MRI-VisAct : a Bowden-cable-driven MRI-compatible series viscoelastic actuator

Abstract

The presence of strong magnetic fields in the magnetic resonance imaging (MRI) environment limits the integration of robotic rehabilitation systems in the MRI process. The tendency to improve imaging quality by the amplification of magnetic field strength further tightens the bidirectional compatibility constraints on MRI-compatible rehabilitation devices. We present the design, control and characterization of MRI-VisAct– a low-cost, Bowden-cable-actuated rotary series viscoelastic actuator that satisfies the bidirectional compatibility requirements to the maximum extent. Components of MRI-VisAct that are placed in the magnet room are built using nonconductive, diamagnetic MRI-compatible materials, while ferromagnetic or paramagnetic components are placed in the control room, located outside the MRI room. Power and data transmission are achieved through Bowden cables and fibre optics, respectively. This arrangement ensures that neuroimaging artefacts are minimized, while eliminating safety hazards, and device performance is not affected by the magnetic field. MRI-VisAct works under closed-loop torque control enabled through series viscoelastic actuation. MRI-VisAct is fully customizable; it can serve as a building block of higher-degrees-of-freedom MRI-compatible robotic devices.

Keywords

MRI-compatible robots rehabilitation robotics bidirectional compatibility series elastic actuation physical human–robot interaction

Introduction

Physical therapies are indispensable in the treatment of neurological problems. Therapies are conventionally delivered via physiotherapists, who provide active assistance or guidance to patients to help promote recovery by fulfilling a set of exercises. The amount of manual labour involved in conventional physiotherapy is a major concern, especially when considered in relation to the ageing trend of world’s population in developed countries (Wolfgang et al., 2008).

Advanced age is known to be one of the leading causes of stroke, a major generator of motor function deficiency (Wolf et al., 1991). An ageing population is expected to generate a larger gap between supply and demand of human labour in the field physiotherapy. Along these lines, robot-assisted rehabilitation systems are becoming essential parts of physical therapy. In addition to reducing the manual work load on therapists, rehabilitation robots also serve to improve the standardization and repeatability of exercises during therapy sessions, and provide quantitative measurements of patient performance.

Many robotic rehabilitation devices are being employed to treat a range of neurological problems, including joint instability, inability to bear weight and loss of limb function. With the proliferation of robotic rehabilitation systems, recent efforts have concentrated on improving efficacy of therapies conducted through use of such devices. Given that neuroplasticity of the brain is considered the main mechanism driving recovery, neuroimaging techniques can provide decisive information to evaluate efficacy of different treatment procedures (Dong et al., 2006).

Among the noninvasive diagnostic methods for imaging the brain, magnetic resonance imaging (MRI) is one of the most preferred. Functional MRI (fMRI), a procedure in MRI studies, measures brain activity associated with blood flow. In particular, activation in an area of the brain causes flow of oxygenated blood cells to that part of the brain to replace deoxygenated cells that display paramagnetic properties and interfere with magnetic signals of the MRI machine. Because of this phenomenon, the activated regions of the brain appear comparatively brighter in MRI scans.

If the rehabilitation devices can be operated during fMRI, the activation of regions in the sensory-motor cortex can be studied during therapies and conclusions about the effectiveness of different rehabilitation treatments can be made. Therefore, fMRI-compatible rehabilitation devices can lead to evidence-based robotic rehabilitation treatments that are personalized according to the needs of each patient and structured to achieve maximum efficacy.

Although the potential of such studies is great, the adaptation of classical rehabilitation devices for MRI environments is not a trivial task. The design of such devices should comply with the narrow dimensions of MRI machines and also ensure successful operation in the presence of strong magnetic fields. For successful operation of a device during MRI, it should satisfy two crucial constraints, which are together termed bidirectional compatibility constraints (Gassert et al., 2008).

The first constraint is to ensure successful realization of MRI procedures without interference from the device. For this, not only should the device not cause any safety hazards for the patient and environment, but it should also not create any disturbances to the quality of images. This compatibility requirement limits the use of standard actuation methodologies, such as direct current (DC) motors. Similarly, utilization of any ferromagnetic materials should be avoided, owing to their high magnetic susceptibility, as they may cause strong magnetic forces to be induced, leading to a missile effect. Another safety hazard can be caused by the heating of conductive materials, owing to eddy currents that develop on them because of the changing magnetic fields. These currents might cause excessive temperature elevations in these parts. In addition to these safety hazards, any other type of actuation and sensing mechanism that contains electric circuitry is not preferred, owing to the external magnetic effects and radio frequency interference that it may create. These types of parasitic effect are known to present themselves in MR images as false-positive activation artefacts, spatial distortion and shading.

The second condition of compatibility with MRI requires that the performance of the device should not be hindered by the high magnetic field of the MRI machine. Actuators and sensors that employ means of electrical actuation and reading are disturbed by the eddy current effects caused by the changing magnetic fields of the MRI machine. Similarly, sensor readings can be distorted by heating the sensors, owing to the same effects.

The strength of the magnetic field generated during fMRI studies is closely related, not only to the imaging quality and the length of image acquisition protocols, but also to the compatibility of mechatronic devices that are used during these procedures. As MRI technology develops, the field strength of the MRI machines also increases. For example, while the first MRI magnets operated at 0.1–0.3 T, currently most commercial devices operate at 1.5–3 T (Le Bihan, 2014). Since higher magnetic fields are preferred for high-quality neuroimaging, bidirectional compatibility requirements are likely to become more challenging in the near future with the spread of machines that use 7 T or higher magnetic field strengths. Such MRI machines are currently used for research (Budinger and Bird, 2017).

We propose MRI-VisAct, a low-cost, force-controlled MRI-compatible actuator that features ideal bidirectional compatibility, to future-proof robot-assisted rehabilitation protocols within MRI. The proposed actuator does not utilize any conductive material or electric circuitry inside the MRI room and can deliver good torque-control performance for safe and effective delivery of robot-assisted rehabilitation.

The rest of this paper is organized as follows. The ‘Related work’ section provides a comprehensive literature review of MRI-compatible devices and outlines the novel aspects of MRI-VisAct. The ‘Design requirements’ section reviews the constraints imposed on MRI-compatible devices, emphasizing the importance of bidirectional compatibility. The ‘Design and implementation’ section presents the mechatronics design and implementation details of the series viscoelastic element, MRI-compatible fibre-optic encoders, sensor processing unit and actuation unit of MRI-VisAct. The ‘Series elastic actuation and torque control’ section reviews series elastic actuation and viscoelastic modelling, and introduces control architecture of the device. The ‘Experimental characterization and verification’ section provides comprehensive evaluation of device performance. Finally, the ‘Discussion and conclusions’ section provides an overall evaluation of the proposed approaches.

Related work

MRI-compatible mechatronic devices have been used for several applications, such as surgery, analysis of haptic perception and rehabilitation. Researchers have proposed various design approaches to address the design challenges induced by harsh compatibility constraints to enable robot-assisted rehabilitation in MR environments. Table 1 summarizes MRI-compatible rehabilitation devices described in the literature. These devices can be loosely categorized according to their actuation scheme.

Table 1.

MRI-compatible human movement pattern or rehabilitation assessment devices.

Reference	Actuation type	Force sensing	Position sensing	Application
Hidler et al. (2006)	No actuation	Nonmagnetic 6-axis load cell	—	Wrist force/moment measurements
Newton et al. (2008)	No actuation	Nonmagnetic 6-axis load cell	—	Ankle, knee and hip torque measurements
Mehta et al. (2009)	No actuation	—	Optical encoder	Pedalling speed measurements
Sergi et al. (2011)	No actuation	—	Optical encoders	Post-rehabilitation efficacy prediction
Menon et al. (2014)	Particle jamming via pneumatic actuation	—	—	Mechanical modulation of device stiffness
Khanicheh et al. (2008)	Electrorheological fluidics actuation	Aluminium strain gauge	Optical encoders	Mechanical modulation of device damping
Hara et al. (2009)	Electrostatic motors	Nonmagnetic force sensor	Synchronous drive	2-dof motion & force rendering joystick
Hollnagel et al. (2011)	Pneumatic actuation	Resistive strain gauges	Optical encoder, foil potentiometer	Analysis of stepping patterns
Gassert et al. (2006)	Hydraulic actuation	Fibre-optic force sensors	Shielded optical encoders	Analysis of reaching movements
Yu et al. (2008)	Pneumatic actuation hydraulic actuation	Optical force sensors	Optical encoders, potentiometers	Comparison of hydraulic potentiometers
Ergin et al. (2014)	Ultrasonic motors	Shielded aluminium strain gauge	Optical encoders	Analysis of pick & place movements
Sergi et al. (2015)	Series elastic actuation with ultrasonic motors	Series elastic force sensing	Optical encoders	Torque-controlled wrist rehabilitation
Li et al. (2009)	Shielded DC motors with cable transmission through carbon fibre rods	DC motors	Optical encoder	Analysis of hand movements
Chapuis et al. (2006)	DC motor cable transmission	Fibre-optic force sensor	Optical encoder	Investigation of cable transmission for MRI
Menon et al. (2016)	Shielded DC motors & transmission using rods	DC motors	Optical encoders	Analysis of haptic perception, motor control
MRI-VisAct (this paper)	Series viscoelastic actuation with Bowden cables	Fibre-optic force sensing via series elasticity	Fibre-optic encoders	Administering torque controlled rehabilitation exercises

dof: degrees of freedom.

The first category is of devices with no actuation (Hidler et al., 2006; Mehta et al., 2009; Newton et al., 2008; Sergi et al., 2011). The purpose of these devices is to measure the interaction forces or movement patterns of patients during, just before or just after the MRI process. The devices in this category are typically equipped with multiple-degrees-of-freedom force sensors or optical encoders that are MRI-compatible. Although these devices help researchers gather data for perception and diagnostic studies, their use for rehabilitation is limited, owing to their inability to assist patients.

The second category is of devices that are capable of passive modulation of their impedance through unconventional techniques, such as particle jamming (Menon et al., 2014) or electrorheological fluidics (Khanicheh et al., 2008). Even though these devices are capable of stiffness or damping modulation, their adaptation for rehabilitation remains limited, as these devices are also incapable of providing active assistance to patients.

The third category includes devices that are actuated with MRI-compatible electrostatic motors (Hara et al., 2009). Electrostatic motors use electrical fields for actuation, where the actuator performance depends heavily on the current flowing inside it. Large electrical currents introduce noise to the environment that might interfere with MR images; hence, electrostatic motors must be placed at a certain distance from the MRI machine (Yamamoto et al., 2005).

Devices that use pneumatic actuation belong to the fourth category. Pneumatic actuation relies on compression of intermediate matter to transfer motion and force between a master system outside of the MRI room and a slave system inside the MRI room. This type of actuation can provide high forces that are adequate for physical rehabilitation and assessment (Hollnagel et al., 2011); however, the compressibility of air, pressure losses in piping or valves and friction in the pistons negatively affects the bandwidth and force-control performance of these devices (Yu et al., 2008). The force-control performance of these devices remains limited without the introduction of force sensors within the MRI room.

The fifth category consists of devices that utilize hydraulic actuation (Gassert et al., 2006). Owing to high friction losses of the hydraulic system, hydraulic actuation requires high internal pressures in the transmission for accurate position control of the system, leading to bulky structures in the construction of the device. The existence of high valve friction in hydraulic systems severely limits their use for force-controlled physical human–robot interaction.

The devices in the sixth category are actuated with ultrasonic motors (Ergin et al., 2014; Sergi et al., 2015). Ultrasonic motors are MRI compatible and possess high output impedance, displaying a good position control performance. However, these actuators are not only of high cost, but also require integration of force sensors for their use in physical human–robot interaction studies. For instance, Sergi et al. (2015) have used ultrasonic motors with bronze springs acting as series elastic elements to render the overall system into a force-controlled series elastic actuator. However, ultrasonic motors inherently contain electric circuitry that introduces noise to the environment and might cause MR image artefacts, especially in the new generation of MRI devices with strong magnetic fields.

The seventh category of devices relies on magnetic shielding to use standard DC motors within the MRI room. In particular, the motors are positioned in Faraday cages, such that MRI compatibility is established to some extent. However, like the case with the electrostatic motors, these systems must be placed a certain distance away from the bore of the MRI machine. Along these lines, both mechanical linkages (Li et al., 2009; Menon et al., 2016) and cable-based transmissions (Chapuis et al., 2006) have been employed for remote location of the actuators. Long linkages and cable-based transmissions both introduce undesired elasticity to the system, and the resulting noncollocation adversely affects the control performance of these approaches. Spaelter et al. (2006) used a fibre-optic force sensor to achieve closed-loop force control.

In this paper, we present the design, force control and experimental characterization of MRI-VisAct, a low-cost, Bowden-cable-actuated series viscoelastic actuator for robot-assisted physical rehabilitation during MRI. This work significantly extends our earlier feasibility studies (Senturk and Patoglu, 2016a,b). Even though Bowden-cable-driven series elastic actuation has found use in different force-controlled robot-assisted rehabilitation devices (Erdogan et al., 2017; Veneman et al., 2006), none of these designs target MRI compatibility. MRI-VisAct is different from these devices in that Bowden cable actuation is proposed to locate actuation units outside the MRI room, while series viscoelasticity results from the intentionally introduced nonconductive leaf spring that enables torque estimations and force closed-loop torque control.

In particular, MRI-VisAct utilizes only nonconductive MRI-compatible materials within the MRI room; hence, it can provide ideal bidirectional compatibility, unlike other closed-loop force-controlled MRI-compatible rehabilitation devices. To eliminate any imaging artefacts due to the device acting under strong magnetic fields, a Bowden-cable-based transmission and custom fibre-optic sensing units are introduced. The use of Bowden cable actuation and fibre-optic signals enables the placement of conventional non-MRI-compatible control or signal-processing units and electric actuators outside the MRI room, as presented in Figure 1, while a series elastic element constructed using polymer leaf springs and fibre-optic encoders enables accurate measurement of interaction torques, without causing any interference within the MRI room. The proposed MRI-compatible actuator is torque-controlled to enable the control of interaction forces with the patient. The torque control is implemented through a cascaded force-motion control architecture to enable high-fidelity control. Furthermore, the proposed device is not only customizable and low in cost, but can also act as a building block for MRI-compatible robotic devices with more degrees of freedom.

Figure 1.

Remote actuator and controller placement using Bowden-cable-based mechanical and fibre-optics-based signal transmissions.

Design requirements

Even though the overall design is customizable, the MRI-compatible actuator presented in this study is designed to deliver single-degree-of-freedom robot-assisted rehabilitation exercises for human forearm–wrist joints. Following the terminology of Merlet (2006), the performance requirements of the MRI-compatible system are categorized into four distinct groups of decreasing importance, namely imperative, optimal, primary and secondary design requirements.

An imperative design requirement is the kinematic compatibility of the device with the targeted joint. Although the kinematics of the human forearm–wrist joint are coupled and complex, dominant movements can be faithfully modelled as three-degrees-of-freedom rotations corresponding to supination or pronation of the forearm, and to flexion or extension and ulnar or radial deviation of the wrist. The proposed device targets each of these movements independently, by properly aligning the axis of rotation of the device with the corresponding axis of rotation of the relevant joint.

Another imperative design requirement dictates that the device should be capable of delivering physical rehabilitation exercises without sacrificing patient safety. Along these lines, a torque-controlled device is designed such that adequate levels of interaction forces between the patient and the rehabilitation device can be ensured at all times.

Table 2 presents the workspace and torque output capabilities of the forearm–wrist complex for a healthy human being. Since the isometric strength of healthy volunteers is unreasonably high for patients to perform activities of daily living, values corresponding to the minimal range of motion and torque limits needed for patients to perform activities of daily living are provided in parentheses. The proposed design needs to ensure that the range of motion and torque capabilities of the human forearm–wrist joint for everyday tasks are covered, by providing a continuous torque output exceeding 0.5 Nm, and a rotary workspace of over ±86°. A motion bandwidth of about 1 Hz is targeted for large rotations to match human performance within the range of motion. Furthermore, an order of magnitude larger motion bandwidth is necessary for small rotation references that are sufficient to cover the allowable deflection range of the elastic element, such that interaction forces can be controlled effectively through series elastic actuation.

Table 2.

Workspace or torque limits of forearm and wrist (Tsagarakis et al., 1999).

Joint	Human isometric strength	Human joint workspace limits
Forearm	9.1 Nm	Supination: $86 \circ$ ( $86 \circ$ )
Supination/pronation	(0.02 Nm)	Pronation: $71 \circ$ ( $71 \circ$ )
Wrist	19.8 Nm	Flexion: $73 \circ$ ( $45 \circ$ )
Flexion/extension	(0.5 Nm)	Extension: $71 \circ$ ( $50 \circ$ )
Wrist	20.8 Nm	Radial dev.: $19 \circ$ ( $19 \circ$ )
Radial/ulnar deviation	(0.5 Nm)	Ulnar dev.: $40 \circ$ ( $40 \circ$ )

Values in parenthesis correspond to the minimal range of motion and torque limits for patients to perform activities of daily living.

Considering the technological push to increase the magnetic field strength within MR machines to increase quality of neuroimaging, bidirectional compatibility is determined as the optimal design requirement. In particular, bidirectional compatibility should be maximized such that neither the device causes any artefacts in the resulting images nor the strong magnetic fields interfere with the proper functioning of the device. The proposed device aims at ideal bidirectional compatibility through the use of only strictly MRI-compatible, nonconductive materials within the MRI room, and remotely located actuation and sensor processing units outside the MRI room. Power and data transmission between the MRI and control rooms are achieved through Bowden cables and fibre optics, respectively.

Small device volume and low mass or inertia are considered as primary design requirements, while low cost, compact and modular designs are taken as secondary design requirements.

Design and implementation

This section details the design and implementation of the mechanical structure, series viscoelastic element, MRI-compatible fibre-optic encoders, sensor processing and actuation units of MRI-VisAct.

Mechanical design

The mechanical design of MRI-VisAct consists of four major plastic parts: support platform, exterior shell, output shaft and end-effector connectors, as presented in Figures 2 and 3. The support platform is arranged to make a $45 \circ$ angle with the horizontal. This angle is chosen to enable easier grip of the handle, when the user is lying on his or her back. The main function of the supporting platform is to constrain all unwanted movements owing to out-of-axis forces or torques applied to the system, while also limiting the movements of the cable housing to enable the relative motion of the inner cable.

Figure 2.

(a) Actuation unit located in control room. (b) MRI-compatible patient interface. (c) Top view: actuation unit. (d) Side view: patient interface. (e, f) Cross-sectional view: bearings, leaf springs, support and output shafts.

Figure 3.

Exploded view of MRI-VisAct.

The support platform is connected to the exterior shell of the device by the support shaft. MRI-compatible polymer glass ball bearings are used between the support shaft and the exterior shell to minimize friction during relative motion. Custom circular grooves are machined on the exterior shell to ensure that the tear-resistant polymer ropes are properly coiled around the exterior shell. Undesired relative motion between the coiled polymer ropes and the shell is hindered by screwing the ropes onto the shell with plastic screws.

The exterior shell is connected to the output shaft through four polymer composite leaf springs. The output shaft is not mounted on the support shaft, so as not to induce any parasitic friction. The output shaft can move relative to the exterior shell through deflection of the compliant leaf springs.

Since the device is intended to be used in the MRI room under physical interaction with the user within a narrow environment, the compliant parts and the output shaft of the device are implemented in a configuration in which they are contained in the rigid exterior shell. With such a configuration, the risk of causing any injury to the user due to jamming of body parts into cavities of the device is minimized.

The output shaft connects to the end-effector connector, through holes on the exterior shell that are designed to be larger than required, to avoid constraining deflections of the spring to some extent. The end-effector connector has two functions: to transfer the rotation of the actuator to suitable end-effectors or handles, by bypassing the support platform, and to act as a hard stop if the rotation is larger than the workspace limits of the user joint. To implement hard stop limits, the dimensions of the end-effector connector are customized based on the range of motion of the targeted joint.

The body of the device is machined from cast polyamide, a rigid engineering polymer known for its electrical resistance and relatively small weight. This part of the device weights about $3$ kg, together with the support platform. Rotating parts of the device weigh less than $1.5$ kg and have a moment of inertia of about $0.01127$ kg $m^{2}$ .

Series viscoelastic element

A series viscoelastic element is implemented to enable MRI-compatible force sensing through fibre-optic encoder readings. polymer composite leaf springs are utilized as compliant elements. Owing to their geometry in the form of a rectangular plate, leaf springs possess high axial, bending, and torsional stiffness to the forces and torques applied along directions other than the desired direction of deflection. As a consequence, only bending torques along the direction of the shaft can result in significant deflections of the compliant element, as shown in Figure 4. In this way, cross-coupling of forces and moments on the sensor, a parasitic effect suffered by many optical force sensors developed for MRI environments (Tan et al., 2011), can be largely avoided.

Figure 4.

Deflections of the series elastic element and deflection measurements.

By adjusting their geometric parameters, the bending stiffness of the leaf springs is designed to be compliant enough to result in large enough deflections that can be measured with sufficient resolution to estimate interaction torques with high fidelity, and large enough to render targeted torque levels and to achieve desired motion or torque-control bandwidths from the device. Deflection measurements are performed by an MRI-compatible linear fibre-optic encoder attached near the outer diameter of the exterior shell.

As with many polymers, polymer composite leaf springs display viscoelastic properties that become more dominant at higher frequencies. Along these lines, we experimentally characterize the viscoelastic behaviour for the leaf springs for use in force estimations during closed-loop torque control.

MRI-compatible fibre-optic encoder

Two MRI-compatible fibre-optic encoders are employed by MRI-VisAct; one to measure the rotations of the external shell for precise motion control, and the other to measure the deflections of the leaf springs to estimate interaction torques.

Standard encoders, which arrange the optical measurement unit and the decoding circuitry in a single compact package, are not preferred for MRI applications, since electrical circuits and metal cables inside the MRI room might lead to imaging artefacts and heating, significantly compromising bidirectional compatibility. Consequently, custom fibre-optic encoders that avoid any conductive material or electric circuitry within the MRI room are developed. These custom fibre-optic encoders, shown in Figure 5, function using the same working principles of a standard quadrature encoder and their signal processing is also performed in a similar manner. The fibre-optic encoders consist of light-transferring fibre-optic cables, an encoder case, an encoder strip within the MRI room, and signal-processing elements and fibre-optic transmitters (sources) and receivers (sinks) located outside the MRI room.

Figure 5.

(a) Cross-section of encoder. (b) Encoder assembly.

Commercial fibre-optic transmitters and receivers rely on light signals to achieve very high communication rates; hence, they are suitable for high-resolution encoder data transmission at update rates of the order of kilohertz. Moreover, fibre-optic cables can transfer data without significant loss over long distances. Furthermore, fibre-optic components featuring plastic or ceramic construction are widespread and low in cost.

Straight-tip, physical-contact cables with a 62.5 $μ m$ core diameter are chosen to implement the MRI-compatible fibre-optic encoders. These cables are available with plastic connection parts, making them suitable for MRI applications. The casings of the encoders are produced from polyoxymethylene, a nonconductive and MRI-compatible material. The casing holds the ceramic ferrules of fibre-optic cables in place with an interference fit, while the encoder strip is positioned between the ferrules, as depicted in Figure 5. Since the distance between lines on the encoder strip should be smaller than the core diameter of the fibre-optic cable, a 62.5 $μ m$ core diameter is suitable for use with 10–12 lines per mm encoder strips. The resolution can be further increased using a fibre-optic cable with a smaller core diameter.

To secure ceramic ferrules with micrometre precision, two sets of opposing holes are machined in the casing using a micro computer numerical control machine. Opposing pairs are machined simultaneously to ensure precise alignment of fibre-optic cores for successful transmission of the light beam. The lateral distance between the centre lines of the hole pairs is chosen to be $(2 k \pm 1 / 2) l$ in order to establish a $\pm π / 2$ phase difference between the A and B signals of the encoder, where l is the length of the transparent and opaque lines of the encoder strip and k is a positive integer. The lateral alignment of the hole pairs is crucial for performing accurate velocity estimation using encoder readings under quadrature decoding.

Sensor processing unit

The sensor processing unit is placed outside the MRI room, since sensor data can be communicated over long distances using fibre optics. The optical signals transmitted to the control room are converted into electrical signals with the help of optical receivers. The processing of these signals is performed via a series of integrated circuit elements to obtain appropriate signal outputs that can be interfaced with standard commercial encoder decoding modules.

The signals received by the fibre-optic receiver are inherently noisy. The main cause of the noise is open-air light transmission. In particular, diffraction occurs in the region where the optic signals exit the transmitter cables, pass through the encoder strip and enter the receiver cable. These multiple diffractions of light causes high-frequency oscillations in the electrical signal, which can be captured by the decoder and incorrectly interpreted as instantaneous direction changes of the encoder strip. Even though this noise is bounded by a single encoder count for position readings, its effect on velocity estimation is more extensive.

To reduce the noise, signal processing is implemented in hardware as follows. Firstly, the signal is passed through an RC circuit that acts as a low-pass filter. Even though most of the high-frequency noise is successfully eliminated by low-pass filtering, remnants of the high-frequency oscillations might still be present on the rising or falling edges of the encoder signals. Secondly, a Schmitt trigger is implemented using a rail-to-rail op-amp, to prevent false readings due to these remnants. The Schmitt trigger acts as a comparator with hysteresis; it not only digitizes the signal, but also hinders low-magnitude oscillations from changing the signal reading. Finally, the signal is fed to a high slew rate (5 V/80 ns) comparator to ensure that the rise and fall behaviours are fast enough to be compatible with the velocity estimation modules of the commercial encoder decoders, which may perform multiple sampling of a single rising or falling edges with low slew rates. Figure 6 presents a sample signal-processing instance for the fibre-optic encoders.

Figure 6.

Sample signal-processing instance for MRI-compatible fibre-optic encoders. Signals between processing steps are recorded at different time instants; however, the rise and fall behaviours are representative of the signal behaviour.

Actuation unit

The actuation unit is placed outside the MRI room, together with the sensing and control equipment. Bowden cables are used to transfer power from geared DC motors to the MRI-compatible device. Remote placement of the actuation unit away from the MRI-compatible human interface not only ensures bidirectional compatibility, but also significantly reduces the size and weight of the device to be placed within the bore of the MR machine.

The current prototype is presented in Figure 7; a 200 W coreless, rare earth magnet DC motor coupled to a harmonic drive with a 1:50 transmission ratio is used to actuate the drive pulley. The pulleys have a 1:1 ratio; hence, a cumulative transmission ratio of 1:50 is implemented between the external shell of the MRI-compatible device and the shaft of the DC motor. The Bowden cable transmission consists of tear-resistant polymer ropes and plastic shielding.

Figure 7.

Prototype of MRI-VisAct. Left: device with its remote actuation unit. Right: interaction with a user.

Series elastic actuation and torque control

This section discusses the advantages of series elastic actuation, introduces the model used to capture the viscoelastic behaviour of the compliant element and reviews the cascaded control architecture used for torque or impedance control of MRI-VisAct.

Series elastic actuation

MRI-VisAct is powered through Bowden-cable-driven series elastic actuation. This type of actuation has been used in rehabilitation robotics (Erdogan et al., 2017; Veneman et al., 2006) to achieve high-fidelity force control with large force-output capabilities and to ensure portability of the human interface. In this study, in addition to these advantages that ensures that the device has a lightweight and portable design with significantly low volume to fit the narrow bore of MRI machines, while simultaneously providing large enough actuation torques, required to assist human forearm–wrist movement by Bowden-cable-driven series elastic actuation is particularly preferred as it enables bidirectional MRI compatibility, by conveniently placing the controller and actuator units outside the MRI room. Furthermore, revoking the need for high precision and inevitably expensive force sensors, actuators and transmission elements, series elastic actuation helps reduce the cost of MRI-VisAct.

The Bowden cables and harmonic drive-reduction unit of MRI-VisAct introduce high friction to the power transmission, resulting in a passively nonbackdrivable system. Safety of the patients necessitates reduction of the output impedance of the system, while high-fidelity force control is required to adequately assist patients during physical rehabilitation exercises. For low-output impedance and high-fidelity torque control, series (visco)elastic actuation relies on compliant elements that are intentionally introduced between the Bowden-cable-driven exterior shell and the output shaft. In particular, the deliberate introduction of compliance between the Bowden-cable-driven actuation unit and the patient-attached output shaft decouples the high-impedance actuator unit from the interface and introduces passive compliance to the system, which acts as a mechanical low-pass filter, for instance under impulsive loads and high-frequency disturbances, such as torque ripple and stick-slip friction originating from the motor or power transmission. Furthermore, the compliant element is also used as the torque sensing unit by measuring its deflections. Compliant elements of series elastic actuators are designed to be orders of magnitude less stiff than commercial force sensors or load cells; hence, these elements experience significantly larger deflections under the interaction forces or torques, such that these deflections can be measured using regular position sensors, for example, optical encoders. Series elastic actuation possesses high-fidelity torque control and active backdrivability within its control bandwidth, while also featuring passive elasticity for excitations above this bandwidth, ensuring safety and robustness throughout the whole frequency spectrum, including hard impacts that may take place (Erdogan et al., 2017; Sensinger and Weir, 2006).

Given the inherent performance limitations of force control imposed by noncollocation between the actuator and the force sensor (Eppinger and Seering, 1987), series elastic actuation trades force-control bandwidth for fidelity, by introducing compliant force or torque sensing elements in the force-control scheme (Pratt and Williamson, 1995). By decreasing the force sensor stiffness (hence, the system bandwidth), higher force-feedback controller gains can be utilized to achieve responsive and robust force controllers within the control bandwidth of the system. Robust control is particularly important for Bowden-cable-driven systems, as the time-dependent and nonlinear friction in these cables are highly unpredictable.

The determination of appropriate stiffness of the compliant element is an important aspect of the design of series elastic actuators, where a compromise solution needs to be reached between force-control fidelity, force-output capability and closed-loop bandwidth. In particular, higher compliance can increase force-sensing resolution, while higher stiffness can improve the control bandwidth and force output of the system.

Viscoelastic modelling of the compliant element

The compliant elements in series elastic actuators are commonly constructed using metal springs with low hysteresis, such that the force–deflection relationship can be captured algebraically through Hooke’s law. Nonmetallic compliant elements have been proposed for use in series elastic actuators to take advantage of their compactness (Austin et al., 2015) and low mass or inertia (Parietti et al., 2011). In this paper, a nonmetallic (polymer-based) series elastic element is utilized to maximize the bidirectional MRI compatibility.

The force–deflection relationship of polymers displays viscoelastic properties that become more dominant at higher frequencies. Among the basic models available to capture viscoelastic behaviour, the Voigt–Kelvin model excels at modelling an asymptotic deflection behaviour under constant force but falls short of modelling instantaneous deflections. The Maxwell model can capture instantaneous deflections and creep, but entails infinite deflection under constant force. A combination of these two models, called the Burgers model, possesses preferable characteristics of both models. However, this model is overly complicated for modelling the compliant element of MRI-VisAct, as no creep behaviour has been observed in the leaf springs during empirical testing. Along these lines, the standard linear model depicted in Figure 8 is used as the underlying viscoelastic model. The standard model can account for instantaneous deflections, while also imposing an upper limit on the deflection of the material under constant force.

Figure 8.

Standard linear model used to capture viscoelastic behaviour of the elastic element.

The force and deflection relationship in the standard linear model is governed by

σ (t) + τ_{σ} \overset{\cdot}{σ} (t) = M_{R} (δ (t) + τ_{δ} \overset{\cdot}{δ} (t))

where $σ$ represents forces and $δ$ denotes deflections. The following definitions hold, given the model parameters depicted in Figure 8

\begin{matrix} τ_{σ} = \frac{η}{k_{1} + k_{2}} \\ τ_{δ} = \frac{η}{k_{1}} \\ M_{R} = \frac{k_{1} k_{2}}{k_{1} + k_{2}} \end{matrix}

Torque control

A real-time cascaded controller is implemented for control of MRI-VisAct, as shown in Figure 9. In this controller, a fast inner loop controls the velocity of the outer shell, rendering it into an ‘ideal’ motion source, while an intermediate-loop controls the interaction torque based on deflection feedback from the compliant element. Finally, an outer loop can be used for impedance control. The cascaded control architecture is advantageous as it allows for utilization of well-established robust motion controllers for the inner loop.

Figure 9.

Cascaded controller architecture with inner velocity, intermediate torque and outer impedance control loops.

In this study, the inner motion control loop is implemented on the motor controller at 10 kHz to compensate for imperfections in the power transmission, such as friction and stiction. The torque and impedance control loops are implemented at 1 kHz. The passivity of the cascaded control architecture of series elastic actuators can be guaranteed with a proper choice of controller gains, as demonstrated elsewhere (Tagliamonte and Accoto, 2014; Vallery et al., 2007).

Experimental characterization and verification

This section presents experimental verification of the fibre-optic encoders and empirical characterization of the viscoelastic compliant element. Furthermore, the control performance of MRI-VisAct is characterized through a comprehensive set of experiments.

Verification of fibre-optic encoders

To verify the data gathered using the custom-built fibre-optic encoders, a series of experiments was conducted, during which the performance of the fibre-optic encoders was compared with a commercial 10 lines per mm encoder. The encoders were positioned in series, such that they read from the same encoder strip.

Arbitrary oscillations up to ±1000 counts amplitude were applied to the test strip for 180 s and data from both encoders were recorded using a real-time I/O control card. Sample data collected during the experiments are given in Figure 10. The root mean square error between the fibre-optic encoder and commercial encoder was found to be 1.4 counts, corresponding to 25 $μ m$ , which is likely to be caused by the mechanical coupling and the possible bending of the encoder strip. The results indicate that the custom-built encoders achieve the desired level of position measurement performance.

Figure 10.

Sample data collected during encoder verification experiments.

Characterization of the compliant element

Experimental characterization of the series viscoelastic element was performed using a force or torque sensor rigidly attached to the output shaft. Sinusoidal torque inputs at different frequencies up to 10 Hz were administered to the system over a period of time corresponding to at least 30 cycles, during which encoder measurements were recorded. Displacement and torque measurements from these experiments are plotted in Figure 11. Since hysteresis is observed in the results, the standard linear model was used to obtain a model for the compliant element.

Figure 11.

Experimental characterization of compliant element and hysteresis compensation using the standard linear model for viscoelasticity.

The three parameters $τ_{σ}$ , $τ_{δ}$ and $M_{R}$ of the model were identified in the frequency domain by inspecting the input and output characteristics of the sinusoidal signal. Since $M_{R}$ characterizes the equivalent stiffness of the two springs $k_{1}$ and $k_{2}$ connected in series, it is identified at low-frequency input signals, where the effect of $η$ can be ignored. Once $M_{R}$ is determined, the remaining model equation becomes linear in $τ_{σ}$ and $τ_{δ}$ and these parameters are identified using the phase difference and amplitude ratio of the input and output signals, measured using a fibre-optic encoder and the torque sensor, respectively. After recording the amplitude ratio and phase shift values for input and output signals for multiple frequencies ranging from 0.1 Hz to 10 Hz, $τ_{σ}$ and $τ_{δ}$ were estimated through a least squares fit, leading to model parameters of $k_{1}$ =1552 Nm/rad, $k_{2}$ =135 Nm/rad and $η$ =38 Nm s/rad.

The model was verified at different frequencies to reduce torque estimation errors due to the hysteresis of the system, as presented in Figure 11. The top row of Figure 11 presents results from experiments at 3 Hz, while the bottom row presents similar results for 6 Hz. At each frequency, torque estimation was performed according to Hooke’s law and the standard linear model, and these results were compared with the force sensor readings. It was observed that, for frequencies greater than 3 Hz, the standard linear model results in a 50% reduction in torque estimation error caused by using Hooke’s model. The difference between these models is less for frequencies less than 3 Hz, where the effects of hysteresis become weaker.

Position tracking performance

The dynamic position control performance of MRI-VisAct was characterized through a set of experiments. Since the performance of the cascaded control architecture highly relies on the performance of the inner motion control loop, the position control bandwidth of the device was first determined.

Figure 12 presents a magnitude Bode plot characterizing the position control bandwidth for the system as 15 Hz, for 5.25° peak-to-peak magnitude sinusoidal inputs. Up to this frequency, MRI-VisAct can be regarded as a perfect motion source, as necessitated by the outer force and impedance control loops of the cascaded controller. This bandwidth is adequate for series viscoelastic actuation, as the deflection of the elastic element is five times less than 5.25° during normal operation with 2 Nm interaction torque.

Figure 12.

Experimental characterization of position bandwidth for 5.25° peak-to-peak magnitude sinusoidal inputs.

The position control bandwidth for 45° peak-to-peak magnitude sinusoidal inputs is greater than 1 Hz, which is also adequate, given the bandwidth limitations of patients.

The position tracking performance of MRI-VisAct for a chirp motion ranging up to 2 Hz with 30° peak-to-peak amplitude is presented in Figure 13. The percentage root mean square error for this experiment is characterized to remain less than 2%.

Figure 13.

Chirp position reference tracking performance for frequency range up to 2 Hz.

Torque tracking performance

The dynamic torque-control performance of MRI-VisAct is presented in Figures 14 and 15. In Figure 14, the set-point torque-control results are reported for three reference torque values; 1 Nm, 2 Nm and 3 Nm. The steady-state torque error for these three references is within the torque sensing resolution, while the 10% to 90% rise time and 5% maximum error settling time are less than 0.09 s and 0.15 s, respectively.

Figure 14.

Set-point torque-control performance for reference force values of 1 Nm, 2 Nm and 3 Nm.

Figure 15.

Chirp torque reference tracking performance for a frequency range up to 4 Hz.

Figure 15 depicts the experimental torque tracking performance of MRI-VisAct for a chirp torque reference signal up to 4 Hz with 2 Nm peak-to-peak amplitude. The percentage root mean square error for this tracking experiment is characterized to remain less than 6%.

Figure 16 presents a magnitude Bode plot characterizing the torque-control bandwidth as 14 Hz for 2 Nm reference torques, which is sufficiently high to deliver rehabilitation exercises. As expected, the torque-control bandwidth of the system becomes closer to the position control bandwidth as reference torque magnitude decreases. These bandwidths may be adjusted by modifying the motion bandwidth of the system. Alternatively, high force bandwidths are also directly linked to the stiffness of the viscoelastic element and can be altered by modifying the stiffness of the compliant element.

Figure 16.

Experimental characterization of the torque-control bandwidth with 2 Nm peak-to-peak torque reference.

Impedance rendering performance

To evaluate the impedance control performance of the device, two virtual fixtures were rendered as torsional springs with stiffness values of 2.5 Nm/rad and 5 Nm/rad, respectively. Figure 17 presents force–deflection data measured for these renderings, by applying known torques to MRI-VisAct and measuring its rotary displacement. Best linear fits on the data are also presented together with $R^{2}$ values characterizing the quality of these line fits. These results indicate that the device can achieve high-fidelity impedance renderings with errors less than 1%.

Figure 17.

Experimental verification of impedance rendering of two virtual torsional springs with 2.5 Nm/rad and 5 Nm/rad.

Discussion and conclusions

The design, control and experimental characterization of a Bowden-cable-actuated, MRI-compatible series viscoelastic actuator are presented. MRI-VisAct features MRI-compatible construction, fibre-optic sensing units and a Bowden-cable-based series viscoelastic actuation, such that it can minimize any interference that can cause imaging artefacts during neuroimaging, and ensure that device performance is not affected by strong magnetic fields.

Schueler et al. (1999) evaluated the bidirectional compatibility of a device with an MRA environment, considering five criteria: device movement, device heating, induced electrical currents, image distortion and device operation. Device movement is due to forces caused by the presence of ferromagnetic materials in an MRI machine. Such forces are not possible with MRI-VisAct, since it is constructed using diamagnetic materials. Device heating stems from electromotive forces acting on conductive elements. Given that all the materials within the MRI room are classified as insulators, such heating cannot take place to cause operational dysfunctions and safety hazards. Furthermore, owing to a lack of conductive materials or circuitry inside the MRI room, there is also no risk of inducing currents that can create artefacts on the image. MRI-VisAct does not distort the magnetic field outside of its volume, regarding its fully diamagnetic construction. Finally, the performance of the device operation is not affected by the MRI procedure, thanks to remote placement of actuation and control or processing units though use of Bowden-cable-based power and fibre-optic data transmission.

Even though the current prototype of MRI-VisAct is implemented as a single-degree-of-freedom actuator built to administer forearm–wrist exercises, this MRI-compatible mechatronic system design is highly customizable and can serve as the building block of higher-degrees-of-freedom MRI-compatible robotic devices. In particular, the stiffness of the series viscoelastic element can be customized by simply changing the geometric parameters of the leaf springs, the resolution of the fibre-optic encoders can be adjusted by employing fibre-optic cables with different core diameters, together with encoder strips of appropriate resolution, and the workspace of the device can be adjusted through the hard stops on the end-effector connector, while the torque output of the device can be adjusted by utilizing more powerful motors or higher transmission ratios within the control room.

Footnotes

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This work was partially supported by Sabancı University.

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