Soft robotics has the potential to enhance dexterous robotics tasks, such as gripping and locomotion, using structures that conform to variable and sensitive environments (Schmitt et al., 2018). While soft robotic actuators offer the high stroke and force-to-weight ratio required for such tasks (Bar-Cohen, 2000; Carpi et al., 2011), the position control of rigid actuators is generally more predictable, and better suited for complex tasks such as path planning and position sensing in sufficiently structured environments (Trivedi et al., 2008). Thus, a significant challenge for soft robotics is the development of control strategies that permit fast and complex motion within changing or unpredictable environments.

Dielectrophoretic Liquid Zipping (DLZ) is a novel actuation concept whereby amplified electrostatic attraction results in high-force electrostatic zipping (Taghavi et al., 2018). In DLZ, a pair of electrodes, electrically insulated from one another, are mechanically arranged in a zipping configuration (Figure 1). If the electrodes are oppositely charged, a strong electric field is developed between them, inducing a strong electrostatic attractive force that causes them to progressively zip together. Although electrostatic zipping has been demonstrated previously in zipping devices (Maffli et al., 2013; Chen et al., 2014; Li et al., 2018), DLZ features a tiny droplet of liquid dielectric (e.g., silicone oil) at the zipping point(s), which considerably amplifies electrostatic force. The electrostatic force between the two electrodes is related to Maxwell pressure, P = εE², where ε is the permittivity of the liquid dielectric and E is the electric field (Suo, 2010). The added liquid dielectric not only has a higher permittivity but also a considerably higher breakdown strength compared with air, allowing stronger fields to be sustained with associated stronger electrostatic zipping forces. Silicone oil, for example, whose respective permittivity and breakdown strength are around 2.7 and 6.7 times greater than air, theoretically implies up to 120-fold amplification of electrostatic force (Taghavi et al., 2018). While this amplification could be achieved by submerging the entire actuator in liquid dielectric, practically only a tiny droplet at each zipping point is required, since coincidentally occurring dielectrophoretic forces (which have the effect of drawing high-permittivity materials toward strong electric fields) help to retain the liquid dielectric at the zipping point (Taghavi et al., 2018).

The simplest embodiment of DLZ is the electro-ribbon actuator (Figure 1). Electro-ribbon actuators are compliant artificial muscles that can be made from any combination of conducting and insulating materials. Various embodiments of this type of actuator can exhibit high tension, high contraction (>99%), or high specific power equivalent to human muscle. These performance metrics make them a promising technology for Soft Robotics, where flexible, low-mass, high-performance actuators are required to deliver useful functions.

Control of soft robots is typically a challenging task due to their continuum structure and inherent compliance when interacting with the environment (Trivedi et al., 2008). Conventional control strategies that assume rigid joints tend to be ineffective at controlling soft robots (Rus and Tolley, 2015). Compared with traditional hard actuators, such as motors, control of soft actuators is often challenging due to their inherent compliance. Closed-loop control of dielectric elastomer actuators has been demonstrated using capacitive self-sensing (Rosset et al., 2013). Self-sensing has also been demonstrated in liquid-filled flexible fluidic actuators (Helps and Rossiter, 2018) and electrically driven HASEL (Acome et al., 2018) and Peano-HASEL (Kellaris et al., 2018) actuators, although full closed-loop control was not demonstrated. Closed-loop control of several parallel-plate electrostatic actuators, such as microelectromechanical systems (MEMS) devices, have been studied in Chu and Pister (1994), Seeger and Boser (1999), and Dong and Edwards (2010).

In this article, we investigate closed-loop control for electro-ribbon actuators. Open-loop control is limited with these actuators due to pull-in instability, resulting in an extremely small range of travel where position may be reliably controlled. However, by modulating the input voltage, a much larger region of stable positions can be achieved. We introduce a closed-loop (Boost-PI) controller, explore the effect of system gains upon output parameters, and configure gains based on a multi-objective parameter-space approach. Finally, we demonstrate system performance, including set point tracking of predetermined trajectories and sinusoidal signals, typical behaviors needed for the actuation and control of soft robots.

The electro-ribbon actuators were made from two electrode ribbons, each of which was comprised of a 50-μm-thick, 10-cm-long, 2.5-cm-wide steel strips (1.1274 carbon steel, h+s präzisionsfolien GmbH, Germany). Each electrode ribbon was insulated using PVC tape (AT7 PVC Electrical Insulation Tape, Advance Tapes, UK). The ends of the electrode ribbons were attached to one another using custom-made plastic clips to ensure a tight zipping point (Figure 2). A drop of silicone oil with viscosity of 50 cSt (# 378356, Sigma-Aldrich, USA) was added to each zipping point prior to each experiment to ensure consistency. High voltage was applied to the electro-ribbon actuators using a high voltage amplifier (5HVA24-BP1, UltraVolt, USA). Inputs were controlled and data was recorded using a National Instrument device (NI USB-6343, National Instruments, USA). A laser displacement sensor (LK-G402, Keyence, Japan) was used to measure actuator displacement, by measuring the height of the suspended mass in the vertical direction at a frequency of 1,000 Hz. For closed-loop control, measured height was used as the feedback variable, with a control loop sample frequency of 32 Hz. The open-loop bandwidth of the actuator has been observed as 10 Hz (Taghavi et al., 2018), thus 32 Hz was considered sufficient.

Isotonic testing was used to investigate the controllability of an electro-ribbon actuator. A rigid acrylic frame was built for the experiments. The center of the upper ribbon of the electro-ribbon actuator was clamped to the top of the rigid frame (Figure 2). This clamp had the advantage of preventing full zipping, which can introduce temporal hysteresis due to adhesive and cohesive forces associated with the liquid dielectric (Taghavi et al., 2018). The bottom ribbon was connected to a rigid bar, prescribed to move vertically by a linear guide, ensuring symmetrical zipping of the electro-ribbon actuator. To apply load to the electro-ribbon actuator, an external mass was hung at the bottom of the rigid bar. In the following experimental results, zero height was set as the position where the two electrodes zipped such that the bottom ribbon touched the clamp, with a 5 mm gap remaining between two electrodes at the center. The initial negative height was set as the resting position of the actuator with a suspended load and without an electrostatic force.

In this article, we explored an approach to control the contraction of an electro-ribbon actuator, which exhibits complex non-linear behavior. Initially, the actuator was tested by applying increasing static voltages to determine the V_pull−in, where the actuator experienced pull-in instability and performed full zipping. V_pull−in depends on the external load; higher loads induce larger extensions and require higher V_pull−in. If voltages below V_pull−in are applied, there exists a very narrow open-loop-controllable range of contractions. Application of a time-varying voltage approach, that is initially above V_pull−in but subsequently steps down to a lower voltage, enables a much wider range of accessible steady-state contractions. However, this approach is challenging because the steady-state contraction reached depends on not only on the applied voltage profile but also the previous steady-state contraction.

We modified a closed-loop PI controller—the Boost-PI controller—with an additional constant voltage term (V_c) to control the actuator. V_c reduces the time taken for the integral term to ramp-up to the voltage required to initialize zipping, resulting in lower rise time. It ensured the controlled voltage was close to V_pull−in, which is dependent to a suspended load (Figure 3B). The Boost-PI controller was studied by varying proportional and integral terms while setting V_c to 90% of V_pull−in.

To select appropriate Boost-PI gains, we implemented a multi-objective parameter-space approach, analyzing rise time, overshoot, steady-state error and settle time of the actuator response as benchmarks. As a result, K_p = 1,200 and K_i = 600 were selected since the resulting actuator was capable of fast rise time (1.45 s or 5.89 mm/s), low overshoot (1.77 mm or 18.6%) and acceptable settle time (38.0 s) for a 9.49 mm setpoint distance step-response task. The Boost-PI controller was used to control an electro-ribbon actuator to perform different control tasks: a staircase and oscillatory task, showing versatility and controllability of electro-ribbon actuators.

The contraction rate of the electro-ribbon actuator increases with increasing supplied voltage (Taghavi et al., 2018). In contrast, its extension rate increases with decreasing supplied voltage and is lower than contraction due to stiction of dielectric liquid and surface tension between two electrodes. Applying high voltage results in high contraction speed but can result in full zipping. Using the presented PI controller enables the actuation speed up to 8.7 mm/s when using K_p = 1,000 and K_i = 60 and holds the actuator at stable height.

While our Boost-PI method demonstrates controllability of the electro-ribbon actuators, we note several limitations based on load, actuator length and the current height. At higher loads, increasing gravitational forces reduce the acceleration of the actuator when traveling upward (against gravity) and increase acceleration when traveling downward (with gravity) and would likely require retuning of controller gains. Furthermore, the sensitivity to variations in load increases when decreasing the bending stiffness of the actuator (a long beam is more sensitive due to the longer moment arm). An additional limitation of Boost-PI is set-point sensitivity. While we show good performance over a large range of travel for our actuator, electrostatic forces increasingly affect controller performance close to full zipping position.

To address these limitations, the gains could be configured to automatically respond to changes in load and height. While height dependent gains could be developed using feedback already present in the system, load dependency could be implemented with a load cell. This approach would allow electro-ribbon actuators to perform over a wider range of loads and set-points, decrease settle-time and mitigate the need to manually reconfigure gains. The electro-ribbon actuator was observed to access the minimum distance of 5 mm away from full zipping position (Figure 5). Automatically tuning control gains based on the current actuator shape could enable the actuator to access a smaller distance closer to the full zipping position.

Alternatively, to improve the actuator to counteract pull-in instability, the controllable range could be increased by implementing a direct charge control strategy that actively controls the level of electrostatic charge rather than voltage, as has been done for other MEMS devices (Bochobza-Degani et al., 2003; Zhang et al., 2014). Due to the novelty of electro-ribbon actuators, analytical models are not yet available, therefore we investigated the performance of our controller using a multi-objective parameter-space approach. We plan to use a model-based approach to control electro-ribbon actuators in future work.

Traditional closed-loop control using self-sensing has been demonstrated in electro-ribbon actuators over a small displacement range (Bluett et al., 2020). Using the capacitance of the actuator measured by a self-sensing unit, which increases with zipping, as a feedback variable for the proposed Boost-PI controller could result in a controlled electro-ribbon actuator without additional sensors, as required for many soft robotics applications.

The demonstrated Boost-PI controller enables closed-loop, high-accuracy, high-working-range displacement control of electro-ribbon actuators. This addresses one limitation of the electro-ribbon actuators and considerably extends the range of applications for this type of DLZ actuator, allowing it to be included in a wide range of soft robotic systems including wearables assist devices, autonomous rescue robots and soft robots for space exploration.

The datasets presented in this study can be found in online repositories. The names of the repository/repositories and accession number(s) can be found at: University of Bristol Research Data Repository (https://data.bris.ac.uk/data) at https://doi.org/10.5523/bris.2sv1xtrsmhoro2qu3io2u244ig.

RD and AF contributed equally throughout developing the presented controller, designing and performing experiments, and collecting and analyzing the data. TH, MT, and JR provided advices along the research project. All authors wrote the manuscript, read, and approved the submitted version.

The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.