Electrically Activated Soft Robots: Speed Up by Rolling

Abstract

Soft robots show excellent body compliance, adaptability, and mobility when coping with unstructured environments and human–robot interactions. However, the moving speed for soft locomotion robots is far from that of their rigid partners. Rolling locomotion can provide a promising solution for developing high-speed robots. Based on different rolling mechanisms, three rolling soft robot (RSR) prototypes with advantages of simplicity, lightweight, fast rolling speed, good compliance, and shock resistance are fabricated by using dielectric elastomer actuators. The experimental results demonstrate that the impulse-based and gravity-based RSRs can move both stably and continuously on the ground with a maximum speed higher than 1 blps (body length per second). The ballistic RSR exhibits a high rolling speed of ∼4.59 blps. And during its accelerating rolling process, the instantaneous rolling speed of the robot prototype reaches about 0.65 m/s (13.21 blps), which is much faster than most of the previously reported locomotion robots driven by soft responsive materials. The structure design and implementation methods based on different rolling mechanisms presented can provide guidance and inspiration for creating new, fast-moving, and hybrid mobility soft robots.

Introduction

The wheeled locomotion is the most common mode and one of the fastest solutions for robots running on the ground. There is another kind of robots different from the traditional wheeled robots, which can also roll fast on the ground. The rolling robot can be defined as one that rolls on its entire outer surface rather than just external wheels and does not need to react any of the rotating torques against the ground. Compared with the traditional wheeled robots or walking robots, the rolling robots have the following advantages: The spherical shell or multilinked closed-loop structure can protect their inside control system and equipment, and also provide better adaptability for uneven or soft surfaces (such as sand, snow, brush, or vegetation and even water); better stability and mobility; easily recovering from collisions, etc.¹ Due to these superiorities, rolling robots are very suitable for use in an unknown and varied but relatively smooth terrain, which can find great potential in scouting, exploration missions, and even entertainment industries.

The rolling mechanism of most reported rolling robots is based on the principle of moving the center of gravity of the robot outside of the contact area, which causes the robot to fall in that direction and thus roll along. It can be conveniently implemented by displacing the center of mass of the robot with respect to its point of contact with the ground or morphing the shape of the robot. Besides, impulse-based dynamic rolling is also an alternative way for rolling locomotion, which can be visualized by actuating a leg to push off the ground that can provide an impulse in the desired direction of motion or lift the robot and put gravitational potential energy into the system, which is then converted into rolling kinetic energy as the robot falls.²

Many rigid ball and loop-like rolling robots have been developed and the proofs of concepts for different rolling mechanisms are verified by different rolling robot prototypes. But the rigid structures and actuators (probably motors) of the rolling robots are often cumbersome, complex, and have poor impact resistance. And the operation of the motors that can generate eccentric and inertial forces could change the motion state of the robot and influence its trajectory, so the rolling control for the rigid rolling robots is difficult.¹ With the development of soft actuator technology, the linkages, gears, motors, and other rigid components in conventional robots are gradually replaced by soft materials and actuators, which results in soft robots with excellent adaptation, sensitivity, and agility when operated in unstructured environments and safe human–robot interaction.^3,4 The soft actuators make the integrated design of actuators and structures in one rolling robot body possible, which may simplify the robot structure and the rolling control.

Based on the impulse-based rolling mechanism, Farias et al.⁵ designed and constructed an untethered soft wheel robot that can be propelled in a fast rolling motion by pneumatically actuated channels. It was able to roll for about 3 min on one 16 g cartridge of CO₂ and was able to achieve a speed of about 6 m/min (0.72 blps). Robertson and Paik⁶ developed a modular vacuum-driven soft continuum robot system that realized a faster rolling gait with the average speed of 60 mm/s (1.33 blps) impulsed by the body deformation. Huang et al.⁷ designed a STAR-shaped rolling soft robot (RSR), which consists of seven curly shape memory alloy (SMA) actuators; the STAR robot can roll over 1 blps (body length per second) by the impulse generated from the unfolding deformation of the actuators.

Based on the gravity-based rolling mechanism, Sugiyama and Hirai⁸ developed a circular soft robot and a spherical deformable robot using SMA coils: The robots can roll steadily and continuously on the ground or slope through deformation of the robot bodies. The circular robot prototype moves 260 mm in 10 s at a speed of 26 mm/s (0.65 blps). Wu et al.⁹ proposed a wheeled robot driven by a liquid-metal droplet; applying voltage to the droplet can alter the robot's center of gravity, which, in turn, generates a rolling torque and induces continuous locomotion at a steady speed of 1.1 blps (tethered) and 0.9 blps (untethered). Through body deformation driven by light, a tubular structure made of polymer/single-walled carbon nanotube bilayers also realizes a fast forward-rolling away from light on a flat surface at the speed of ∼6 cm/s (3 blps).¹⁰

In addition, a different ballistic rolling mechanism inspired by the caterpillar was explored by Lin et al.,¹¹ and a soft-bodied rolling robot “GoQBot” was developed based on this mechanism by using SMA. GoQBot can reach a forward velocity over 0.5 m/s within the first 200 ms during one ballistic rolling, which is considered a very fast moving speed among soft robots. But GoQBot does not have a righting reflex to recover from each ballistic roll and all ballistic rolling events end with an unpredictable tumble. Another different rolling mechanism is the passive rolling driven by the external magnetic field. Hu et al.¹² designed a magneto-elastic soft millirobot and realized a fast rolling motion at the speed of ∼5.89 blps, but it requires bulky setups to generate the external magnetic fields, and the mobile scope of the robot is limited.

Dielectric elastomer (DE), as one of the few artificial muscle materials that can be comparable to the natural muscle, has been widely explored to replace conventional actuators and transducers for developing various robotic applications, especially soft robots. This soft active material possesses remarkable traits, including large actuation strain, high energy density and electromechanical efficiency, inherent compliance, light weight, fast response, and silent operation.^13–16 And it simply consists of an elastomer membrane sandwiched by compliant electrodes on both sides. When applying voltage on the electrodes, charges accumulate on the top and bottom surfaces of the membrane. The opposite charges induce electrostatic pressure in the membrane, which results in an increase in the area and shrinkage in the thickness. Based on this simple actuation mechanism, many soft robots with biomimetic locomotion (such as swimming,^17,18 peristalsis,^19,20 legged walking,^21,22 crawling,^23–25 hopping-running,²⁶ and sliding²⁷) have been developed by using dielectric elastomer actuators (DEAs), which exhibit improved mechanical robustness and environmental adaptability. Moreover, the DE-based soft robots also have demonstrated respectable moving speed compared with other soft actuator-based robots, due to the lightweight and fast response of DEs. For example, an inchworm-inspired crawling soft robot can run 4 times its blps,²⁵ and a hopping–running robot inspired by the rabbit reaches a high speed of 51.83 cm/s (6.10 blps)²⁶ when their DEA bodies or legs are excited by periodic high voltage with high frequency.

Combining the fast-response DE with the rolling locomotion mechanism, which is one of the most promising solutions for high speed motion systems, fast RSRs can be developed. Artusi et al.²⁸ proposed an inflated deformable rolling rover actuated by four DEA sectors, but due to the cumbersome rigid frame and inflated body, the robot moves slowly at a speed of 43 mm/s (0.40 blps). Rosset and Shea²⁹ developed a rolling robot “Rupert” using a DEA motor; it can roll steadily on a customized metallic rail at a high speed typically between 100 and 200 mm/s, but it is not a strictly soft robot and cannot roll on the ground. Li et al.³⁰ presented a fast RSR driven by a multisegment annular DEA. The robot rolls at a speed of 36.27 mm/s (0.73 blps), and the maximum speed reaches ∼0.95 blps. These three RSRs driven by DE are all based on the center of gravity-based rolling mechanism. A few studies have been concerned with the RSRs driven by DE based on other rolling mechanisms.

In this article, three fast RSRs with different rolling mechanisms (impulse based, gravity based, and ballistic) are developed based on dielectric elastomer minimum energy structure (DEMES). The impulse-based rolling soft robot (IRSR) consists of a wheeled sponge body and several DEMES joint legs. Its wheel center is elaborately designed to coincide with its center of gravity, so the robot can roll stably on the flat ground by the continuous impulse generated from the DEMES legs kicking quickly on the ground. The gravity-based rolling soft robot (GRSR) also has a wheeled body, but its shape is deformable and controllable. With six DEMESs integrated in it, continuous changes of the robot's center of gravity can be induced by the active body deformations. So the RSR can realize dynamic rolling on the ground due to the moment generated by the gravitational force. The ballistic rolling soft robot (BRSR) has a rollable multisegment DEMES body and electroadhesion actuator (EA) feet. By the fast unfolding and curling deformations of the body and the controllable anchoring operations of the feet, the robot can eject itself quickly and then roll fast on the ground by the inertia. Corresponding to different RSRs, the DEMES acts in different structural and actuation modes for the different rolling mechanisms. Its good compliance, large bending deformation, fast response, light weight, silent operation, and other excellent properties are all fully utilized to realize the fast rolling speed and good compliance for the RSRs. In the Dielectric Elastomer Actuators section, the basic structure and actuation mechanism of dielectric elastomer actuators are described. The conceptual designs and rolling mechanisms, along with the corresponding control patterns and rolling tests for the three RSRs are listed and illustrated in RSRs with the Different Rolling Mechanisms section, respectively. The discussion and conclusion are presented in the Discussion and Conclusion section.

Dielectric Elastomer Actuators

Recently, DEMES has been widely used to design and drive soft robots for its good compliance, design flexibility, easy fabrication, and actuation.^17,23–25 As shown in Figure 1a, a DEMES rotary joint consists of a prestretched DE membrane bonded to a planar flexible frame with an open section. The area of the DE membrane with painted compliant electrodes is covered exactly on the open section, which deforms into an out-of-plane saddle shape after release of the elastomeric prestrain. Simultaneously, the tension force in the prestretched DE membrane makes the flexible frame buckle out of plane and then bend to a minimum energy state of the film-substrate system. Application of voltage on the DE membrane shifts the system's minimum energy state, resulting in the unfolding of the buckled frame.

FIG. 1.

Structures and actuation characteristics of three DEAs. (a) Bending deformation of the DEMES rotary joint. (b) Unfolding deformation of the rollable multisegment DEMES. (c) Shape deformation of the multisegment annular DEA. DEA, dielectric elastomer actuator; DEMES, dielectric elastomer minimum energy structure. Color images are available online.

When subject to voltage, the electric-field-induced Maxwell stress σ in the membrane can release some of its pretension, which results in the frame unfolding to a new equilibrium angle with a smaller bending angle θ. The Maxwell stress is related with the applied voltage¹³ $σ = ɛ_{r} ɛ_{0} E^{2} = ɛ_{r} ɛ_{0} {(\frac{V}{t_{m}})}^{2}$ (1)

where ɛ_r is the relative dielectric constant of the elastomer, ɛ₀ is the permittivity of vacuum, E is the electric field, V is the applied voltage, and t_m is the thickness of the DE membrane. So, different voltages can control different bending angles. The angle shift process is the actuation stroke of the DEMES rotary joint.

When the flexible frame of the DEMES is a strip with several same open sections distributed uniformly on it and the DE film is painted with multiple groups of electrode regions corresponding to the open sections (shown in Fig. 1b), after release of the bonded prestretching DE film, a rollable multisegment dielectric elastomer minimum energy structure (MDEMES) is obtained by self-assembly.³¹ The rollable MDEMES can be regarded as forming from mechanically linking several independent single-segment DEMES rotary joints; its initial state o is a curly configuration with a large curvature. When activating all the DE segments (a–f) simultaneously, the curly strip uncurls and allows for a large actuation stroke, which has fully functioned in the design of soft grippers.^31,32

As shown in Figure 1c, an annular DEA can be simply fabricated by connecting the two ends of a rollable MDEMES. The initial configuration of the annular DEA is a circle; when activating different groups of DE segments, various shape deformations can be achieved. For example, its shape can change to an ellipse after applying voltage on two opposite DE segments in the DEA. More information about the active deformation performance of the annular DEA is provided in Ref.³³ The actuation performances of the DEMES rotary joint and the rollable MDEMES are shown in Figure 2. We can find that both the DEAs respond to the applied voltage within 40 ms, and achieve a big deformation after 300 ms, as shown in Figure 2a and b. When the voltage applied to the DEMES rotary joint increases from 0 to 5 kV, the steady bending angle θ of the joint reduces from the initial 79° to about 16°, and the blocking force increases from 0 to 103.4 mN; the response curve of the blocking force when subjected to 5-kV high voltage is also shown in Figure 2c. For the rollable MDEMES, it begins to unfold when the voltage is 5 kV, as shown in Figure 2d; as the voltage increases to 7 kV, the unfolding range x extends from 75.6 to 126.5 mm, and the corresponding response time quickens from 1.7 to 0.34 s. Higher voltage can generate bigger Maxwell stresses in the DE film, thus releasing more prestress in the DE film of DEMESs. Under the combined action of the elastic restoring force of the flexible frame, the actuator can obtain bigger deformation acceleration. So, high voltage leads to faster response of the MDEMES. The multisegment annular DEA can also rapidly respond to the excitation voltage within 50 ms, and it can achieve various shape deformations by actuating different DE segments.³³ It can be seen that the design principles and fast actuation characteristics of the DEAs provide a simple and effective method for converting the lateral expansion of DE film into different deformations that can be used as actuators for soft robots.

FIG. 2.

Actuation performances of the DEAs. (a) Photo sequences of a DEMES rotary joint during bending deformation. (b) Photo sequences of a rollable MDEMES prototype during unfolding deformation. (c) Steady bending angle and blocking force of the DEMES rotary joint varying with different applied voltages. (d) Unfolding range and the corresponding response time of the rollable MDEMES under different applied voltages. MDEMES, multisegment dielectric elastomer minimum energy structure. Color images are available online.

RSRs with Different Rolling Mechanisms

Based on the DEAs, we have developed three RSRs with different rolling mechanisms, which, respectively, are impulse-based rolling, gravity-based rolling, and ballistic rolling. Every rolling mechanism and control pattern corresponding to the three RSRs along with the robot prototypes and main experimental results are described later. The DEAs used to build the robot prototypes were mainly fabricated from attaching prestretched acrylic elastomer film (VHB tape from 3M) on the laser-cut polyethylene terephthalate (PET) frames; carbon grease (MG Chemicals) was smeared on both sides of the elastomer film as the compliant electrodes, as shown in Figure 1. We used these readily available commercial materials in our study mainly to conduct the proof-of-concept research on developing and characterizing RSRs with different rolling mechanisms using DEAs.

Impulse-based rolling soft robot

Conceptual design and rolling mechanism

As the DEMES rotary joint can generate a bending deformation and actuation torque when subject to voltage, an IRSR driven by multiple DEMES rotary joints was designed. As shown in Figure 3, the IRSR mainly comprises a wheeled robot body and several DEMES legs that are evenly distributed around the middle block of the body. Here, a robot prototype with four DEMES legs (A–D) was fabricated for the impulse-based rolling test, as shown in Figure 3b.

FIG. 3.

IRSR. (a, b) Structure design and prototype of the IRSR. (c) Impulse-based rolling mechanism. (d) Voltage pattern for rolling control. (e) Photo sequence during a rolling test of the IRSR prototype. IRSR, impulse-based rolling soft robot. Color images are available online.

The rolling mechanism of the IRSR is illustrated in Figure 3c; at the initial state, the robot rests on the ground with DEMES leg A approaching the ground; then actuating it to push off the ground, the output force generated by the DEMES leg can drive the robot to rotate clockwise. Assuming the DEMES leg deforms from initial 90° to 180° (fully unfolded) during every impulse step, the impulse accelerates the robot to rotate angle Φ. The force analysis of the robot is shown in Figure 3c. When the DEMES leg acts on the ground, the motion equation of the IRSR can be given as $f_{l} - f_{b} = m r β$ (2)

J β = N_{l} d + f_{b} r - f_{l} r

(3)

where f_l and N_l are, respectively, the friction and reaction forces exerted on the DEMES leg by the ground; f_b and N_b are, respectively, the friction and reaction forces exerted on the wheel by the ground; J and β are, respectively, the rotational inertia and the angular acceleration of the robot; r is the radius of the wheeled body; d is the horizontal distance between the contact point P and the robot's center of gravity G, and it increases during the actuation of the leg. The rolling condition is f_l > f_b, namely, N_lμ_l > mgμ_b, where μ_l and μ_b are, respectively, the friction coefficients of leg to ground and the wheeled body to ground. Combing the two equations cited earlier, β is obtained by $β = \frac{N_{l} d}{J + m r^{2}}$ (4)

The reaction force N_l can be acquired from the blocking force of the DEMES leg, as shown in Figure 2c; then, the angular velocity ω of the robot can be determined by $ω = \sqrt{2 ϕ β}$ . The rolling speed of the IRSR can be simply improved by increasing the reaction force N_l, which can be implemented by increasing the applied voltage or optimizing the structure of the DEMES legs. After each acceleration rolling induced by the impulse from the DEMES leg, the robot then slows down by the friction f_b, until the next step of impulse-based rolling. After the first actuation step, the robot rolls and DEMES leg B rotates to the initial position of the leg A. Then, actuating leg B can make the robot accelerate rolling to the right again. So, the IRSR can roll on the ground continuously by actuating the four legs in an appropriate time sequence. Figure 3d gives two voltage patterns for the rolling control. Continuous rolling can be simply controlled by actuating the four legs in sequence by four control signals. On the contrary, actuating two opposite legs one time can reduce the four control signals to only two for the rolling control, which can also simplify the control system.

Rolling performance

The weights of every DEMES leg and the robot body are 1.1 and 7.8 g, respectively. So the assembled IRSR prototype weights 12.2 g totally, and the diameter of its wheeled body is 106 mm. Every DEMES leg was connected to a multiplex high-voltage control system by wires and can be actuated independently. Figure 3e shows a sequence of photos of the IRSR prototype during a rolling test and the corresponding speed curve when actuated by a high-voltage control signal with amplitude 5 kV and period T = 2 s. The IRSR prototype moves about 226.6 mm in 1.8 s. So the average rolling speed of the prototype is about 125.9 mm/s, and its speed-diameter ratio is 1.19 blps. The rolling distances and speeds of the prototype at different time intervals are also listed in Table 1. We can see that at the initial time interval 0–0.5 s, the average speed of the prototype is 1.04 blps, which is relatively slow; then during the next time interval 0.5–1.0 s, the speed reaches the instantaneous maximum 1.43 blps. The four DEMES legs were actuated in sequence by the time interval of 0.5 s (an open-loop control signal) during the experiment, whereas the rolling of the robot was not a uniform motion, so it could not ensure that every DEMES leg can provide an impulse for the rolling when it was actuated.

Table 1.

Distances and Speeds of the Impulse-Based Rolling Soft Robot Prototype at Different Time Intervals

Time, T (s)	Distance, S (mm)	Average speed, v (mm/s)	Speed-diameter ratio, v_r (blps)
0–0.5	55.3	110.6	1.04
0–1.0	131.3	131.3	1.24
0–1.8	226.6	125.9	1.19
0.5–1.0	76.0	152.0	1.43

blps, body length per second.

Actually, the robot prototype was only accelerated by the impulse from DEMES legs A and B during the rolling test, respectively, at 0 and 0.5 s. So after twice acceleration, the instantaneous maximum speed occurred at the time interval 0.5–1.0 s. If the position of every DEMES leg can be identified by sensors, then a dynamic rolling with faster speed can be realized by the accurate closed-loop control signal. Using DEMES legs with multilayer elastomer or improved structure design,³⁴ and applying higher voltage to provide a bigger impulse, or increasing the number of the legs can also make the rolling motion of IRSR faster and smoother. Moreover, since the position of the robot's center of gravity barely changes, it is possible to develop an untethered fast rolling robot by integrating the power and miniature control system in the center of the robot body.

Gravity-based rolling soft robot

Conceptual design and rolling mechanism

A GRSR is designed based on the annular DEA, which can be seen as the GRSR when standing on the ground as shown in Figure 4a. The six DE segments a–f can be actuated separately. However, the structure of the GRSR can be regarded as forming from mechanically linking six general DEMESs. Applying voltage on different DE segments can induce different shape changes of the circular robot, which has been verified and investigated in our previous work.^30,33

FIG. 4.

GRSR. (a) Structure design and prototype of the GRSR. (b) Gravity-based rolling mechanism. (c) Two voltage patterns for rolling control. (d) Photo sequence during a rolling test of the GRSR prototype. GRSR, gravity-based rolling soft robot. Color images are available online.

When a circular robot is stable on the ground as illustrated in Figure 4b, the active shape change of the robot can alter the position of its center of gravity; thus, the robot can roll to the right due to the moment generated by the gravitational force around the contact point O between the robot body and the ground. The motion equation of the robot is simply given as $J_{G} α = m g x + N x - T y + I$ (5)

where J_G is the rotational inertia of the robot; α is the rolling angular acceleration (x, y), is the coordinate of the center of gravity CG relative to the contact point O; N and T are, respectively, the normal force and traction exerted on the robot by the ground; and I is the torque generated by the two activated DE segments a and b. The unfolding deformations of the DEMES segments a and b can exert the torque I on the rest part of the robot body, which can push the robot to the forward direction.³⁵ One active deformation of the robot can lead to single-step rolling; due to the circular and symmetric structure of the robot, continuous rolling motion can be controlled by the successive and periodic actuation of DE segment groups, which would result in the successive and periodic deformations of the robot. Figure 4 gives two voltage patterns for the rolling control: They are, respectively, actuating two opposite and adjacent DE segments in sequence.

Rolling performance

A prototype with diameter 49.7 mm was fabricated. When activating two opposite DE segments, the GRSR changes from a circle to an ellipse, thus inducing the location shift of its center of gravity. By actuating three groups of DE segments (every opposite DE segments in one group) in sequence as the left voltage pattern shown in Figure 4c, the GRSR prototype has realized a continuous and stable rolling motion on level ground in our previous work; the average speed is 36.27 mm/s, and the speed-diameter ratio is about 0.73 blps.³⁰ In this work, we investigated a different actuation sequence of the DE segments for rolling control as the right pattern shown in Figure 4c. The adjacent two DE segments were actuated in sequence by a 3.2-kV high voltage provided by the multiplex high-voltage control system. Figure 4d shows the photo sequence of the robot rolling under this new voltage pattern. The GRSR prototype moves about 68.5 mm in 1.8 s. So, the average rolling speed of the prototype is about 38.1 mm/s, and its speed-body length ratio and speed-mass ratio is 0.77 blps.

The rolling distances and speeds of the prototype at different time intervals are also listed in Table 2. We can see that at the time intervals 0–0.6 and 1.2–1.8 s, the average speed of the prototype is about 1.07 and 1.58 blps, which are much higher than the 0.73 blps achieved in our previous work. Abnormally, we can see from the speed curve shown in the inset in Figure 3d that the rolling distance at 0–1.2 s is 21.5 mm, which is smaller than 31.9 mm at 0–0.6 s, and this is mainly because the time interval 0.6–1.2 s is the transition period of the two actuation steps for DE segments ab and bc. During this period, the applied voltage is removed and the shape of the robot returns to its initial circle, while the robot still has a rolling speed. If the actuation time sequence is not appropriate, the shape restoration process of the robot may constrain it from rolling forward and even drive it back like the experimental result shown here.

Table 2.

Distances and Speeds of the Gravity-Based Rolling Soft Robot Prototype at Different Time Intervals

Time, T (s)	Distance, S (mm)	Average speed, v (mm/s)	Speed-diameter ratio, v_r (blps)
0–0.6	31.9	53.2	1.07
0–1.2	23.7	19.8	0.40
0–1.8	68.5	38.1	0.77
1.2–1.8	47.0	78.3	1.58

Due to the limitation of control precision of the developed control system and the rough open-loop voltage pattern used here, the robot prototype rolls back at 0.6–1.2 s, which affects the average rolling speed of the robot. However, the robot has achieved a higher rolling speed under this different voltage pattern, which is probably because the common contributions from the location shift of its center of gravity and the mechanism of stiffness distribution control for the rolling locomotion (the stiffness of the activated DE segments is changed).³⁵ Specifically, under voltage pattern I, the two opposite DE segments are activated; the torques generated by the DE segments are symmetric to the center of gravity of the robot, so their effects on the rolling are cancelled out; the robot can be only accelerated to roll by its gravitational torque. While under the control of voltage pattern II, the torque exerted on the remaining part of the robot by the two adjacent DE segments can accelerate the rolling as the force analysis shown in Figure 4b. So, the rolling speed of GRSR is promoted under the combined action of the gravitational torque and the actuation torque.

Ballistic rolling soft robot

Conceptual design and rolling mechanism

Figure 5a shows the design of a BRSR, which simply consists of a rollable multisegment DEMES and two EAs. The EA is adopted here, because it is actuated by high voltage that is compatible with DEs, and it also possesses advantages including robust anchoring on various surfaces, low power consumption, lightweight, speed, and quiet operation.^23,24 Only one EA is mounted on one side of the MDEMES for simplicity in the fabricated BRSR prototype. The connection position for them is set at the middle of the first two DE segments for enabling the MDEMES to unfold unimpededly when it is actuated. Figure 5b shows the mechanism of the EA, which can be simply illustrated as the effect of the electroadhesion force between the polarized charges on the surface of the ground and the electrodes.²³

FIG. 5.

BRSR. (a) Structure design and prototype of the BRSR. (b) Mechanism of the EAs. (c) Ballistic rolling mechanism. (d) Voltage pattern for rolling control. (e) Photo sequence during a rolling test of the BRSR prototype. BRSR, ballistic rolling soft robot; EA, electroadhesion actuator. Color images are available online.

As described in the Dielectric Elastomer Actuators section, the initial state of the rollable MEDMES is a curly configuration with large curvature (nearly a circle with an opening). When applying high enough voltage on the DE segments, the curly strip uncurls rapidly, which can generate a momentum. Combined with the controllable anchoring realized by the EA, the uncurling momentum can be transformed into a ballistic rolling locomotion for the robot. The detailed ballistic mechanism and rolling process is illustrated in Figure 5c. During the whole process of every ballistic rolling locomotion, the robot can be accelerated three times, respectively, in three steps. In step 1, the BRSR is anchored stably on the ground by the activated EA. Then actuating the MDEMES, the ground reaction forces (shear adhesion force F_t and normal adhesion force F_n) acting on the MDEMES can ensure it unfolds rapidly and steadily with its one end fixing, and a momentum can be generated during this step. In the next step 2, deactivating the EA while maintaining the MDEMES activated, the left end of the MDEMES detaches from the ground; under the action of the strip's inertia and gravity, the robot accelerates, rotating to the right. Then in the final step 3, removing the voltage applied on the MDEMES, the elastic restoring process of the flexible actuator produces a momentum again for the rolling. After the three-time acceleration, the BRSR recovers to the initial circular configuration and launches itself into a fast rolling. Figure 5e gives the corresponding voltage pattern for the MDEMES and the EA during this ballistic rolling process. An optimal rolling performance can be obtained by adjusting the pulse time of every step.

Rolling performance

The assembled BRSR prototype weighs 1.02 g totally with the MDEMES 0.98 g and EA 0.04 g. Its diameter is about 49.4 mm. The prototype was first placed on a piece of paper, and the EA was laid flat on the paper for obtaining a stable and reliable adhesion force. Then, a 5.4 kV high voltage was applied to the EA to anchor one end of the MDEMES. The actuating voltage for unfolding the MDEMES is 6.8 kV, and the duration time is t_M = 0.22 s. During the unfolding deformation process of the MDEMES, the EA foot is first deactivated; after a short time delay Δt = 0.02 s, the MDEMES begins to curl. Controlled by the voltage pattern given in Figure 5d, the snapshots of the prototype during one ballistic rolling locomotion are shown in Figure 5e, and the corresponding speed curve is plotted in Figure 6e. Due to the unfolding and curling deformations of the MDEMES during the rolling process, it is difficult to define the real rolling displacement of the BRSR. Here, we use the right side contact point between the robot body and the ground as the baseline for measuring the rolling displacements.

FIG. 6.

Effects of control parameters on the rolling performance of the BRSR prototype. (a) Rolling process when the EA foot is off. (b) Rolling process when reducing the voltage duration applied on the MDEMES (V_MDEMES = 6.8 kV, V_{EA foot} = 5.4 kV, t_M = 0.18 s, Δt = 0.02 s). (c) Rolling process when reducing the voltage amplitudes applied on the MDEMES and the EA foot (V_MDEMES = 6.5 kV, V_{EA foot} = 5 kV, t_M = 0.22 s, Δt = 0.02 s). (d) Rolling process when reducing the voltage amplitudes and increasing the voltage duration applied on the MDEMES and the EA foot (V_MDEMES = 6.5 kV, V_{EA foot} = 5 kV, t_M = 0.26 s, Δt = 0.06 s). (e) The rolling speed curve of the rolling test shown in Figure 5e. (f–h) The rolling speed curves, respectively, corresponding to the rolling tests shown in (b–d). Color images are available online.

The BRSR prototype moves about 158.8 mm in 0.7 s with the average rolling speed 226.9 mm/s, and its speed-diameter ratio is about 4.59 blps. The rolling distance is a bit larger than the perimeter of the MDEMES, which is 155 mm, except for the error from measurements; slides between the robot body and the ground during the rolling could also cause the difference. The corresponding rolling steps are framed by the same colors, respectively. In the first 200 ms, the MDEMES unfolds rapidly while maintaining one end of the strip anchoring on the ground. Actually, the robot does not move in step 1 until the EA is detached from the ground, which occurs between 200 and 220 ms. Subsequently, the robot begins to roll fast after the third acceleration by the elastic recovering of the MDEMES in steps 2 and 3. The recovering process of the MDEMES basically ends at 280 ms; in addition, the robot begins to move at 200 ms, so the time interval 200–280 ms is the accelerating rolling process. During this process, the robot prototype moves about 64.6 mm; its average rolling speed and speed-diameter ratio, respectively, reach 652.5 mm/s (13.21 blps), which is much faster than previously reported RSRs. When the BRSR is anchored on the ground by the activated EA, it is considered that the rolling has not yet occurred. The actual rolling begins from 200 ms, so we can recalculate the rolling speed from 200 to 700 ms; the average rolling speed of the BRSR is 317.6 mm/s (6.43 blps).

The rolling distances and speeds of the prototype at different time intervals are listed in Table 3. The BRSR has achieved a very fast rolling speed by this simple structure design and rolling mechanism. Moreover, we can see from the snapshots at 0 s and 700 ms in Figure 5e or from the Supplementary Videos, after a ballistic rolling, that the BRSR returns to its initial state with the EA lying flat on the ground, which means that the BRSR can be launched again by actuating the MDEMES and EA using the same voltage pattern. Although the BRSR shows potential in continuous rolling, there are still some limits for the practical implementation. For example, the EA foot of the BRSR must be right at the bottom of the robot body and close to the ground after each ballistic rolling, so that it can re-attach on the ground for the next ballistic rolling. The severe tangle of the power wires for the robot is also a big problem for the continuous rolling, which can generate remarkable resistance for the rolling and lead to a short circuit. The control signals for the MDEMES and EA are time pulse with high voltage and low current, so the control system can be unified; once the untethered system is developed, the continuous ballistic should be realized easily.

Table 3.

Distances and Speeds of the Ballistic Rolling Soft Robot Prototype at Different Time Intervals

Time, T (s)	Distance, S (mm)	Average speed, v (mm/s)	Speed-diameter ratio, v_r (blps)
0–0.2	0	0	0
0–0.7	158.8	226.9	4.59
0.2–0.7	158.8	317.6	6.43
0.2–0.28	52.2	652.5	13.21

To reveal the effects of control parameters on the rolling performance of the BRSR prototype, we have conducted several rolling tests by changing the voltage amplitudes and durations applied on the MDEMES and the EA foot. Figure 6a shows the rolling state when the EA foot is inactive; when the rollable MDEMES is actuated by a high-voltage pulse signal (V_DEMES = 6.8 kV, t_M ≈ 0.38 s), the BRSR first tumbles to the right, and it then rolls back to the initial position automatically due to the gravitational potential energy converted from the deformation. So we can see, without the anchoring and release control from the EA foot, that the rapid unfolding and curling deformations of the MDEMES cannot be converted to the rolling motion successfully. Compared with the fast rolling test shown in Figure 5e, Figure 6b shows the rolling process when reducing the voltage duration applied on the MDEMES. When the duration time is reduced from 0.22 to 0.18 s, the time delay between the deactivations of the EA foot and the MDEMES remains unchanged Δt = 0.02 s; so, the unfolding time for the anchored MDEMES is shortened, which can reduce the acceleration a₁ in step 1 and the rotating velocity in step 2, as shown in Figure 5c. Shorter duration time t_M also means an earlier curling deformation of the MDEMES; it has an effect on the effective acceleration a₃ for the forward rolling in step 3.

Figure 6f plots the corresponding speed curve of the rolling test, shown in Figure 6b, the BRSR prototype rolls 157.0 mm in 1.1 s, and the average speed is 142.7 mm/s (2.89 blps). We can see that the rolling speed obviously slows down from 0.6 s; the average speed in the first 0.6 s is 202.0 mm/s (4.09 blps), which is mainly because the robot is crossing the gap part of the MDEMES during 0.6–0.7 s. The imperfect circle body has a big effect on the free rolling of the robot. The voltage also plays an important role in the ballistic rolling, as shown in Figure 6c; when we reduce the voltage amplitude to 6.5 kV for the MDEMES and 5 kV for the EA foot, and keep t_M and Δt unchanged. Compared with the rolling test shown in Figure 5e, the robot cannot achieve a complete rolling; it rolls only 110.3 mm and stops in 0.7 s with the EA foot far from the ground. The corresponding average speed is 157.6 mm/s (3.19 blps), as shown in Figure 6g; it is easy to understand that the deformation speed and range of the MDEMES are smaller under lower voltage (as shown in Fig. 2d), and the adhesion force of the EA is also reduced, so the accelerations in the three steps are all weakened, which results in the limited rolling speed and distance. If we keep the low voltage and appropriately increase the t_M from 0.22 to 0.26 s and increase Δt from 0.02 to 0.06 s, then the robot can complete the whole rolling as the high-voltage case does.

As shown in Figure 6d and h, the robot moves about 160.7 mm in 1 s, and the average speed is 160.7 mm/s (3.25 blps). The MDEMES can get a greater degree of unfolding deformation with the increase of t_M and Δt, so more elastic energy can be stored in steps 1 and 2. Then, the larger elastic energy can be converted to a bigger kinetic energy for the rolling motion, which explains the faster rolling speed and longer distance during the rolling test shown in Figure 6d compared with that in Figure 6c. From the experiments, we know that the timing sequence and amplitude for the control voltage pattern have important effects on the ballistic rolling of the robot. Lots of tests have been done for realizing the high speed of rolling locomotion for the robot prototype. A more precise control system and scheme should be developed for further studying and optimizing its rolling performance.

Discussion and Conclusion

Using DEAs, three prototypes were designed and fabricated based on the impulse-based, gravity-based and ballistic rolling mechanisms, respectively. They have the common unique advantages, including simplicity, lightweight, silent operation, fast rolling speed, good compliance, and shock resistance, which attribute to the excellent properties of DE and the fully flexible structures. Table 4 lists the comparisons between our RSRs and other high-speed RSRs driven by different soft actuators. It can be seen that the rolling robots reported in this article have high rolling speed. The IRSR consists of a wheeled robot body and four DEMES legs that can generate impulses to rotate the robot on the ground. The robot has a wheeled body, thus an integrated control system with a power source can be mounted in it. Moreover, four photoelectric sensors can be, respectively, set at the position of every DEMES leg and fixed on the robot body; then the reflected signal from the ground can determine which leg is in contact with the ground, and thus it can help the control system decide which DEMES leg should be actuated for a rolling motion; the heavy power source and control system mounted on the robot body around its center of gravity can be protected from damage; and little work has to be done for overcoming their weight when the robot is rolling on the ground. In addition, the photoelectric sensors are conveniently used to acquire the rolling state of the robot, which could be beneficial to the precise closed-loop control for the rolling locomotion.

Table 4.

Comparison of High-Speed Rolling Soft Robots Driven by Soft Actuators

Rolling soft robot	Rolling mechanism	Actuation method	Body length (mm)	Weight (g)	Average speed (blps)	Maximum speed (blps)	Untethered
IRSR	Impulse-based rolling	DE	106.0	12.2	1.19	>1.43	No
GRSR	Gravity-based rolling	DE	49.7	0.88	0.77	1.58	No
BRSR	Ballistic rolling	DE+EA	49.4	1.02	4.59	13.21	No
GoQBot¹¹	Ballistic rolling	SMA	100.0	>5	—	>5	No
STAR⁷	Impulse-based rolling	SMA	50.0	16.4	>1.00	—	No
Circular soft robot⁸	Gravity-based rolling	SMA	40.0	3.6	0.65	—	No
V-SPA⁶	Impulse-based rolling	Vacuum	45.0	225	1.33	—	No
Soft wheel robot⁵	Impulse-based rolling	Pneumatic	139.7	1469	0.72	—	Yes
Wheeled robot⁹	Gravity-based rolling	Liquid metal	45.0	11.27	1.10	1.25	No
Wheeled robot⁹	Gravity-based rolling	Liquid metal	45.0	11.27	0.90	1.25	Yes
Light motor¹⁰	Gravity-based rolling	Remote light	20	—	∼3.00	—	Yes
Magnetic millirobot¹²	Passive rolling	Magnetic field	3.7	—	∼5.89	—	Yes

BRSR, ballistic rolling soft robot; DE, dielectric elastomer; EA, electroadhesion actuator; GRSR, gravity-based rolling soft robot; IRSR, impulse-based rolling soft robot; SMA, shape memory alloy.

The average and maximum speeds of the IRSR prototype reach about 1.19 and 1.43 blps, which are higher than most reported soft robots with other locomotion mechanisms such as creeping and peristalsis. The IRSR is faster than most of the RSRs driven by other soft actuators, except the light and magnetic field actuation methods. However, the wheeled body also makes the IRSR hard to climb a slope, unless enhancing the output torque of the DEMES rotary joints to generate a bigger impulse for the rolling. The robot can achieve higher rolling acceleration by a bigger impulse at each actuation step, and the right timing for each DEMES leg to push the ground during the dynamic rolling process also plays an important role in accelerating the rolling. Fast-rolling velocity resulted from the dynamic impulse rolling, which can help the robot to rush on the slope. The DEMES leg reaches out at the appropriate time, and this can also help to brake the rolling or help the robot to stand stably on a slope. So, the IRSR will be an interesting platform to study the rolling control for rolling robots.

The GRSR is an annular structure with six DE segments that can be actuated separately to shift the shape of the robot, thus altering the position of its center of gravity. Due to the moment generated by the gravitational force, the GRSR can realize a continuous and stable rolling with a high speed on the ground. The average speed of the GRSR prototype reaches about 0.77 blps, which has been verified to be higher than other similar GRSRs.³⁰ During the rolling process, the maximum speed reaches 1.58 blps at the time interval 1.2–1.8 s, which is about twice of the average speed. It indicates that there is still a big room for improvement on the rolling speed of the GRSR. Except that the peak rolling speed is higher than most of the RSRs listed in Table 4, the GRSR is the lightest one, so it has a very large speed-weight ratio. However, its locomotion ability in unstructured terrain is still weak now. According to the relevant research on the loop-structure locomotion robots,^36,37 the obstacle-crossing ability of the GRSR can be improved by increasing the number of the segments and modifying the gait planning for different goals. More segments of the robot body can result in smoother locomotion for variable terrain environments, but the rolling speed may be limited, for a lower stiffness and response speed of the robot structures. The structure design, control scheme, and gait planning of the GRSR need to be optimized and improved in future work for better locomotion performance.

The BRSR consists of a rollable MDEMES and an EA, which can realize controllable anchoring with the ground. By actuating the MEDMES and the EA in a specific time sequence, the BRSR has realized a ballistic rolling locomotion and shown great potential in continuous rolling. It exhibits a high rolling speed of 4.59 blps, which is much faster than previously reported electrically activated RSRs, as listed in Table 4. The average rolling speed of a magnetic millirobot is about 5.89 blps, which is a little bigger than BRSR, but this robot relies on the passive rolling whose speed is determined by the moving speed of an external magnetic field. Further, during the accelerating rolling process (at time interval 200–280 ms), the rolling speed of the BRSR prototype can reach 652.5 mm/s (13.21 blps).

The unfolding and curling speed of the MDEMES plays an important role in the rolling speed of the BRSR; faster deformations of the MDEMES lead to larger acceleration and initial velocity for the ballistic rolling. So, the ballistic rolling can be controlled by the deformation speed of the MDEMES to some extent; higher applied voltage can lead to faster response and greater dynamic deformation for the robot. Besides, the initial shape and center of gravity of the BRSR can also affect the stability and smoothness of the rolling locomotion. The shape is closer to a circle and the center of gravity is closer to the center; the free rolling after ballistic of the BRSR could be smoother and faster.

The EA also has a remarkable effect on the ballistic rolling, especially the detaching timing during the unfolding process of the MDEMES. Detaching should be set near the moment when the unfolding speed of the MDEMES achieves its maximum, so a faster initial speed can be continued for the rolling. The EA can also act as a brake during the rolling, thus a controllable tumble and rolling of the robot can be realized. Due to the high rolling speed, the stability of rolling for the BRSR may be no better than the IRSR and GRSR. The possibilities of developing untethered systems for the GRSR and BRSR are harder than the IRSR for their deformable and soft bodies. With the developments of flexible electronics and micro power, we believe the untethered systems for GRSR and BRSR can be realized. Moreover, the prototypes built in this work used the most common acrylic elastomer (3M VHB) and the carbon grease (MG Chemicals) electrodes for the purpose of proof-of-concept investigations. We believe the silicone-based DEAs may further improve the rolling performance of the robots for their faster response time and higher elasticity modulus.

In summary, in this article, we developed three RSRs with different rolling mechanisms by using DEAs. Three fabricated robot prototypes exhibit superiorities of fast rolling, simplicity, lightweight, good compliance, and shock resistance, which can find potential future use in scouting and exploration missions. Especially, the RSR with the ballistic rolling mechanism has demonstrated that the soft mobile robot can also achieve a comparable moving speed to rigid robots. Moreover, the structure designs and implementations for different rolling mechanisms in this article may provide guidance and inspiration for creating new, fast-moving, and hybrid mobility soft robots.

Experimental Section

Fabrications of DEAs and RSR prototypes

The elastomer films and compliant electrodes used in the experiments were commercially available VHB 4910/4905 tape (3M) and carbon grease (MG Chemicals 846-80G), respectively. The flexible frames were made of laser-cut PET sheet (Dupont) with different thicknesses. For the fabrication of the DEMES rotary joint, VHB 4910 tape was prestretched with 400% biaxial prestrain; the geometry of the PET frame is l₀ × w × t = 60 × 49 × 0.178 mm, and the dimension of the open section is s = e = 20 mm, as shown in Figure 1. An improved design with a larger output torque for the DEMES rotary joint was used, and more detailed design parameters of the frame and the electrode pattern can be seen in Ref.³⁴ The IRSR prototype was fabricated by mounting four DEMES rotary joints on a wheeled body, which consists of two wheels (diameter 106 mm, thickness 15 mm) and a middle block (30 × 30 × 70 mm), as shown in Figure 3b. The components of the body were assembled by glue and made of polyethylene foam cotton, except the 3-mm-thick EVA sponge tape (3M) adhered outside the wheels. The robot body is deformable and has good impact resistance, as shown in the inset in Figure 3b.

For the rollable MDEMES, it was fabricated from bonding a single layer of elastomer film (VHB 4910) with prestretch 650% × 300% to a laser-cut PET strip (0.2 mm in thickness). The prestretch ratio of the elastomer film was selected after trial and error. Six hundred fifty percent was the main prestretch and along the longitudinal direction of the strip, which ensured the circularly curly configuration of the MDEMES. However, the prestretch in the transverse direction should be as large as possible for increasing the electric-induced deformation of the DE segments, with little effect on the curly configuration of the MDEMES.^13,38 The dimensions of the strip and the six square open sections are 155 × 30 and 20 × 20 mm, respectively. The electrode patterns are corresponding to the open sections and connected in a series on each side of the elastomer film. The BRSR was simply fabricated by bonding a piece of EA to one side of the rollable MDEMES (Fig. 5a). The EA was made by smearing two paralleled rectangle electrodes (carbon grease) on a piece of silicone membrane (0.1 mm in thickness), which was then covered by a thin film (VHB 9473) as shown in Figure 5b.

The annular DEA or the GRSR prototype was fabricated by bonding a single layer of elastomer film (VHB 4905) with prestretch 550% × 300% to a laser-cut PET strip (0.178 mm in thickness). The strip is a 162 × 32 mm rectangle, and six 20 × 20 mm square open sections are evenly distributed in it along its length. Six groups of square electrode patterns were smeared on both sides of the elastomer film corresponding to the regions of the strip open sections. The prestretch ratios of the DE elastomer are also selected by giving consideration to both curly configuration with little twist for the rollable MDEMES and enough electric-induced strain of the DE segments. After release of the prestretch, both ends of the strip were connected together by adhesive tape to form a closed-loop structure. More fabrication details are provided in Ref.³⁰

Measurements of the actuation performances of DEAs

A high-voltage amplifier (TREK MODEL 20/20C-HS) was used to actuate the DEAs through amplifying the control voltage from a function generator (Tektronix AFG3022C). The dynamic deformation of DEAs was recorded by a digital camera (Canon 550D) with a frame rate of 50 fps. For the measurements of steady deformation, images were taken at each voltage step 30 s after application of the voltage increment to allow the DEAs to reach the steady state, and they were then analyzed by ImageJ. The blocking force was measured by a load cell (Futek LSB-200) with a probe, as shown in the inset of Figure 2c; the probe is perpendicular to the PET frame and 10 mm away from its edge. Data were then acquired by a signal acquiring system (DH5902) continuously, and they were then analyzed through Matlab. Reproducibility had been checked by three independent measurement sets for every experiment.

Measurements of the rolling performances of RSR prototypes

A multiplex high-voltage control system was used for the rolling control for robot prototypes. A DC high voltage generated by the high-voltage amplifier was switched by high-voltage reed relays to different DEAs, and the control signal was programmed by a micro-control unit. More details about the control system can be seen in Ref.³⁰ So, the four DEMES legs in the IRSR prototype, the six DE segments in the GRSR prototype, and EA and MDEMES in the BRSR prototype can be actuated independently by programmed time sequences. Then, the rolling tests were recorded by the camera and analyzed.

Footnotes

Acknowledgments

The authors gratefully acknowledge the supports by the National Natural Science Foundation of China under grant 91748118, the National Postdoctoral Program for Innovative Talents under grant BX20190201, the Program of Shanghai Key Laboratory of Spacecraft Mechanism, and the National Natural Science Foundation for Distinguished Young Scholars of China under grant 11625208.

Author Disclosure Statement

No competing financial interests exist.

Funding Information

This work was funded by the National Natural Science Foundation of China under grant 91748118, the National Postdoctoral Program for Innovative Talents under grant BX20190201, the Program of Shanghai Key Laboratory of Spacecraft Mechanism, and the National Natural Science Foundation for Distinguished Young Scholars of China under grant 11625208.

Supplementary Material

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Supplementary Material

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