Small-Scale Soft Terrestrial Robot with Electrically Driven Multi-Modal Locomotion Capability

Abstract

Small-scale soft robots, despite their potential for adaptability in unknown environments, often encounter performance constraints due to inherent limitations within soft actuators and compact bodies. To address this problem, we proposed a fast-moving soft robot driven by electroactive materials. The robot combines the advantages of dielectric elastomer actuators (DEAs) and shape memory alloy (SMA) spring actuators, enabling its high-performance multi-modal locomotion in a small and lightweight design. Theoretical models were constructed for both DEAs and SMA spring actuators to analyze the performance of the designed robot. The robot’s design parameters were optimized based on these models to improve its running and jumping performance. The designed robot has a size of 40 × 45 × 25 mm and a weight of 3.5 g. The robot can achieve a running speed of 91 mm/s, ascend a 9° slope, and execute turning motions via an asymmetrical actuation of SMA spring actuators. The robot also demonstrates high-performance jumping motions with a maximum jumping height of 80 mm and the ability to jump over a 40 mm high obstacle. This work introduces a novel approach to designing small-scale soft terrestrial robots, enhancing their agility and mobility in obstacle-laden environments.

Introduction

Small-scale soft terrestrial robots (1 mm < body length < 100 mm) have become one of the most popular research topics in the robotics community. These robots utilize the soft actuators to achieve performance comparable with that of rigid robots, while also allowing for more flexible body designs in limited size scales. This makes them particularly suitable for locomotion tasks inside constrained unstructured environments such as search-and-rescue,^1–3 pipe inspection,^4–6 and medical treatment.^7–10 Among these robots, terrestrial robots are most widely studied because of their low energy consumption, simpler designs, and wide application scenarios.

In the past decade, different designs were utilized to enable small-scale soft robots with better terrestrial locomotion capabilities, including legged locomotion modes^11–13 and whole-body locomotion modes.^14,15 Actuator performance is one of the key factors in deciding the robot’s locomotion capabilities (speed, terrain adaptability, etc.). To improve the locomotion performance of the robots, different actuation technologies were applied to drive the robots, such as pneumatic actuation,¹⁶ magnetic field actuation,¹⁷ and electrical actuation using dielectric materials^18,19 or piezoelectric materials.²⁰ Despite all the progress, the robot’s size and the actuators’ energy output are still the main limitations of these robots’ performance. Meanwhile, small-scale robots also have difficulties navigating through obstacle-laden environments. Different designs have addressed the problem to enable the robot’s jumping^21,22 or wall-climbing motion.^23–25 However, the specific design of the actuation mechanisms, such as a latch-release mechanism for jumping robots or an attach-detach mechanism for wall-climbing robots, make these robots limited to a specific locomotion mode and less adaptable to the change of terrains.

Nature is one of the most important sources of inspiration for robot designs. Almost all animals can switch between different locomotion modes to adapt to changing environments. Many researchers have been learning from nature to enable multi-modal locomotion capability in small-scale soft robots. Some existing designs utilize the high output force of soft actuators to achieve crawling and jumping motion in small-scale robots.^19,26–28 However, these designs did not fully unleash the capabilities of soft actuators in each locomotion mode. Their designs use the same actuator for different locomotion modes, making compromises during the design. One way to improve the performance of multi-modal locomotion of robots is to combine different actuators together, each responsible for the specific locomotion mode. This design methodology has been proven successful in some robots^29,30 with larger size scales (>100 mm). However, this method is difficult to apply to small-scale robots due to their size and weight limitations. How to realize multi-modal locomotion without hugely impacting the performance of small-scale robots remains an open research problem.

To address the aforementioned problems, this work designed a small-scale soft terrestrial robot utilizing the high-frequency actuation dielectric elastomer actuators (DEAs) and high energy storage of shape memory alloy (SMA) spring actuators. Both actuators are designed to be compact and lightweight, allowing better performance for running on flat terrain and jumping over obstacles. To achieve the optimal design parameter, analytical models are proposed for the actuators used in the robot, and their design parameters are optimized. Experiments are carried out to show the effectiveness of the proposed design methodology.

Robot Design and Locomotion Strategies

The overall design of the robot is illustrated in Figure 1a. The robot is mainly constructed in two parts. The first part is the bistable structure at the front of the robot, which is made of several units with two SMA spring actuators and one polyimide (PI) elastic plate in the middle. The second part is the DEA-driven joint made of PI elastic frames and a pre-stretched dielectric elastomer (DE) membrane. The SMA bistable structures and the DEA-driven joint will bend in the unactuated state, forming the robot’s front and hind legs. Fasteners connect the two parts. A soft foot pad is added at the bottom of the hind leg to increase friction with the ground.

FIG. 1.

Overall design and locomotion strategies of the proposed robot. (a) The overall structure of the designed robot. (b) The schematic of the robot’s running motion. Dotted lines with different colors show different phases in one gait cycle. (c) The schematic of the robot’s left-turning motion with the SMA spring actuators actuated on the upper-right and bottom-left sides. (d) The robot’s motion when jumping over an obstacle.

The robot can realize a fast-running gait by actuating the DEA with high-voltage signals. When the voltage is turned on, the instant actuation of DEA will send the robot into a leaping motion, as shown in Figure 1b. The voltage will be turned off during the leaping phase, and the hind leg is contracted. Finally, the robot finishes one running step by landing on the ground and preparing for the next gait cycle. The robot’s turning motion is explained in Figure 1c with the example of the left-turning motion. By actuating the left SMA spring actuator on the upper side and the right one on the bottom side, the front part of the robot will be twisted, and the left side of the hindfoot will be lifted. In this state, the friction force generated by the soft pad is biased to the right side, generating a left-turning momentum. Right turning can also be achieved by actuating the SMA spring actuators in symmetric positions.

In the presence of obstacles, the robot can switch to the jumping motion with the help of energy storage and release of SMA bistable structures, as illustrated in Figure 1d. The robot will first get into a preparation pose by actuating all the SMA spring actuators on the upper side. Afterward, the SMA spring actuators on the upper side will be turned off, and those on the bottom will be turned on. In this process, the bistable structure will slowly bend downwards. The structure will then undergo a snap-through process, instantly releasing the elastic energy stored in the actuated SMA spring actuators and sending the robot into the air. The jumping angle can be controlled with the help of DEA. By actuating the DEA, the contact angle between the hindfoot and the ground can be adjusted, which changes the direction of the jumping force applied to the robot during the jumping motion.

Analytical Modeling

Dynamic modeling of the DEA-driven joint

Gent constitutive model is used to describe the hyperelastic property of the DEA. The strain energy density is a function of three principal stretches (λ _x , λ _y , λ _z ). The DE membrane forms a saddle shape in the designed structure. This geometric nonlinearity makes it hard to explicitly describe the strain distribution across the membrane at the state of large deformation. Therefore, a simplified method is used in this work to construct the model.

The geometric model used for the proposed design is illustrated in Figure 2. The octagon-shaped DE membrane is divided into nine sections. Assuming the principal strains are the same for every point inside each section, the stretch distribution on the membrane can be described by the design parameters of DEA shown in Figure 2a and the deformation variables of the elastic frame and DE membrane as shown in Figure 2b. For the three sections in the middle row along the x-axis (sections 4, 5, and 6) and y-axis (sections 2, 5, and 8), its strain along x- and y-axis can be calculated from the length of arc C_x and C_y formed by these sections (the red dashed line in Figure 2b) respectively as $C_{x} = 2 \arcsin (\frac{L_{x}}{H_{x} + \frac{L_{x}^{2}}{4 H_{x}}}) (\frac{H_{x}}{2} + \frac{L_{x}^{2}}{8 H_{x}}), λ_{x, i} = λ_{x, pre} \frac{C_{x}}{d_{1} + 2 d_{2}}, i = 4, 5, 6,$ (1) $C_{y} = 2 \arcsin (\frac{L_{y}}{H_{y} + \frac{L_{y}^{2}}{4 H_{y}}}) (\frac{H_{y}}{2} + \frac{L_{y}^{2}}{8 H_{y}}), λ_{y, i} = λ_{y, pre} \frac{C_{y}}{2 w_{2} + w_{3}}, i = 2, 5, 8,$ (2)where L_x and L_y are the chord lengths and H_x and H_y are the arc heights in each arc. All the chord lengths and arc heights can be expressed by the design parameters in Figure 2a and the deformation variables h and θ in Figure 2b. Therefore, the arc lengths and principal strains in Equations (1) and (2) can be written as functions of h and θ.

FIG. 2.

Modeling of the DEA-driven joint. (a) Design parameters of DEA-driven joint and sectioning of the DE membrane to calculate its strain distribution. (b) Deformation variables of the elastic frame and the DE membrane. The deformed DEA-driven joint is shown in two different viewing angles, with h marked in the front view and θ marked in the side view. (c) Visco-hyperelastic model of DE based on the Gent model.

For other sections, the corresponding strains in x- and y-direction are assumed to be the average of each point’s strains in each section. The strain on the edges connected with middle sections is the same as the values calculated in Equations (1) and (2), and the strain on the edges connected with the outer frame remains constant as the pre-stretch value λ _x,pre and λ _y,pre . By integrating each point’s strain over each section, we get $\begin{array}{l} λ_{x, i} = \frac{2}{3} λ_{x, j} + \frac{1}{3} λ_{x, pre}, i = 1, 3, 7, 9, j = 4, 5, 6, \\ λ_{y, i} = \frac{2}{3} λ_{y, j} + \frac{1}{3} λ_{y, pre}, i = 1, 3, 7, 9, j = 2, 5, 8, \\ λ_{x, i} = \frac{1}{2} λ_{x, j} + \frac{1}{2} λ_{x, pre}, i = 2, 8, j = 4, 5, 6, \\ λ_{y, i} = \frac{1}{2} λ_{y, j} + \frac{1}{2} λ_{y, pre}, i = 4, 6, j = 2, 5, 8. \end{array}$ (3)

The stretch in the z-direction can be computed as λ _z,i = 1∕(λ _x,i λ _y,i ) in incompressive materials.

A dissipative model based on the Gent model is used for the modeling of the visco-hyperelastic property of the DE membrane.³¹ This model describes the material as a system of nonlinear springs and dashpots in x- and y-directions as illustrated in Figure 2c. The strain density function of the model can be written as $\begin{array}{l} W_{strain} (λ_{x}, λ_{y}, ξ_{x}, ξ_{y}) = - \frac{μ^{α} J_{lim}^{α}}{2} \ln (1 - \frac{λ_{x}^{2} + λ_{y}^{2} + λ_{x}^{- 2} λ_{y}^{- 2} - 3}{J_{lim}^{α}}) \\ - \frac{μ^{β} J_{lim}^{β}}{2} \ln (1 - \frac{λ_{x}^{2} ξ_{x}^{- 2} + λ_{y}^{2} ξ_{y}^{- 2} + λ_{x}^{- 2} λ_{y}^{- 2} ξ_{x}^{2} ξ_{y}^{2} - 3}{J_{lim}^{β}}), \end{array}$ (4)where μ and J_lim are shear moduli and strain limits of two Gent springs. The strains in the x- and y-direction of the upper spring are λ_x and λ_y, while the strains of the lower spring are λ_x/ξ_x and λ_y/ξ_y, respectively. ξ represents the stretch ratio of the dashpot.

Euler-Lagrangian equation of motion is used for the dynamic modeling of the DEA-driven joint. The Euler-Lagrangian formulation of a nonconservative system can be written as $\frac{d}{d t} (\frac{\partial L}{\partial \dot{q}}) - \frac{\partial L}{\partial q} + \frac{\partial D}{\partial \dot{q}} = 0,$ (5)where the Lagrangian L = T − U with T being the kinetic energy and U = U_strain + U_Maxwell being the potential energy of the system, which is the sum of strain energies induced by the elastic deformation and the Maxwell strain. D = D_VE + D_frame is the dissipation function of the system, which is the sum of the dissipation energies in the viscoelastic DE and the elastic frame. q is the generalized coordinate of the system and $\dot{q}$ is its time derivative.

By choosing q = [h, θ, ξ_x_,1,ξ_y_,1,…,ξ_x_,9,ξ_y_,9] ∈ ℝ²⁰, the total strain energy of the system can be written as $U_{strain} = \sum_{i = 1}^{9} W_{strain} (λ_{x, i}, λ_{y, i}, ξ_{x, i}, ξ_{y, i}) A_{i} t + \frac{Y I_{ME}}{2 d_{1}} θ^{2},$ (6)where strain energy density W_strain is from Equation (4). A_i is the area of each section, and t is the thickness. Y and I_ME are Young’s modulus and cross-section inertia of the elastic frame in the structure. λ_x,i and λ_y,i are both functions of h and θ according to Equations (1), (2), and (3). The dimension of the generalized coordinate can be reduced from 20 to 10 by using the following equation derived from the symmetric property of the structure $\begin{array}{l} ξ_{x, 4} = ξ_{x, 6}, ξ_{y, 4} = ξ_{y, 6}, \\ ξ_{x, 2} = ξ_{x, 8}, ξ_{y, 2} = ξ_{y, 8}, \\ ξ_{x, 1} = ξ_{x, 3} = ξ_{x, 7} = ξ_{x, 9}, \\ ξ_{y, 1} = ξ_{y, 3} = ξ_{y, 7} = ξ_{y, 9} . \end{array}$ (7)

The electrical strain energy density function induced by Maxwell strain can be expressed as $W_{Maxwell} (λ_{x}, λ_{y}) = - \frac{1}{2} ε_{r} ε_{0} E^{2} λ_{x}^{2} λ_{y}^{2} .$ (8)

Here, E = Φ/t denotes the electric field across the DE membrane, where Φ is the electrical potential difference between two sides of the membrane, and t is the pre-deformation thickness of the membrane. Consequently, the total electric potential energy can be formulated as $U_{Maxwell} = \sum_{i = 1}^{9} W_{Maxwell} (λ_{x}, λ_{y}) A_{i} t .$ (9)

The charging and discharging time of the capacitor is neglected in the model, as the DEA’s capacitance is around 100 pF and the resistance of the flexible electrodes is around 100 kΩ, which leads to a resistor-capacitor time constant of around 10 μs. This value is much smaller than the actuation speed of the mechanical system (around 100 ms).

By considering one end of the DEA-driven joint being fixed, the kinetic energy of the system equals the kinetic energy of one side of the elastic frame rotating around the joint’s hinge with angular velocity $\dot{θ}$ , which can be written as $T = \frac{1}{2} J {\dot{θ}}^{2} + \frac{1}{2} M {\dot{θ}}^{2} r^{2},$ (10)where J is the mass moment of inertia, M is the mass of the frame, and r is the distance between the center of mass of the moving frame and the joint’s hinge.

For the dissipation function, the energy dissipation inside DE (D_VE) can be calculated using the Rayleigh dissipation function $D_{VE} = \sum_{i = 1}^{9} A_{i} t (\frac{1}{2} η {\dot{ξ}}_{x, i}^{2} + \frac{1}{2} η {\dot{ξ}}_{y, i}^{2}) .$ (11)

The energy dissipation in the rotating joint (D_frame) can be approximated using the term α as following: $D_{frame} = α I_{ME} {\dot{θ}}^{2},$ (12)where α is an unknown constant that will be fitted with experimental data.

Energy-based modeling of the SMA bistable structure

An energy-based model is built for the SMA bistable structure to predict its quasistatic deformation and jumping performance. The two-state model³² is used to model SMAs. This model considers only the full martensite state at low temperatures and the full austenite state at high temperatures. The force-displacement curve of SMA springs described by the two-state model is shown in Figure 3a. This relationship can be seen as linear when the SMA is in a full austenite state with small shear strains (<1%).

FIG. 3.

Modeling of the SMA bistable structure. (a) Two-state model of SMA spring actuators. (b) Geometry of the deformed bistable structure.

The elastic strain energy of SMA spring actuators on both sides is $U_{SMA} (θ) = \int_{0}^{L (θ) - L_{0}} F_{up} (δ, T) d δ + \int_{0}^{L_{max} - L_{0}} F_{bottom} (δ, T) d δ,$ (13)where F_up(δ, T) and F_bottom(δ, T) are the forces of SMA spring actuators at the upper and bottom side of the bending frame, δ is the length change of the springs, and T is the temperature of the SMA. L(θ) and L_max are the lengths marked in Figure 3b, where L(θ) is the function of the bending angle θ. L₀ is the natural length of SMA springs. The elastic strain energy of the bending frame is $U_{frame} (θ) = \frac{Y I_{BF}}{2 L_{max}} θ^{2},$ (14)where I_BF is the cross-sectional area moment of inertia of the bistable frame. The total energy of the bistable structure is U_total(θ) = U_SMA(θ) + U_frame(θ). The structure’s equilibrium points are the total energy’s local minima.

Model-Based Design Optimization

Design optimization of the DEA-driven joint

The visco-hyperelastic parameters for the 3M VHB elastomer are determined using the stretching test result from Ref.³³ The particle swarm algorithm is used from the MATLAB toolbox (R2022b, MathWorks Inc.) to search for the best-fit parameters. The fitted curves are plotted in Figure 4d.

FIG. 4.

Model verification and design optimization of the DEA-driven joint. (a) Testing of a DEA-driven joint with a width of 45 mm and a length of 75 mm with DC voltages from 1 to 4 kV. (b) The FEM simulated deformation of the prototype. (c) The comparison of quasistatic response calculated by the geometrically simplified analytical model and the FEM with DEA pre-stretched at different ratios. (d) The curve-fitting result of the visco-hyperelastic model of DE using stretch test data with different stretch speeds. The parameter values are μ_α = 17.73 kPa, μ_β = 37.93 kPa, $J_{lim}^{α} = 203.22$ , $J_{lim}^{β} = 62.02$ , η = 62.27 MPa·s. (e) The fitting of dissipation parameter α in the rotational frame using experimental data with α = 2.862 × 10⁸ kg·m⁻²·s⁻¹. (f) The Pareto front plot of the MOGA optimization process with a population size of 50 and a total generation of 100. The values of the objective functions of the five best individuals from the last generation are marked with stars.

The experimental results of the quasistatic response with DC voltages from 1 to 4 kV are shown in Figure 4a. The finite element method (FEM)-based results are shown in Figure 4b, where the constitutive model of DEA is described using user-defined materials (UMAT)³⁴ in Abaqus 2021 (Dassault Systèmes Simulia Corp.). The results based on the analytical model in Equation (5) are calculated using fmincon in MATLAB by letting the time derivatives of all the generalized coordinates be zero. The voltage-angle relationships at different pre-stretch ratios from the analytical model and FEM are compared in Figure 4c. These results show that the analytical model can fit the nonlinear response of DEA at different conditions, with the error of the bending angle less than 0.23 rad for all the points under 5 kV. The computation time of the voltage-angle relationship for each pre-stretch condition using the analytical model is 36 s on a desktop (with Intel Core i7 14700 CPU, 32GB RAM). Meanwhile, getting the same result costs 21 min using FEM on the same computer, which is 35 times slower. Therefore, the analytical model provides a much faster design optimization process.

The unknown frictional parameter α in Equation (12) is fitted with the experimental data by actuating the DEA-driven joint with 3 kV square wave signals at frequencies between 2 and 20 Hz. The fitted result is plotted in Figure 4e.

Using the fitted dynamic model, the robot’s running speed is optimized using two objective functions. The first is the total weight of the robot f_obj1 = m_DE + m_SMA, where m_SMA is estimated as 1.5 g. The second is the opposite of the maximum output speed of the joint, which is calculated as $f_{obj 2} = - S_{max} = - max_{f} f θ_{amp} (f) L,$ (15)where f and θ_amp are the actuation frequency and the corresponding angular amplitude of the DEA-driven joint, and L is the length of the leg. The amplitude of the actuation voltage is limited in the optimization, so the peak electrical field in DEA is lower than 80 MV/m to avoid electrical breakdown.

The optimization uses the multi-objective genetic algorithm in MATLAB. The Pareto front during the optimization is plotted in Figure 4f. The five best individuals are selected from the last generation, and their parameters are listed in Table 1. Among these individuals, D is selected to be the parameters used for the final version of the robot. Although E has a higher locomotion speed, its weight is also much higher, which will reduce the achievable jumping height.

Table 1.

Best Individuals from Gen 100 of MOGA Optimization

Individual	λ _pre	t_vhb (mm)	t_PI (mm)	w₁ (mm)	w₂ (mm)	w₃ (mm)	d₁ (mm)	d₂ (mm)	d₃ (mm)
A	4.3	0.5	0.1	6.2	1.5	5.4	5.8	2.5	1.7
B	3.5	1.0	0.1	5.8	2.6	6.1	5.9	2.5	4.8
C	4.0	1.0	0.1	9.9	3.2	10.8	3.0	9.6	12.5
D	3.7	1.5	0.2	6.9	9.0	9.6	5.7	9.6	14.6
E	3.5	2.0	0.2	8.3	10.4	10.2	5.9	11.9	18.6

MOGA, multi-objective genetic algorithm.

Design optimization of the SMA bistable structure

The energy-based model of the SMA bistable structure describes the maximum possible jumping height of the robot. The robot’s jumping height is proportional to N-times of the energy barrier ΔU_total of the bistable structure (as shown in Figure 5a) divided by the total mass M_t of the robot, where N is the number of bistable units in the structure. The mass of the DEA-driven joint is estimated to be 3 g. The optimization variables are selected as w_BF and L as shown in Figure 5b, because these parameters significantly influence the energy barrier of the bistable structure and can be easily modified in the fabrication process. The optimization problem can be described as $\begin{array}{l} \max_{w_{BF}, L} G (w_{BF}, L) = N \frac{Δ U_{total} (w_{BF}, L)}{M_{t} (w_{BF}, L, N)} \\ = N \frac{U_{total}^{θ = 0} (w_{BF}, L) - U_{total}^{θ = θ_{eq}} (w_{BF}, L)}{M_{t} (w_{BF}, L, N)}, \\ s . t . N \leq (w_{body} + {\underline{d}}_{mid}) / (w_{BF} + {\underline{d}}_{mid}), N \in ℕ^{+}, \\ L_{SMA} \leq L \leq L_{lim}, \\ w_{SMA} \leq w_{BF} \leq w_{body}, \\ U_{total}^{θ = 0} \leq U_{total}^{θ = \hat{θ}}, \forall \hat{θ} \in T, \end{array}$ (16)where d _mid is the lower bound of the gap distance d_mid between the bistable units to avoid interference of bending motion, and w_body is the total body width of the robot, as shown in Figure 5b. In the constraint conditions of Equation (16), L_SMA represents the natural length of SMA spring actuators under room temperature, L_lim represents the elastic length limit of SMA springs, and $T$ represents the set of θ values where the structure bends toward unactuated SMA springs. The last constraint ensures that the structure can bend through the point of θ = 0.

FIG. 5.

Design parameter optimization of SMA bistable structure. (a) The plot of energy functions of one SMA bistable unit with the SMA spring actuator on one side actuated. The energy barrier ΔU is decided by the total energy at θ = 0 and the equilibrium point with lower total energy (equilibrium point 2). (b) Geometric parameters are used to describe the optimization problem. (c) Plot of the values of the optimization goal function G from the grid search of w_BF and L.

The optimization problem is solved by carrying out a grid search of w_BF and L. d _mid and w_body are predetermined as 1.5 mm and 40 mm, respectively. The elastic frame’s thickness is 0.4 mm, and its Young’s modulus is 2 GPa. To calculate the energy difference of SMAs between θ = 0 and θ = θ_eq, only the actuated SMA springs need to be considered. The lengths of unactuated SMA springs remain unchanged as L between θ = 0 and θ = θ_eq. The force of SMA spring actuators at full austenite state is linearly estimated as F(δ) = k_ausδ. The spring constant k_aus is experimentally determined as 0.34 N/mm. The result is shown in Figure 5c, where the goal function reaches maximum at w_BF = 11.5 mm and L = 34 mm. With this designed size, the maximum shear strain inside actuated SMA springs is estimated to be around 0.6%, which is inside the linear range of the two-state model described in Section “Energy-based Modeling of the SMA Bistable Structure.”

Locomotion Capability Test

Robot fabrication

The robot with optimized design parameters was fabricated using the process depicted in Figure 6a. PI films with thicknesses of 0.2 and 0.4 mm were laser cut for the elastic frame and the robot fixture, respectively. Two layers of dielectric films with a thickness of 1 mm (3M VHB 4910) were pre-stretched by 4 × 4, and electrodes made by multi-walled carbon nanotubes (MWCNTs, Suzhou Tanfeng Graphene Technology Co., Ltd.) were brushed on both sides through a masking layer. Afterward, two layers were stacked together and stuck to a PI elastic frame and fixtures after removing the masking layer. The SMA springs (Shenzhen Superline Technology Co., Ltd.) with a wire diameter of 0.3 mm, a coil diameter of 3 mm, and a natural length of 12 mm were fixed with nylon bolts and nuts through pre-cut holes on PI frames. Nylon bolts were used to avoid electric connections between different SMA springs. The foot structure at the hind leg was made by a 0.4 mm PI plate and bounded to the end of the DEA-driven joint along with a 1 mm thick silicone-made friction pad using double-sided tapes. The total weight of the assembled robot is 3.5 g.

FIG. 6.

Fabrication process and experimental setup. (a) Fabrication process of the robot. Each step of the fabrication process is boxed with dotted lines. (b) Experimental setup for the multi-modal locomotion test of the robot.

Experimental setup

The electronic peripherals were designed to control the high-voltage signal for DEAs and the DC currents for SMA spring actuators. A 10 kV DC-DC amplifier (UltraVolt 10A12-P4, Advanced Energy) was used to supply the high voltage. A custom-built optocoupler circuit based on the design of Mitchell et al.³⁵ was built to achieve high-speed control of DEAs.

The currents in the SMA springs were controlled by MOSFET (IRFR024N, International Rectifier) arrays with pulse-width modulated signals. Hall-effect-based current sensors (ACS712, Allegro Microsystems) provided feedback on actual currents.

All the actuation circuits were connected to a single Cortex-M3-based microcontroller (STMicroelectronics). Locomotion data of the robot was captured using a high-speed camera (iPhone XR, Apple Inc.) at 240 fps and analyzed with Tracker software. The schematic of experiments is illustrated in Figure 6b.

Running motion test

The robot’s forward-running motion on a PVC surface is shown in Figure 7a. The square wave signal with frequencies between 2 and 20 Hz was used to control the optocouplers, where the voltage of the DC amplifier was set to 5 kV. The relationship between the control frequency and the robot’s speed is plotted in Figure 7b. The robot achieved the maximum running speed of 91 mm/s at 12 Hz, which was 2.02 times the body length per second (BL/s).

FIG. 7.

Experimental results of the robot’s running motion. (a) Demonstration of the robot’s forward-running speed on a flat PVC surface. (b) Relationship between the frequencies of the applied control signal and the running speed of the robot on a flat PVC surface. (c) The maximum running speed tested on different material surfaces. (d) Trajectories of the robot carrying out left and right turning motions on a flat PVC surface. The turning radius of the robot is marked on the right turning trajectory. (e) The robot ascending a 9° slope on a PVC surface. (f) The robot running on a flat PVC surface carrying a 10 g payload.

The robot’s turning ability was tested under the same setting, with SMA spring actuators selectively actuated with 500 mA current based on the desired turning direction as described in Section “Robot Design and Locomotion Strategies.” Results of the robot carrying out left and right turning motions are shown in Figure 7d. After carrying out five repeated tests in each direction, the average turning radius (R_turn) achieved by the robot was measured as 208 mm, which was 4.6 times the body length of the robot.

The forward-running motion test was repeated on other materials, including glass, printing paper, steel, and wood, to show the robot’s adaptability on different terrains. These materials covered a wide range of different surface roughness and hardness. Figure 7c shows the maximum speeds achieved on these surfaces. The robot achieved higher maximum speeds on PVC and wood, while the speeds on the glass and steel were significantly lower. This was due to the lower surface friction between the silicone pad and the glass or steel surface. The slope climbing test was also carried out on a PVC surface with slope angles of 5°, 9°, and 15°. The robot was able to ascend on the slope of 5° at an average speed of 52 mm/s, and on the slope of 9° at an average speed of 30 mm/s (Figure 7e). It failed to ascend the slope of 15°.

The robot’s load-carrying ability is also tested to show its future possibility to fully carry the weight of its power source and control board. The robot is loaded with metal payloads weighing 5 g, as shown in Figure 7c. Running speeds were tested under each condition. The result shows that the robot could run under 5 and 10 g loads, with an average speed of 58 and 34 mm/s, respectively. This shows the robot’s good potential for future untethered operation.

Jumping motion test

The SMA control signals used in the jumping motion test with their corresponding temperature changes are illustrated in Figure 8a. During the test, the SMA springs were actuated using DC currents of 800 mA. A certain time delay was given between the upper and bottom springs’ actuation. Changing the length of the time delay can adjust the amount of released energy during jumping.

FIG. 8.

Testing of the robot’s jumping motion. (a) The control signals and the temperature change of SMAs on the top and bottom sides. A_f and M_f represent the temperature at which the austenite and martensite transformations are finished. (b) The vertical jumping performance of a standalone SMA bistable structure and the robot. (c) The jumping trajectories of the robot with the DEA actuated with different DC voltages. (d) The robot’s forward jumping motion over a 40 mm high obstacle. (e) The robot’s vertical and forward jumping motion carrying a 5 g payload.

Different time delay values were tested in the vertical jumping motion. The robot reached a maximum jumping height of 80 mm with a time delay setting of 2 s. This jumping performance is compared with that of the standalone SMA bistable structure to show the influence of adding the DEA structure on the robot’s jumping performance as shown in Figure 8b. The SMA bistable structure alone reached the maximum jumping height of 96 mm. This height is slightly higher than that of the designed robot, considering the lighter weight of the SMA bistable structure (2.3 g).

The jumping height and forward distance can be controlled by applying different voltages on the DEA. This changes the contact angle of the hind foot with the ground, affecting the friction force generated during jumping. Figure 8c illustrates the measured jumping trajectories. The average jumping height with V_DEA = 0, 2.5, and 5 kV are 78, 69, and 60 mm, respectively. The corresponding jumping distances are 14, 31, and 49 mm. The robot’s obstacle-crossing capability was shown with the DEA actuated at 5 kV over an obstacle with a height of 40 mm as shown in Figure 8d. In some experiments, the robot landed upside down because of the rotational momentum generated during the jumping motion. The control of landing pose is out of the scope of this research. Nevertheless, the robot’s pose can be flipped back by repeating the jumping motion.

Adding payloads will reduce the robot’s jumping height. This influence was tested with 5 and 10 g payloads added to the robot. With a 5 g payload, the robot could vertically jump to a height of 52 mm and jump across a 25 mm obstacle as shown in Figure 8e. However, the robot could not carry out significant jumping motion when the payload weight was increased to 10 g.

Energy cost analysis

The energy consumption associated with the robot’s various modes of motion is essential for enabling untethered locomotion, particularly when operating with a limited power supply. The energy cost of the SMA spring actuators can be calculated by measuring electrical currents I_k(t) flowing through k-th SMA spring in real-time. The resistance of each SMA spring is estimated to be constant R. The power cost of the SMA springs is then presented as $P_{SMA} (t) = \sum_{k = 1}^{6} I_{k}^{2} (t) R$ . The power cost of the DEA is calculated with the supplied current I_DEA(t) and U_DEA(t) from the DC high-voltage power supply as P_DEA(t) = U_DEA(t)I_DEA(t). The total energy cost for each locomotion time period is then given by the time integration of the power $E = \int_{0}^{T} (P_{S M A} (t) + P_{D E A} (t))$ .

For straight-line running motion, only DEA is actuated. At maximum running speed, the average energy cost of a 10 s period was measured to be around 1.5 mJ. By dividing the total energy by the product of mass and traveled distance, the corresponding cost of transport (CoT) is calculated as 7.69 J/(kg·m). The energy cost of the jumping motion was calculated from the energy used by all SMA springs during one jumping cycle as shown in Figure 8a. The average energy used in one jumping cycle was around 90.08 J. These results show the significant advantage of having DEA in the robot, which has a much lower energy cost.

Sensing ability demonstration

To show the robot’s sensing ability, a 60% humidity indicator was pasted on the back of the robot, as shown in Figure 9. The robot carried the indicator inside the target area, and the change of color on the indicator successfully showed the rise of the humidity in the air. Other possible sensors to be carried on the robot include light, chemical, and temperature sensors. Some lightweight inertial measurement units are also available within the robot’s load-carrying capability, which will give the robot the ability to navigate intelligently in complex environments.

FIG. 9.

Demonstration of the robot’s sensing ability. The robot carries a humidity indicator to detect the change in environmental humidity.

Conclusion

This article designed a small-scale soft robot with high-performance multi-modal locomotion capability. The robot utilized the advantage of the large deformation and energy storage capability of SMA spring actuators and the high-frequency output of DEAs to achieve better performance in running, turning, and jumping motions. The theoretical model of the robot was constructed using an energy-based model for the SMA bistable structures and a visco-hyperelastic model for the DEA-driven joint. A geometrical simplification was made to calculate the strain distribution in the DE membrane under nonlinear deformation, which improved the calculation speed by 35 times while preserving accuracies for quasistatic and dynamic analysis. Based on these models, the robot’s performance in running and jumping motion was optimized. The optimized design of the robot achieved a maximum running speed of 91 mm/s (2.02 BL/s), a maximum jumping height of 80 mm (1.78 BL), and an obstacle-crossing height of 40 mm. The robot could also carry out turning motions with an average turning radius of 208 mm (4.6 BL) and ascend a slope of 9° at 30 mm/s speed. The performance of the designed robot is compared with other related works as listed in Table 2. Most works with multi-modal locomotion capabilities use single actuation methods, therefore are only optimally designed for one locomotion mode. This work combines the strength of different actuators in a small and lightweight design, achieving performance comparable with other small-scale robots in both running and jumping locomotion modes. This overall performance makes the robot more suitable for exploration in complex terrains with obstacles while still capable of high-speed locomotion with low CoT.

Table 2.

Comparison of Robot’s Performance with Related Works

Literature	Actuation	Locomotion modes	Body length/mm	Weight/g	Speed/mm⋅s⁻¹ (BL⋅s⁻¹)	Peak jump height/mm (BL)	Untethered
Nishikawa et al.³⁶	SMA	Jump	50	1.2	/	130 (2.6)	×
Zhao et al.¹⁸	DEA	Run	85	6.5	518 (6.09)	/	×
Tang et al.¹⁶	Pneumatic	Run	70	45	174.4 (2.49)	/	×
Mao et al.¹⁷	Magnetic	Run, jump, swim	9	0.2	630 (70)	4 (0.44)	×
Mao et al.¹⁷	Magnetic	Run, jump, swim	9	0.7	10.8 (1.2)	/	✓
Duduta et al.¹⁹	DEA	Crawl, jump, roll	50	0.9	20 (0.4)	87 (1.74)	×
Zhakypov et al.²⁶	SMA	Crawl, jump, walk	58	9.7	0.55 (0.009)	140 (2.41)	✓
This Work	DEA + SMA	Run, jump	45	3.5	91 (2.02)	80 (1.78)	×

BL, body length; DEA, dielectric elastomer actuator; SMA, shape memory alloy.

One of the limitations of the current robot design is the need for tethers for power supply and control. In the future, it is possible to make this robot fully untethered by lowering the DEA’s actuation voltage and properly designing a powering and control circuit. Also, this work’s theoretical model did not consider the robot’s interaction with the ground. Although the methods used in this work provide enough accuracy for the design optimization, a more accurate dynamic model can give the robot more adaptive locomotion strategies on different terrains to further improve its performance.

Footnotes

Author Disclosure Statement

No competing financial interests exist.

Funding Information

This work was supported in part by the Natural Science Foundation of China under Grant 62225309, U24A20278, 62361166632, and U21A20480.

Supplementary Material

References

Chen

, Liang

, Miao

, et al. Elevation control of a soft jumping robot. In: 2021 IEEE International Conference on Robotics and Automation (ICRA), Xi’an, China; 2021, pp. 11843–11849.

Wharton

, You

, Jenkinson

, et al. Tetraflex: A multigait soft robot for object transportation in confined environments. IEEE Robot Autom Lett, 2023; 8(8):5007–5014.

Talas

, Baydere

, Altinsoy

, et al. Design and development of a growing pneumatic soft robot. Soft Robot, 2020; 7(4):521–533.

Tang

, Du

, Jiang

, et al. A pipeline inspection robot for navigating tubular environments in the sub-centimeter scale. Sci Robot, 2022; 7(66):eabm8597.

Adams

, Sridar

, Thalman

, et al. Water pipe robot utilizing soft inflatable actuators. In: 2018 IEEE International Conference on Soft Robotics (RoboSoft), Livorno, Italy; 2018, pp.321–326.

Lin

, Xu

, Juang

. Single-Actuator soft robot for in-pipe crawling. Soft Robot, 2023; 10(1):174–186.

, Lum

, Mastrangeli

, et al. Small-scale soft-bodied robot with multimodal locomotion. Nature, 2018; 554(7690):81–85.

Zhao

, Dai

, Yao

. Liquid-Metal magnetic soft robot with reprogrammable magnetization and stiffness. IEEE Robot Autom Lett, 2022; 7(2):4535–4541.

Han

, Guo

, Chen

, et al. Submillimeter-scale multimaterial terrestrial robots. Sci Robot, 2022; 7(66):eabn0602.

10.

, Wu

, Nishikawa

, et al. Soft robotic origami crawler. Sci Adv, 2022; 8(13):eabm7834.

11.

, Liu

, Cacucciolo

, et al. An autonomous untethered fast soft robotic insect driven by low-voltage dielectric elastomer actuators. Sci Robot, 2019; 4(37):eaaz6451.

12.

Drotman

, Jadhav

, Karimi

, et al. 3D printed soft actuators for a legged robot capable of navigating unstructured terrain. In: 2017 IEEE International Conference on Robotics and Automation (ICRA), Singapore; 2017, pp. 5532–5538.

13.

Matia

, Kaiser

, Shepherd

, et al. Harnessing nonuniform pressure distributions in soft robotic actuators. Adv Intell Syst, 2023; 5(2):2200330.

14.

Chen

, Yuan

, Guo

, et al. Legless soft robots capable of rapid, continuous, and steered jumping. Nat Commun, 2021; 12(1):7028.

15.

Lin

, Leisk

, Trimmer

. GoQBot: A caterpillar-inspired soft-bodied rolling robot. Bioinspir Biomim, 2011; 6(2):26007.

16.

Tang

, Chi

, Sun

, et al. Leveraging elastic instabilities for amplified performance: Spine-inspired high-speed and high-force soft robots. Sci Adv, 2020; 6(19):eaaz6912.

17.

Mao

, Schiller

, Danninger

, et al. Ultrafast small-scale soft electromagnetic robots. Nat Commun, 2022; 13(1):4456.

18.

Zhao

, Zhang

, McCoul

, et al. Soft and fast hopping-running robot with speed of six times its body length per second. Soft Robot, 2019; 6(6):713–721.

19.

Duduta

, Berlinger

, Nagpal

, et al. Tunable multi-modal locomotion in soft dielectric elastomer robots. IEEE Robot Autom Lett, 2020; 5(3):3868–3875.

20.

Liang

, Wu

, Yim

, et al. Electrostatic footpads enable agile insect-scale soft robots with trajectory control. Sci Robot, 2021; 6(55):eabe7906.

21.

Ahn

, Liang

, Cai

. Bioinspired design of light-powered crawling, squeezing, and jumping untethered soft robot. Adv Mater Technol, 2019; 4(7):1900185.

22.

Baek

, Yim

, Chae

, et al. Ladybird beetle–inspired compliant origami. Sci Robot, 2020; 5(41):eaaz6262.

23.

Chen

, Tao

, Cao

, et al. A soft, lightweight flipping robot with versatile motion capabilities for wall-climbing applications. IEEE Trans Robot, 2023; 39(5):3960–3976.

24.

Tang

, Zhang

, Lin

, et al. Switchable adhesion actuator for amphibious climbing soft robot. Soft Robot, 2018; 5(5):592–600.

25.

Zhang

, Yang

, Yan

, et al. Inchworm Inspired Multimodal Soft Robots With Crawling, Climbing, and Transitioning Locomotion. IEEE Trans Robot, 2022; 38(3):1806–1819.

26.

Zhakypov

, Mori

, Hosoda

, et al. Designing minimal and scalable insect-inspired multi-locomotion millirobots. Nature, 2019; 571(7765):381–386.

27.

Patel

, Huang

, Luo

, et al. Highly dynamic bistable soft actuator for reconfigurable multimodal soft robots. Adv Mater Technol, 2022; 8(2):2201259.

28.

Yun

, Liu

, Leng

, et al. A millimeter-scale multilocomotion microrobot capable of controlled crawling and jumping. Soft Robot, 2024; 11(2):361–370.

29.

Misu

, Yoshii

, Mochiyama

. A compact wheeled robot that can jump while rolling. In: 2018 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS). Madrid, Spain; pp. 7507–7512.

30.

Spiegel

, Sun

, Zhao

. A shape-changing wheeling and jumping robot using tensegrity wheels and bistable mechanism. IEEE/ASME Trans Mechatron, 2023; 28(4):2073–2082.

31.

Chiang Foo

, Cai

, Jin Adrian Koh

, et al. Model of dissipative dielectric elastomers. J Appl Phys, 2012; 111(3):34102.

32.

, Ryu

, Cho

, et al. Engineering design framework for a shape memory alloy coil spring actuator using a static two-state model. Smart Mater Struct, 2012; 21(5):55009.

33.

Plante

, Dubowsky

. Large-scale failure modes of dielectric elastomer actuators. Int J Solids Struct, 2006; 43(25–26):7727–7751.

34.

Zhao

, Suo

. Method to analyze programmable deformation of dielectric elastomer layers. Appl Phys Lett, 2008; 93(25):251902.

35.

Mitchell

, Martin

, Keplinger

. A pocket-sized ten-channel high voltage power supply for soft electrostatic actuators. Adv Mater Technol, 2022; 7(8):2101469.

36.

Nishikawa

, Arai

, Niiyama

, et al. Coordinated use of structure-integrated bistable actuation modules for agile locomotion. IEEE Robot Autom Lett, 2018; 3(2):1018–1024.

Supplementary Material

Please find the following supplemental material available below.

For Open Access articles published under a Creative Commons License, all supplemental material carries the same license as the article it is associated with.

For non-Open Access articles published, all supplemental material carries a non-exclusive license, and permission requests for re-use of supplemental material or any part of supplemental material shall be sent directly to the copyright owner as specified in the copyright notice associated with the article.

0.00 MB