Design and Evaluation of a Balance Assistance Control Moment Gyroscope

Loss of balance accounts for a significant proportion of injuries among all age groups, but is known to be particularly detrimental among the elderly [1,2] and those with sensory deficit disorders such as stroke survivors and patients with Parkinson's disease [3,4]. Several factors associated with balance control have been found to increase the risk of falling, such as impaired stability when leaning and reaching, impaired gait and mobility, impaired ability in standing up, and impaired ability with transfers [2].

Multiple hardware solutions for balance assistance are discussed in the literature; currently, advanced wearable actuation technologies [5] and orthotic systems have been developed to assist locomotion, such as the wearable Cyberlegs hip orthosis [6] or exoskeletons such as the MindWalker [7], eLEGS (Ekso Bionics, Richmond, CA), or the ReWalk (Argo Medical Technologies, Israel). So far, these require bulky mechanical constructions attached to multiple segments of the body in order to deliver moments to individual joints of the body. Furthermore, they do not primarily target balance control, sometimes requiring the use of crutches.

Momentum exchange devices such as reaction wheels (RWs) and control moment gyroscopes (CMGs) present an attractive solution for human balance assistance. These devices can produce effective free moments on a body without the need of a coupled inertial frame. RW systems exert moments by accelerating or decelerating the spinning wheel and CMGs exert moments by rapidly changing the orientation of the spinning wheel about an orthogonal gimbal axis [8]. Even though RW systems are much simpler to control and construct, their effective output moment is relatively small if a light and minimalistic construction is desired [9]. In contrast, CMGs present moment amplification capabilities, i.e., given the same wheel actuator as a RW, CMGs can produce higher moments with a relatively small gimbal torque input, making them better candidates for minimalistic assistive devices for human balance. In addition, CMG used in assemblies can exert controlled moments about any direction. Unfortunately, these assemblies are prone to singular configurations in which the desired exerted moment cannot be produced. However, several steering laws have been proposed for spacecraft applications [10–12], and recently for CMGs as balance assistance devices [13].

In the past several years, a number of minimalistic support devices for human balance assistance based on RWs and CMGs have been proposed. Wojtara et al. constructed a RW-based prototype consisting of a single large flywheel embedded in a corset [14,15]; although the prototype is specifically designed as balance aid, the assistive torque has to be generated by the flywheel motor, making it bulky if higher moments are required. Theoretical examples of CMG-based devices include gyrostabilizers envisioned in belts or canes [16], or on patient's legs to assist joint motion [17] and haptic devices such as the iTorqU for torque feedback [18], or in intravehicular space suits for sensorimotor adaptation [19–21]. Recently, we proposed an upper body CMG-based wearable device, utilizing multiple CMGs to reduce mass and provide balance assistance in any direction [22]. This study was elaborated by Chiu and Goswami [23], who constructed the first CMG-based human balancing prototype which consisted of a symmetric (scissored) pair of CMGs with a mechanical constraint to synchronize gimbal motions; although this gives credence of the use of CMG technology toward gyroscopic human balancing, no experimental data are reported regarding balance capabilities of the device. Moreover, important design specifications such as the dynamic effect induced by the wearers movement, flywheel aerodynamic behavior, and internal loads due to gimbal actuation and gyroscopic moment are not addressed. These issues pose an important design challenge as they have great influence on material and actuator selection which as a consequence have a direct impact on output assistive moment, power consumption, size, and weight.

In contrast to the previously reported CMG devices for human balance, we present a detailed design methodology of a single CMG (Fig. 1), where the aforementioned design challenges have been addressed. Selection of the actuators was based on the aerodynamic behavior of the flywheel and the influence of the wearer's motion (i.e., parasitic moments). In addition, a structural analysis is reported, which is set to comply with the European directives for medical electrical equipment [24], accounting for the loads induced due to the gyroscopic moment and centrifugal acceleration. Based on this methodology, a single CMG was built and tested in a dedicated test setup.

A CMG is a momentum exchange device which consists of a fast spinning wheel supported by one or more gimbal structures as shown in Fig. 2, where the gyroscopic moment τ_CMG is given by the rate of change of angular momentum of the spinning wheel [8,25]. Using Euler's equations of rotational motion, the dynamic equilibrium of a single gimbal CMG (SGCMG) is expressed as [9]

where I_s, I_t, and I_g are the combined moments of inertia of the flywheel and gimbal structure about the flywheel spin axis $g⃗̂s$⁠, output moment axis $g⃗̂t$⁠, and gimbal axis $g⃗̂g$⁠, respectively. The term I_Ws denotes the flywheel inertia about the spin axis $g⃗̂s$⁠. γ, $γ˙$⁠, and $γ¨$ are the gimbal angular position, velocity, and acceleration, respectively; $ϕ, ϕ˙$⁠, and $ϕ¨$⁠, are the body angular position, speed, and acceleration about the transverse axis $b⃗̂v$⁠, respectively; and Ω is the flywheel angular speed. Note that we constrained our analysis to fall in the sagittal plane (i.e., the $b⃗̂u−b⃗̂w$ plane), with body angular velocity $ω=ϕ˙b⃗̂v$⁠.

where τ_CMG and τ_GM are the magnitudes of the gyroscopic moment and the torque exerted by the gimbal actuator, respectively. Note that the component about the falling axis (the transverse axis $b⃗̂v$⁠) of the gyroscopic moment τ_CMG depends on how the flywheel is oriented with respect to it, as determined by the gimbal angle γ.

As the gimbal angle γ increases, a higher gimbal angular rate $γ˙$ is necessary to produce the same desired torque. Special care must be taken when γ = ±π/2. In that case, no gyroscopic moment can be exerted in the transverse axis, as the flywheel spin axis $g⃗̂s$ is aligned with the transverse axis $b⃗̂v$⁠. When the gimbal is in such configuration it is said to be in a singularity. Thus, the desired gyroscopic moment has to be generated within a range free of singularities, i.e., −π/2 < γ < π/2.

For our design, we based our calculations on the CMG output torque required to counteract the effect of gravity in a fall, when no other balance-recovering actions are applied (e.g., use of crutches, fixed supports, or reflexes) and the body is in an out-of-balance state. To obtain quantitative requirements, we simplify a human as an inverted pendulum (IP), where the hip and knee joints are stiff, and no torques are applied about the ankles. It is thus assumed the person falls while pivoting about a horizontal edge. Previously, we estimated that a continuous moment of 280 N·m, generated by a set of three CMGs, applied for 0.1 s is sufficient to reorient the human body vertically, based on the same model of a rigidly falling human body with an initial inclination of 10 deg with respect to the vertical z axis. In that analysis, we assumed a human mass of 70 kg and height of 1.7 m [22].

Based on these findings, for an assembly of three CMGs, the design of a single CMG was developed aiming for about one-third of the reported gyroscopic moment, i.e., 90 N·m. It should be noted that even though this first proof of principle is not intended as a full wearable device, size and safety-factor constraints were imposed in the design of the CMG as a first step toward an improved wearable design.

We assume that the CMG should eventually be enclosed in a regular 50 l backpack. Therefore, an outer radius of 200 mm was set as size limit for the device envelope. A safety-factor lower limit of four was chosen against structural failure of the rotating components (i.e., flywheel and gimbal bearings) as well as the enclosing structure, complying with the European directives for medical electrical equipment [24].

In order to store higher angular momentum, the flywheel's moment of inertia was chosen to be as high as possible satisfying the given size constraint and readily available material. A classic disk-with-rim flywheel geometry was chosen as its shape and velocity factors are similar to those of an ideal thin rim [26] and also due to manufacturing practicality. Thus, it is desired that its mass is distributed as far as possible from the spinning axis (i.e., at the outer perimeter of the flywheel). Moreover, the width of the flywheel would need to be as large as possible, such that the rim inner radius R_i of the wheel can be as large as possible for a given outer radius R_o. Considering that the wheel needs to rotate also about the gimbal axis, increasing overall volume of the construction, we chose the maximum acceptable rim width h = 70 mm and outer radius R_o = 100 mm. As material, we chose the readily available aluminum 7075-T6. Moreover, as the device is to be wearable, mass of the wheel was limited to 2.5 kg. This resulted in a rim inner radius of R_i = 78 mm and a moment of inertia of I_Ws = 0.02 kg m²

To couple the rim with the motor, a constant-thickness thin disk was preferred due to manufacturing practicality and weight reduction. A hub was also included such that it could incorporate the motor within the flywheel itself as seen in Fig. 3. Further weight reduction was performed by removing material from the thin disk leading to a rim-with-spokes flywheel. However, the presence of these spokes is undesirable in the flywheel geometry due to significant increase of frictional drag while spinning. In order to diminish this effect, thin-plastic disks were placed on each side of the flywheel to cover the spokes after the material was removed.

To compute the needed power, an analysis of the different friction sources was performed. The main friction source was expected to be the flywheel's frictional drag.

A 120 W Maxon EC 4-pole 22 brushless motor was selected as flywheel actuator given size constraints in the flywheel's hub. A mechanical power of 108 W was estimated taking into account the losses due to the motor efficiency η_FM = 90%. Thus, a maximum angular speed of Ω = 5408.8 rpm was estimated from Eq. (10). For the chosen hybrid bearings, the frictional torque can be computed as τ_f,HB = 0.5μ_HBPd_b, according to the specification sheet, where μ_HB is the constant coefficient of friction for the bearing, P is the dynamic bearing load, and d_b is the bearing bore diameter. Thus, the frictional torque was τ_f,HB = 3.6 × 10⁻⁵ N·m, adding an extra 0.02 W of power at nominal speed. So, this confirms the assumption that the power to overcome friction in the bearings and the rotor in the motor is indeed negligible compared to the power required to overcome frictional drag at maximum speed.

To evaluate the mechanical strength of the flywheel under nominal operation, the maximum flywheel angular rate Ω = 5408.8 rpm in addition to the maximum designed gyroscopic moment of 90 N·m was used. Due to the complexity of the flywheel geometry, finite element method (FEM) analysis was performed using ANSYS Workbench and its static structural module. As the CMG is not used in reaction wheel mode (i.e., the flywheel angular rate remains constant in nominal operation), the imposed condition over the model is constant rotational speed. To validate the FEM results, a simplified model keeping the same overall dimensions but using only centrifugal loads was simulated and compared with analytical results. FEM analysis of the simplified model showed good agreement with the analytic radial and tangential stresses with root-mean-square error (RMSE) values of σ_r,RMSE = 0.07 MPa and σ_θ,RMSE = 0.13 MPa.

Using the same simulation parameters and boundary conditions and including the load due to the gyroscopic moment, the flywheel geometry as shown in Fig. 3 was used to perform the FEM analysis. Figure 4 shows the equivalent (von Mises) stress, where the maximum of 50.24 MPa is much lower than the yield strength of the flywheel material (aluminum 7075—T6, S_y = 503 MPa), giving a safety factor of 10 against the combined centrifugal and gyroscopic loads.

In addition to the stress analysis, it is necessary to assess the critical speed, since the flywheel can experience several types of vibrations with shaft whirl, lateral and torsional vibrations being the most important ones [29]. This critical speed must be avoided, since the resulting deflections might cause stresses beyond the strength of the material. The ANSYS Workbench modal analysis module was used to perform the critical speed analysis given the complexity of the flywheel geometry. Shaft whirl and lateral vibration effects were neglected as the flywheel was thoroughly balanced after manufacturing and the deflection of the shaft is very small at the flywheel location during bending due to the gyroscopic moment. Thus, Torsional vibrations were analyzed using the same parameters and boundary conditions as the static structural analysis, where the modal analysis results showed a minimum critical speed of 200,778 rpm, giving a margin of 37 when compared with the intended rotational speed (Ω = 5408.8 rpm).

The gimbal structure consists of a 6-mm-thick Al7075-T6 high-strength aluminum case which encloses the whole flywheel. In addition, extra 3-mm-thick Al7075-T6 high-strength aluminum plates were placed to reinforce the structure and prevent access to the flywheel from the exterior as shown in Fig. 5. The flywheel is supported by a pair of hybrid bearings ensuring low rolling friction and better performance at high speeds than those of conventional materials, allowing higher top speeds and lower power consumption. These bearings are responsible for transferring the gyroscopic moment to the gimbal structure, thus they have to withstand the dynamic loading of the gyroscopic moment. The bearings are symmetrically mounted in the flywheel with a distance d = 92.5 mm separating them (see Fig. 3). Based on the desired gyroscopic moment of 90 N·m and the distance between bearings d, the loading in each bearing is thus 973 N. Hybrid bearings were selected with a minimum safety factor of 4, leading to a load rating higher than 3892 N. The selected bearings (GMN HY-KH 61910) are able to withstand 3900 N of dynamic loading, complying with the designed safety factor against failure for dynamic loading due to the transfer of the gyroscopic moment to the gimbal structure.

The gimbal structure is at the same time supported by a pair of self-aligning bearings (SKF-2200), which are responsible for the transfer of the gyroscopic moment from the gimbal structure to the environment. The self-aligning bearings are mounted apart along the gimbal axis, symmetrically at 133 mm from the flywheel spinning axis (i.e., 266 mm from each other) as shown in Fig. 5. The dynamic loading withstood by each bearing is hence 349.62 N. Dynamic loading rate for each bearing is reported to be 5530 N, giving a safety factor of 15.8 against dynamic loading produced by the gyroscopic moment.

The second term in Eqs. (12) and (13) shows the influence of the body motion $ϕ˙$ on the gimbal torque and power. This is shown in Table 1, where the influence of the body motion considerably affects the required power of the gimbal motor. Based on the required power to exert the desired gyroscopic moment of 90 N·m when falling during walking, as shown in Table 1, the combination Maxon RE 40 150 W direct current motor with a 126:1 planetary gearhead (Maxon GP 52 C) was chosen accounting for a combined mechanical and electrical efficiency of η_GM = 73.6% providing a maximum mechanical power of 110.4 W. Both gimbal and flywheel motors are driven each by a Maxon ESCON 50/5 pulse-width modulation (PWM) servo controller set in current mode. Renishaw RMB20 encoder modules were placed in the gimbal axis (13-bit absolute RMB20SC) and the flywheel axis (9-bit incremental RMB20IC).

To evaluate the capabilities of the CMG, an experimental platform consisting of a single-degree-of-freedom inverted pendulum was built, which might emulate a rigid human falling in the sagittal (anterior–posterior) or coronal (medio-lateral) planes. The structure consists of a 1-m-long aluminum profile attached to a hinge joint, in which the CMG and electronics (motor drives and microprocessing unit) are mounted as shown in Fig. 6(a). In addition to the main aluminum profile, two safety end-stops are coupled to it in order to constrain the tilting angle of the pendulum. Absolute encoders are placed in the pendulum hinge joint and gimbal axis. The CGM was mounted at the top of the pendulum as shown in Fig. 6(b). Note that moments about the $b⃗̂u$- and $b⃗̂w$-axis are supported by the hinge joint. These moments were quantified from Eqs. (2) and (12) giving a maximum of 15.5 N·m about the $b⃗̂w$-axis due to the gimbal motor actuation and 45 N·m in the $b⃗̂u$ direction due to the projection of the gyroscopic torque within a gimbal range of operation of −45 deg < γ < 45 deg to avoid singular configurations. Thus, the combined reaction moment supported by the hinge joint is 47.43 N·m which is less of 50% its load capacity of 100 N·m against bending moments.

A pair of ESCON 50/5 servo-controllers was used to drive the gimbal and flywheel motors. These servo-controllers are set in current-control mode and receive a reference signal as PWM. A custom-made board (3Mxl) was used to command the PWM reference signals to the servo controllers and read the signal from the encoders. matlab xPC target was used as prototyping platform where the target personal computer (PC) is connected to the 3Mxl via RS485 (Quatech Serial Universal PCI Board) as shown in Fig. 7. High- and low-level controllers were implemented in matlab simulink running at a sampling rate of 1000 Hz.

Figure 8 shows the general control scheme of the setup. The high-level controller is responsible for keeping the inverted pendulum balanced. As a proof of concept, a springlike behavior, similar to the ankle strategy while maintaining balance in quiet stance, was implemented. Thus, the desired gyroscopic moment about the transverse axis is given by $τIP,ref=−kIPϕ$⁠, where k_IP is the desired emulated stiffness.

Once the desired gyroscopic moment is set by the high-level controller, the desired instantaneous gimbal rate $γ˙ref$ is computed from Eq. (5). The low-level controller is then responsible for tracking this gimbal rate, so the desired gyroscopic moment is generated. A proportional-integral controller was implemented to track the commanded gimbal speed. The low-level control law is then expressed as $τGM,ref=kpeγ˙+ki∫eγ˙dt$⁠, where $eγ˙=γ˙ref−γ˙$ is the error between the desired reference gimbal rate $γ˙ref$ minus the actual gimbal rate $γ˙$⁠.

To avoid singular configurations, the CMG initial position is set as γ = 0 (i.e., $g⃗̂t∥b⃗̂v$⁠), constraining the gimbal to an operation range of −45 deg < γ < 45 deg as shown in Fig. 6(b). Once the gimbal has reached the limit of the range, gimbal actuation is overridden and the gimbal stops, acting as a saturation in the gimbal angle γ. Only actuation leading to movement in the direction of the operation range is allowed from the saturated position.

Tests were performed with the inverted pendulum oriented at an inclination angle of $ϕ=0deg$ and with different virtual stiffnesses implemented (600, 800, 1000, and 1200 N/rad). Once the CMG low level controller was enabled, the inverted pendulum was manually perturbed.

As outcome measures to quantify performance of the device, we used the achieved maximum speed of the flywheel and the tracking performance of the balancing controller. In addition to the RMSE of the gyroscopic moment compared to the reference, we estimated the maximum achieved gyroscopic moment in the experiment via $τ̂CMG=IWsΩγ˙$ from measured flywheel angular speed Ω, gimbal angular position γ, and speed $γ˙$⁠.

A maximum speed of 5400 rpm at 118.56 W was reached in the flywheel. Figure 9 shows the tracking results for different virtual stiffnesses, from 600 N·m/rad to 1200 N·m/rad which were emulated accurately with a maximum RMSE of 0.55 N·m. Furthermore, gyroscopic moments up to 70 N·m were reached in the $b⃗̂v$-axis.

The implemented controller successfully tracked the reference virtual stiffnesses, while keeping the inverted pendulum within its equilibrium position $ϕ=0$⁠. Even though no damping was emulated in the controller, dry friction was present due to the inherent mechanical construction of the pendulum hinge joint. This resulted in a dead band behavior in the vicinity of the equilibrium point where the pendulum angular velocity was very low. This effect can be seen in Fig. 9 where the shaded regions showing the tracked stiffness seem to have a slight offset compared to the reference stiffness represented by the solid line. Note that the offset slightly changes as the stiffness tracking passes the equilibrium position showing the effect of the dead band caused by the dry friction in the hinge joint.

Despite the rather heavy weight of our device, it showed a substantially better gyroscopic-torque to weight ratio against the only other comparable device reported in the literature (7 N·m/kg versus 3.4 N·m/kg by Chiu and Goswami [23]), although the target gyroscopic moment of 90 N·m was not reached in this specific experiment. To improve the generated gyroscopic moment, we presume that the implementation of a partial vacuum flywheel chamber could considerably diminish the effect of the aerodynamic drag as lower air density can be achieved, decreasing even more power consumption and weight, and increasing top speed, thus producing higher angular momentum. Further improvements in weight reduction can be made using different material and geometry selection for the flywheel, where higher moment of inertia can be achieved with a smaller wheel size using materials with higher density (e.g., steel, iron, and tungsten). This could have a direct impact on the size and weight of the gimbal structure as well as on aerodynamic drag in the flywheel given that it increases rapidly with the peripheral speed. This reduction in aerodynamic drag implies at the same time a reduction in the power requirement for the flywheel motor.

Although the presented aerodynamic analysis is based on rather simple flywheel geometry, experimental results (Ω = 5400 rpm at 120 W) agree with the estimated maximum speed (⁠$Ω̂=5408.8rpm at 118.56 W$⁠), validating the assumptions of turbulent flow, merged boundary layers, and estimated consumed power. Special care must be taken in the aerodynamic analysis if a partial vacuumed flywheel chamber is implemented, as some of the assumptions presented in this paper might no longer hold, such as merged boundary layers and aerodynamic regime type.

As our prototype was conceived as wearable device, safety requirements were set to comply with directives for medical devices. Thus, pilot tests could be conducted to assess how humans react to transmitted moments in the upper body.

Finally, the setup used to evaluate the capabilities of the CMG as balance assistance device is rather simplistic, as it is based on an overly simple human model. Future research should involve tests with more realistic experimental platforms, for example emulating falls in all directions using a set of two or more CMGs in a 2DOF inverted pendulum.

By including the aerodynamic behavior of the spinning wheel and the induced dynamics of the wearer, we demonstrated that, with the proposed design methodology, a CMG-based human balance assistance device can be built to comply with the designed specifications given a proper selection of the actuators. We showed that our device is capable of producing up to 70 N·m with a total weight of approximately 10 kg.

This research was supported by the U.S. Department of Education, National Institute on Disability and Rehabilitation Research, NIDRR-RERC, Grant No. H133E120010, the Marie-Curie career integration Grant No. PCIG13-GA-2013-618899, and the Innovational Research Incentives Scheme Vidi with Project No. 14865, which is (partly) financed by The Netherlands Organisation for Scientific Research (NWO). The authors would also like to thank Ines Santos for her contribution in the conceptual design of the experimental setup and Guus Liqui Lung, Andries Oort, Nisse Linskens, and Simon Toet for technical support.

• Directorate-General for Research and Innovation (Marie-Curie Career).

• National Institute on Disability and Rehabilitation Research (Grant No. H133E120010).

• Nederlandse Organisatie voor Wetenschappelijk Onderzoek (VIDI Project No. 14865).