- Email: [email protected]
Force Control of an Underwater Vehicle Equipped with a Robotic Manipulator
Copyright @ IFAC Robot Control, Vienna, Austria, 2000
POSITION/FORCE CONTROL OF AN UNDERWATER VEHICLE EQUIPPED WITH A ROBOTIC MANIPULATOR Philippe FRAISSE, Lionel LAPIERRE, Pierre DAUCHEZ [email protected] [email protected] dauchez@lirmmJr LlRMM - UMR 5506 CNRS / Universite Montpellier 11 161 rue Ada - 34392 Montpellier CEDEX 5 - France
Abstract: This paper proposes a new control method applied to an underwater vehicle equipped with a robot manipulator. This method is based on force control to stabilize the vehicle when the manipulator works in free or constrained space. The torque produced by the arm on the vehicle is estimated with a force sensor installed between the base of the manipulator and the vehicle. This allows correcting the position errors of the vehicle using an external force control loop. This paper presents this control law and shows some simulation results. Copyright © 2000 IFAC Keywords : Robotic manipulator, Force control.
1.
INTRODUCTION In a fluid the specific phenomena like added mass, buoyancy, drag forces, current loads make up the main disturbance. In fact, the motion of the arm in the fluid creates a torque that modifies the vehicle attitude (see Fig. I.). Building a vehicle rather large compared to the arm is a first way to avoid this problem. But this IS not always possible. Measurements and compensation of the reacting forces is the second way to eliminate it. This is the choice we have made and we present in a first part of the paper a control scheme that would theoretically allow us to compensate for, or at least minimize the reaction forces. The control method has been implemented and first simulation results confirm that it improves the stability of the vehicle during the arm motion. This paper is organized as follows. The principles of the control method are first described. To validate thi s theoretical study, we have developed with MA TLAB-SIMULlNKH' the dynamic model of a submarine robot constituted by a spherical vehicle and a two degree-of-freedom manipulator. We have considered the hydrodynamic disturbances acting on every element of the robot. This model has been
An underwater mobile manipulator is composed of two different parts: the vehicle and the manipulator. The global system is dynamically non-homogeneous and the problem to couple these two elements brings phenomena of mutual disturbances. Moreover, there are some specifications of the submarine environment, and most of the phenomena that are neglected in the air have to be specifically considered in the sea. In the air, the torque produced by the arm on the vehicle is generally neglected, because of the large mass of the vehicle compared to that of the arm and the forces exerted on the arm.
Fig. I. Am1-Vehicle disturbances
513
fluid flow . We obtain the equation:
validated by comparing its behavior to other experiments ran on the subject (N ewman, 1977; Yuh, 1990, Scholberg, 1990; McMillian, et aI. , 1995). The simulator is presented and we show some simulation results .
2.
following dynamic
F=A{P) . P+H(P ,P)
(I)
P=[X Y e e, e:l is a position vector, F=[F, F, TT, Tj' is a force vector, A(P) is a 5x5 inertia matrix including the added mass phenomenon,H(P, P) is a
CASE STUDY
The subject of this study concems the general problem of mobile manipulator control. Every environment (terrestrial, spatial, sub-sea) has its own specifications. This involves that, in front of the same question, there are different solutions to solve the problem of regulation of the dynamic coupling between the arm and the vehicle. We diagnostic the physical origins of the action of the arm. Some specific phenomena characterize the sub-sea environment. We can analyze the consequences of these phenomena on the behavior of the robot. Unlike the spatial domain, modeling the sub-sea environment is very complex. The main problem encountered is the precision of the estimation of the hydrodynamic coefficients. Furthermore, the coefficients vary according to the temperature, depth, salinity and winds. We propose to present simulation results of a submarine robot equipped with a manipulator as depicted in figure 2. We show the disturbances produced by the arm on the vehicle. We propose a solution to decrease these disturbances by controlling the interacting forces .
vector including the Coriolis, hydrodynamic and gravity effects.
Initial position
Desired position
Fig. 3. Open loop test A force sensor is added in the simulator as an elastic transmission between the arm and the vehicle. Consequently, we measure the torque and the forces produced by the arm on the vehicle. A preliminary test of the vehicle is presented when a PlO control law controls the arm (see Fig. 3 .). The vehicle is not controlled in this test. The desired position of the arn1 is Pd
=[0
0
0
~ ~J
The simulation results are presented in figures 4 (ideal motion) and 5 (real motion). The final arm positions is reached in 15s. The orientation of the vehicle tends to about 6 radians, which is of course not acceptable. Motions
effector Fig. 2. The undersea vehicle Fig. 4. Arm motion The Lagrange method has been used to develop the dynamic model of the robot. We have chosen to consider only three hydrodynamic phenomena: added mass, drag and buoyancy. The calculation of drag forces acting on the elements of the arm has to be integrative along the length of the links (Kiener. 1996). Newman showed (1977) that the added mass phenomenon. which is directly taken into account in the Lagrange development as the kinetic energy of the surrounding fluid, can be written under the form of virtual mass called added mass. The model chosen for the drag effect imposes for the robot to keep the absolute velocities of all its elements under a maximum value, to stay in a laminar regime of the
A solution to eliminate this problem is to get a mass of the vehicle higher than the arm. However, this solution decreases the workspace of the arm . Another possibility is to define a robust position control law to stabilize the vehicle. But the main problem is the low precision and bandwidth of the absolute position sensors used on undersea vehicles. Therefore, a priori, a robust position control law is not enough to stabilize the vehicle when the arm moves. In order to improve the results, we propose to add an external force control law on the position loop to minimize the interaction forces between the vehicle and the arm .
514
X axis (m)
sampling period. The desired force vector Fd =[000 00)'. The control vector Fecan be written as:
Y axis (m)
(4)
, ,'--TLi~~-e-i~' s-e-c-·~-n-d-sN--'
p; -
With P= P . The desired force vector has to be equal to zero to eliminate the interaction force between the manipulator and the vehicle.
Ti~e i~ sec~nds·
() vehicle orientation (rad) ' r---~---------------------~
Two simulation tests are presented. First of all, a motion of the arm without external force loop. In other words, only a position control loop of the vehicle is activated. The initial and desired configurations of the system are that of section 2. As foreseen, the position control loop is not robust when the arm moves (see Fig. 7.). In figure 8, we obtain some interesting results, using external force control loop. This force control loop reduces the disturbances . The position errors of the vehicle are globally divided by 1000. The external force control loop is a great improvement for underwater mobile manipulator.
Time in seconds Fig. 5. Open loop result, motion of the vehicle
3.
COMPENSATION IN FREE SPACE
The compensation of the disturbances when the arm moves in the free space is obtained by an external force control loop implemented on the vehicle only (see Fig. 6.). The force values are measured with a force sensor installed on the link between the arm and the vehicle. The goal of this compensation is to eliminate the interaction force between the manipulator and the vehicle.
X axis (m) o
~0+---7"""---:;; " ---:.,,---,-:;; o -~
Time in seconds
Time in seconds
e (rad)
0 05
os
-0
·0.1 - O lS
·0 ' · 0 25 0
Fig. 6. External force control law
)
·0 lSo! -----7"----:,':o:""- - - 7 , , ,-------,,:'::"o- - - - !,,.
Time in seconds
The force vector read on the sensor is defined as:
Fig. 7. Without external force loop As a matter of fact, the cause of the vehicle positioning error is the disturbance force/torque vector due to the arm motion . If we use position control of the vehicle, we use the consequence of the disturbance. Since there is a delay between the cause and the consequence, we obtain large positioning errors during the movement. Of course, after a while, we can have zero steady-state error if we use a good position control law. Now, if we use force control, we directly measure the cause of the problem and the positioning errors are drastically reduced. However, force control alone cannot guarantee a zero steady-
The desired position of the vehicle is computed as follows:
~
Where
D.Pd
= K p. F+ K,
.
I/n ·Te
(3)
n=O
With F = Fd - Fr is the force error vector, Kp and K, are (5x5) diagonal matrices, namely proportional and integral gain matrices, respectively, and Te is the
515
The arm-vehicle model when the manipulator pushes on the environment is given in figure 11.
state position error. This is why a position/force control scheme seems to be the solution. ~ axis (IO-".m)
.Y axis ( 10. 5 .m)
Time in seconds e (10.5 .rad)
Fig. 11. Contact model Time in seconds The equations are:
'r-----------------------------------,
-
F;; -K< ·X" -K,' )("" -D,' Xap -Mh ·)(" =0
where Fa is a force due to the actuators of the arm, Ke is the stiffness of the environment, K, is the stiffness of the link between the arm and the vehicle (force sensor), D, the damping friction, Ma the mass of the ann, Mp/ the mass of the vehicle, :pj the force of the
60~------7-----~~----~~--~~----~"
Time in seconds
vehicle due to the thrusters and X ap = X a Fig. 8. With external force loop
4.
(5)
-
X
p'
By
rnaking t tending towards infinity, equations (5) allows us to determine that it is necessary to verify the following equality to force control the mobile rnanipulator:
FORCE CONTROL LAW
The previous solution allows to compensate the disturbances caused by the movement of the arm. This solution can be used to control the force exerted by the manipulator on the environment. An external force loop is also used to control the manipulator (Figure 9). We propose to modify the previous control equation (4) to obtain a satisfying response of the robot during the task described in figure 10.
fd is the desired force on the environment along the
X axis. This result allows us to determine the following equations.
J'
Fr = [Fx
FI
rr
rI
r
FJ = [FxJ
F,d
0
rlJ
r2.t! .
(7)
[:J=;t .[;:] With J ' is the (2x2) Jacobian matrix of the arm . Using equations (2) and (3) with the vector F we obtain a force control vector similar to that of equation 4. The main difference between the position (free space) a~d the force control law is the force R
error vector F. We have a hybrid position/force control equation for underwater mobile manipulator based on external force control. We can define a generalized vector Fr to control in position and force ;he mobile manipulator such that:
R.
Fig. 9. Generalized external force control law
Thruster Frocc~
z with a= I in force control , and a=0 in position control to compensate for the interacting forces between the arm and the vehicle. Fig. 10. Mobile manipulator in constrained space
516
Fossen T.I., "Guidance and Control of Ocean Vehicles", John Wiley and Sons, New York, 1st. ed.,1994 Kiener 1., "Coupled Vehicle and Manipulator Modeling and Control : Scope of the Work", UNION Project, ESPRlT BRA #8972 - D5 .6, 1996 Yuh 1., "Control of Underwater Robotic Vehicles", IEEE Transactions on Systems, Man, and Cybernetics, Vo120, No. 6,1990
o~~~~--~--~--~--~--~--~
o
20
40
60
80
'00
'20
'40
'60
Time in seconds
Scholberg I., Fossen T.I., 'Modelling and Control of Underwater Vehicule-Manipulator Systems", Technical report, Department of Engineering Cybernetics, Norwegian Institute of Technology, Trondheim, Norway, 1990 McMillian S., Orin D.E., Mc Ghee R.B ., "Efficient Dynamic Simulation of an Underwater Vehicle with a Robotic Manipulator", IEEE Transactions on Systems, Man and Cybernetics, Vo!. 25, No. 8, 1995, pp. 1194-1206
Fig. 12. Force control A simulation result is presented in figure 12. The mobile manipulator pushes on the environment along the X axis. We obtain a satisfying force response of the arm on the environment . The arm pushes on the environment and the thrusters of the vehicle compensate for the action of the arm at its base, fixed on the vehicle. The vehicle keeps its situation stable while the arm is working. This implies for the vehicle to exert the desired force on the base of the manipulator (equation 6).
5.
loi K., Itoh K., "Modelling and Simulation of an Underwater Manipulator, Advanced Robotics, Vo!. 4, 1990, pp. 303-317
CONCLUSION Yamamoto Y., Yun X., "Coordinating Locomotion and Manipulation of a Mobile Manipulator", Proc. of the 31" Conf. on Decision and Control, Tucson, Arizona, 1992, pp. 2643-2648.
This paper aimed at proposing and analyzing a control method to compensate for the disturbances produced by a manipulator motion on the underwater vehicle carrying it. Simulation results performed with a realistic simulator have proved the efficiency of our approach. However, we are aware that real tests will have to be performed in the future . With this goal in mind, we work in close relationship with the French Institute for Marine Research (IFREMER) that owns a small submarine equipped with a 7-axis Mitsubishi PA-1O manipulator. However, it is not reasonable to install on this system a force sensor between the vehicle and the manipulator. Therefore, we are currently investigating the performance we could obtain if only joint torque sensors can be used.
Yamamoto Y., Yun X., "Control of Mobile Manipulation Following a Moving Surface", Proc. of the 1993 IEEE Int. Conf. of Robotics and Automation, Atlanta, Georgia, 1993, pp. 1-6. Mahseh H., Yuh 1., Lakshrni R., "A Coordinated Control of an Underwater and Robotic Manipulators", Journal of Robotic Systems, Vo!. 8, No. 3, 1991, pp. 339-370
REFERENCES Newman J.N., "Marine Hydrodynamics", Cambridge, MIT Press, 1st. ed., 1977 Faltinsen O.M ., "Sea Loads on Ships and Offshore Structures", Cambridge University Press, 1st. ed., 1990 Goldstein RJ ., "Fluid Mechanics Measurements", Hemisphere Publishing Corporation, 1st. ed., 1976
517
POSITION/FORCE CONTROL OF AN UNDERWATER VEHICLE EQUIPPED WITH A ROBOTIC MANIPULATOR Philippe FRAISSE, Lionel LAPIERRE, Pierre DAUCHEZ [email protected] [email protected] dauchez@lirmmJr LlRMM - UMR 5506 CNRS / Universite Montpellier 11 161 rue Ada - 34392 Montpellier CEDEX 5 - France
Abstract: This paper proposes a new control method applied to an underwater vehicle equipped with a robot manipulator. This method is based on force control to stabilize the vehicle when the manipulator works in free or constrained space. The torque produced by the arm on the vehicle is estimated with a force sensor installed between the base of the manipulator and the vehicle. This allows correcting the position errors of the vehicle using an external force control loop. This paper presents this control law and shows some simulation results. Copyright © 2000 IFAC Keywords : Robotic manipulator, Force control.
1.
INTRODUCTION In a fluid the specific phenomena like added mass, buoyancy, drag forces, current loads make up the main disturbance. In fact, the motion of the arm in the fluid creates a torque that modifies the vehicle attitude (see Fig. I.). Building a vehicle rather large compared to the arm is a first way to avoid this problem. But this IS not always possible. Measurements and compensation of the reacting forces is the second way to eliminate it. This is the choice we have made and we present in a first part of the paper a control scheme that would theoretically allow us to compensate for, or at least minimize the reaction forces. The control method has been implemented and first simulation results confirm that it improves the stability of the vehicle during the arm motion. This paper is organized as follows. The principles of the control method are first described. To validate thi s theoretical study, we have developed with MA TLAB-SIMULlNKH' the dynamic model of a submarine robot constituted by a spherical vehicle and a two degree-of-freedom manipulator. We have considered the hydrodynamic disturbances acting on every element of the robot. This model has been
An underwater mobile manipulator is composed of two different parts: the vehicle and the manipulator. The global system is dynamically non-homogeneous and the problem to couple these two elements brings phenomena of mutual disturbances. Moreover, there are some specifications of the submarine environment, and most of the phenomena that are neglected in the air have to be specifically considered in the sea. In the air, the torque produced by the arm on the vehicle is generally neglected, because of the large mass of the vehicle compared to that of the arm and the forces exerted on the arm.
Fig. I. Am1-Vehicle disturbances
513
fluid flow . We obtain the equation:
validated by comparing its behavior to other experiments ran on the subject (N ewman, 1977; Yuh, 1990, Scholberg, 1990; McMillian, et aI. , 1995). The simulator is presented and we show some simulation results .
2.
following dynamic
F=A{P) . P+H(P ,P)
(I)
P=[X Y e e, e:l is a position vector, F=[F, F, TT, Tj' is a force vector, A(P) is a 5x5 inertia matrix including the added mass phenomenon,H(P, P) is a
CASE STUDY
The subject of this study concems the general problem of mobile manipulator control. Every environment (terrestrial, spatial, sub-sea) has its own specifications. This involves that, in front of the same question, there are different solutions to solve the problem of regulation of the dynamic coupling between the arm and the vehicle. We diagnostic the physical origins of the action of the arm. Some specific phenomena characterize the sub-sea environment. We can analyze the consequences of these phenomena on the behavior of the robot. Unlike the spatial domain, modeling the sub-sea environment is very complex. The main problem encountered is the precision of the estimation of the hydrodynamic coefficients. Furthermore, the coefficients vary according to the temperature, depth, salinity and winds. We propose to present simulation results of a submarine robot equipped with a manipulator as depicted in figure 2. We show the disturbances produced by the arm on the vehicle. We propose a solution to decrease these disturbances by controlling the interacting forces .
vector including the Coriolis, hydrodynamic and gravity effects.
Initial position
Desired position
Fig. 3. Open loop test A force sensor is added in the simulator as an elastic transmission between the arm and the vehicle. Consequently, we measure the torque and the forces produced by the arm on the vehicle. A preliminary test of the vehicle is presented when a PlO control law controls the arm (see Fig. 3 .). The vehicle is not controlled in this test. The desired position of the arn1 is Pd
=[0
0
0
~ ~J
The simulation results are presented in figures 4 (ideal motion) and 5 (real motion). The final arm positions is reached in 15s. The orientation of the vehicle tends to about 6 radians, which is of course not acceptable. Motions
effector Fig. 2. The undersea vehicle Fig. 4. Arm motion The Lagrange method has been used to develop the dynamic model of the robot. We have chosen to consider only three hydrodynamic phenomena: added mass, drag and buoyancy. The calculation of drag forces acting on the elements of the arm has to be integrative along the length of the links (Kiener. 1996). Newman showed (1977) that the added mass phenomenon. which is directly taken into account in the Lagrange development as the kinetic energy of the surrounding fluid, can be written under the form of virtual mass called added mass. The model chosen for the drag effect imposes for the robot to keep the absolute velocities of all its elements under a maximum value, to stay in a laminar regime of the
A solution to eliminate this problem is to get a mass of the vehicle higher than the arm. However, this solution decreases the workspace of the arm . Another possibility is to define a robust position control law to stabilize the vehicle. But the main problem is the low precision and bandwidth of the absolute position sensors used on undersea vehicles. Therefore, a priori, a robust position control law is not enough to stabilize the vehicle when the arm moves. In order to improve the results, we propose to add an external force control law on the position loop to minimize the interaction forces between the vehicle and the arm .
514
X axis (m)
sampling period. The desired force vector Fd =[000 00)'. The control vector Fecan be written as:
Y axis (m)
(4)
, ,'--TLi~~-e-i~' s-e-c-·~-n-d-sN--'
p; -
With P= P . The desired force vector has to be equal to zero to eliminate the interaction force between the manipulator and the vehicle.
Ti~e i~ sec~nds·
() vehicle orientation (rad) ' r---~---------------------~
Two simulation tests are presented. First of all, a motion of the arm without external force loop. In other words, only a position control loop of the vehicle is activated. The initial and desired configurations of the system are that of section 2. As foreseen, the position control loop is not robust when the arm moves (see Fig. 7.). In figure 8, we obtain some interesting results, using external force control loop. This force control loop reduces the disturbances . The position errors of the vehicle are globally divided by 1000. The external force control loop is a great improvement for underwater mobile manipulator.
Time in seconds Fig. 5. Open loop result, motion of the vehicle
3.
COMPENSATION IN FREE SPACE
The compensation of the disturbances when the arm moves in the free space is obtained by an external force control loop implemented on the vehicle only (see Fig. 6.). The force values are measured with a force sensor installed on the link between the arm and the vehicle. The goal of this compensation is to eliminate the interaction force between the manipulator and the vehicle.
X axis (m) o
~0+---7"""---:;; " ---:.,,---,-:;; o -~
Time in seconds
Time in seconds
e (rad)
0 05
os
-0
·0.1 - O lS
·0 ' · 0 25 0
Fig. 6. External force control law
)
·0 lSo! -----7"----:,':o:""- - - 7 , , ,-------,,:'::"o- - - - !,,.
Time in seconds
The force vector read on the sensor is defined as:
Fig. 7. Without external force loop As a matter of fact, the cause of the vehicle positioning error is the disturbance force/torque vector due to the arm motion . If we use position control of the vehicle, we use the consequence of the disturbance. Since there is a delay between the cause and the consequence, we obtain large positioning errors during the movement. Of course, after a while, we can have zero steady-state error if we use a good position control law. Now, if we use force control, we directly measure the cause of the problem and the positioning errors are drastically reduced. However, force control alone cannot guarantee a zero steady-
The desired position of the vehicle is computed as follows:
~
Where
D.Pd
= K p. F+ K,
.
I/n ·Te
(3)
n=O
With F = Fd - Fr is the force error vector, Kp and K, are (5x5) diagonal matrices, namely proportional and integral gain matrices, respectively, and Te is the
515
The arm-vehicle model when the manipulator pushes on the environment is given in figure 11.
state position error. This is why a position/force control scheme seems to be the solution. ~ axis (IO-".m)
.Y axis ( 10. 5 .m)
Time in seconds e (10.5 .rad)
Fig. 11. Contact model Time in seconds The equations are:
'r-----------------------------------,
-
F;; -K< ·X" -K,' )("" -D,' Xap -Mh ·)(" =0
where Fa is a force due to the actuators of the arm, Ke is the stiffness of the environment, K, is the stiffness of the link between the arm and the vehicle (force sensor), D, the damping friction, Ma the mass of the ann, Mp/ the mass of the vehicle, :pj the force of the
60~------7-----~~----~~--~~----~"
Time in seconds
vehicle due to the thrusters and X ap = X a Fig. 8. With external force loop
4.
(5)
-
X
p'
By
rnaking t tending towards infinity, equations (5) allows us to determine that it is necessary to verify the following equality to force control the mobile rnanipulator:
FORCE CONTROL LAW
The previous solution allows to compensate the disturbances caused by the movement of the arm. This solution can be used to control the force exerted by the manipulator on the environment. An external force loop is also used to control the manipulator (Figure 9). We propose to modify the previous control equation (4) to obtain a satisfying response of the robot during the task described in figure 10.
fd is the desired force on the environment along the
X axis. This result allows us to determine the following equations.
J'
Fr = [Fx
FI
rr
rI
r
FJ = [FxJ
F,d
0
rlJ
r2.t! .
(7)
[:J=;t .[;:] With J ' is the (2x2) Jacobian matrix of the arm . Using equations (2) and (3) with the vector F we obtain a force control vector similar to that of equation 4. The main difference between the position (free space) a~d the force control law is the force R
error vector F. We have a hybrid position/force control equation for underwater mobile manipulator based on external force control. We can define a generalized vector Fr to control in position and force ;he mobile manipulator such that:
R.
Fig. 9. Generalized external force control law
Thruster Frocc~
z with a= I in force control , and a=0 in position control to compensate for the interacting forces between the arm and the vehicle. Fig. 10. Mobile manipulator in constrained space
516
Fossen T.I., "Guidance and Control of Ocean Vehicles", John Wiley and Sons, New York, 1st. ed.,1994 Kiener 1., "Coupled Vehicle and Manipulator Modeling and Control : Scope of the Work", UNION Project, ESPRlT BRA #8972 - D5 .6, 1996 Yuh 1., "Control of Underwater Robotic Vehicles", IEEE Transactions on Systems, Man, and Cybernetics, Vo120, No. 6,1990
o~~~~--~--~--~--~--~--~
o
20
40
60
80
'00
'20
'40
'60
Time in seconds
Scholberg I., Fossen T.I., 'Modelling and Control of Underwater Vehicule-Manipulator Systems", Technical report, Department of Engineering Cybernetics, Norwegian Institute of Technology, Trondheim, Norway, 1990 McMillian S., Orin D.E., Mc Ghee R.B ., "Efficient Dynamic Simulation of an Underwater Vehicle with a Robotic Manipulator", IEEE Transactions on Systems, Man and Cybernetics, Vo!. 25, No. 8, 1995, pp. 1194-1206
Fig. 12. Force control A simulation result is presented in figure 12. The mobile manipulator pushes on the environment along the X axis. We obtain a satisfying force response of the arm on the environment . The arm pushes on the environment and the thrusters of the vehicle compensate for the action of the arm at its base, fixed on the vehicle. The vehicle keeps its situation stable while the arm is working. This implies for the vehicle to exert the desired force on the base of the manipulator (equation 6).
5.
loi K., Itoh K., "Modelling and Simulation of an Underwater Manipulator, Advanced Robotics, Vo!. 4, 1990, pp. 303-317
CONCLUSION Yamamoto Y., Yun X., "Coordinating Locomotion and Manipulation of a Mobile Manipulator", Proc. of the 31" Conf. on Decision and Control, Tucson, Arizona, 1992, pp. 2643-2648.
This paper aimed at proposing and analyzing a control method to compensate for the disturbances produced by a manipulator motion on the underwater vehicle carrying it. Simulation results performed with a realistic simulator have proved the efficiency of our approach. However, we are aware that real tests will have to be performed in the future . With this goal in mind, we work in close relationship with the French Institute for Marine Research (IFREMER) that owns a small submarine equipped with a 7-axis Mitsubishi PA-1O manipulator. However, it is not reasonable to install on this system a force sensor between the vehicle and the manipulator. Therefore, we are currently investigating the performance we could obtain if only joint torque sensors can be used.
Yamamoto Y., Yun X., "Control of Mobile Manipulation Following a Moving Surface", Proc. of the 1993 IEEE Int. Conf. of Robotics and Automation, Atlanta, Georgia, 1993, pp. 1-6. Mahseh H., Yuh 1., Lakshrni R., "A Coordinated Control of an Underwater and Robotic Manipulators", Journal of Robotic Systems, Vo!. 8, No. 3, 1991, pp. 339-370
REFERENCES Newman J.N., "Marine Hydrodynamics", Cambridge, MIT Press, 1st. ed., 1977 Faltinsen O.M ., "Sea Loads on Ships and Offshore Structures", Cambridge University Press, 1st. ed., 1990 Goldstein RJ ., "Fluid Mechanics Measurements", Hemisphere Publishing Corporation, 1st. ed., 1976
517