Analysis of Manipulator Arm Steadiness During Ship-Hull Mine Neutralization by a UUV

Analysis of Manipulator Arm Steadiness During Ship-Hull Mine Neutralization by a UUV Mathieu Kemp Bradley Richardson, Lonnie Love Bluefin Robotics C...
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Analysis of Manipulator Arm Steadiness During Ship-Hull Mine Neutralization by a UUV Mathieu Kemp

Bradley Richardson, Lonnie Love

Bluefin Robotics Corporation Quincy, MA, USA [email protected]

Oak Ridge National Laboratory Oak Ridge, TN, USA

Tony Rodgers, Kurt Nelson, Tracy Dixon Orca Maritime, Inc Imperial Beach, CA, USA Abstract— Accurate tool placement is an essential element of teleoperated ship-hull mine neutralization. In this article we present a framework to analyze the stability of a UUV-mounted manipulator arm during neutralization. Our principal result is a relationship between rate of arm motion and minimum vehicle thrust required to maintain steadiness. Keywords: ship-hull inspection, mine neutralization, UUV, manipulator arm, modeling.

I.

INTRODUCTION

Vaganay [1] achieved a landmark demonstration of 100% automated sonar coverage of a ship hull’s Non-Complex Areas using the Hovering Autonomous Underwater Vehicle (HAUV) in 2008. This achievement paved the way to recent efforts aimed at extending the reach of inspection to Confined Areas [2,3,4], and at performing tether-less inspection [5]. After a ship hull mine has been detected, it must be neutralized – i.e. rendered safe. Current search and neutralization procedures consist of sending divers to scan the hull for targets, mark them, and neutralize them. Neutralization is achieved by carefully placing an explosive tool on the target, bringing back the firing wire, and finally remote-initiating the tool. This procedure has several drawbacks: it places Explosive Ordnance Disposal (EOD) personnel in direct contact with an explosive device; it is performed in limited-tozero visibility, forcing divers to combine their sense of touch with visual cues to reacquire and neutralize the target; it is time-consuming in a time-critical situation; and it requires a large amount of resources. A system that could allow EOD personnel to conduct the entire search-locate-neutralize sequence from a safe standoff distance would be a considerable improvement over the current procedure. In response to this need, the Office of Naval Research initiated a program aimed at developing a tele-operated shiphull mine neutralization capability. This system, called HUNS (Hull UUV Neutralization System), will combine the HAUV with a lightweight and dexterous underwater manipulator arm (Figures 1 and 2). An initial demonstration of this capability is planned for 2013.

Figure 1. HUNS architecture. Topside consists of the display/control interfaces for the arm and vehicle. Wetside consists of the vehicle, the manipulator arm, the overview PTZ and wrist-mounted cameras, and the passive stabilizer. Communication is done over a thin fiber optic tether.

Figure 2. HUNS manipulator arm. The base is attached to the vehicle. The upper arm has both a yaw and a pitching joint at the shoulder and a humeral rotator near the elbow. The forearm is actuated at the elbow. The endeffector (not shown) will be actuated in yaw, pitch, and roll. Arm design, based on novel meso-fluidic actuation methods and involute-cam joints, will take advantage of additive manufacturing techniques to achieve a high performance-to-weight ratio at a low cost.

The central technical objective of HUNS is accurate placement of the neutralization tool – the device that renders the mine safe. The generic problem of end-effector stabilization for an underwater vehicle was investigated by

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McLain et al. [6-8], where dynamic control techniques were shown to provide a six-fold reduction in motion amplitude. Because the placement requirements for mine neutralization are very stringent, HUNS will rely on a passive truss structure instead of dynamic control to achieve stabilization. In this paper we present a framework to analyze passive stabilization. Our main result is a relationship between the rate of arm motion and the minimum vehicle thrust required to maintain steadiness. A thorough discussion of the results, including response to cross-current, will be presented elsewhere. The paper is organized as follows: Section II sets up the arm steadiness problem. Section III addresses the kinematics of the arm. Section IV discusses the loads on the vehicle due to arm motion. Section V addresses the stabilizer response to the load. Section VI presents the steadiness criteria. Finally, Section VII shows some steadiness predictions during tool placement. II.

ARM STEADINESS

III.

The arm consists of seven links, L=1:7. Each link has a center-of-mass position relative to the inertial frame, the rate of change is the velocity, and the second derivative is the acceleration. Each link also has an ortho-normal body frame: the rotational rate of change defines the angular velocity, and the derivative is the angular acceleration: X L , VL ≡ d dt X L iL

McLain analyzed single-link end-effector stabilization using dynamic control techniques, and showed that feedforward is effective [6-8]. In this paper we examine a different approach, where stabilization is achieved passively, by thrusting into the hull via a truss structure (Figure 1). Figure 3 shows the analysis framework we developed. The operator commands individual arm joint trajectories θ ( t ) . The arm kinematics block generates the individual arm link velocities, accelerations, angular velocities, and angular accelerations: V , A, ω , α . The inertia, drag, and ideal fluid blocks generate the individual link loads ( f ,τ ) using link

established hydrodynamics models. These loads are summed, and the sum is passed to the stabilizer response block, which decomposes it into individual truss loads. Finally, the steadiness criteria block determines if the vehicle remains in contact with the hull (no-tipping) without moving (no-sliding).

, AL ≡ d dt VL

, ωL ∧ iL ≡ d dt iL , α L ≡ d dt ω L

(1)

where we used the Dirac bra-ket notation to frame the analysis in coordinate-independent language, and where ω ∧ is the wedge product and iL is the ith basis vector for link L. Link 2 rotates on top of link 1, link 3 on top of 2, etc. Because of this embedding, the angular velocity of any link L depends on links 1, 2, ... L-1. Formally:

Large hydrodynamic forces and torques develop when the manipulator arm moves. These forces and torques cause the vehicle to move, inducing unwanted motions on the endeffector. Divers have the same problem. To steady themselves, they may place a magnet on the hull and use their other arm to place the tool. HUNS does not have a second arm. Consequently, something else is needed to steady the vehicle.

ARM KINEMATICS

ωL = ωL −1 +ν Li iL where d dt [TL ] ji = [TL ] jk ( ε kmiν Lm )

(2)

iL ≡ [TL ] ji jL −1 where we used the Einstein summation convention. ε is the Levi-Civita anti-symmetric tensor, ν L = ν Li iL is the Lth joint velocity, and TL defines the rotation of link L relative to L-1. Projecting these equations in each frame yields a hierarchy of equations for the rotational variables: ω L = TL+ ω L −1 + ν L α L = TL+ α L −1 + ν& L + ω L × ν L

(3)

and for the translational variables: VLE = TL+ VLE−1 + ω L × l L A EL = TL+ A LE−1 + α L × l L + ω L × ( ω L × l L ) VL = TL+ VLE−1 + ω L × h L

(4)

A L = TL+ A LE−1 + α L × h L + ω L × ( ω L × h L )

{

where ω L = ωLi ≡ iL ωL

Figure 3. The framework developed to analyze arm steadiness during neutralization.

} is the array of components of

vector ωL , ν& = d dtν is the joint velocity, lL = lLi iL is the vector joining the origin of link L with its end, and hL = hLi iL is the vector joining the origin of link L with its center-of-mass. Note that the translational hierarchy has two parts: a hierarchy for the end-points, and a hierarchy for the center-of-masses. The latter depends on the former. The i L

i L

2

hierarchy starts at link 0, the base, which is fixed on the vehicle. The matrix and vectors TL , ν L , ν& L are computed from the joint axis nL ≡ nLi iL and the joint angle and angular rates θ ,θ&,θ&& as follows:

+ sin (θ L ) n L ×

L

IV.

L

(5)

L

LOADS DUE TO ARM MOTION

f denotes force and τ denotes torque. As shown in Spong et al. [9], the force applied to link L-1 by link L has three parts: the force applied by link L+1 to link L, the external force on link L, and the inertia of link L: f L-1 by L ≡ f L −1 = f L + f LX − mL AL

(6)

(7)

d LL dt

where a term due to the link-to-link force appears, and where the last term is the rate of change of angular momentum:

LL = [ J L ]ij ωLj iL

(8)

where J L is the moment of inertia of link L. These equations yield a hierarchy that runs in reverse from the kinematics hierarchy, i.e. from the end-effector to the base. The external loads, f LX and τ LX , are hydrodynamic, and have three parts: ideal fluid terms (i.e. added mass and Munk moments); viscous terms (i.e. drag); and buoyancy, which are neglected since each link is neutrally buoyant by design. Newman shows that the ideal fluid loads are of the form [10]: f L = − d dt ⎡⎣([ M L VL ]i + [ N L ω L ]i ) iL ⎤⎦ τ L = − d dt ⎡⎣([ PL VL ]i + [QL ω L ]i ) iL ⎤⎦ - VL ∧ ([ M L VL ]i + [ N L ω L ]i ) iL

(10)

where the first axis is the along the cylinder. Jones [11], Allen and Perkins [12], and Prestero [13] present models for the viscous terms. To a good approximation:

⎡ diag ⎡⎣0, V2 V2 , V3 V3 ⎤⎦ ⎡f ⎤ ⎢ 3 ρ C Rl = − T ⎢τ⎥ ⎢l ⎣ ⎦ ⎢⎣ 32 diag ⎡⎣0, ω2 ω2 , ω3 ω3

⎤ ⎥ ⎥ ⎤⎦ ⎥ ⎦

(11)

where CT = 1.1, and where the axial and rolling drag are neglected. STABILIZER RESPONSE

The stabilizer has N trusses, each terminated by a friction pad. To determine steadiness, we need to resolve the load applied by each truss to the hull. This is a structural problem, and we formulate it as such.

τ L-1 by L ≡ τ L −1 + τ LX − −hL ∧ f L −1 −

Q ≈ (π 12 ρ R 2 l 3 ) diag (0 1 1) .

V.

where mL is the mass of link L. Similarly for the torque:

= τ L + lL − hL ∧ f L

M ≈ (πρ R 2 l ) diag (0 1 1) N =P=0

TL = cos (θ L ) I + (1 − cos (θ L ) ) n L n +L ν L = θ&L n L ν& = θ&& n

The matrices M, N, P, and Q are 3x3 constants attached to the frame of link L. The second term in the torque equation is the Munk moment. For cylinders of long aspect ratio,

(9)

In the HAUV coordinate system, the end of truss T is the vector sum of its origin plus a vector tangent to its axis: XT = XTO + lT t T

(12)

Where lT is the length of the truss. Small translations/ rotations of the vehicle cause the truss to compress and bend by an amount linear in vehicle displacement: δTC = − ⎡⎣ tT t T+ A⎤⎦ δV ≡ − AC δV

δTB = − ⎡⎣( I − tT tT+ ) A⎤⎦ δV ≡ − AB δV ⎡δX ⎤ A ≡ [ I − XT ×] ; δV ≡ ⎢ V ⎥ ⎣ δθV ⎦

(13)

Assuming linear response, and using K C and K B for the compressive and bending stiffnesses, the counter force/torque applied by the hull to the vehicle through truss T is:

KC AC + K B AB ⎡ ⎤ FT = ⎢ ⎥ δV ≡ KT δV ⎣ KC ( XT ×) AC + K B ( XT ×) AB ⎦

(14)

i.e. a truss stiffness matrix multiplied by the vehicle displacement. The total stabilizer stiffness is the sum of the 3

individual truss stiffnesses: K = ∑ KT . For a cylindrical truss, the ratio of bending to compressive stiffness is 2 K B K C = 1.5 ( R l ) where R is the truss radius and l is its length. The load applied to the vehicle by the arm is transferred to the hull by the stabilizer. The load applied to the hull by individual trusses is:

FT = KT K −1Fapplied .

(15)

Note that the stiffness matrix K must have full rank – else certain vehicle displacements cannot be countered. The minimum number of trusses is consequently three.

The stabilizer consists of three trusses forming an equilateral triangle, with K B K C = 1.5 x10 −4 . The thrusters are engaged forward. Representative values for the coefficient of static friction range from 0.6 for rubber on wet pavement to 0.2 for brake material on wet metal [14]. In what follows 0.2 is used. Figure 4 shows the amount of thrust required when the tool moves side-to-side relative to the target (top figure) and backand-forth (bottom figure). In both cases, the wrist moves at 35°/s (A=5° at T=1s). For side-to-side motion, 25N of thrust (6lbs) is needed to cancel out the forces due to arm motion; for back-and-forth motion, 4N is needed (1 lbs). This level of thrust output is well within the range achievable by HAUV, implying that steadiness is expected to occur.

STEADINESS CRITERIA

VI.

There are two modes of failure: failure in tipping, where any of the trusses loses contact with the hull, and failure in sliding where any of them slides. The no-tip criterion requires that the force perpendicular to the hull be positive for all trusses. The no-slip criterion requires that the force parallel to the hull be smaller than that allowed by static friction: + T

τ Fapplied > 0

(16)

+ Fapplied ΣT Fapplied > 0

LT ≡ ( I

where

0 ) KT K −1 , τ T ≡ L+T 1L ,

ΣT ≡ ( LT ) diag ⎡⎣ μ s2 , −1, −1⎤⎦ LT +

and

T>

(

b 2 − 4ac − b

.

) ( 2a )

no tipping no sliding

a = tˆ + ΣT tˆ b = 2tˆ + ΣT A c = A + ΣT A d = τ T+ A e = τ T+ tˆ

The side-to-side thrust requirement is dictated by the sliding criterion. This is expected, since side-to-side motion of the arm causes a large torque on the vehicle: this can only be countered by shifting forces between trusses, which makes the vehicle more vulnerable to sliding.

where

The applied load has two parts, one due to the arm and one due to the thrusters, Fapplied = A + Ttˆ , where T , tˆ are the thrust magnitude and direction. Separating these contributions yields the thrust required to null the effect of the arms: T > −d e

Figure 4. Thrust required to maintain steadiness during a 35°/s wrist oscillation. Top: tool moving side-to-side. Bottom: tool moving back-andforth.

(17)

VIII. SUMMARY We presented a framework to analyze the steadiness performance of a passive stabilizer during neutralization. We have shown how arm motion relates to stabilizer performance, going from arm kinematics to drag, added-mass, and inertia, to loading of the vehicle, to loading of the trusses, and finally to the tipping and sliding criteria. Our main result is a relationship between rate of arm motion and minimum vehicle thrust required to maintain steadiness. We applied the framework to a typical tool placement case, and showed that for typical wrist rates steadiness is expected to occur. This framework can be used elsewhere, for example to analyze the effect of elbow and shoulder motion during arm deployment, maximum lifting capacity, and the effect of crosscurrent. This will be discussed elsewhere. ACKNOWLEDGMENTS

VII. APPLICATION TO TOOL PLACEMENT To apply this framework, a target located on the vertical side the hull will be considered, and the case of small adjustments of the tool using wrist motions of amplitude aw and frequency fw:

θ ( t ) = aw sin ( 2π f wt )

(18)

This work was funded by the Office of Naval Research under contract N00014-11-C-0143. We thank Brian Almquist, Victoria Steward, EODC John Fleming, and EOD1 Jami Souffront for insightful comments on current and future ship hull neutralization practice. REFERENCES [1]

J. Vaganay, "HAUV System Improvement for Use by EOD Units", Proceedings of 2009 ONR Unmanned Systems Review.

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[2]

[3] [4] [5]

[6]

[7]

R. Eustice, "Real-time visual feature-based navigation for hull search and inspection with the Bluefin HAUV", Proceedings of 2011 ONR Unmanned Systems Review. S. Reed, "Autonomy capability for the ship hull inspection problem", Proceedings of 2011 ONR Unmanned Systems Review. J. Leonard, "Acoustic feature-based navigation and control on a ship hull", Proceedings of 2011 ONR Unmanned Systems Review. P. Beaujean, "High-data rate acoustic communications for transmission of ATR images, mosaics, 3-D images and vehicle status in complex and non-complex search areas", Proceedings of 2011 ONR Unmanned Systems Review. T.W. McLain, "Modeling of Underwater Manipulator Hydrodynamics with Application to the Coordinated Control of an Arm/Vehicle System", PhD dissertation, Stanford University, 1995. T.W. McLain, S.M. Rock, and M.K. Lee, "Experiments in the Coordinated Control of an Underwater Arm/Vehicle System", Autonomous Robots 3, 1996, pp. 213-232.

[8]

[9] [10] [11] [12] [13] [14]

T.W. McLain, and S.M. Rock, "Development and Experimental Validation of an Underwater Manipulator Hydrodynamic Model", International Journal of Robotics Research, Vol. 17, No. 7, 1998, pp. 748-759. M. W. Spong, S. Hutchinson, M. Vidyasagar, Robot Modeling and Control, John Wiley and sons, 2006. J. N. Newman, Marine hydrodynamics, MIT Press, 1977. R. T. Jones, "Effect of sweepback on boundary layer and separation", NACA technical report 884, 1947. H. J. Allen, E.W. Perkins, "Characteristics of flow over inclined bodies of revolution", NACA RM A50L07, 1951. T. Prestero, "Verification of a 6 DOF simulation model of the REMUS AUV", MIT master thesis, 2001. Online Engineer's handbook, www.engineershandbook.com/ Tables/frictioncoefficients.htm.

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