Actuator Sizing and Utility Assessment of Control Moment ...

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

International Conference on Environmental Systems

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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.


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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.


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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.


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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.


12

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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