Nonbiomorphic Passively Adaptive Swimming Robot Enables Agile Propulsion in Cluttered Aquatic Environments

Abstract

Aquatic swimmers, whether natural or artificial, leverage their maneuverability and morphological adaptability to operate successfully in diverse, complex underwater environments. Maneuverability allows swimmers the agility to change speed and direction within a constrained operating space, while morphological adaptability allows their bodies to deform as they avoid obstacles and pass through narrow gaps. In this work, we design a soft, modular, nonbiomorphic swimming robot that emulates the maneuverability and adaptability of biological swimmers. This tethered swimming robot is actuated by a two degree-of-freedom (2-DOF) cable-driven mechanism that enables not only common maneuvers, such as undulatory surging and pitch/yaw rotations, but also a roll rotation maneuver that is steady and controllable. This simple 2-DOF system demonstrates full 3D swimming abilities in a space-constrained underwater test bed. The soft compliant body and passive foldable fins of the swimming robot lend to its morphological adaptability, allowing it to move through narrow gaps, channels, and tunnels and to avoid obstacles without the need for a low-level feedback control strategy. The passive adaptability and maneuvering capabilities of our swimming robot offer a new approach to achieving underwater navigation in complex real-world settings.

Introduction

Maneuverability and adaptability are essential features of underwater swimmers. In nature, biological swimmers rely on their maneuverability to chase prey or avoid predators in open water, and leverage the adaptability of their compliant bodies to navigate cluttered areas of seaweed bush on ocean floors or hide in narrow gaps between coral reefs and rocks (Supplementary Movie S1). Underwater robots, which are designed for various tasks, including tracking evasive moving targets, exploring complex underwater environments, and accessing hard-to-reach underwater areas for industrial or search-and-rescue operations,^1–5 require levels of maneuverability and adaptability similar to those of biological swimmers. As such, robotics researchers have sought to replicate the locomotion capabilities of fish, eels, dolphins, and other aquatic animals using multiple approaches.^6–11

Most underwater remotely operated vehicles (ROVs) are designed to be maneuverable and agile in open waters. One approach that researchers have taken to enable controllable agile maneuvers is to utilize six or more actuators, as seen in several research^12,13 and commercial¹⁴ ROVs. These holonomic underwater vehicles can perform 6-degree-of-freedom (DOF) independent maneuvers such as sways/slips (lateral movement), heaves (vertical movement), surges (forward and backward movement), and turns in place, providing them levels of free-space agility sometimes greater than that possessed by many natural swimmers (e.g.). Despite their superior capabilities in open water, it is not clear that underwater ROVs can sustain such functionality in space-constrained, real-world environments, as their nonholonomic, biological counterparts can. In fact, the rigid construction and large form factors of ROVs may significantly limit their ability to navigate obstacle-laden terrain in field applications, and the amount of hardware and energy required for practical use could pose feasibility challenges.

Natural swimmers can achieve agile maneuverability and adaptation in cluttered environments by leveraging their compliance and specialized anatomical features. Although many biological swimmers are not able to perform 6-DOF maneuvers (e.g., sway/slip, heave)^15,16 as effectively as underwater ROVs, they are known to effectively navigate complex aquatic environments by changing their locomotion strategies and leveraging their passive mechanical properties. Moray eels exploit undulating motions and their slender flexible bodies to pass through small gaps in coral reefs as they evade predators (Supplementary Movie S1), and octopi can contort their bodies to fit through into crevices much smaller than they are (Supplementary Movie S1).¹⁷ Animals like alligators, dolphins, and sea otters use their long, flexible vertebral structures and specialized features (i.e., fins, flippers, and tails) to achieve complex roll rotations using combinations of relatively simple maneuvers (Supplementary Movie S1).^18,19 Such rolling or spinning maneuvers help these animals quickly reorient themselves and execute tight turns as they pursue prey, elude predators, and avoid obstacles.

Motivated by the robustness and versatility of biological swimmers in diverse underwater settings, bioinspired robots have been designed with active adaptability, or the ability to plan paths and avoid obstacles using feedback control, and passive adaptability, which relies on mechanical compliance and underactuation to avoid obstacles and facilitate agile maneuvers in cluttered environments.

Active obstacle avoidance has been studied on several bioinspired swimming robots,^20–24 and commonly involves the use of sensors and cameras, computer vision, and closed-loop feedback control. Active obstacle avoidance has proven useful in navigating unknown underwater environments containing various terrains and changing currents, but is not as effective in obstacle-laden environments where the range and accuracy of sensors and cameras can be diminished.

In cases where sensing is occluded, open-loop control approaches can be used, granted that a robot has been designed with body adaptability. Swimming robots with body passive adaptability have been developed using several methods, including integrating soft materials or soft actuators into otherwise rigid body structures to increase mechanical compliance,^25–30 and by increasing the number of DOFs along the body to enable contortion and movement around physical impediments^9–11 (originated from compliant elongated-body robots^31–34). Although some reports on flexible, passively adapting swimming robots have demonstrated their robustness to intermittent encounters with obstacles, there appear to be no examples of robots exhibiting passive adaptability in dense patches of underwater obstacles, or while passing through gaps, holes, channels where a robot is frequently in contact with physical barriers.

In this work, we present a nonbiomorphic (i.e., not necessarily copying a biological swimmer's body structure, actuation mechanisms, and maneuvers) swimming robot capable of facilitating maneuvers essential to passive adaptive navigation in space-constrained, cluttered aquatic settings without the need for holonomic motion or closed-loop feedback control (Fig. 1A). To discover an effective swimming robot design solution, we methodically explored several body component types and actuation strategies using an experimental learning approach^35,36 often referred to as robophysics.^37,38

FIG. 1.

Two DOF modular soft swimming robot. (A) The 2-DOF modular soft swimming robot consists of a flexible vertebral structure, foldable fins, and two waterproof servos as actuators. (B) The compliant body components allow the robot to bend and twist, facilitating passive adaptability. The frame-by-frame shows the process of passing through straight channel (left) and rectangular hole (right, marked by red dash lines). (C) The swimming robot can perform multiple maneuvers (undulatory surge, yaw, pitch, and roll rotation) and can swim up to 7 m deep underwater. With its intrinsic morphological adaptability and spatial maneuverability, the swimming robot moves agilely in cluttered aquatic environments, even without feedback control. The assembled robot is 22.0 ± 0.1 cm in width, 47.0 ± 0.1 cm in BL, and 409.2 ± 0.1 g in weight (head 218.7 ± 0.1 g, tail 190.5 ± 0.1 g). BL, body length; DOF, degree-of-freedom.

The resulting mechanical design of the robot mimics the long, compliant vertebral structure and flexible fins seen in agile biological swimmers. These features help the passively to accommodate mechanical perturbations. With only two actuated DOFs, the robot can perform not only basic surge, yaw/pitch turning maneuvers but also roll rotations (Fig. 1C). With such maneuvers, the robot can swim in up to 7 m deep water in complex trajectories. Compared to current swimming robots, our swimming robot's passive adaptability allows it to navigate gaps, holes, and channels narrower than itself (Fig. 1B) and swim through complex 3D tunnels effectively, without low-level, individuated control of its many joints. We believe that such underactuated, maneuverable swimming robot designs are a viable solution to achieving the agility and versatility required for underwater tasks in complex, austere real-world settings.

Design

Swimming robot design and fabrication

The swimming robot has a fish vertebra mimicking morphology, formed by cascaded segments. Each segment includes a rigid spine bone, elastomer joints as intervertebral soft tissue, and four foldable fins (Fig. 2A–F).

FIG. 2.

The design, fabrication steps, actuation mechanism, and control system of the swimming robot. (A) The soft joints are cast from silicone in 3D printed molds. By changing the mixing ratio of 2 silicone materials (Dragon skin 10 [Shore A Hardness: 10A] and Smooth-Sil 960 [Shore A Hardness: 60A]; Smooth-On, Inc.), the joint stiffness can be tuned. (B) The foldable fin consists of a flexible plastic sheet layer (Stretchlon^® 200 Bagging Film, thickness: 0.381 mm) sandwiched by several 3D printed rigid fin frame parts. (C) The small torsion spring (spring constant: 0.121 lbf·in/360°, maximum torque: 0.042 lbf·in) inside enables it to fold in when encountering external force and expand back when no force is applied. (D, E) The soft swimming robot is formed by repeated cascaded segments. Each segment consists of soft silicone joints, 3D printed rigid spine bone, and four passive foldable fins. (F) The flexible vertebra structure can both bend and twist, which together with foldable fins contributes to passive adaptability. (G) The wire-driven robot is actuated by two waterproof servos. Each servo controls the yaw and pitch bending, respectively. By programming the actuation pattern, the robot can perform multiple maneuvers. Here shows how Yaw bending is generated when the blue wire controlling yaw is actuated/dragged. (H) The robot is controlled by a microcontroller for simple open-loop maneuver performance. It can also be switched to manual mode for remote control using a joystick.

The Acrylonitrile Butadiene Styrene 3D printed rigid spine bone supports the body structure and holds the soft joints and fins. The soft joints are cast from silicone in 3D printed molds. Their stiffness can be controlled by changing the mixing ratio of two silicone materials (Dragon skin 10 [Shore A Hardness: 10A] and Smooth-Sil 960 [Shore A Hardness: 60A]; Smooth-On, Inc.). In this study, we created five stiffness sets with a mixing mass ratio of 0:4, 1:3, 2:2, 3:1, and 4:0, respectively. By selecting stiffer silicone joints close to head and softer silicone joint close to tail, the robot body has a certain stiffness gradient, which enables the robot body to bend easier on tail side than head side.

The foldable fin consists of a flexible plastic sheet layer (Stretchlon^® 200 Bagging Film, thickness: 0.381 mm) sandwiched by several 3D printed rigid fin frame parts. The small torsion spring (spring constant: 0.121 lbf·in (pound-force inch)/360°, maximum torque: 0.042 lbf·in) inside enables it to fold in when encountering external force and expand back when no force is applied. The compliance of the vertebra structure and foldable fins contribute substantially to the passive adaptability of the robot.

The assembled robot size is 22.0 ± 0.1 cm in width, 47.0 ± 0.1 cm in body length (BL), and 409.2 ± 0.1 g in weight (head 218.7 ± 0.1 g, tail 190.5 ± 0.1 g).

Actuation mechanism

The 2-DOF cable-driven swimming robot is actuated by two pairs of nonstretchable wire (Ashconfish PE braided fish line, 90LB), to avoid any actuation delay caused by elastic cable. Each pair of wire lies in same plane and connects the rear body segment and is controlled by a separate servo (Fig. 2G). One servo-wire pair controls the yaw bending, while another pair controls the pitch bending. Having only two actuators lends to the simplicity of swimming robot, yet facilitates multiple maneuvers in 3D space, including surging and roll/pitch/yaw turning maneuvers.

Experiments and Results

This simple 2-DOF soft swimming robot can effectively perform surging motions and roll/pitch/yaw maneuvers in 3D space underwater. The adaptability of the flexible body and fins allows it to pass through obstacles and gaps smaller than itself.

Multiple maneuver performance

In this study, we focused on the most basic swimming robot maneuvers, including undulatory surging, pitch, yaw, and roll rotation (Supplementary Movie S2). Undulatory surging and roll rotation maneuvers are studied in a long rectangular water tank (120 × 45 × 30 cm). Two types of turning maneuvers, “tuna-like” yaw and “dolphin-like” pitch turns, were studied in a large water pool (Intex^® Rectangular Frame Pool, 300 × 200 × 75 cm) for adequate space.

We studied the maximum undulatory surging velocity achievable by the swimming robot at different servo actuation frequencies (Fig. 3A). Surging maneuvers are generated by actuating one of the two cable-driving servos in a sinusoidal sweeping pattern, with a frequency range of 0.08–2.06 Hz. Surging velocity is compared with our previous robot's performance (with 1-DOF, unstretchable wire, and a servo that rotates slower at high frequencies).³⁵ We recorded the system input power by measuring input current I and voltage U (11.0 ± 0.1 V) at certain actuation frequencies. The cost of transport (COT) is calculated as COT = (UI)/(mν), where m is robot mass and ν is surging velocity. Current and COT values at various frequencies are shown in Figure 3B. We also compared the COT versus velocity between our 2-DOF soft swimming robot and other robot systems (Fig. 3C).²⁵

FIG. 3.

Undulatory surging maneuvers performance. (A) Undulatory surging LV versus frequency. This maneuver is generated by actuating one servo in a sinusoidal sweeping pattern along frequencies between 0.08 and 2.06 Hz. The orange points indicate the performance achieved with our previous swimming robot version.³⁵ (B) The robot system's input current and COT for the undulatory surging maneuver at f = 0.34, 0.69, 1.03, 1.38, 1.72, 2.07 Hz. (C) A comparison of the COT versus velocity between our 2-DOF soft swimming robot and other swimming robot data from Ref.²⁵ Data points in (A, B) are the average of three trials, with standard deviation error bars. COT, cost of transport; LV, linear velocity.

In the study of undulatory surging (Fig. 3A), as the frequency increases, the surging velocity initially increases and then plateaus around 18.5 ± 0.8 cm/s (or 0.39 ± 0.02 BL/s), due to the output power limitations of the servo. Compared to our previous robot's performance (with 1-DOF, unstretchable wire, and a servo that rotates slower at high frequencies),³⁵ the maximum surging speed is increased from 12.1 ± 0.4 cm/s (or 0.26 ± 0.01 BL/s) to 19.3 ± 0.5 cm/s (or 0.41 ± 0.01 BL/s), a 59% improvement. At higher frequencies (1–2 Hz), the current robot swims two to three times more effectively, with a speed around 17–19 cm/s compared with previous version (around 5–7 cm/s). The COT of undulatory surging motion decreases as frequency increases and reaches a plateau at 207.7 ± 8.4 J/(m·kg), with a minimum COT of 198.5 ± 0.1 J/(m·kg), as shown in Figure 3B. By comparing the COT and surging velocity (BL/s) with other robot systems (Fig. 3C), our robot lies at the middle of both COT and velocity.

The robot can turn laterally (yaw) or dorsoventrally (pitch) by actuating yaw/pitch servos. As the yaw and pitch turning actuators are identical and axisymmetric to each other, we only tested the lateral (yaw) turning in horizontal plane as a representation. We studied the swimming robot's ability to perform two types of turning patterns. The “tuna-like” yaw turn (Fig. 4A) involves the robot flapping its tail laterally (horizontally) by sweeping the yaw servo in a sinusoidal wave, with a specific wave offset (25% of maximum servo range), while the pitch servo is set at the midpoint of maximum servo range steadily. The “dolphin-like” yaw turn (Fig. 4B) involves the robot flapping its tail dorsoventrally (vertically) by sweeping the pitch servo in a sinusoidal wave, with the yaw servo set at 25% of maximum servo range steadily. Both turning patterns are evaluated for turning angular velocity (AV) and turning radius versus actuation frequency, which ranged from 0.08 to 1.90 Hz. We also compared the turning AV versus turning radius between our 2-DOF soft swimming robot and biological systems (Fig. 4C).^39–45

FIG. 4.

“Tuna-like”/“dolphin-like” turning maneuvers performance. (A) AV and turning radius of the “tuna-like” turning maneuver versus frequency. The robot flapping its tail laterally (horizontally). (B) AV and trajectory radius of “dolphin-like” turning maneuver versus frequency. The robot flaps its tail dorsoventrally (vertically). (C) A comparison of the turning AV and turning radius between our 2-DOF soft swimming robot and biological systems.^39–45 Data points in (A, B) are the average of three trials, with standard deviation error bars. AV, angular velocity.

Comparing the yaw and pitch turning maneuvers (Fig. 4A, B), both angular velocities increased as actuation frequency increased. The “dolphin-like” pitch pattern reached a higher AV, 44 ± 1 deg/s, than the “tuna-like” yaw pattern, 35 ± 1 deg/s. However, the yaw pattern achieved a turning radius of 18.9 ± 0.6 cm (or 0.40 ± 0.01 BL) at higher frequencies, while the pitch turn radius remains the same at roughly 31.3 ± 1.3 cm (or 0.67 ± 0.03 BL) across the entire actuation frequency range. The slower “tuna-like” yaw turning velocity and larger turning radius at higher frequencies (>1.5 Hz) may be attributed to the yaw servo's inability to generate enough force or sweeping amplitude at high frequency to turn as effectively as expected. Comparing our robot's turning performance with other biological systems, the robot turning radius (BL) is relatively small and close to many other biological systems, which promotes movement in cluttered underwater environments. However, the turning rate is much slower than most biological systems.

We studied changes in roll rotation velocity at different actuation frequencies and phase lags (Fig. 5). Roll rotation is generated by two sinusoidal signals applied to pitch and yaw servos (Fig. 5C). The signals have identical amplitude and frequency but a quarter cycle phase lag. This pattern creates a circular trajectory (phase lags other than quarter cycle create elliptical trajectories) at the end effector (tail), which generates body roll rotation. The sign of the phase lag determines both the elliptical trajectory direction and the body roll direction. The roll rotation maneuver is accompanied by surging motion, which is caused by the roll rotation's propulsive force and the tail's circular sweeping. The roll rotation's AV and linear velocity (LV) with respect to actuation frequency at a quarter cycle phase lag are shown in Figure 4A. We recorded the system input current I and the COT for the surging motion that accompanied roll rotation at various frequencies, as shown in Figure 5B. Figure 5D shows the side view of a roll rotation maneuver, and Figure 5E shows the top view of roll rotation accompanied by surging and body twisting at f = 1.20 Hz.

FIG. 5.

Roll rotation (or spinning) maneuver performance. (A) The roll AV and accompanying surging LV versus different actuation frequencies and a performance comparison with the previous swimming robot.³⁶ (B) The robot's input current and COT for roll rotation and surging motion at f = 0.34, 0.69, 1.03, 1.38, 1.72, 2.07 Hz. (C) The roll rotation actuation maneuver, generated by applying two sinusoidal signals with a +/− quarter period phase lag to the yaw and pitch servos. The sign of the phase lag will decide the elliptical trajectory direction and, consequently, the body roll rotation direction. (D) Side view of the roll rotation maneuver at f = 1.20 Hz. The swimming robot rotates clockwise, and the orientation is marked by red dash arrow. The blue dash arrow points out the sequence of subfigures. (E) The top view of roll rotation accompanied by surging and body twisting at f = 1.20 Hz. The body twisting is shown by the helical alignment of fins marked by red dash line. Data points in (A, B) are the average of three trials with standard deviation error bars.

For the roll rotation maneuver performance shown in Figure 5A, the AV increases in a near linear manner as actuation frequency increases, before reaching a peak velocity, then begins to decrease due to the power limitations of servos. The LV of the accompanying surging motion increases as frequency increases and reaches a plateau. The AV and accompanying LV are significantly improved compared to previous results,³¹ especially for the roll AV which increases from 41 ± 1 to 107 ± 1 deg/s, a 161% improvement. The COT of accompanied surging motion decreases as frequency increases and reaches a plateau at 236.6 ± 9.4 J/(m·kg), as shown in Figure 5B.

A hypothesis for the roll rotation phenomenon with a theoretical model and experimental verification

We formed a hypothesis for the mechanism behind roll rotation based on our observations of the swimming robot and the following three facts: (a) compared to most fish vertebra (1-DOF), the soft swimming robot has a flexible vertebra articulation (2-DOF), enabling bending in 2D, (b) the robot fins orientation is passive, (c) the “no-fin” configuration test shows higher roll rotation performance compared to the “fins applied” configuration.

The hypothesis is based on the angular momentum conservation instead of the torque generated by fins. When the robot is actuated by the roll rotation signal pattern, the body motion resembles a “hooping motion” and can be decoupled to two kinematic components. One component is spinning along the vertebra, $ω$ , which is generated by actuation pattern directly from the view in relative coordinate that the curved body only spins but stays still. The spinning velocity $ω = 2 π f$ . Another is the body rotation along center of mass, $Ω$ , which is the curved body rotation in the world coordinate, besides spinning component $ω$ . To maintain conservation of angular momentum (supposing the robot started with 0 angular momentum while sitting still), the two kinematic components rotate in reverse directions, countering the angular momentum generated by each other. When there exists a body bending angle $θ$ between each segment, $ω$ would exceed $Ω$ , which consequently generates the body's overall roll rotation $Ψ_{r o l l}$ , where the AV $Ψ_{r o l l} = ω - Ω$ .

In this study, we show the roll rotation ratio simulation results for two simplified models, a robot with 2 segments (shown in Fig. 6A, B) and a robot with 10 segments (shown in Fig. 6A, and blue curve in Fig. 6C). The ratio $Ψ_{r o l l} ∕ ω$ (or can be rewritten as $Ψ_{r o l l} ∕ 2 π f$ ) is matching the output body's overall roll rotation $Ψ_{r o l l}$ to input spinning velocity $ω$ or servo input frequency f, which indicates how much percentage of the robot input spinning velocity/frequency is converted to global roll rotation AV.

FIG. 6.

Hypothesis and simulation model explaining the roll rotation mechanism. (A) The simplified 2-segment model and the 10-segment model for the real swimming robot. Each spine bone segment is a homogeneous cylinder with a radius r and height h = 2r. When performing roll rotation maneuver, there exists a bending angle $θ$ between adjacent segments. (B) The two-segment model theoretical relation curve of the ratio $Ψ_{r o l l} ∕ ω$ versus bending angle $θ$ . The ratio increases from 0 to an upper limit boundary of 1 when the bending angle $θ$ increases from 0 (straight body configuration) to $π$ (fully bent body configuration). (C) The 10-segment model theoretical relation curve of the ratio $Ψ_{r o l l} ∕ ω$ versus bending angle $θ$ , and the experimental ratio results at different bending angles ( $θ$ = 2.7°, 5.7°, 9.3°, 12.2°, 14.2°) and different frequencies (f = 1.38 and f = 2.06 Hz). The experimental results show a similar trend with divergence from the theoretical curve. (D) The experimental results of the ratio $Ψ_{r o l l} ∕ ω$ versus frequency at bending angle $θ$ = 14.2° body configuration. Data points in (C, D) are the average of three trials, with standard deviation error bars.

The simplified-model assumptions include the following: (a) the mass of each cylindrical spine bone segment is homogeneous, while the mass of bendable joints and head servo are ignored; (b) the simple kinematic model ignores the dynamic influence of external forces (e.g., water resistance, gravity, and buoyancy torque) and internal body forces (e.g., wire tension); (c) the robot is actuated by pitch and yaw servos with sinusoidal output of the same amplitude, but with a quarter period phase lag; and (d) the cascaded spine bone model bends homogenously in a plane. Details of the two-segment model equation derivation are shown in the Hypothesis-Supporting Theoretical Sodeling and Analysis section in Supplementary Information.

To verify the theoretical curve of the 10-segment model in Figure 6C experimentally, the pure roll rotation AV of no-fin configuration robot is tested at different bending levels from 1 to 5 (corresponding average bending angles of 2.7° ± 0.1°, 5.7° ± 0.1°, 9.3° ± 0.1°, 12.2° ± 0.1°, and 14.2° ± 0.1°) and two frequency sets (f = 1.38 and f = 2.06 Hz) (Fig. 6C orange and green dots and Supplementary Movie S3 shows the experiment demo).

As there exists a stiffness gradient along the body bending segments (stiffer near the head and softer by the tail), the bending is not homogenous at low bending levels. The average bending angle $θ$ at each bending level is approximately measured by the angle difference between the first and last segment divided by number of soft joints (for the 10-segment configuration, there are 9 soft joints). As shown in the figure, both frequency sets lie below the theoretical curve. This divergence is mainly caused by the nonhomogeneous distribution of mass, especially caused by the heavy mass of the servo head. However, both experimental results show a trend similar to the simulation result, which indicates that higher body bending amplitude results in higher roll rotation velocity converting ratio.

We also tested the body overall roll rotation $Ψ_{r o l l}$ and the ratio $Ψ_{r o l l} ∕ ω$ versus frequency ranging from 0.17 to 2.06 Hz, with a number 5 body bending level configuration (average bending angle is 14.2° ± 0.1°), as shown in Figure 6D. Both the $Ψ_{r o l l}$ and $Ψ_{r o l l} ∕ ω$ show two different trends for low and high frequencies, separated by the green line, which is defined as the “buoyancy-gravity torque barrier.”

At the low frequency region before the barrier, the input frequency (or power) cannot generate enough torque to exceed the buoyancy-gravity torque barrier. At that moment, the robot would only perform body spinning $ω$ , but not perform body rotation $Ω$ , which means $Ψ_{r o l l} = ω = 2 π f$ . As a result, the $Ψ_{r o l l}$ —frequency curve exhibits a roughly linear relationship, while the $Ψ_{r o l l} ∕ ω$ —frequency curve value is close to 1. At the frequency region after the barrier, soon after the torque generated by input frequency (or power) exceeds the buoyancy-gravity torque barrier, the robot would be able to perform both body spinning $ω$ and body rotation $Ω$ simultaneously, which means $Ψ_{r o l l} = ω + Ω$ . As a result, the $Ψ_{r o l l}$ —frequency curve shows a new approximate linear relationship with a lower slope, while the $Ψ_{r o l l} ∕ ω$ —frequency curve value reaches a new plateau close to 0.80 ± 0.02. As soon as the robot has enough input power to go over such buoyancy-gravity torque barrier, the ratio $Ψ_{r o l l} ∕ ω$ is a constant and is independent from input actuation frequency.

According to our theoretical hypothesis and model simulation, we believe such roll rotation mechanism requires a flexible vertebra structure which can bend in both yaw and pitch direction. As this roll maneuver is very similar to the “death roll” used by alligators during spin-feeding,¹⁸ we believe that this roll rotation mechanism can also be performance by nature swimming animals with flexible vertebral structures (e.g., alligator, dolphin, and sea otter) and might be regarded as parts of contribution to their spinning maneuvers.

Intrinsic morphological passive adaptability enables agile propulsion through multiple types of obstacles without feedback control

In this study, we focused on testing the swimming robot's passive adaptability in various obstacle-laden environments using undulatory surging and rolling maneuvers.

We decomposed the obstacle passing procedure (with unavoidable body collision) into three steps: Step 1—locate obstacles using sensors/cameras and adjust body orientation toward entrances or gaps between obstacle clusters, Step 2—the robot head successfully enters the entrance or gap, accompanied with unpredictable body collisions, and Step 3—the body passes through the obstacle successfully.

In real operations, there might be cases where sensors are not working well, leading to the failure of obstacle location in step 1. Even when obstacles are located successfully, the robot's head may be lodged before the body enters the obstacle field in step 2, or the body may get lodged in step 3. With so many uncertainties underwater, the robot should benefit from its intrinsic morphological passive adaptability to pass through obstacle clutter, especially for step 2 and step 3. The robot body is made flexible using silicone joints and a cascaded vertebral structure, allowing it to bend and twist its body to adapt to external forces when engaging obstacles or to squeeze through tortuous channels. Foldable fins can collapse passively, enabling the robot pass holes or gaps smaller than its body size. These features, together, contribute to its intrinsic morphological passive adaptability.

To measure the obstacle passing ability of the swimming robot, we first established test criterion. We developed several obstacle configurations with high collision probabilities in an underwater test bed. The obstacle configurations, representative of environmental obstructions common to complex underwater settings, are parallel bar (Fig. 7A), rectangular hole (Fig. 7B), straight channel (Fig. 7C), and meandering tunnel sets (Fig. 8A–C, F).

FIG. 7.

The obstacle pass-through experiments in bar, hole, and channel obstacle configurations. (A) The parallel bars configuration. The bars are marked by red dash line, with a 15.5 ± 0.5 cm spacing. (B) The rectangular hole configuration. The hole is marked by red dash lines, with a side length of 15.5 ± 0.5 cm. (C) The straight channel configuration. The channel, 15.5 ± 0.5 cm wide and 24.5 ± 0.1 cm long, is marked by red dash lines, with a side length of 15.5 ± 0.5 cm. The bars, holes, and channel spacings are narrower than robot's body cross-section width (22.0 ± 0.1 cm). (D–F) Shows the entry rate (D), pass rate (E), and average pass time (F) of undulatory surging (pitch) and roll maneuver. The number of trials (or sample size) in (D, E) is n = 40. The average pass time data in (F) are the average of 40 repeated trials with error bars as standard deviation.

FIG. 8.

The obstacle pass-through experiments in tunnel obstacle configurations. (A–C, F) are the planar “I,” “Z,” “U,” and 3D complex tunnel configurations. The tunnel is built by bendable ducts with an inner diameter of 25.4 ± 0.1 cm, slightly wider than the robot's body cross-section width (22.0 ± 0.1 cm). (D, E) Shows the pass rate and average pass time of undulatory surging (pitch/yaw) and roll maneuver for planar “I,” “Z,” “U” tunnel configurations (boxed in orange line). (G, H) Shows the pass rate and average pass time of undulatory surging (pitch) and roll maneuver for 3D complex tunnel configuration (boxed in blue line). The number of trials (or sample size) in (D, G) is n = 10. Data in (E, H) are the average of 10 repeated trials with error bars as standard deviation. (I) The yaw/pitch/roll direction definition.

To test the robot's ability to self-fold and pass through the gaps/holes narrower than its body cross-section width (22.0 ± 0.1 cm), we chose 15.5 ± 0.5 cm as the width of the gaps/holes/channels, which is about 70% of the robot's width. To control variables for different obstacle settings, we kept the same width for parallel bar (width 15.5 ± 0.5 cm), rectangular hole (side length 15.5 ± 0.5 cm), and straight channel (width 15.5 ± 0.5 cm, length 24.5 ± 0.1 cm) obstacle configurations. Considering the robot's axisymmetric shape and actuation patterns, we used vertical parallel bars and vertical channel configurations as the representation for all orientation cases of bars and channels. The meandering tunnel sets were built using bendable ducts (inner diameter 25.4 ± 0.1 cm) which are formed into planar “I” (Fig. 8A), “Z” (Fig. 8B), and “U” (Fig. 8C) tunnel configurations, as well as a 3D complex tunnel configuration (Fig. 8F) with several acute bends/corners.

The robot's obstacle passing ability is quantified by two attributes: successful pass rate and pass time. For swimming tasks that do not concern time and energy limitations, the pass rate would be regarded as the most essential aspect. However, if time or energy is limited, passing time would also be important.

The obstacle pass rate is composed of two measures: the first is the entry rate, which means the ability to successfully enter the entrance passively without any feedback control, corresponding to the obstacle passing procedure described in step 2. To measure the entry rate, the robot is placed facing the obstacle entrance from 10 to 30 cm away with an arbitrary position (for bars, rectangular hole, and straight channel configurations). Without any environmental information or feedback control, the robot swims toward the obstacle's entrance and the success of entering the entrance is recorded. The second measure is the pass-through rate, which means the ability of the robot to pass through the entrance after successfully finding it, corresponding to the obstacle passing procedure mentioned in step 3. To measure the pass-through rate, the experimental protocol assumes that the robot has successfully located the entrance. The robot starts from rest with its head inside the entrance. Each passing attempt is regarded as successful if the robot does not get stuck and is finally able to clear the obstacle within twice the averaged pass time; otherwise, it would be regarded as a fail case.

Another performance measure, the obstacle pass time, represents how effective the passing process is and shares the same experimental protocol with the pass-through rate. The time cost of an obstacle pass-through is measured from the start of robot movement toward the obstacle to the moment when the whole body has passed through and successfully cleared an obstacle.

In theory, the entry rate can be improved by adding proximity sensing and closed-loop feedback control, while the pass-through rate and pass speed are mainly influenced by the passive adaptability/flexibility and swimming maneuvers of the robot.

The obstacle pass-through experiments were conducted using two maneuvers: the undulatory surging maneuver and the roll rotation maneuver. For the 2D meandering tunnel sets, the body bending direction of undulatory surging maneuver would have an influence on both pass rate and pass time, and we tested yaw (horizontal bending) and pitch (vertical bending) undulation surging maneuvers separately during these experiments.

Figures 7D–F and 8D, E, G, and H show the obstacle pass-through experiment result of entry rate, pass rate, and pass time in bar, hole, channel, and tunnel obstacle configurations for different maneuvers. As shown in the experiment (Supplementary Movie S4), the swimming robot encounters each type of obstacle physically with passing duration and the body deformation level in varying degrees. With the help of the passive adaptability enabled by compliant body and different swimming maneuvers, the robot can pass through the obstacle sets with a relatively high success rate (Figs. 7D, E and 8D, G).

In addition, each maneuver (undulatory surging by pitch/yaw servo, roll rotation) performs differently in different obstacle configurations. The obstacle pass time results (Figs. 7F and 8E, H) show that the undulatory surging (pitch) maneuvers work better in narrow, parallel obstacle configurations, such as bars and channels, while the roll rotation maneuver's pass-through rate exceeds the other gaits and passes faster through the narrow hole and tunnel configurations.

For the complex 3D tunnel configuration (Fig. 8F), there exist five 90° corners in various directions that require drastic reorientations of a robot navigating through it. It is a challenge for the undulatory surging maneuver's (thunniform) 2D planar head sweeping motion to navigate through 3D turns and for the 2D planar body bending to adapt to 3D turns. This is evidenced by the divergence of yaw/pitch undulatory surging maneuver performance in the 2D planar tunnel sets (Fig. 8D, E). The pitch (vertical bending) undulatory surging maneuver does not accommodate horizontal corners well, which leads to lower pass rate and longer average pass time compared to yaw (horizontal bending) undulatory surging maneuvers. By comparison, the circular head sweeping motion and rotating body bending generated by the roll rotation maneuver help the robot reorient itself and adapt its body configuration to find openings and pass through the 3D tunnel turns of various orientations.

Swimming performance demonstration

The high maneuverability and passive adaptability of the swimming robot allow it to perform and follow complex motion trajectories and complete tasks involving frequent encounters with obstacles. In this study, we provide two physical experiment records that demonstrate these capabilities (Fig. 9 and Supplementary Movie S5): the first experiment involves the diving and ascent of the robot in a 7 m deep water pool and required the robot to execute roll, pitch, and yaw maneuvers to swim in a complex route (Fig. 9A). In this experiment, the robot is controlled remotely using a joystick. The second experiment involves robot swimming toward a tunnel and adjusting its body position and orientation to enter a hole on the right side of the meandering tunnel (Fig. 9B). Once it enters the hole, the robot executes roll rotation maneuvers to successfully pass through the narrow and winding 3D tunnel. In this experiment, the robot operates in open-loop mode, constantly performing roll rotations until it passed through the tunnel.

FIG. 9.

Two sets of sequenced images demonstrating the robot swimming performance. (A) A time sequence trajectory showing swimming performance in 7 m deep water tank. (B) A time sequence images of swimming toward the tunnel and pass it with the contribution of roll rotation maneuver and compliant body. The upper and lower sets of images are from two cameras and two perspectives simultaneously.

Discussion and Conclusion

Our swimming robot can swim through complex, obstacle-laden underwater environments due to its high maneuverability and passive adaptability.

The soft swimming robot can perform basic swimming maneuvers such as surges, pitches, and yaws and can also achieve a unique roll rotation maneuver generated by asynchronous actuation of its two cable-driving servos.

The COT for surging motions from undulatory maneuvers (Fig. 3B) is always smaller than those from the roll rotation maneuver (Fig. 5B). One explanation for this phenomenon is that as part of the roll rotation maneuver input power is transferred to roll angular motion, while most of the input power of undulatory maneuvers is mainly transferred to surging.

In addition, we developed a naive kinematic model to explain how the intrinsic roll rotation maneuver is generated and how the body curvature (Fig. 6C) and servo input frequency (Fig. 6D) would affect the roll rotation velocity (in additional data A Hypothesis for the Roll Rotation Phenomenon with a Theoretical Model and Experimental Verification section). Based on the model and validation experiment, we find two general conclusions for this roll rotation maneuver: (a) Higher body bending curvature results in higher roll rotation velocity; (b) the ratio $Ψ_{r o l l} ∕ ω$ is constant at certain bending angle configurations and is independent from input actuation frequency. Both the model and conclusions can be expected to be generalized to represent other similar roll rotation system and replicate such roll rotation maneuver.

We tested the roll angular rotation velocity for no-fin configuration and it reaches 582 deg/s at f = 2.03 Hz (Fig. 6D), which is more than five times the maximum roll rotation performance (108 deg/s, shown in Fig. 5A) of the fin-expanded configuration. Compared to roll rotation capabilities achieved in previous swimming robot research (204 deg/s),⁴⁶ our robot can achieve a higher roll rotation AV with fewer actuators (six servos were used⁴⁶). Such high-performance roll rotation maneuvers would be essential for fast body orientation adjustments or other possible tasks requiring high roll rotation velocity.

The multiple maneuvers discussed in this article not only enable free-space swimming underwater but also together with the compliant body contribute to agile propulsion in cluttered aquatic environments. As we found from our preliminary obstacle-passing tests (Figs. 7 and 8), different types of maneuvers benefit different obstacle configuration passing effectiveness (in both time and success rate). According to obstacle passing results, a possible multimaneuver combination strategy aimed for certain classified types of obstacle clutters can be programmed and controlled to achieve higher passive adaptability in real cluttered aquatic environments in the future.

As there is a high chance of encountering known or unknown randomly distributed obstacles underwater, our soft swimming robot is expected to be a good solution for many underwater tasks, such as exploring complex seabed environments, inspecting underwater equipment, and rescuing people who get trapped in an underwater cave.

Currently, the robot is still a tethered version and does not have any feedback control, which would limit its mobility space and active adaptability. By converting the robot to an untethered version, adding vision, orientation, pressure feedback, and high-level dynamic control, our swimming robot would be more controllable and capable for real tasks.

Footnotes

Acknowledgments

The authors thank Prof. Daniel Goldman for lending 3D printing machine and fish tank for both design and parts of experiments. The authors also thank the George W. Woodruff School of Mechanical Engineering and Prof. Francois Guillot for using acoustic water tank and space for parts of experiments.

Authors' Contributions

B.L. designed the swimming robot and carried the experiments. Both authors contributed to conceiving of the research and writing of the article.

Author Disclosure Statement

No competing financial interests exist.

Funding Information

Supported by George W. Woodruff School of Mechanical Engineering.

Supplementary Material

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Supplementary Material

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