Development and Modeling of a Biomimetic Punting Unmanned Underwater Vehicle

This thesis details the development of a novel propulsion system for unmanned underwater vehicles (UUV’s) inspired by the punting locomotion of the ‘Little Skate’. The hybrid legged, gliding and punting gait is a potential enabling technology for UUV access to complex littoral environments. Design, development and initial trials with the prototype vehicle are presented. A combination of video motion capture and on-board inertial sensing is validated and used for preliminary analysis of a limited set of punting gaits. The results indicate the importance of matching vehicle morphology and kinematics to achieve effective locomotion and that the prototype is viable to be used as a validation tool for a general punting dynamic model that is in development. A practical method for modeling the vehicle is also presented with results comparing the model to experimental trials.

. Flapping foils in the lab  and in the field, , , and [Ade], have been implemented in vehicles using various swimming schemes, such as those akin to the ray , tuna , or turtle .

Motivation
Complex underwater environments are difficult to navigate through, hindering efforts of robotics to operate in these areas. Over time, aquatic animals have adapted different forms of propulsion to move through these complex undersea environments. Littoral zones, specifically, frequently have strong currents, and obstacles, and their shallow depths limit operations of UUVs in these areas. Researchers in the past have taken inspiration from ocean creatures to design vehicles better suited for specific environments. Taking motivation from the 'Little Skate', a prototype 'punting' vehicle was designed, developed and tested with the goal of improving access to near bottom and near shore environments. It is hypothesized that this propulsion method will improve the ability of underwater vehicles to move along the sea floor in complex environments in the hopes of aiding in scientific study or military operations.

Thesis Content
The following chapter, Chapter 2, is a review of literature pertaining to underwater vehicles, the Little Skate, and its mode of locomotion termed 'punting'.
The background information is provided to give context the work presented in this paper. Chapter 3 details the development and testing of the mechanical prototype punting vehicle. Chapter 4 provides an introduction to modeling the punting vehicle and results obtained. Chapter 5 provides insight into sources of error and future work. Finally, the conclusions drawn from the present work are stated, followed by the bibliography.    Listak et al. [2007] developed a bio-inspired fish-like vehicle prototype for environmental monitoring shown in Figure 2.1.1. The 16 kilogram, 1.5 meter long vehicles consists of 3 flippers. One, located at the rear, acts as a rudder and provides the main propulsion, while the other two are used for additional propulsion and depth control. The vehicle has active buoyancy control, an inertial measurement unit, cameras and sonar, and can be towed using the flippers solely for depth control . The vehicle was tested in its towing configuration to analyze its ability to submerge and ascend using its fins. When towed, it was found the vehicle was suitable for near bottom visual inspections in areas of volatile sediments with the ability to submerge and ascend at adequate speeds to follow the irregular bottom.   Flipperbot, shown in Figure 2.1.2, is a vehicle developed to study the mechanics of the terrestrial locomotion with flippers. ] The vehicle's design is based on sea turtle hatchlings and their movement through sand.
The vehicle is 40cm wide by 19cm long and consists of an aluminum body with four servo motors attached. Two motors lift the arms up and down while the other two move the flippers forward and backward. The servos are used together to create different gaits to propel the vehicle over a sand-like medium. The vehicle was used to gain insight into the principles of flipper-based locomotion on granular media. FlipperBot was tested with two different wrist configurations and various gaits.
A free wrist configuration where the flipper that sinks into the sand is allowed to rotate with respect to the arm that drives it was found to to greatly outperform a fixed wrist that is rigidly attached to the arm. The performance of the vehicle was also sensitive to flipper penetration where a slight decrease in penetration led to a greater decrease in step displacement. This vehicle is not ready to be deployed in open ocean environments but these tests have given insight into amphibious propulsion of marine vehicles.   The Institute of Computer Science and Foundation for Research and Technology in Heraklion, Greece has developed a multi-functional robot inspired by the octopus. The vehicle body is made of PMC-746 urethane rubber, cast to form interior spaces that hold the electronics and buoyancy elements. 8 legs, each 20cm long and driven by its own waterproof micro-servomotor, are arranged symmetrically about the body. The vehicle propels itself by moving its 8 arms in a synchronous sculling motion with a fast propulsion phase and slow recovery phase, taking advantage of the large inertial forces incurred through large accelerations.
The vehicle is able to achieve speeds of 0.26 body lengths per second and can perform turning maneuvers through asymmetric movement of the legs. The vehicle is also able to grasp objects between two of its legs and propel itself forward with the remaining limbs to carry an object through the water. This prototype has great potential for future vehicles that can adapt to a variety of tasks and would perform well in stealth operations where its biomimetic movement would hide it from investigation.   Punning et al. [2004] details the development of a ray like vehicle built using Electroactive polymers (EAPs). EAPs are materials whose shape can be alter by the direct application of an electric field and are used to mimic the behavior of muscles.  uses 16 of these artificial muscles in a vehicle that replicates the rajiform locomotion used by ray and skates. In rajiform swimming, the animals propel themselves by passing waves through their pectoral fins. With 8 of these EAP muscles in each wing, the vehicle was able to propel itself by coordinating the contraction of the muscles to create thrust generating waves in the latex fins. This vehicle still has offboard computing and power, but the prototype shows the potential of this type of propulsion mechanism.
These vehicles are all examples showing the variety of vehicles that have been biologically inspired and many can provide benefits to a vehicle designed to perform a specific task or operate in a specific environment. The aim of the vehicle in this paper is to operate in the near-bottom or near-shore complex environments such as the surf zone, rivers, or estuaries.

Crawling Vehicles
There has been active interest in designing vehicles to operate in these complex environments near shore environments, not all of which has centered on biologically  MARC-1 can be controlled from shore or floating platform in depths up to 5 meters and distance from the control station ranging up to 165 meters. The vehicle is equipped with sensors to gather environmental data along the shoreline.   Scripps Institute of Oceanography  has developed a deepsea bottom crawler that provides a stable platform for data collection to depths of 6,000 meters for up to 6 months. The vehicle can be used for a wide variety of boundary-layer measurements near the sea floor and can collect water samples and oxygen concentrations. Wood et al. [2013] at FIT also developed a remotely operated crawler/flyer that moves along the bottom collecting data or investigating areas of interest but also has the ability to inflate additional buoyancy bladders and move through the water column with thrusters. This allows the vehicle to move quickly over adverse terrain and avoid sensitive areas such as reefs without damaging the sea life.

Underwater Walking Vehicles
Aside from crawlers researchers have also looked toward walking vehicles for access these complex regions.   Another amphibious hexapod robot is AmphiHex-I developed by Zhang et al.
[2016]. This vehicle is very similar to AQUA but has legs than can transform from the curved legs used by RHex to flat flipper like appendages that can be used to swim through the water. The vehicle performed well in difficult terrain, passing through soft muddy or sandy bottoms as well as being able to propel itself in water.
Figure 2.3.4: 3D models of attachable walking skid for sea bed ROV's.  Further research into sub sea walking vehcles lead to the development of the adaptable walking skid by  which also uses the hexapod configuration to move along the sea floor. The skid can be attached to ROV's giving them the ability to walk underwater. The skid has higher degrees of freedom in the legs than seen in Aqua or Amphihex. The skid provides a stable platform that is resistant to seabed currents when performing sub-sea operations such as data collection or pipeline inspection.
Whether crawling or walking, underwater vehicles have trade-offs in obstacle avoidance, payload sizes, mission times, or resistance to currents and waves that make no one vehicle perfect for exploring the surf zone.

Little Skate
This  In order to gain fundamental insight into punting as a method of vehicle locomotion, a legged mechanical prototype was designed and constructed.   side profile is that of a NACA 4412 airfoil and was chosen for its significant camber to provide increased lift during the glide phase. The body was 3D printed from ABS plastic in ten separate pieces which can then be assembled into four sections: a front section, back section, and the left and right wings. After printing but before being assembled, the pieces were waterproofed by subjecting the parts to an acetone vapor bath which dissolved the outer layer of the ABS pieces enough to allow it to flow and seal the microscopic holes that form between layers during the printing process. The pieces were also covered with several coats of polyurethane and waterproof paint to further prevent water from penetrating into the ABS.           When the vehicle is at rest it reaches an equilibrium between the spring in the tail and the hydrostatic wrench where the vehicle has a constant pitch angle before the legs kick. The tail also tends to impact the floor as the vehicle glides downwards.

Design and Construction
The spring in the tail works to soften the impact, decreasing any jerks imparted on the vehicle. The tail is also equipped with foam to make it neutrally balanced to eliminate any gravitational forces from the tail on the body.

Testing
In order to evaluate the performance of the mechanical prototype it was subjected to in-water trials at the University of Rhode Island wave tank facility. A characteristic motor speed of two revolutions per second was chosen and the vehicle was run for two successive kick cycles with a varying pause length between the cycles. Initial tests were limited to two kicks due to limits imposed by the field of view of the camera and to limit the effect of variations in the (    The experimental setup is shown in Figure 3.2.3. The vehicle was placed on a solid, level floor covered with a non-slip material for the vehicle feet. Starting blocks were added to provide a repeatable kickoff and the scaffolding above the test area was used for tether management. The tether was required to provide power and communication to both the motor and on-board sensors.

Data Analysis
The vehicle trajectory was captured with a Go-Pro 3+ video camera and then the motion was extracted from the video using a Speeded Up Robust Feature (SURF) tracker. The Go-Pro has a fish eye lense allowing it a larger than normal field of view, however the distortion must be removed before an analysis can be done on the video. Using multiple calibration images such as that in Fig     last. These images also show evidence of some roll instability which will cause some error in the pitch and height data extracted from the video.     to 1200ms. This figure shows a plot of the pitch at the end of the first glide versus the pitch at the end of the second glide. A tight cluster corresponds to a higher repeatability in the second kick and glide phases. The pause length of 1200ms was found to have the tightest cluster of trials and therefore the greatest similarity in movements across all trials.

Discussion
From these results the following can be shown: 1. Different pause lengths have a significant effect on the trajectory and speed over ground of the vehicle.
2. The vehicle does not passively return to the same pitch at the end of each kick and glide phase.
3. Ground contact between successive kicks affects the repeatability of the kick and glide phase motions.
The different pause lengths have a considerable effect on the trajectory of the vehicle. If the pause is too short, the feet will not contact the ground. If the pause length is too long the vehicle will contact the ground before kicking, effectively halting the forward motion of the vehicle, as seen in Figure 3.3.7. Figure 3.3.8 shows a peak in speed over ground at a pause length of 1000ms and shows a trend of increasing speed over ground with an increase in pause length. For the longer pauses, the vehicle pitches down after leg contact so that when the legs kick, it propels the vehicle at a lower angle, as can be seen in the trajectories in To achieve stable, steady propulsion the vehicle must return to its initial pitch angle over the kick and glide phase. shows the smallest change in pitch angle but achieves a lower speed over ground than the other pause lengths. The spread decreases as the pause length increases which appears to indicate that at longer pause lengths the vehicle spends more time in contact with the bottom which levels out any variations in roll and pitch that occurred while the vehicle was gliding and the vehicle begins to return to its static initial orientation before the legs come in contact with the ground initiating the second kick phase. While this provides a repeatable kick and glide phase, it is not energetically desirable as it implies a stop-start motion with energy lost at every contact.

Introduction of a Practical Modeling Approach for a Punting Vehicle
From the video collected in the testing of the prototype, the motion of vehicle could be separated into different phases. Each of these phases require their own model to predict the motion.

Glide Phase
A simplified 2-dimensional model was developed in order to provide insight into the vehicle dynamics during the glide phase of the 'punting' motion as well as to provide a theoretical reference for the results obtained through experiment.

Kinematics
The general equations of motion for the vehicle in 2 dimensions are as follows .
Where u is surge, v is heave, w is sway, p is roll, q is sway, and r is pitch. The distance from the origin to the vehicle's center of gravity are x g , y g , and z g . (d) The origin is at the center of gravity: x g = 0, y g = 0, z g = 0 3. The tail has no effect during the glide phase.

The vehicle can be treated as an ellipsoid of similar dimensions
After applying assumptions items 2a to 2d, eqs.

Added Mass
To find an approximate added mass of the vehicle, assumption 4 allows us to calculate it as an ellipsoid as shown in Figure 4.4.1. with R 1 = .35m, R 2 = .07m, and R 3 = .305m. Added mass coefficients for 3 dimensional bodies can be calculated by using strip theory which integrates the added mass coefficients of the cross sections along one axis to give an approximate coefficient for the entire body.  Integrating along R 1 gives a cross section in the shape of an ellipse with radii R 2 and R 3 . The added mass coefficients for an ellipse are shown in Figure 4.4.2 with m 11 being a force in the horizontal direction due to a unit acceleration in the horizontal direction, m 22 is a vertical force due to vertical acceleration and m 66 being a moment due to unit rotational acceleration about the origin.   The added masses for the vehicle were calculated with the integrals shown in eqs. (7) to (9) where ρ is the density of water.

Moment of Inertia
The rotational moment of inertia, I zz of the vehicle about its center of gravity was obtained from a 3 dimensional model of the vehicle body created in Solidworks, where the volume of the vehicle, V veh and center of buoyancy were obtained from a Solidworks model, d b is distance between the center of gravity and the center of buoyancy and g is the acceleration due to gravity.

Lift and Drag
Due to the irregular shape of the vehicle and the dynamic motion of the vehicle, modeling of the vehicle as a static foil failed. Instead the fluid force were modeled as only drag on a body. Vertical and horizontal drag coefficients were found using flow simulations on the solidworks model.

Munk Moment
The Munk moment is a moment imparted on slender bodies when the body travels at an angle of attack to the flow . The moment tends to drive the body broadside to the flow with a magnitude described in equation eq. (14).

Force Balances
The forces are added to the kinematic equations, eqs.

Iterative Calculations
Using the simplified equations of motions, defined coefficients and specified forces, the motion of the vehicle was modeled in steps with a time increment of .01 seconds.

Body Referenced Accelerationṡ
2. Body Relative Velocities 3. Position 4. Inertial Frame Velocities The results were plotted as followed and compared to the trial data extracted from video.       The results from the modeling compared to the data extracted from the trial videos are shown in figs. 4.9.1 to 4.9.9. The model is able to predict the general trends captured in the video, however, the magnitudes of the accelerations do not match, and the error in acceleration propagates through to the other modeled values. Throughout the process of modeling the vehicle, the forces were estimated in multiple different ways but varied little between methods. The coefficients of added mass for the vehicle affected the greatest change in accuracy in the modeling, better calculations or measurements of these coefficients would greatly improve the modeling of the vehicle.

Results and Discussion
CHAPTER 5

Sources of Error and Future Work
There are several sources of error that affect the results shown in the paper.
Error in the modeling is likely caused by the irregular shape of the vehicle and the lack of an accurate method estimate the lift, drag and added mass forces on the vehicle. The data collected from the video could also be inaccurate due to motion into or out of the frame that cannot be captured by one camera alone. The current prototype can be used for investigation into varying morphologies and gaits to maximize speed and minimize transport cost. The prototype was designed with large amounts of variability that allow for a wide range of possible experiments.
Further investigation can also be performed to determine the effect due to a change in ballast as well as the relation between the center of gravity and the force vector

CHAPTER 6 Conclusions
This thesis details the development and preliminary dynamic trials of a punting underwater vehicle along with preliminary modeling of motion of the vehicle.
In-water trials showed that the motion capture algorithm can accurately measure vehicle position and velocity which can be used to validate hydrodynamic models.
The development has also provided insight and experience that will be used in the design of future punting vehicles. The trials also identified an optimal pause between kick cycles to maximize speed over ground, however at this point in time it does not lead to a steady state condition across successive kicks. Open loop control was chosen for simplicity in the design of the prototype and also to observe the passive stability of the vehicle. The results show that the vehicle will require feedback in both pitch and altitude to provide adequate control of a punting vehicle. A practical method for modeling of the vehicle is presented and based on the current results, further refinement is needed to accurately predict the motion of the vehicle. The vehicle can be optimized to lessen the extreme changes in pitch and increase glide time to improve performance. From the insight gained with this prototype, future vehicles can be designed to be more easily modeled. Finally, the vehicle has proven that punting is a feasible method of propulsion for undersea vehicles and the platform provides multiple avenues for future work.