mass off-set implemented is equal to the mass-offset applied for the crew member
rescue mission in which the center of mass of the system is translated one meter in all three axes. The second mission
action corresponds to the requirement of the Jetpack to provide a stiff work platform despite astronaut-induced
disturbance torques throughout an EVA mission. Instead of just comparing the CMG system with a single Jetpack
design point, two Jetpack implementations were simulated: one with a large deadband of 30 degrees, and another with
a small deadband of 2 degrees.
Figure 7 depicts the comparison of average (root-mean squared) attitude error and fuel consumption for the three
systems during a translation of 25 meters in 300 seconds, both with and without a mass off-set. At the top of the figure,
there is a plot that shows the linear position of the system in order to give context to the attitude error and fuel
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consumption plots below. Even for the tight deadband thruster implementation, CMGs provide significantly better
pointing accuracy as expected for continuous actuators that aren’t limited by a deadband. This comparison of attitude
accuracy is seen in the top of Figure 7. The fact that more fuel is consumed in the case that the system’s center of mass
is displaced is an expected consequence of an astronaut carrying a large or heavy object during a translation maneuver,
though it is encouraging to see that the optimal CMGs succeed in maintaining precise attitude control throughout the
maneuver. For the case of no mass off-set, fuel consumption for the wide and tight deadbands (the solid blue and red
lines, respectively) is roughly equivalent, with CMGs displaying significantly (>60%) greater fuel economy. The same
trend exists for the case of a mass off-set, though in this situation the tight deadband thruster requires far more fuel
than either the wide deadband thruster or the most fuel economic CMG option.
Figure 8 shows the second constituent mission action simulated for the three systems: an attitude hold with periodic
astronaut motions over the course of an hour’s time. The attitude accuracy plot displays the same behavior as mission
action 1: both the wide and tight deadband thruster attitude control systems successfully maintain their deadbands, but
are far from achieving the pointing accuracy of the CMG system. Once again, the principle advantage of using CMGs
is demonstrated and the system is shown to be capable of maintaining precise pointing and a correspondingly stiff
work platform by rejecting external disturbances. At the bottom of the figure, the fuel consumption difference is also
stark: while the wide deadband thruster ACS uses slightly less fuel than the tight deadband, both use far more fuel
than the CMG implementation, which hardly ever uses fuel, except for desaturation purposes.
Figure 7 Mission Action 1 Results. Linear translation of 25 meters. RMS attitude error and fuel
consumption shown for a wide deadband thruster ACS (blue), a tight deadband thruster ACS (red) and
CMG ACS (green), for the case of no mass off-set (solid lines) or a mass off-set (dotted lines).
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B. Mass-to-Orbit Projections
Significant differences are indicated in both attitude error and fuel consumption rates as indicated by the
comparison of the top performing CMGs and a thruster attitude control system Jetpack explored above. While the
contrast in attitude error provides the best indication of relative control performance and system stability, the
difference in fuel consumption profiles can be used to perform preliminary mass-to-orbit requirements analysis. Such
an analysis is useful to see at what point in the lifetime of the MAJIC system would the increased fuel economy of
CMGs be enough to require less overall mass to be brought to orbit than would otherwise be required for a Jetpack.
The comparison made is between the sum of the CMG subsystem mass and thruster fuel mass for MAJIC with total
thruster fuel mass for a Jetpack that does not include CMGs. Table 3 shows the results of this analysis.
In order to arrive at the values shown in Table 3 several assumptions are taken. First, a single mission is assumed
to consist of three EVAs, each 6 hours in duration. Furthermore, it is assumed that two astronauts conduct each EVA,
and that both astronauts are using a Jetpack. Each mission is assumed to be 50% translation split 75%-25% between
Figure 8 Mission Action 2 Results. Attitude hold with periodic astronaut motions. RMS attitude error
and fuel consumption shown for a wide deadband thruster ACS (blue), a tight deadband thruster ACS (red)
and CMG ACS (green).
Table 3. Mass-to-Orbit Mass Projections for a Jetpack with and without CMGs.
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no mass off-set and a mass off-set; the other 50% of the mission is assumed to compose of attitude hold during
astronaut motions. Next, the overall CMG system mass including CMG actuators, control electronics and extra battery
mass is assumed to have a mass of 20 kg per MAJIC system. Finally, a 100 gram per hour desaturation budget for
each astronaut is added to CMG figures.
In reality, nearly 100% of an EVA would require disturbance rejection actuation to account for astronaut motions
and mass properties would be changing nearly continuously as the astronaut moves his or her limbs and interacts with
low gravity objects. With this in mind, the projections are conservative in nature and so the indication that CMGs
could “pay for their weight” after only five missions is an exciting prospect.
VI. Conclusion
Technology options can be constrained by mission architecture, but the opposite is true as well: mission
architecture options can be constrained by technology. CMGs for satellites as discussed in the literature are constrained
by specific mission architecture. This is usually the case when mission goals are well-defined and a method to
accomplish those goals is decided upon early in the conception and design processes. CMGs for MAJIC, on the other
hand, are not constrained in the same way. Instead, it is the mission architecture, or mission goals, that become
constrained by the technological capability of CMGs. A larger and more responsive system will enable the use of
heavier, more powerful tools; likewise, in the event of a crew member becoming incapacitated, the control authority
of the MAJIC system will dictate the speed and ease with which a second astronaut can collect the incapacitated crew
member and return him or her to safety.
When viewed in this light, the lack of well-defined performance requirements for the MAJIC system should not
be viewed as a hindrance for optimization, but as an opportunity to explore architectures that utilize a Jetpack. This
situation is similar to the one faced by human exploration in general: with no clear best-option architectures there is
an opportunity to develop cross-cutting and enabling technologies that might be useful for any number of potential
futures that might be pursued by NASA and other space agencies.
Even with these uncertainties, it is possible to design the next generation back-mounted Jetpack for astronaut EVAs
around low gravity objects. The analysis contained in this paper demonstrates the potential of a CMG-integrated
Jetpack system to provide a stable and responsive work platform that enables precise EVA tasks that include asteroid
sampling and scientific equipment installation or maintenance. Future work will include optimizing the MAJIC
system’s control logic as well as thruster number, placement and orientation. In addition, improvements to the
simulation environment can be made that would increase realism including the addition of sensor noise and actuation
delay for CMGs. The design point for a CMG system identified in this represents a promising base from which further
studies can be conducted to refine the MAJIC concept. Already the latest sizing study has resulted in a CMG design
that is superior to the previous sizing effort described in [11] and has provided physical insight to the design objectives
that are most important for the MAJIC application.
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