Optimum positioning of an underwater intervention robot to maximise workspace manipulability

Mechatronics 15 (2005) 747–766

Technical Note

Optimum positioning of an underwater intervention robot to maximise workspace manipulability T. Asokan, G. Seet *, M. Lau, E. Low Robotic Research Centre, School of Mechanical and Aerospace Engineering, Nanyang Technological University, Singapore 639 798, Singapore Received 8 August 2003; accepted 15 December 2004

Abstract Underwater robotic vehicles (URV) are extensively used for inspection and intervention tasks of subsea facilities. To enable dexterous manipulations, the URV is required to be firmly attached to the structure. The choice of docking point is very important. An inappropriate choice would necessitate multiple re-dockings. This significantly increases the duration and cost of the mission. In this paper, we present a method of assisting the URV operator to identify the most appropriate docking position in the context of a desired dexterous workspace. The method draws upon classical procedures developed, predominantly, for industrial robotics. Currently, the operator intuitively determines docking positions. A positioning strategy, based on the type of task to be carried out, is proposed. Inspection of a subsea weld joint, using a compact URV and a specially designed and optimised, dexterous, 7 d.o.f., manipulator, is considered as a test case. Dexterity of manipulator at the target location is taken as the optimisation criterion. As a measure of manipulator dexterity, the condition number of the manipulator is adopted here. Manipulator joint limits and workspace constraints are taken into account. Theoretical analysis and simulation results are presented. Ó 2005 Elsevier Ltd. All rights reserved.

*

Corresponding author. Tel.: +65 6790 5600; fax: +65 6793 5921. E-mail address: [email protected] (G. Seet).

0957-4158/$ - see front matter Ó 2005 Elsevier Ltd. All rights reserved. doi:10.1016/j.mechatronics.2004.12.003

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Keywords: Underwater manipulation; Dexterity; URV; Optimum positioning; Condition number; Singularity

1. Introduction Underwater robotic vehicles (URV) are widely used for subsea inspection and intervention tasks such as cleaning, salvage, and repair of submerged structures. A typical scenario of using a URV for subsea application is shown in Fig. 1. URV with the onboard intervention system is deployed from the base station and remotely navigated to the target location. At the target location, URV is positioned and attached to a structure. The intended tasks are then completed through remote operation or autonomously. In the successful completion of a subsea task, the choice of URV docking point is very critical. A poor choice would not permit the dexterous manipulation of the workspace and would necessitate multiple re-dockings. This significantly extends the entire process and imposes a high workload on the remote operator, severely affecting the efficiency of the system. To utilise the resources efficiently, it is necessary to dock the URV at an optimum location so that the tasks can be completed with minimum re-positionings. In this paper, we present a method of assisting the URV operator to identify the most appropriate docking position in the context of a desired workspace. This research work is undertaken as part of an ongoing research program at the Robotic Research Centre of Nanyang Technological University, Singapore. The program focuses on development of technologies and systems for the advancement of knowledge and for possible commercial exploitation relevant to the oil and gas industry. Under this program, a compact URV and a unified pilot training and control system have been developed [1]. A dual stage, hybridly powered, dexterous manipulator has also been designed as the intervention arm of the URV [2]. The dexterous manipulator is expected to increase the URV capabilities in intervention tasks. Developmental studies on URV deployment, station keeping, and task execu-

Fig. 1. A typical scenario of a URV deployed for intervention tasks.

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tion are going on at the Centre. One of the major issues we encountered, in the deployment simulations of URV with the intervention systems onboard, is the determination of the best possible deployment location for URV, to carry out a given task. A wrong choice may lead to many re-positionings, which are costly and tedious. Identifying an optimum location will help to increase the operational capabilities of the vehicle and reduce operator fatigue. The choice of looking for an optimised location, however, depends on many factors, predominantly, 1. The nature of URV task, i.e. cleaning, inspection, repair etc. 2. Operating environment, i.e. constrained by surrounding structures, easily accessible, obstructions in the manipulator path etc. 3. Kinematic structure, over all length, and control strategies of on board manipulator. The criticality of docking position, with respect to the given task, is to be assessed and decision needs to be taken whether to optimise or not. For some simple operations, like salvage of sunken objects, docking position may not be critical, whereas it becomes highly critical in inspection of a weld joint. Similarly, if the surroundings of the target space are highly constrained, with limited accessibility and docking positions, optimisation may not be viable. Hence, it is necessary to define the proposed task and analyse it with respect to the URV and manipulator functionality and limitations, before optimising the location. The objective in optimising the docking position is to identify the best possible location for the URV to manipulate a given work space, in order to complete an assigned task with ease. This position is a subset of the position and orientation of URV that provides maximum orientability with respect to an operating point. In this paper we have addressed this problem for a specific task, i.e. inspection of welded joints of underwater pipelines. A special purpose, 7-d.o.f. manipulator, designed for underwater inspection, is considered as the intervention arm of URV. Since the manipulator plays a vital role in URV positioning, link lengths of the manipulator has been optimised to get maximum dexterity at the inspection location [3]. Following assumptions, valid for the specific task assumed, are made in the analysis. 1. The manipulator is directly mounted on the URV, with the origin of coordinate frames of both the URV and the arm coinciding, without any rotation, as shown in Fig. 2. 2. URV can be navigated and positioned anywhere near the target space, without any obstruction. 3. The URV will be able to maintain its commanded position with the help of mechanical constraints, overcoming the effects of sea conditions. The positioning strategy, optimisation, and simulation results are presented in the following sections.

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Fig. 2. Manipulator onboard the URV.

2. Positioning strategy There are many reported works in the field of underwater robotics that address the trajectory tracking and navigational problems of URV, for example [4,5]. However, not much work has been reported in the literature addressing the positioning problem of URV. This is mainly due to the academic importance given to the navigational and control aspects, leaving positioning as an issue to be addressed at the operational level. (Recently, General Robotics (UK), a pioneer company in underwater robotics, has reported that they are working on an algorithm, based on neural networks, to address the positioning problems of URV in deployment. No more details are available at present.) At the optimum location, URV and the onboard manipulator system should satisfy the following conditions: (1) all or maximum of the target points should lie within the manipulator workspace. (2) None of the target points should lie on the manipulator singular surfaces. (3) Optimisation criteria to be satisfied. Though it is difficult to find a universal criterion for optimal positioning, there were many proposed methods in literature, addressing the positioning problem of land based robotic applications. Placement for avoiding interference between manipulator links [6,7], reachability of manipulator [8], service sphere [9], and dexterity of manipulator at the target point [10] were some of them. A positioning strategy, drawn up from some of these classical methods, comprising the following steps, has been proposed for the URV. 1. Define the manipulator kinematics, its workspace and boundaries. 2. Move the URV towards the target space to bring the target points within the manipulator workspace. 3. Optimise the URV position. 4. Check for singular positions and modify base position accordingly. These steps are illustrated in the following sections.

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3. Seven d.o.f. underwater manipulator The manipulator considered here for analysis is a 7 d.o.f., 2-stage manipulator specially designed for underwater inspection of weld joints. The first two d.o.f. acts as a launching-stage manipulator, which will be used for suitably posing the base of the manipulator with respect to the target. The remaining 5 d.o.f. is used for the inspection of welded structures. The kinematic chain of the manipulator is sketched in Fig. 3 [2]. The two-stage design has been adopted to increase the dexterity of the manipulator without affecting its total reach. DH parameters [11] of the manipulator and the range of joint angles are given in Table 1. 3.1. Workspace analysis For the simplicity of analysis, the workspace of the manipulator has been divided into two, namely, wrist point access space (WPAS) and wrist space (WS). The wrist space represents the workspace of the wrist joints (O5,O6,O7) while the wrist point access space represents the set of points that can be reached by the wrist point (O5). The boundary of these sub-spaces and the surface patches representing the singular surfaces within these are analytically determined using the method presented by Karim and Yeh [12]. Let q = [q1


q7]T represent the joint variables of the manipulator and q 2 R7 Using the DH representation method, a position vector X = [x, y, z]T can be written as X ¼ UðqÞ

ð1Þ

Z

O2

d1

d7

a2

a1

O3

Y

O4

O5

O6

O7

O1

X Fig. 3. Kinematic chain of 7 d.o.f. manipulator.

Table 1 DH parameters and joint angles Joint no.

Joint type

Limits, deg

a, mm

d, mm

1 2 3 4 5 6 7

Rotary Rotary Rotary Rotary Rotary Rotary Rotary

±p/2 ±p/2 ±3p/4 ±3p/4 ±3p/4 ±p/3 ±p

50 650 502 355 192 0 0

250 60 0 0 0 0 300

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where U : R7 ! R3 is a smooth vector function defined as a subset of Euclidean space. The homogeneous transformation matrix [11], 0T7, represents the position and orientation of the end point frame of the manipulator with respect to the base frame. The transformation can be represented as
0  R7 0 P7 0 T7 ¼ ð2Þ 0 1 where, R is the rotation matrix and P is the position vector. Thus, the seven axis manipulator may be partitioned using the homogeneous transformation matrix relating the end-effector and the wrist to the reference frame such that 0

T7 ¼ 0 T4 4 T7

ð3Þ

The wrist point accessible space of the manipulator can be determined using the equation 0

xq ¼ 0 R4 4 xP w þ 0 P4

ð4Þ

where, 0xq is the vector describing the wrist accessible output set of the wrist point and 4 xP w is the vector describing a point resolved in the reference frame of link 4. For a given configuration of the manipulator, the generalised coordinates satisfy independent holonomic kinematic constraint equations of the form UðqÞ ¼ 0 xq  0 R4 4 xP w  0 P4 ¼ 0

ð5Þ

The generalised coordinates q are subject to inequality constraints, qmin < q < qmax, representing joint limits. This inequality can be transformed in to an equation using a generalised coordinate k, (in the field of optimisation, k are usually called slack variables) as qi ¼ ai þ bi sin ki

ð6Þ

where   =2; þ qmin ai ¼ qmax i i

  bi ¼ qmax =2  qmin i i

ð7Þ

Equating the determinant of the Jacobian of the mechanism to zero and then computing the roots can compute the workspace-boundary singularities and workspaceinternal singularities. The constraint Jacobian of the constraint function U(q) for a certain configuration q0 is the matrix U q q0 ¼

oU 0 q oq

ð8Þ

The Jacobian with respect to the new coordinates, k, can be written as U k ¼ U q qk

ð9Þ

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Singularities are determined by equating the determinant of Uk to zero such that F ðkÞ ¼ jUq qk j ¼ 0

ð10Þ

These singularities represent the boundary and/or the internal singularities. Surface patches corresponding to these singularities represent the singular surfaces within the workspace. As it is impossible to move the tip of the manipulator along the singular surfaces, no matter which joint rates are selected, they are to be avoided during manipulation. Any point lying on a singular surface will have zero manipulability. 3.1.1. Wrist point access space The boundary of the wrist point access space and the singular surfaces within this space (referred as surface patches and represented as ni) are determined using the method described in the previous section. The 4-d.o.f. manipulator that represents the arm, can be simplified in to a 3-dof system by assuming the joint angle h2 to be constant. This assumption is valid due to the fact that, during an inspection process, this joint will be stationary. Thus the arm reduces to a 3-d.o.f. system and the boundary and surface patches can be easily calculated. The homogeneous transformation matrix 0T4 representing the position and orientation of wrist point is given as
0  Rw 0 Pw 0 T7 ¼ ð11Þ 0 1 where 0 Pw ¼ ½ P x obtained as

Py

P z T . For the 3-d.o.f. manipulator, components of 0Pw can be

P x ¼ cos h1 ða4 cosðh2 þ h3 þ h4 Þ þ a3 cosðh2 þ h3 Þ þ a2 cosðh2 Þ þ a1 Þ P y ¼ sin h1 ða4 cosðh2 þ h3 þ h4 Þ þ a3 cosðh2 þ h3 Þ þ a2 cosðh2 Þ þ a1 Þ

ð12Þ

P z ¼ a4 sinðh2 þ h3 þ h4 Þ þ a3 sinðh2 þ h3 Þ þ a2 sinðh2 Þ þ d 1 The constraint equation given by Eq. (5) can be written as 2 3 X  Px 6 7 UðqÞ ¼ 4 Y  P y 5

ð13Þ

Z  Pz subject to the parameterized constraints p sin k1 2 3p sin k3 q3 ¼ 0 þ 4 3p sin k4 q1 ¼ 0 þ 4

q1 ¼ 0 þ

ð14Þ

The constrained Jacobian Uk, given by Eq. (8), can be determined by evaluating Uq and qk as

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2

S 1 ða4 C 234 þ a3 C 23 þ a2 C 2 þ a1 Þ C 1 ða4 S 234 þ a3 S 23 Þ C 1 ða4 C 234 Þ

6 Uq ¼ 4 C 1 ða4 C 234 þ a3 C 23 þ a2 C 2 þ a1 Þ 0

S 1 ða4 S 234 þ a3 S 23 Þ a4 C 234 þ a3 C 23

3

7 S 1 ða4 C 234 Þ 5 a4 C 234 ð15Þ

2p

cos k1

62 6 6 0 qk ¼ 6 6 4 0

0

0

3p cos k3 4

0

0

3p cos k4 4

3 7 7 7 7 7 5

ð16Þ

where, C12. . . = cos (h1 + h2 +


); S12. . . = sin (h1 + h2 +


). By equating the determinant, jUqqkj to zero, we get jUq qk j ¼

9 3 p cos k1 a24 C 234 cos k3 cos k4 a3 S 4 32 9  p3 cos k1 a23 C 23 cos k3 cos k4 a4 S 4 32 9  p3 cos k1 a2 C 2 cos k3 cos k4 a3 a4 S 4 32 9  p3 cos k1 a1 a3 a4 cos k3 cos k4 S 4 ¼ 0 32

ð17Þ

By solving the above equation, singularities can be obtained. These computed singularities are given as sin h4 ¼ 0 ! h4 ¼ 0; p cos k1 ¼ 0 ! k1 ¼ p=2; ) h1 ¼ p=2 cos k23 ¼ 0 ! k3 ¼ p=2; ) h23 ¼ 3p=4 cos k4 ¼ 0 ! k4 ¼ p=2; ) h4 ¼ 3p=4

ð18Þ

Substituting the singular value of the joint variable in Eq. (12), and implementing the inequality constraints for the other joint variables can obtain the singular surface due to a particular singularity. All the singular surfaces due to the singularities obtained in Eq. (18) are obtained by this method. They are represented analytically as shown below 2 3 0 6 7 h1 ¼ p=2 ) n1 ðq3 ; q4 Þ ¼ 4 a4 C 234 þ a3 C 23 þ a2 C 2 þ a1 5; ð19Þ a4 S 234 þ a3 S 23 þ a2 S 2 þ d 1 subjected to the limits, 3p/4 < h23 < 3p/4, 3p/4 < h4 < 3p/4 2 3 0 6 7 h1 ¼ p=2 ) n2 ðq3 ; q4 Þ ¼ 4 a4 C 234  a3 C 23  a2 C 2 þ a1 5; a4 S 234 þ a3 S 23 þ a2 S 2 þ d 1

ð20Þ

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subjected to the limits, 3p/4 < h23 < 3p/4, 3p/4 < h4 < 3p/4 2 3 C 1 ða4 cosðh4  3p=4Þ þ a3 cosð3p=4Þ þ a2 þ a1 Þ 6 7 h23 ¼ 3p=4 ) n3 ðq1 ; q4 Þ ¼ 4 S 1 ða4 cosðh4  3p=4Þ þ a3 cosð3p=4Þ þ a2 þ a1 Þ 5; a4 sinðh4  3p=4Þ þ a3 sinð3p=4Þ þ a2 þ a1 ð21Þ subjected to the limits, p/2 < h1 < p/2, 3p/4 < h4 < 3p/4 2

C 1 ða4 cosðh4 þ 3p=4Þ þ a3 cosð3p=4Þ þ a2 þ a1 Þ

3

6 7 h23 ¼ 3p=4 ) n4 ðq1 ; q4 Þ ¼ 4 S 1 ða4 cosðh4 þ 3p=4Þ þ a3 cosð3p=4Þ þ a2 þ a1 Þ 5; a4 sinðh4 þ 3p=4Þ þ a3 sinð3p=4Þ þ a2 þ a1 ð22Þ subjected to the limits, p/2 < h1 < p/2, 3p/4 < h4 < 3p/4 2

3 C 1 ða4 cosðh23  3p=4Þ þ a3 cosðh23 Þ þ a2 þ a1 Þ 6 7 h4 ¼ 3p=4 ) n5 ðq1 ; q3 Þ ¼ 4 S 1 ða4 cosðh23  3p=4Þ þ a3 cosðh23 Þ þ a2 þ a1 Þ 5; a4 sinðh23  3p=4Þ þ a3 sinðh23 Þ þ a2 þ a1 ð23Þ subjected to the limits, p/2 < h1 < p/2, 3p/4 < h23 < 3p/4 2

3 C 1 ða4 cosðh23 þ 3p=4Þ þ a3 cosðh23 Þ þ a2 þ a1 Þ 6 7 h4 ¼ 3p=4 ) n6 ðq1 ; q3 Þ ¼ 4 S 1 ða4 cosðh23 þ 3p=4Þ þ a3 cosðh23 Þ þ a2 þ a1 Þ 5; a4 sinðh23 þ 3p=4Þ þ a3 sinðh23 Þ þ a2 þ a1 ð24Þ subjected to the limits, p/2 < h1 < p/2, 3p/4 < h23 < 3p/4 2

C 1 ða4 cosðh23 Þ þ a3 cosðh23 Þ þ a2 þ a1 Þ

3

6 7 h4 ¼ 0 ) n7 ðq1 ; q3 Þ ¼ 4 S 1 ða4 cosðh23 Þ þ a3 cosðh23 Þ þ a2 þ a1 Þ 5;

ð25Þ

a4 sinðh23 Þ þ a3 sinðh23 Þ þ a2 þ a1 subjected to the limits, p/2 < h1 < p/2, 3p/4 < h23 < 3p/4. The surface patches n1 to n7 represent the singular surfaces of the manipulator and are numerically determined. Boundary surfaces, n1, n2, and n7, are plotted in Figs. 4 and 5. The combination of all the surfaces represents the WPAS of the manipulator (Fig. 6), with n1, n2, and n7 forming the boundary and the rest internal singular surfaces. 3.1.2. Wrist space Using the same method explained in the previous section, the singularities of the wrist joint could be analysed. This is plotted in Fig. 7.

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Fig. 4. Singular surfaces n1 and n2.

Fig. 5. Singular surface n7.

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Fig. 6. Wrist accessible space with internal singularities.

Fig. 7. Wrist space singularities.

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4. Moving URV to the target In order to optimally locate the URV, it has to be moved from the base position towards the targets, as a first step. As the URV is moved forward, the WPAS associated with the manipulator also moves. URV has to be moved until all the target points are reasonably well inside the WPAS. An analytical criterion to ensure this condition is given below. Let the target points are given as Pj, where, P ¼ ½ P x P y P z T and j = 1, 2, . . . that represents the number of points to be reached by the manipulator, with respect to the local navigation frame, XnYnZn. In order to make sure that the target points are within the workspace, the absolute distance between the target points and the workspace boundary nI should be greater than a specified minimum value [10] such as kPj  fi k P e

ð26Þ

where kÆk represents the Euclidean norm; e, a small positive value and fi the generalised surface given by 1i ¼ Rða;b;cÞ
ni þ Pbðxw ;y w ;zw Þ

ð27Þ

Here, R and Pb are used to represent the orientation and position of the URV with respect to the navigation frame. Thus, the six generalised variables used to track the URV motion is given as w ¼ ½ xw

yw

zw

a b c T

ð28Þ

If the target points satisfy Eqs. (1) and (26), the points will lie within the workspace of the manipulator.

5. Optimum positioning of URV It is difficult to find a universal criterion for optimisation of URV position. A suitable criterion, based on the application, is to be chosen. Here, we are considering dexterity of the manipulator at the target location as the criterion for optimisation. Since the onboard manipulator is used for manipulating the inspection surface, dexterity of the manipulator at the inspection point is found to be most appropriate. Dexterity of a manipulator is a measure of its accessibility to a point and depends on the kinematic structure and link lengths of the manipulator. Different methods are suggested in the literature for assessing and maximising the dexterity of a manipulator, for a given configuration. Some of the earlier works concentrated on workspace volume, reachability, and manipulability [13,14]. Kim and Khosla [15] introduced a number of dexterity measures, an analytical expression for measure of manipulability, condition number independent of the scale of manipulator etc. Kinematic isotropy and kinematic conditioning index (KCI) was used by

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Angeles and Lo´pez-Caju´n [16] to measure the dexterity of a manipulator. Karim et al. [17] used a dexterity measure, which uses an augmented Jacobian to calculate dexterity. The augmented Jacobian takes into consideration all joint limits and singular configurations of manipulator. As a measure of dexterity, kinematic conditioning index of the manipulator is adopted here, which is based on the condition number [18] of the augmented Jacobian matrix. The condition number of a square matrix is a measure of the relative round-off error amplification of the computed results, upon solving a linear system of equations, associated with that matrix, with respect to the relative round-off data [19]. The condition number is known to vary between unity and infinity, matrices with a unity condition umber being called isotropic. Kinematic isotropy has been used widely in design of serial and parallel manipulators [16,20]. The kinematic conditioning index of the 7-d.o.f. manipulator is defined as W¼

100 jg

ð29Þ

where jg is the condition number of the augmented Jacobian, Jg, based on the Frobenious norm, and is given as [19] jg ¼ kJ g kF
kJ 1 g kF

ð30Þ

where rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 trðJ g J Tg Þ kJ g kF ¼ 2 Augmented Jacobian, Jg, is given by [17]
 Uq 0 Jg ¼ I qk

ð31Þ

ð32Þ

In order to optimise the dexterity at all the target points, a weighted dexterity function g(q) has been defined as ... X gðqÞ ¼ qi W ð33Þ i¼1;2;...

where, qi, i = 1, 2, . . . are the specified weights at each target point. The above function is maximised to obtain the optimum location of the URV, subjected to the following conditions: (1) target points are inside the workspace, (2) target points are not on the singular surfaces, (3) manipulator is constrained and (4) URV motion is within a constrained space.

6. Algorithm for optimisation The algorithm for positioning of URV to maximise dexterity at the given target points is given in Fig. 8 as a flow chart. The initial position and orientation of

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Fig. 8. Positioning algorithm for maximising dexterity.

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URV, target points, dexterity weights at each point and the boundary surface details of the manipulator are given as input data. The URV base is moved incrementally in small steps of Dw from the base position and the new boundaries of the manipulator are calculated using Eq. (27) and checked for the conditions given by Eqs. (1) and (26). Once the target points are inside the workspace of the manipulator, optimisation of this position (wI) is carried out using the cost function given by Eq. (33). For the optimised position wo the manipulator boundaries are again calculated and checked for the conditions specified in Section 5. Simulation results of the above algorithm are presented in the following section.

7. Simulation The algorithm presented in Section 6 has been simulated to find out the optimum position of URV for a given target location. Three target points to be reached by the URV for an inspection process have been given as 2 3 3:7 3:0 4:0 6 7 Pt ¼ 4 3:5 3:3 4:2 5 ð34Þ 3:9 3:4 4:5 Equal dexterity weights are assumed at all points and the URV base position is given as wb ¼ ½ 0 0

0

0

0

0

T

ð35Þ

Using the algorithm, URV base is moved incrementally towards the target and the normalised distance from the boundary surface n7 to the target points is calculated and plotted as shown in Fig. 9. When all these values crosses a particular minimum threshold, (this value depends on the accuracy of result required, set as 0.1 in this case) the target points can be assumed to be within the boundary surface. The base position corresponding to this is taken as the intermediate position, wI of the URV and is found to be corresponding to wI ¼ ½ 3:15

2:55

3:4

0:72 

0 0

T

ð36Þ

KCI at this location is found to be ½ 4:59 5:66 2:05 . Fig. 10 shows the initial and final position and orientation of WPAS corresponding to the above motion of URV. Constrained optimisation of the URV position for maximising KCI was carried out using the objective function given by Eq. (33). The variation of cost function value and the dexterity measure at each of the target points during the optimisation are plotted in Fig. 11. The optimised position is obtained as wo ¼ ½ 3:74

2:17

4:25

0

0

0:72 T

ð37Þ

Fig. 12 shows the initial, intermediate and optimal position and orientation of the WPAS corresponding to the URV position. The conditioning index at the optimised

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Fig. 9. Variation of normalised distance between the boundary surface and targets.

Fig. 10. Positioning of WPAS to reach out to the target.

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Fig. 11. Variation of dexterity measure during optimisation.

Fig. 12. Position and orientation of WPAS corresponding to optimum location of URV.

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location is found to be [6.54 6.54 6.51], which is much higher than that at the intermediate position. Thus, the algorithm provides an efficient method to position a URV in a constrained environment to have optimum dexterity at the operating points. It is to be noted that the optimised position is not unique. Based on the criteria chosen, there can be more than one position and orientation at which the manipulability is maximum. Optimised position depends more on the manipulator kinematics and does not take into account the vehicle properties. In many instances, the vehicle may not be able to position and dock itself at the specified location due to its size and accessibility. It may be necessary to re-calculate the position, taking into account the new positional constraints introduced due to vehicle limitations. Also, any variations in the vehicle position, during a task, may affect the dexterity at the target points. 7.1. Graphical modelling A three dimensional model of the URV deployment and inspection environment was developed using Pro-Engineer and ported to a simulation package developed with Sense 8—WorldToolKit graphics toolkit. The simulation package can simulate

Fig. 13. Virtual environment display.

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various deployment strategies under different environmental conditions for the URV and the onboard manipulator, and can be used for analysing and improving the URV and the manipulator path planning and motion control strategies. This package was used to simulate the optimum positioning strategy of the URV. Target inspection points for the URV were specified to the system and the URV was commanded to autonomously position itself for the task. Using the strategy discussed in this paper, URV was able to position autonomously for the task. The simulation was also useful in studying the environmental issues in the positioning strategy. Fig. 13 shows the virtual environment display of the URV in a positioning task.

8. Conclusions A method for determining the optimal docking position of an underwater robotic vehicle for intervention tasks was presented here. The method is based on the kinematic structure of the manipulator onboard the vehicle and maximises the dexterity of it at the target points. Theoretical analysis as well as simulation results was presented to verify the method. The results presented show that the underwater vehicle can be positioned at an optimum location so as to have maximum operational capability in terms of manipulation. Even though the manipulator constraints are fully implemented, the environmental constraints are implemented partially only. This is mainly due to the uncertainty in the environmental conditions. Further work on this aspect of the problem is under progress.

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