Bioinspired Soft Spine Enables Small-Scale Robotic Rat to Conquer Challenging Environments

Abstract

For decades, it has been difficult for small-scale legged robots to conquer challenging environments. To solve this problem, we propose the introduction of a bioinspired soft spine into a small-scale legged robot. By capturing the motion mechanism of rat erector spinae muscles and vertebrae, we designed a cable-driven centrally symmetric soft spine under limited volume and integrated it into our previous robotic rat SQuRo. We called this newly updated robot SQuRo-S. Because of the coupling compliant spine bending and leg locomotion, the environmental adaptability of SQuRo-S significantly improved. We conducted a series of experiments on challenging environments to verify the performance of SQuRo-S. The results demonstrated that SQuRo-S crossed an obstacle of 1.07 body height, thereby outperforming most small-scale legged robots. Remarkably, SQuRo-S traversed a narrow space of 0.86 body width. To the best of our knowledge, SQuRo-S is the first quadruped robot of this scale that is capable of traversing a narrow space with a width smaller than its own width. Moreover, SQuRo-S demonstrated stable walking on mud-sand, pipes, and slopes (20°), and resisted strong external impact and repositioned itself in various body postures. This work provides a new paradigm for enhancing the flexibility and adaptability of small-scale legged robots with spine in challenging environments, and can be easily generalized to the design and development of legged robots with spine of different scales.

Introduction

Improving the flexibility of bioinspired legged robots to better adapt to the environment, particularly in narrow spaces, is a key issue in the field of bioinspired legged robots.^1–5 Legged animals of different scales can flexibly use their spine and legs to adapt to unstructured environments.^6,7 In nature, cheetah's flexible spine could absorb kinetic energy so they can decelerate sharply and rapidly, which enable much tighter turns in hunting.^8–10 Dogs could keep the center of mass in a nearly constant position relative to the thorax by controlling their limbs and spine when trotting.¹¹ Rats could use lateral spine movement to reduce vertical oscillation and side-to-side fluctuation.¹² In recent years, researchers have attempted to combine spine motion and leg motion in legged robots to enhance their mobility.

In MIT cheetah, the legs and spine are connected in parallel through the differential so that the hindlegs of the robot can use the spine spring to store energy during impact with the ground and release it in the subsequent acceleration swing.¹³ Zhao et al. verified the effect of active spine motion on driving a robot through a bouncing experiment using the quadruped robot Kitty.¹⁴ In a further study, Zhao et al. used a single-joint spine-type robot model driven by pneumatic muscles in parallel and found that the robot ran fastest when the active spine and legs were triggered simultaneously.¹⁵ Khoramshahi et al. found through Bobcat that as the spine is involved in motion, the absolute swing of the legs relative to the ground is increased so that a lower leg swing angle (relative to the body) can be obtained for an equal or higher robot speed.¹⁶

The aforementioned robots demonstrated the positive effect of the spine on the speed performance of robot locomotion. However, the physical size of these robots is too large for them to operate in a narrow space and their researchers have not verified whether the spine can increase the robot's adaptability in unstructured environments.

In terms of small-scale spine-type legged robots, Tang et al. achieved spine-driven running through a spine-inspired bistable soft actuator, with a movement speed of 2.68 body lengths per second.¹⁷ The insect-scale soft robot developed by Wu et al. achieved a moving speed of 20 body lengths per second through a piezoelectric structure, which is the fastest measured value among published artificial insect-scale robots.¹⁸ However, these small robots are unable to power themselves, and external tethers limit their applications.

In summary, the large-scale legged robots mostly integrate a drive mechanism into an originally rigid body to enhance their physical performance and robustness, and the related works mostly focus on rigid-flexible coupling control. As for the small-scale legged robots with spine, they are mostly soft bodies driven by the pneumatic or piezoelectric actuator with a tether connected to an external power, and the related works focus more on design and fabrication of the actuator. As we mentioned before, neither of them is able to operate independently in narrow space. For most confined spaces, centimeter-scale is an ideal robot size. Robots of this size can flexibly enter narrow spaces, such as ruins and pipelines, with a power source. However, it is a great challenge to achieve high bioinspired mobility without a tether in a limited volume.

Inspired by small legged animals in nature, we found that the rat's adaptability is particularly prominent in narrow spaces because of its unique body structure.¹⁹ The narrow and long body allows the rat to pass through narrow pipes and holes. The cooperation of the spine and legs allows the rat to flexibly combine lateral bending, sagittal bending, and long-axis rotation, which give it the ability to traverse complex terrain. In our previous studies, we developed wheeled and legged robotic rats.^20,21 The wheeled robotic rat can imitate the behavior of a rat, however, its driving mechanism makes it difficult to cross obstacles, which limits the application environment of the robot.

In our previous legged robotic rat SQuRo, which included four legs and one spine, we simplified the rat spine into two rotation joints with axes perpendicular to the lateral plane and connected by rigid links,²² which made the spine function limited to the turning motion of the robotic rat in the lateral plane, and this greatly limited the spatial flexibility of the robot.

In this article, we propose a bioinspired soft spine and integrate it into our previously developed robotic rat (SQuRo). The new version of the robotic rat is called SQuRo-S. SQuRo-S includes two main parts: (1) a bioinspired soft spine design based on the anatomy of the rat spine, and (2) spine-leg coupling motion planning and control. As a result of the aforementioned work, SQuRo-S is more adaptable to the environment than existing state-of-the-art small-scale legged robots and we present a detailed comparison in the Discussion section. We experimentally verified the environmental adaptability of SQuRo-S. It successfully crossed obstacles higher than its own height (1.07 body height). Second, SQuRo-S traversed a narrow space composed of a wall obstacle and thin plate obstacle whose width was less than its own width (0.86 body width). Third, SQuRo-S repositioned itself in different body postures.

Finally, SQuRo-S passed through various rough terrain, such as pipelines, mud-sand, and slopes. Remarkably, SQuRo-S resisted external impact while walking. The superior performance of SQuRo-S is mainly attributed to two aspects. One is the soft flexible spine designed to imitate the biological mechanism of the rat spine, which greatly improves the flexibility of SQuRo-S. Second, we adjusted the motion parameters of the spine and legs, and coordinated the coupled motion of the spine and legs. Our design can be easily generalized to other designs of bioinspired legged robots.

Materials and Methods

The spine of SQuRo-S is driven by four geared stepper motors. These four motors are driven by two control boards, which are installed at the top of the front trunk and top of the hind trunk. The control board at the front controls the relative long-axis rotation of the forelegs and the spine, and the lateral bending of the spine. The control board at the hind controls the relative long-axis rotation of the hindlegs and the spine, and the sagittal bending of the spine. The two control boards operate independently and are supplied with 7.4 V lithium rechargeable batteries.

The STM32F103RG microcontroller is connected to the LORA communication module to send and receive commands wirelessly. This setup can be used to implement wireless control so that the user can send commands to the module and drive the actuator to perform the desired action. The control boards of geared stepper motors have their own communication circuit, which can send commands through a signal generator to adjust the speed and the direction of motor rotation.

Each servo motor on the leg of the robot rotates periodically as the robot moves with a certain gait. We designed the foot trajectory according to the following rules: when the robot steps forward, the leg can be lifted higher, and when the robot pushes back, the leg can be as smooth as possible. The foot trajectory is thus designed to be a cycloid forward followed by a smooth ellipse backward.

The cycloid equation is as follows: $\{\begin{matrix} x = \frac{S [4 π t - sin (4 π t)]}{2 π} \\ y = \frac{H [1 - cos (4 π t)]}{2 - h} \end{matrix}$ (1)

The elliptic equation is as follows: $\{\begin{matrix} x = \frac{S [4 π t - sin (4 π t)]}{2 π} \\ y = \frac{H [1 - cos (4 π t)]}{2 - h} \end{matrix}$ (2)

where S is the step length, H is the lifting height of foot (leg-end), b is the height range of the ellipse, and h is the height from the hip joint to the leg-end at the initial position of the leg.

Then, according to the relationship between the foot position and the angle of the servo motor, the angle of the servo motor is inversely determined. The equations for the motor angle and front foot position are as follows: $\{\begin{matrix} x = L cos ((60 - y_{q}) \frac{π}{180}) - L sin ((30 - x_{q}) \frac{π}{180}) \\ y = - L sin ((60 - y_{q}) \frac{π}{180}) - L cos ((30 - x_{q}) \frac{π}{180}) \end{matrix}$ (3)

The equations for motor angle and hind foot position are as follows: $\{\begin{matrix} x = L sin ((30 + x_{h}) \frac{π}{180}) - L cos ((60 - y_{h}) \frac{π}{180}) \\ y = - L cos ((30 + x_{h}) \frac{π}{180}) - L sin ((60 - y_{h}) \frac{π}{180}) \end{matrix}$ (4)

where x and y are the coordinates of the foot trajectory, x_q and y_q are the corresponding angles of the foreleg servo motor, L is the leg link length, and x_h and y_h are the corresponding angles of the hindleg servo motor.

Results

Bioinspired spine conformation

As shown in Figure 1, we designed the kinematic joints of the spine of SQuRo-S by analyzing X-ray images and anatomical maps of rats. The main basic movements of the rat (lateral bending, sagittal bending, and long axis rotation) are accomplished with the assistance of the spine, as shown in Figure 1a. In the anatomy of the rat spine, we found that the bending and rotation movements of the spine are achieved by flexion-extension, abduction-adduction, and protraction–retraction of the muscles on the periphery of the spine. These muscles are divided into erector spinae muscles (ESMs) and deep back muscles. The ESMs of the spine are mainly used to generate the aforementioned movements (Fig. 1b) and the deep back muscles are responsible for maintaining the posture of the spine. A coupling relationship exists between the legs and spine to achieve the basic motions of the rat, which is shown in Figure 1c.

FIG. 1.

Mechanism configuration of the spine of SQuRo-S based on analysis of rat spine X-ray recordings^21,22 (a). Rat spine functional group anatomy (b). The basic motions of the rat mainly depends on the three-dimensional (lateral bending, sagittal bending, and long-axis rotation) spine movement, and the mapping relationship between the basic motions and functional groups of the rat is shown in (c). To ensure the similarity with the spinal movement of rats, we set four DOFs for the spine of the SQuRo-S. The blue active joints are for the long-axis rotation between the spine and the trunk of forelegs and hindlegs. The retractable muscle-like lines and the passive elastic joints are for lateral bending and sagittal bending (d). DOFs, degrees of freedoms; ESMs, erector spinae muscles. The basic motions of SQuRo-S are shown in Supplementary Video S1. Image Credits: Anatomical images of rats, biosphera3d.com

According to the aforementioned motion mechanism of the rat spine, we configured the spine with four degrees of freedom (DOFs), including two DOFs for lateral bending and sagittal bending, and two DOFs for relative rotation between the spine and legs, which is shown in Figure 1d. The integration of four spinal DOFs in a limited volume requires a compact actuation mechanism. We previously developed rigid spine joints with two DOFs,^23,24 however, a soft spine can better help robots to adapt to environments because of its compliance and flexibility. Existing soft body bending actuation mechanisms mainly include pneumatic-driven bending,^25–27 cable-driven bending,²⁸ and twisted-and-coiled actuator (TCA)-driven bending.²⁹ Pneumatic-driven bending and TCA-driven bending usually require a tether to connect to the power supply system, and this system usually cannot fit into the robot body because of its power-to-mass ratio.

Untethered pneumatic-driven meter-scale soft robots have also been proposed in recent years;³⁰ however, it is still difficult to integrate pneumatic devices in centimeter-scale robots to achieve excellent environmental adaptability.^31,32 Considering that our robot needs to operate without a tether,³³ we chose the actuation mechanism of cable-driven bending. The two DOFs for lateral bending and sagittal bending are driven by cables to induce passive deformation of the spine, which mimics the motion mechanism of rat ESMs and vertebrae. The other two DOFs for relative rotation between the spine and legs are achieved by motors embedded in the trunks of the forelegs and hindlegs. Then, we designed and manufactured a bioinspired soft spine for SQuRo-S through engineering process. The spine dimensions and its mechanisms of motion are shown in Figure 2.

FIG. 2.

Overall design of SQuRo-S. (a) 3D model and dimensions of the soft spine. (b) The driving mechanism of soft spine bending motion. (c) Exploded view of soft spine (1) Flange, (2) End cap, (3) Compression block, (4) Reel, (5) Geared motor, (6) Motor fixing ring, (7) Cable, and (8) Soft support bone. (d) 3D assembly model and dimensions of the SQuRo-S. (e) Engineering prototype of the SQuRo-S.

Force and bending characterizations

We conducted experimental tests on soft spines with different hardness values and central radial dimensions, and the construction of the experimental platform is described in detail in the Supplementary Data. The hardness range was 50–80 A (Shore hardness), and the central radial dimension range of the spine was 14—18 mm, which are shown in Figure 3c. Figure 3d–g shows that as the bending angle of the soft spine increased (from 0° to 60°), the torque gradually increased, but the rate of torque increase gradually decreased. At the same hardness value, as the central radial dimension of the spine increased, the value of the torque required to achieve the same bending angle increased. At the same central radial dimension of the spine, as the hardness value increased, the value of the torque required to achieve the same bending angle increased.

FIG. 3.

Experimental characterization of spine bending. (a) Bending deformation measurement platform for soft spine. (b) A measurement cycle of soft spine bending deformation. (c) Hardness and dimensions of soft spines measured in bending deformation experiments. (d–g) The relationship between the bending deformation torque and the bending angle of spines with different dimensions under 50–80 A hardness. (h) Boxplots of the maximum torque generated by the bending deformation of the soft spines under 50–80 A hardness.

Figure 3h shows the mean torque required for the spine (corresponding to three central radial dimension of 14, 16, and 18 mm at each hardness) to bend to the maximum angle at 50, 60, 70, and 80 A hardness, and the rate of increase of the mean torque required to the maximum bending angle increases with increasing hardness. The soft spine with high hardness and large central radial dimension can enhance the whole-body stiffness of the robot, but it will increase energy consumption and reduce the robot's load capacity. On the contrary, choosing a soft spine with low hardness and small central radial dimension will reduce the whole-body stiffness of the robot, but it will reduce energy consumption and increase body flexibility.

Jumping locomotion analysis

SQuRo-S formed a stable triangular support area on the ground through the hindlegs and hips, and then lifted the forelegs through the sagittal bending of the spine, as shown in Figure 4a. In this state, SQuRo-S pushed its hindlegs backwards to achieve the jumping action. We changed the position of the center of mass of the robot by changing the sagittal bending angle of the spine. Because the position of the contact points of the hindlegs did not change, the relative position of the center of mass and the contact points of the hindlegs changed. This changed the reaction force of the foot end during the jumping process, which resulted in the change of the jump trajectory (Fig. 4b).

FIG. 4.

Jumping performance characterization. (a) The sagittal bending angle of the SQuRo-S for preparation of jumping. (b) Jumping trajectory of the head of the SQuRo-S at different sagittal bending angles of the soft spine. (c) Histogram with standard deviation of the mean impulse values of the force points on the two hindlegs along the Z-axis during the jumping at different sagittal bending angles (25°–55°). (d–g) The initial jumping position and the highest jumping position of the SQuRo-S at different sagittal bending angles (25°–55°), and we measured the force on the contact point of hindlegs during the jumping process.

We obtained the joint positions of SQuRo-S and the force values of the contact points during the jumping process. We labeled the thigh joint, calf joint, foot end, and head of SQuRo-S with markers, and captured the motion trajectory of the markers using a motion capture system. SQuRo-S finished the jumping action on the force platform to accomplish the sampling of the force value of the foot end of the hindlegs. Figure 4d–g shows the robot's initial position and the highest position of the spine at the sagittal bending angles of 25°, 35°, 45°, and 55°, and the corresponding force on the foot end of the hindlegs.

We found that, as the spine sagittal bending angle increased, the maximum jump height of SQuRo-S increased. This is because the impulses of the Z-axis supporting force varied with spine sagittal bending angles during the jumping up process (jumping from initial position to the highest position). Figure 4c shows that as the spine sagittal bending angle increased, the impulse of the Z-axis supporting force during the jumping up process also increased.

Obstacle crossing

Through the motion planning of the spine and legs of SQuRo-S, the robot achieved obstacle crossing at a height of 75 mm (higher than 70 mm for SQuRo-S), which is shown in Figure 5a. Because of the scale constraints of the robot, it was difficult to attach a high-power motor to it to achieve airborne jumping. We explored a way for the spine and legs to cooperate with each other to cross obstacles, and achieved the movement of the forelegs and hindlegs in the sagittal plane of the robot. The specific motion phase sequence is shown in Figure 5b–l and described as follows.

FIG. 5.

Obstacle crossing characterization and analysis. (a) The height comparison between the SQuRo-S and the obstacle. (b–l) Video snap-shots and state analysis of surmounting the obstacle. The crossing of the obstacle was accomplished by coordinating the movement of spine and legs of the SQuRo-S. Each subfigure represents 1 of the 11 motion states. To better understand the motion state, a simplified profile of the SQuRo-S from the side view shown at the bottom left or right part of each subfigure. This figure corresponds to the Supplementary Video S2.

First, the hindlegs of the robot extended forward in the standing state so that the hip of the robot touched the ground. Then, the body of the robot tilted forward and the spine performed a sagittal bending motion to lift the forelegs of the robot. At this time, the center of mass of the robot was in the triangular support area formed by the hindlegs and hip. Then the hindlegs of the robot pushed off the ground, and the robot jumped forward and up. After the jump, the forelegs of the robot draped over the obstacle and the hindlegs touched the ground. The sagittal bending angle of the spine adjusted to prepare the robot position for the next jump. Again, the hindlegs of the robot extended forward and then pushed off the ground.

After the second jump, the robot's forelegs crossed the obstacle and made contact with the ground, and the spine made contact with the obstacle while the hindlegs were suspended. Then, the robot's hindlegs were raised by the sagittal bending of the spine, whereas the hindlegs were straightened. In this state, the forelegs of the robot were controlled to gradually free the spine and hindlegs from the obstacle so that the robot could finish the obstacle crossing.

Turning locomotion

SQuRo-S performed the turning motion through the lateral bending of the spine in the trot gait. By observing the rat's movement in X-rays, we found that the inside legs was lower than the outside legs when the rat turned, and we used this phenomenon in the turning motion planning of SQuRo-S. During the turning motion, SQuRo-S's body and the ground formed a lean angle ψ = 10° (Fig. 6a), and there was a distance of d_turn = 13 mm between the inside foot and outside foot within one gait cycle (Fig. 6b). When the spine was bent to the extreme position of 90°, the minimum turning radius of SQuRo-S was 0.42 body lengths. The turning motion process is shown in Figure 6c.

FIG. 6.

Turning locomotion characterization and analysis. (a) The SQuRo-S has a lean angle between its body and the ground during the turning action. (b) Distance between the inside foot of the turning and the outside foot of the turning. (c) Turning process and minimum turning radius when the spine of the SQuRo-S is bent 90°. (d) Thigh and calf rotation angle during one turn cycle in the trot gait. (e) The initial phase of the inside legs in turning and the process of joint rotation in the trot gait. This figure corresponds to the Supplementary Video S4.

SQuRo-S adopted a trot gait when turning, and the phase difference of the trotting legs was half a cycle. The rotation angle values of the thigh joint and calf joint of a single leg in one trot cycle are shown in Figure 6d. Figure 6e shows the initial joint position of the inside legs during turning and the dynamic changing process of the joint rotation angle in one cycle.

Narrow space traversing

Traversing narrow space is a challenging task for legged robots. Through the motion planning of the spine and legs of SQuRo-S, the narrow space formed by a thin plate and wall obstacle can be traversed. Because the width of SQuRo-S (76 mm) was larger than the width of the narrow space (65 mm), the robot could not travel in a straight line normally. We established a strategy for matching the spine and legs to traverse the narrow space. The specific motion sequence is shown in Figure 7. The motion of lifting the forelegs is consistent with the obstacle-crossing experiment.

FIG. 7.

Narrow space traversing characterization and analysis. (a) Schematic illustration of the SQuRo-S traversing through the narrow space composed of wall obstacle and thin plate obstacle. (b–j) Video snapshots and state analysis of traversing a narrow space. The traversing of the narrow space was accomplished by coordinating the movement of spine and legs of the SQuRo-S. Each subfigure represents one of the nine motion states, and each subfigure includes side-view and top-view perspectives of the narrow space traversing. This figure corresponds to the Supplementary Video S3.

The robot twisted the trunk of forelegs so that it could move through the narrow space, and then the robot jumped forward and up. After the jump, the robot's forelegs and part of its spine had traversed the narrow space, while the robot twisted its trunk of forelegs to the initial position. Then, the robot twisted its trunk of hindlegs so that it could traverse the narrow space. The prostrate motion of the forelegs made the hindlegs traverse the narrow space, and then the robot twisted its trunk of hindlegs to reposition itself, thus, the robot completely traversed the narrow space.

Reposition ability

SQuRo-S can reposition itself in a fall by twisting the spine relative to the trunk of forelegs and hindlegs. The trunks of the forelegs and hindlegs are equipped with geared motors (deceleration ratio 210:1), which have good self-locking ability. Figure 8a shows the different long-axis rotation joint states. The long-axis rotation joint of the trunk of the hindlegs locked when the long-axis rotation joint of the trunk of the forelegs rotated, and the trunk of the forelegs rotated with respect to the spine. The long-axis rotation joint of the trunk of the forelegs locked when the long-axis rotation joint of the trunk of the hindlegs rotated, and the trunk of the hindlegs rotated with respect to the spine.

FIG. 8.

Characterization and analysis of reposition ability. (a) Spine rotation joints arrangement classification. (b–i) Video snapshots and state analysis of repositioning. The repositioning was accomplished by long-axis rotation of spine and legs of the SQuRo-S. Each subfigure represents one of the eight motion states, and each subfigure shows the whole-body state of the SQuRo-S during the repositioning process, and we annotated the spine state corresponding to the whole-body state. This figure corresponds to the Supplementary Video S9.

The long-axis rotation joints of the trunks of the forelegs and hindlegs rotated simultaneously (in the same direction and with the same angular velocity), and the spine rotated relative to the trunks of the forelegs and hindlegs. When the two long-axis rotation joints of SQuRo-S's spine were in the state of self-locking, the trunk of the forelegs, trunk of the hindlegs, and spine did not rotate relative to each other. Figure 8b–i shows the state analysis of the robot repositioning itself using long-axis rotation.

Adaptability to complex terrain

We selected four representative types of complex terrain to verify the environmental adaptability of SQuRo-S, including a circular pipe, steep slope, mud and sand, and impact by an object.

PVC pipe is widely used in the mechanical and electronic manufacturing industries. Because of the steel wire embedded in this pipe to enhance its resistance to deformation, the arc surface inside the pipe is uneven. Existing detection robots have high requirements for the flatness of the arc surface in pipes, which makes it difficult to detect PVC pipe. SQuRo-S, with its long and narrow body shape and soft flexible spine, can perform inspection tasks in this type of pipeline.

We bent a PVC pipe with an inner diameter of 114 mm to the limit position, and made the inlet and outlet of the pipe's different heights within three-dimensional space. Thus, we simulated the most difficult scenarios that SQuRo-S may encounter when performing pipe-line inspection tasks. In experiments, SQuRo-S passed through the pipeline smoothly (Fig. 9a), which shows the ability to perform inspection tasks in complex pipelines.

FIG. 9.

Adaptability experiments to complex terrain. (a) The SQuRo-S passed through the PVC pipe with a diameter of 114 mm wound into a three-dimensional spiral in a crawling gait. (b) The SQuRo-S successfully climbed a slope with a gradient of 20° with the spine bending, which is impossible without the spine bending. (c) The SQuRo-S passed through rough terrain with mud and sand, benefiting from excellent passive compliance of the spine. (d) The SQuRo-S successfully resisted the impact of the external impact while walking and kept going. This figure corresponds to the Supplementary Videos S5–S8.

For the slope, we improved the adaptability of the robot by flexibly adjusting the posture of the spine. We set up a steep slope (20° to the ground) with a smooth surface. In experiments, when the SQuRo-S's spine did not bend, it was difficult for SQuRo-S to climb up the slope. In the control group experiment, we bent SQuRo-S's spine so that the central part of the spine was close to the ground, and SQuRo-S successfully climbed up the steep slope in this state (Fig. 9b). This shows that the bending posture of the spine affects the adaptability of the robot for slope climbing.

Terrain consisting of mud and sand is a perennial challenge for legged robots. Because the spine of traditional legged robots is rigid, most of them adapt to this type of terrain through active adjustment control of their gait.³⁴ However, this adjustment requires complex calculations, and small-scale legged robots cannot have an on-board processor that provides sufficient computing power because of volume constraints. To solve this problem, we adapted SQuRo-S to this environment through passive compliance of the soft spine. In experiments, when passing through mud and sand, because of the flexibility of the robot spine, the robot adapted to the terrain through the relative motion of the legs and spine (Fig. 9c).

We also applied the compliance of the soft spine to the robot's ability to resist external impact. A balance algorithm is usually required for robots to maintain their balance under external impact during walking. As mentioned above, we used passive adaptation to solve this problem. In the experiment, we allowed the robot to adopt two gaits, crawling and walking, to observe its ability to resist external impact. The experimental results demonstrated that, thanks to the excellent compliance of the spine, SQuRo-S maintained its balance when subjected to external impact and maintained a normal walking state after impact (Fig. 9d).

Discussion

We selected representative advanced small-scale legged robots for comparison, which are listed in Table 1. Compared with our previous-generation legged robotic rat SQuRo, SQuRo-S is longer, wider, and lower. This is mainly because that the increase of DOFs led to an increase in the number of drive motors and peripheral drive circuit. In terms of environmental adaptability, SQuRo-S is a qualitative leap compared with SQuRo. SQuRo-S can cross obstacles of 75 mm (higher than its own height 70 mm), which is 2.5 times the height of obstacles crossed by SQuRo. In addition, SQuRo-S can traverse a narrow space of 85% of its own width and climb a steep slope with a gradient of 20°. These environmental adaptability capabilities are not available in SQuRo.

Table 1.

Comparisons to Other Small-Scale Legged Robots

Name	Dimensions (mm)	DOFs No.	Obstacle height (BH)	Narrow space width (BW)
SQuRo-S	238 × 76 × 70	14	1.07	0.86
SQuRo	188 × 55 × 90	12	0.33	≥1
WR-1	270 × 130 × 110	15	—	≥1
WR-2	240 × 70 × 90	15	—	≥1
NeRmo	227 × 91 × 90	13	—	≥1
Little dog	300 × 180 × 260	12	0.46	≥1

BH, body height; BW, body width; DOF, degrees of freedom.

Other types of small-scale legged robots, such as the untethered-bioinspired quadrupedal robot based on double-chamber precharged pneumatic soft actuators with a highly flexible trunk,³⁵ NeRmo,³⁶ Cheetah-Cub,³⁷ and Cheetah-Cubs³⁸ have cable-driven elastic leg structures, which improve energy efficiency and exhibit excellent variable stiffness performance; however, they have single-DOF or rigid spines, hence, their ability to cross obstacles and traverse narrow spaces is limited. WR-1³⁹ and WR-2⁴⁰ have 15 DOFs in their entire bodies, however, they are mainly oriented to interactions with laboratory rats and do not have strong environmental adaptability. Small-scale legged robots equipped with spinal joints enable faster speed and higher energy efficiency,^41–43 however, the adaptability of these robots in unstructured environments has not been verified.

As a small-scale legged robot with strong environmental adaptability, the little dog can cross obstacles with a height of 120 mm,⁴⁴ which is lower than its height (260 mm). Regarding a large-scale legged robot with strong obstacle-crossing ability, MIT Cheetah 2 can jump over obstacles with a height of 400 mm (80% of the leg length of Cheetah 2) using the planning frame-work.⁴⁵

By comparison, we found that our proposed SQuRo-S has better environmental adaptability, which benefits from its soft and flexible spine design. In addition, our method of combining spine motion and leg motion enables SQuRo-S to finish challenging tasks in complex environments.

Conclusion

In this study, we developed a bioinspired small-scale legged robotic rat with a four-DOF soft spine by analyzing rat movements in X-rays and rat anatomy. Spine-leg coupling motion planning and control provide SQuRo-S with a strong ability to adapt to challenging unstructured environments. We verified this through a series of experiments, such as the robot crossing obstacles higher than its own height, traversing a narrow space whose width was less than its width, repositioning itself in various body positions, and passing through various rough terrains. Compared with existing state-of-the-art small-scale legged robots, SQuRo-S has stronger environmental adaptability. Our design method is suitable to be applied to other legged robots.

Footnotes

Acknowledgments

The authors appreciate the support and funds.

Authors' Contributions

R.W: Conceptualization, Methodology, and Writing original draft. H.X: Methodology, Visualization, and Validation. X.Q. and J.G: Methodology and Visualization. T.F.: Methodology and Visualization. Q.S.: Conceptualization, Supervision, and Writing—review and editing.

Author Disclosure Statement

No competing financial interests exist.

Funding Information

This study was funded by the National Natural Science Foundation of China under Grant 62022014 and 62088101, and the Science and Technology Innovation Program of Beijing Institute of Technology under Grant 2022CX01010.

Supplementary Material

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