© 2002 by The Society for Integrative and Comparative Biology
Maneuvering and Stability Performance of a Robotic Tuna1
1 Mechanical and Instruments Division, Charles Stark Draper Laboratory, 555 Technology Square, Cambridge, Massachusetts 02139
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The Draper Laboratory Vorticity Control Unmanned Undersea Vehicle (VCUUV) is the first mission-scale, autonomous underwater vehicle that uses vorticity control propulsion and maneuvering. Built as a research platform with which to study the energetics and maneuvering performance of fish-swimming propulsion, the VCUUV is a self-contained free swimming research vehicle which follows the morphology and kinematics of a yellowfin tuna. The forward half of the vehicle is comprised of a rigid hull which houses batteries, electronics, ballast and hydraulic power unit. The aft section is a freely flooded articulated robot tail which is terminated with a lunate caudal fin. Utilizing experimentally optimized body and tail kinematics from the MIT RoboTuna, the VCUUV has demonstrated stable steady swimming speeds up to 1.2 m/sec and aggressive maneuvering trajectories with turning rates up to 75 degrees per second. This paper summarizes the vehicle maneuvering and stability performance observed in field trials and compares the results to predicted performance using theoretical and empirical techniques.
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INTRODUCTION |
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SYNOPSISINTRODUCTIONVCUUV SYSTEM DESCRIPTIONFIELD TRIALSMANEUVERING RESULTSHYDRODYNAMIC MODELSTABILITYMANEUVERINGDISCUSSIONSUMMARYReferences |
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Unmanned Undersea Vehicle (UUV) technologies have evolved in recent years to produce highly functional and capable platforms for a wide variety of undersea missions. As supporting technologies have progressed, so have the mission requirements. Today's UUV missions require a variety of capabilities which in some cases can be mutually exclusive: high transit speed, long range and duration, maneuverability and station keeping ability. Fish and marine mammals have captured the interest of vehicle designers as they are able to cruise great distances at significant speed, maneuver in tight spaces and accelerate and decelerate quickly from rest or low speed with the same integrated propulsion and steering system. Although trade-offs exist between efficient transit and maneuverability in marine animals (Webb, 1994
), engineers have the luxury to select the most desirable attributes to mimic in their designs.
In recent years, research in the fluid flow mechanisms used by fish and marine mammals for propulsion and maneuvering has demonstrated the utility of bio-propulsion for undersea vehicles. Barrett and his collegues (Barrett, 1996; Barrett et al., 1999) illustrated with his RoboTuna apparatus that manipulation of the body of an undersea vehicle in a fish-like manner could enhance energetic performance significantly. Wolfgang et al. (1999) showed that unsteady fish-like movements produce large fluid dynamic effects which can dramatically affect propulsion and maneuvering performance.
Conventional methods for improving unmanned undersea vehicle (UUV) performance (low drag hull profiles, propeller design, energy storage technology) have made little progress in improving propulsive efficiency and maneuverability. Conventional UUVs employ a long slender hull with a propeller as the main propulsor and moveable lifting surfaces which provide maneuvering control. Although several advanced demonstrations have been made in recent years with conventional designs, these types of vehicles are fundamentally limited in their maneuvering performance. Typically requiring several body lengths turning diameter, these vehicles can have fatally poor performance at low speeds. Attempts to improve low speed performance by using cross-axis thrusters have been effective but the net result is loss of useful hull volume and degraded performance at higher speeds.
In this paper we present results and analysis of the first engineering demonstrations of the Draper Laboratory Vorticity Control UUV (VCUUV), a prototype flexible-hull UUV which propels and maneuvers like a tuna. Named after the vorticity control flow control mechanisms employed by fishes to propel and maneuver, the VCUUV is an engineering approximation of the form and movement of a large yellowfin tuna (Thunnus albacares). Across the broad spectrum of fish form and movement, the tuna was selected as our natural model to emulate as they are streamlined, possess a rigid forebody and propel with low amplitude movements in conjunction with a high performance hydrofoil (caudal fin) (Dewar and Graham, 1994). Renowned as a highly efficient cruising fish, the tuna is not considered a highly maneuverable fish compared to other fishes (Blake et al., 1995). Despite their maneuvering limitations, tunas outperform conventional rigid undersea vehicles by a large margin, even at low speeds where maneuverability generally suffers.
Fish-like propulsion and maneuvering is suited to meet the challenges of today's undersea missions. These missions often require long transit, long duration on site, loitering without loss of power, operation in close proximity to objects for docking, tagging, etc., and in dynamic environments such as in shallow water near the beach zone. Fish-like propulsion and maneuvering may prove to be essential in realizing these missions in that fish-like maneuverability may not be as energetically taxing as conventional means of generating large side forces (such as thrusters) in varying conditions. Fish are not poor performers at low velocities like conventional vehicles. In fact, speed is not a requirement for maneuverability as illustrated with the rigid-bodied boxfish (Walker, 2000) and the fast start acceleration of fish from rest (Domenici and Blake, 1997). Fish-like propulsion and maneuvering marries the benefits of range and speed of conventional low drag hulls driven by propellers, with the ability to maneuver precisely when necessary. Although design trade-offs between transit and maneuverability performance must be made, flexible fish-like hulls provide more engineering options for vehicle design.
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VCUUV SYSTEM DESCRIPTION |
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Recent work at MIT with the RoboTuna apparatus (Barrett, 1996; Barrett et al.,
1999) inspired construction of the 2.4 m, 173 kg VCUUV prototype (Fig. 1). The VCUUV is fully autonomous and is a major departure from the externally manipulated and powered MIT RoboTuna apparatus. Although not intended as an ocean-going vehicle, the VCUUV contains all of the components required to execute autonomous missions: onboard energy, actuation and control. Figure 2 illustrates how the vehicle length is divided equally between a rigid forebody which houses the electronics, batteries, ballast and hydraulic unit, and a flexible articulated tail-caudal fin assembly.
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The VCUUV is an engineering approximation of the yellowfin tuna. The body shape was directly scaled from a casting of a 1 m long animal obtained specially for this purpose. No corrections were made to adjust for changes in body shape between the 1 m fish and the 2.4 m vehicle. To replicate the fin geometries, photographs of recently captured specimens were scaled and major fin geometries were averaged. Standard symmetric airfoil sections (NACA 0015) were utilized for all the fin profiles based on chord and thickness measurements. Although an engineered system such as the VCUUV can never be completely true to the natural model, the VCUUV is an excellent replica. Small deviations from the natural model were made in the pectoral fins, the size of the dorsal and anal fins, and the omission of the first dorsal fin, pelvic fins and finlets. We believe these deviations have a small effect on overall performance due to the small projected areas involved compared to the tail and caudal fin. Barrett (1996)
also produced good results with a tuna platform which also ignored these elements.
The vehicle has been successfully operated in shallow, controlled environments to evaluate its propulsion/maneuvering system. Vehicle design and fabrication issues including sizing of actuators, design of articulated body, pressure hull design, and on-board intelligence, sensors and power are described in detail by Anderson and Kerrebrock (1997, 1999). The VCUUV was designed to operate in freshwater environments at depths less than 10 m at typical live animal cruise speeds near one body length per second.
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FIELD TRIALS |
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Early field trials (April–June, 1998, at University of New Hampshire test tank) focused on engineering diagnostics and tuning of the hydraulic system and control system performance. Hydraulic pressure, control gains, and desired tail kinematics were adjusted to give good tracking performance for frequencies up to 1 Hz. Tail oscillations above 1 Hz were not pursued due to larger than expected forces which led to poor tail control performance. Simple maneuvers were explored including coasting turns and biased swimming movement resulting in circular trajectories. Because of the short distances available in the UNH tank, steady state swimming at terminal velocity could not be achieved. Thus, field trials were moved to local freshwater lakes for longer duration and higher speed tests.
During the summer and fall of 1998, the VCUUV was tested in freshwater lakes in Hopkinton State Park and Nickerson State Park. These sites were chosen for their proximity to Draper Laboratory and their clean, undisturbed fresh water. A systematic study of straight swimming parameter variations was completed as well as several basic open and closed loop horizontal plane maneuvers. The swimming parameter study involved variations around a baseline parameter set based on the best results reported by Barrett (1996) for self-propelled optimal motion. Approximately 20 straight swimming cases were studied including variations of frequency of oscillation, amplitude of caudal lateral movement, caudal fin angle of attack, and caudal fin phase with respect to the body wave. Maneuvering experiments were done for straight swimming with varying linkage bias angles and full deflection coasting turns.
A typical experimental run began with the vehicle at rest and submerged approximately 1.5 m while baseline inertial data were collected. The vehicle then began the swimming tail motion that accelerated the vehicle to steady state velocity. The typical acceleration period was 20–30 sec for 1 Hz tail oscillation. After swimming for a total of one minute, the vehicle coasted to a stop while the tail was held in a straight position. The tail movement for swimming adhered as well as possible to the kinematics reported by Barrett (1996) for optimal performance of the RoboTuna.
The maximum speed attained in the field trials was 1.25 m/sec (2.4 knots) at 1 Hz tail oscillation while under heading control (closed loop control using compass feedback). Without heading control, the maximum speed attained was 1.19 m/sec (2.3 knots). We do not report statistical variances on our results as speed measurements were only made during a few select runs by the addition of a small external speed sensor mounted to the top of the pressure hull, protruding beyond the estimated boundary layer thickness. The speed sensor was a custom designed calibrated free-wheeling propeller which was instrumented with four magnets attached to its shaft. A Hall-effect sensor was used to count the rotations of the propeller shaft to obtain speed. Calibration by timed distance confirmed that the velocity error was less than 5%.
The measured vehicle speed was 16% less than that predicted by Strouhal scaling of the MIT RoboTuna results which may be due to differences in the kinematics between the VCUUV tail motion and that of the RoboTuna. Although morphologically similar, the VCUUV and RoboTuna are not identical platforms. The VCUUV utilizes four active links to achieve the desired body undulation whereas the RoboTuna has eight, six of which are independently controlled. Thus, exact duplication of the kinematics was not possible. Using the same length reference (L, length from nose to caudal fin pivot), the VCUUV achieved 0.61 lengths per second (L/sec) whereas the RoboTuna achieved 0.65 L/sec. Unfortunately, degraded performance of the hydraulic system above 1 Hz did not allow the VCUUV to achieve the design speed of 1.0 L/sec. Acceptable linkage trajectory tracking performance above 1 Hz could not be achieved because of phase lag caused by the high loads at those frequencies.
The VCUUV was very stable in straight, forward motion. A small amount of yaw oscillation was present during swimming (2–3° amplitude) and it decreased with increased velocity. This amount of yaw is consistent with that observed with live animals by Dewar and Graham (1994). Roll perturbations were imperceptible, presumably due to the large metacentric height and the significant roll damping from the large caudal and pectoral fins. Significant pitch oscillation (5–10° amplitude) during swimming was problematic in certain cases, largely due to the vertical separation of the center of thrust from the caudal fin-tail assembly and the center of gravity. The thrust oscillation cycle coupled into the pendulous pitch mode. The effect of specific parameters on pitch oscillations was not explored due to limited test time. However, it was noted that some cases consistently produced pitching and that the maximum pitch was somewhat dependent on initial conditions.
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MANEUVERING RESULTS |
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The VCUUV possesses excellent maneuverability that approaches the performance of live animals. Blake et al. (1995)
report average turning diameters for small Thunnus albacares (14 cm length) to be 0.94 body lengths. Although we did not vary the kinematics in search of the minimum turning diameter, we found that simple biases on the straight swimming kinematics produced turning diameters on the order of a body length (2.4–3.0 m) consistent with Blake et al. (1995). Several maneuvering trajectories were explored including abrupt discrete turns and continuous turning which yielded circular and 2-dimensional spiral trajectories. Turning diameters were estimated visually by comparing the turn diameter to the vehicle length. Figure 3 illustrates the heading angle measured during a coasting turn. The vehicle attained maximum speed (1.2 m/sec) after 60 sec of straight swimming, and then coasted with full body deflection to a stop. Two measurements are indicated in the Figure 3: the integral of the heading gyro yaw rate and the absolute heading (yaw) angle measured by the compass. The compass is mounted in a pendulous gimbal such that when subjected to high angular rates, the compass swings in its mount. Thus, the compass slightly over predicts turn rates. The gyro has much better precision in rapid maneuvers but is subject to drift over time. The combination of the two sensors gives a good approximation of the actual turn dynamics. The data from both sensors are in agreement and indicate that the vehicle turned through approximately 160 degrees in 10 sec.
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The maximum measured yaw rate during this maneuver was 75°/sec. As a point of comparison, our own calculations (presented in Fig. 9) have shown that a conventional UUV with control surfaces turns at approximately 3 to 5°/sec at that speed, often requiring several body lengths and as long as a minute to complete a reversing turn. This radical improvement in maneuverability may enable mission elements previously considered beyond the capabilities of UUVs including close inspection and rapid course change tasks, operation in highly perturbed environments and launch and recovery to a moving submarine.
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Figure 4 illustrates the heading angle achieved in an aggressive course-changing trajectory. The vehicle swam straight for 20 sec to attain steady state velocity and then swam zigzag courses at ±45 degrees from the initial heading with 10 sec spent on each segment. The vehicle maintained forward velocity during the maneuver at 1.2 m/sec. The maximum yaw rate for this maneuver was approximately 30°/sec which also outperforms conventional systems by several factors. The zigzag maneuver indicates the level of performance that can be achieved in simple search patterns or in close inspection missions. The vehicle can make aggressive course changes in-stride while effectively preserving forward speed. Conventional UUVs slow down considerably during a turn maneuver due to increased drag forces due to angle of attack on the hull and increased drag of deflected control surfaces (Society of Naval Architects and Marine Engineers, 1989
).
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HYDRODYNAMIC MODEL |
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A preliminary hydrodynamic model for the VCUUV was constructed using a corrected and updated version of the Submarine Hydrodynamic Analysis Tool (SUBHAT) (Boeing Computer Services Company, 1987
) that is used at Draper Laboratory for conceptual designs of conventional UUVs. This code originated in the Hydrodynamic Analysis Techniques (HYDAT) system of computer programs developed by the Naval Coastal Systems Center (1983). These tools estimate relevant hydrodynamic coefficients (force and moment derivatives) using semi-empirical methods, which utilize both theoretical analysis and experimental data. They include added mass, drag, and lift coefficients and take into account all of the important effects: potential or inviscid effects, fluid acceleration effects, and viscous effects. Much of the background needed to understand these tools can be found in the books by Hoerner (1965, 1975) and Newman (1977). These references have gathered theory and experimental data from various sources and presented them in a concise manner.
We adhere to standard naval architecture conventions (Society of Naval Architects and Marine Engineers, 1952) and assign a body centric coordinate system as illustrated in Figure 5. The x-axis points forward and the surge velocity in this direction is u. The y-axis points starboard and the sway velocity in this direction is v. The z-axis points downward and the heave velocity is w. As indicated in Figure 5, positive rotational velocities about these axes are p (roll), q (pitch) and r (yaw), respectively.
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The Draper version of SUBHAT was exercised for the VCUUV hull and fin geometries illustrated in Figure 6 in plan and elevation views. For the simplified analysis presented here, we assume that the body remains fixed to the centerline and completely rigid and that the caudal fin rotates rigidly about its pivot. In the actual system, the aft half of the body undulates with a traveling wave of increasing amplitude envelope as described in Anderson and Kerrebrock (1997)
. Although this analysis approach is simplistic, it fits readily into the framework with which we characterize the stability and maneuvering performance of conventional undersea vehicles. This analysis produces conservative maneuvering performance estimates since body articulation increases the effective rudder control authority.
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The VCUUV caudal fin model is a simplified representation of the actual fin comprising two rudder surfaces as illustrated in Figure 6. The actual caudal fin of the vehicle is wholly moveable and more accurately represents the actual animal's lunate caudal profile. The pectoral fins are similarly modeled as canards (bow planes) as illustrated. Dorsal and anal fins are assumed as fixed surfaces although on the actual vehicle they are deflected with the tail segment to which they are attached.
Using SUBHAT, we produced a complete set of hydrodynamic coefficients. These coefficients provide the hydrodynamic forces and moments that are used in the 6-DOF equations of motion for the vehicle such as presented by Feldman (1979). Most of the hydrodynamic forces and moments are represented in terms of hydrodynamic coefficients and combinations of the vehicle rates (u, v, w, p, q, r) and control surface (fin) deflections (
r for rudder, s for stern plane, and a for aileron). For example, a major contribution to the pitch moment is
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where Mw is a hydrodynamic coefficient. The non-dimensional coefficient is obtained by dividing the hydrodynamic coefficient with a dimensionally appropriate factor, e.g.,
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where 
is the fluid density, and L is the vehicle characteristic length.
A major contribution to Mw is known as the Munk's moment and is the difference between the z- and x-direction added masses (m33 – m11). Here, m11 is the added mass in the x-direction (forward) and m33 is the added mass in the z-direction (downward). Munk's moment destabilizes the vehicle in that turning tends to increase turn rate, causing the vehicle to turn further. Similarly, there is a Munk's moment in the yaw direction included in the term
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where (m11 – m22) is the Munk's moment contribution to Nv. m22 is the added mass in the y-direction.
As with Munk's moments, there are other contributions to hydrodynamic forces and moments from added mass. The added-mass tensor mij is constant for a given vehicle geometry and can be computed from standard formulas based upon shape of the body, e.g., ellipsoidal (Kochin et al., 1964), spheroidal, cylindrical, or strip theory (Newman, 1977). The added mass tensor reflects the potential flow contribution to both the acceleration and the velocity coefficients. The following equations give the added mass contributions to the hydrodynamic forces (F) and moments (M):
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A dot over a variable represent the rate of change with respect to time; thus 
is the vehicle's acceleration along its x-axis.
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STABILITY |
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A trade-off relationship exists for sizing maneuvering surfaces for an undersea vehicle. For given expended power, larger control surfaces produce greater drag in headway motion, leading to smaller attainable maximum speeds. Larger control surfaces make the vehicle more stable and also reduce its maneuverability. In contrast, overly small control surfaces can destabilize the vehicle. Maneuvering coefficients for the VCUUV provide drag, stability coefficients and turning diameters. Simple measures for static stability are the values for
and 
, the static pitch and yaw moment coefficients. A negative value for and a positive value for indicate static stability. High aspect ratio vehicles are generally statically unstable because of the Munk's moment effect.
Another more quantitative measure of vehicle stability (or maneuverability) is given by dynamic stability coefficients Gv in the vertical plane and Gh in the horizontal plane. These are computed as (Humphreys and Watkinson, 1992):
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Here m' is the non-dimensional vehicle mass and the other non-dimensional hydrodynamic coefficients have similar meaning to M
and N
(Feldman, 1979). A vehicle is unstable in the respective planes if the coefficients Gv or Gh are negative. It is statically stable if coefficients are greater than 1 and dynamically stable for values between 0 and 1. As explained by Humphreys and Watkinson (1992), equations (2) and (3) are derived by a series of approximations making an "infinite speed" approximation, which neglects any buoyancy restorative effects due to the separation of centers of gravity and buoyancy. If a vehicle is dynamically stable as indicated by equations (2) and (3) it will be dynamically stable at all ahead speeds as the neglected terms increase dynamic stability.
Table 1 compares pertinent hydrodynamic and dynamic stability coefficients computed with equations (2) and (3), for the VCUUV and for comparison, a generic highly-maneuverable axis-symmetric UUV. The selected generic UUV has properties that resemble several research and development UUVs and is substantially larger than the VCUUV. As all results are normalized for the vehicle length, comparison can be made without concern for the actual size. The generic UUV is 6.1 m long with a maximum diameter of 53 cm and has a mass of 1327 kg and a maximum thrust of around 334 N. Four symmetrical moveable fins at its stern provide maneuvering forces and moments.
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The stability coefficients in Table 1 indicate that the VCUUV is dynamically stable in the horizontal plane and dynamically unstable in the vertical plane. The vertical plane instability of the VCUUV is mitigated mechanically by separating the centers of gravity and buoyancy. This large metacentric height acts as a spring against pitch and roll motions. The generic UUV is slightly stable in both planes as is typical of most UUVs. It is designed to be highly maneuverable and has an autopilot to control its maneuvers.
To illustrate the contributions of fins to the stability of the complete VCUUV vehicle, contributions to the pertinent hydrodynamic coefficients of various vehicle elements (hull alone, pectoral fins, dorsal fin, anal fin, and caudal fin) are listed in Table 2. Stability coefficients for different combinations of components are also computed and listed in Table 3. Results show that hull alone is highly unstable (Gv = –140 and Gh = –167) because of the large Munk's moment in both the vertical and the horizontal planes. Pectoral fins increase M by 64% (add 0.0128 to 0.01999) as these fins are ahead (towards bow) of the hull center of buoyancy and thus decrease stability in the vertical plane. Conversely the vertical lift force coefficient Z of pectoral fins is 31 times the lift force coefficient of bare hull and this makes the vehicle more stable in the vertical plane. Gv still has unstable values, equal to –4.46. Dorsal and anal fins add stability in the horizontal plane, as they are aft of the center of buoyancy of the hull. They reduce the magnitude of by 12%, adding 0.00375 to –0.03256 to obtain –0.02881.
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The horizontal stability coefficient is still computed to be unstable at –15.87 as the horizontal force coefficient Y
due to these fins is only 3.4 times the horizontal force coefficient due to hull alone. Addition of caudal fins decreases the magnitude of N
by an additional 93% adding 0.02672 to –0.02881 to obtain –0.00209. The horizontal stability coefficient is now stable and is calculated to be 1.00. Horizontal dynamic stability of the VCUUV is primarily due to the large caudal fin. |
MANEUVERING |
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Hydrodynamic coefficients computed above were used to compute vehicle turning diameters. Nonlinear computations of turning diameters include cross-flow drag moments along with uv, ur, and u2
r terms in the summation for total yaw moment. For a given rudder (caudal fin) deflection, r, sideslip angle and yaw rate are adjusted to produce zero total yaw moment. Under these conditions, the yaw rate and forward speed are used to compute the turning diameter. We assume for simplicity that the vehicle follows a circular trajectory with no loss of speed in the turn (i.e., constant yaw rate).
Figures 7 and 8 present horizontal turning diameters and yaw rates of the VCUUV vehicle for different caudal fin (rudder) deflections at 1.2 m/s. Turning diameter decreases from 70 lengths at 1 degree of fin deflection to 3.2 lengths at 30-degrees fin deflection. A nonlinear cross-flow drag model is used in these calculations (Chhabra and Scholten, 1997).
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To turn on smaller turning circles, the yaw rate must correspondingly increase as illustrated in Figure 8. To compare with experimental data, we use a 25° caudal fin deflection as a representative value. This is the maximum value that the fin was allowed for turn bias angle. Some caudal deflection range was reserved for the swimming motion upon which the turn was superposed. The actual angles achieved on a given turn were selected by a proportional control algorithm which acted on the heading error. At this caudal fin deflection, the theoretical model predicts the rigid VCUUV's turning diameter at 1.2 m/sec is 3.7 body lengths and the vehicle yaw rate is 16.9°/sec. Sideslip angle (hull angle of attack in the yaw plane) for this maneuver is 16°, independent of speed.
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DISCUSSION |
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Yaw rates for the actual VCUUV during autonomous maneuvers were significantly higher than those predicted from the above rigid body model. Although the theoretical model assumes constant yaw rate, the measured rates are highly dynamic. When entering a turn, the yaw rate peaks, and then quickly decays. For the full stop bias turn illustrated in Figure 3, the peak yaw rate entering the turn was 75°/sec and by the end of the maneuver 10 sec later, the yaw rate was essentially zero. For repeated zigzag maneuvering at 1.2 m/sec (Fig. 4), the VCUUV turned at approximately 30°/sec entering the turn, with decay to zero yaw rate approximately 5 sec into each trajectory segment. The turning diameter for this case was approximately one body length (by visual observation).
Although our measured peak yaw rates do not correspond directly with the constant yaw rates we predict with our theoretical model, some general observations can be made. The theoretical model of the rigid VCUUV with 25° fin deflection produces turning rates of only 16.9°/sec which as expected, under predicts the measured peak rates of 30–75°/sec. This indicates that the unmodeled body deflection may significantly increase the fin effectiveness. In order to predict the turn rates observed in the field, the required rudder moment is roughly double that produced by the caudal fin alone. With this model correction, the turning diameter is two body lengths, which is larger than our rough visual estimate. A possible explanation is that the assumption of constant yaw rate does not apply exactly for this trajectory.
Hydrodynamic coefficients used to predict turning diameters are generally independent of speed, except cross-flow drag coefficients. Thus, yaw rate is nearly linear with speed. Figure 9 illustrates this trend for the corrected rigid VCUUV model and for the generic UUV presented previously. At 1.2 m/sec, the VCUUV has 7.5 times more yaw rate than the generic UUV. For this case at the 25° rudder deflection, the generic UUV has a sideslip angle of 8.2 degrees and a turning diameter of 5.4 body lengths.
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SUMMARY |
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SYNOPSISINTRODUCTIONVCUUV SYSTEM DESCRIPTIONFIELD TRIALSMANEUVERING RESULTSHYDRODYNAMIC MODELSTABILITYMANEUVERINGDISCUSSIONSUMMARYReferences |
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The VCUUV has demonstrated the utility of fish-like propulsion and maneuvering for improving undersea vehicle performance. The VCUUV propels and maneuvers stably in the horizontal plane, with performance surpassing conventional axis-symmetric designs. In field trials, the VCUUV achieved 1.2 m/sec and turn rates up to 75°/sec. On aggressive repetitive maneuvers, the VCUUV turned at 30°/sec without loss of forward speed. Conventional vehicles cannot achieve this trajectory due to their low yaw rate of 4°/sec. For this maneuver, a generic UUV has turning diameter of 5.4 body lengths whereas the VCUUV has turning diameter of approximately two body lengths.
A simplified hydrodynamic model was developed within the framework customarily used for conventional vehicle hydrodynamic analysis. Based on the assumption that the VCUUV body remains rigid and only the caudal fin deflects, hydrodynamic and stability coefficients were calculated. As expected, the caudal fin stabilizes the VCUUV in straight-ahead motion. The VCUUV is hydrodynamically unstable in the vertical plane. The rigid VCUUV model does not capture the added effectiveness of the body undulation as a rudder and under predicts the actual maneuverability by roughly a factor of two.
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ACKNOWLEDGMENTS |
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The research described in this paper was funded internally by the Charles Stark Draper Laboratory.
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FOOTNOTES |
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1 From the Symposium Stability and Maneuverability presented at the Annual Meeting of the Society for Integrative and Comparative Biology, 3–7 January 2001, at Chicago, Illinois.
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References |
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