KR101249853B1 - Approximated modeling method of generalized drag torque acting on multi-joint links underwater robot - Google Patents

Abstract

The present invention provides an approximate modeling method of a fluidized force acting on a link of an articulated subsea robot moving to walking and swimming using a articulated walking leg on the sea floor and a generalized fluid force torque acting on a joint.
The approximate modeling method of the fluid force torque acting on the multi-moveable multi-sea subsea robot according to the present invention is an approximate modeling method of the fluid force that can be used for the equation of motion of the closed articulated articulated link. And determining an application range of the fluid force coefficient according to the cross-section of the articulated link of the walking robot. Approximating a fluid force acting on the articulated link moving in the fluid; Calculating fluid force torque acting on the joint coordinate system through fluid force acting on the articulated link; And converting the fluid force acting on the coordinate system into a fluid force acting on the joint axis and calculating the fluid force torque by all the links after the joint.

Description

APPROXIMATED MODELING METHOD OF GENERALIZED DRAG TORQUE ACTING ON MULTI-JOINT LINKS UNDERWATER ROBOT}

The present invention relates to an approximate modeling method of a generalized fluid resistance torque acting on the articulated link. More specifically, the articulated seabed moves in the water by walking and swimming by reaching the sea floor using the articulated walking leg. The present invention relates to an approximate modeling method of a fluid resistance torque acting on a multi-joint subsea robot capable of multiple movements on a joint due to the fluid force acting on the articulated link of the robot and the fluid force acting on the articulated link.

The Korea Ocean Research & Development Institute started to develop multi-joint combined mobile subsea robot since 2010. The purpose of the articulated submarine robot is to investigate and work on the seabed, mainly to study the seabeds of heavy seas and bad-clocks, such as the western coast of Korea, which is difficult to carry out by conventional ROV (remotely operated vehicle) or AUV (autonomous underwater vehciel). It is to conduct an exploration with minimal disturbance. Multi-joint submarine robot is a new concept of submarine robot that moves to submarine walking or swimming by using multiple legs, unlike the existing ROV or AUV that propulsion is promoted by propeller. Crab and Lobster The robot is named 'Crabster' because it is similar in shape and moving.

Subsea robots have relative dynamics with fluids in an underwater environment with a density of 1000 times that of air. How to analyze, model, and use the fluid forces acting on underwater robots is one of the main factors that distinguish underwater robot technology from airborne robot technology. When maintaining posture and walking or swimming with multi-joint multi-joints in water with velocity, consideration of the fluid force is essential and the modeling of the fluid force acting on the link must be preceded. In the case of the articulated link moving underwater, the motion characteristics are more complicated than the robot moving in the air due to the complex and various nonlinear fluid forces, but there are relatively few studies.

A study that classifies and organizes the major forces acting on underwater rigid bodies has been disclosed [J. Yuh, "Modeling and control of underwater robotic vehicles," IEEE Transaction on Systems, Man and Cybernetics, vol. 20, pp. 1475-1483, November / December 1990, T.I. Fossen, Guidance and Control of Ocean Vehicles, Chichester, John Wiley & Sons Ltd., 1994.]. Also disclosed is a method for estimating the resistance torque acting on a square beam in water [Benoit L'evesque and Marc J. Richard, "Dynamic analysis of a manipulator in a fluid environment," International Journal of Robotics Research, vol. 13, no. 3, pp. 221-231, June 1994.]. The data disclosed above use the cross-flow principle to obtain the pressure-resistance acting on a beam that translates at a certain angle to Hoerner's free stream. The resistance acting on the fragment of the square beam was estimated, and the resistance acting on the long beam was estimated using the strip theory. In addition, a study that extends traditional N-E (Newon-Euler) mechanics to the case of an underwater robot arm has been disclosed [K. Ioi and K. Itoh, "Modeling and simulation of an underwater manipulator," Advanced Robotics, vol. 4, no. 4, pp. 303-317, 1990.]. In addition, a simulation algorithm for a submersible equipped with a robotic arm has been disclosed based on the NE formula for an underwater robotic arm [McMillan, D. E Orin and CSG Lee, "Efficient dynamic simulation of an underwater vehicle with a robotic manipulator," IEEE Transaction on Systems, Man, and Cybernetics, vol. 25, no. 8, pp. 1194-1206, Aug. 1995.]. In addition, a kinematic model of a submersible with a robotic arm has been disclosed using Kane's method [T. J. Tarn, G. A. Shoults and S. P. Yang, "A dynamic model of an underwater vehicle with a robotic manipulator using Kane's method", Autonomous Robots 3, pp. 269-283, 1996.]. In addition, studies have been conducted to show that the interaction between the robot arm and the submersible can be large by experimentally examining the behavior of added mass and fluid resistance coefficient for a single link [T. W. McLain and S. M. Rock, "Experiments in the coordination of underwater manipulator and vehicle control," Journal of Autonomous Robots, vol. 3, no. 2, pp. 139-158, June / July 1996.]. These previous studies were approaches to numerically model underwater robotic arms, but they did not provide a closed form dynamic equation for the generalized coordinate system variables and the underwater joints represented by their first and second derivatives. However, there is a problem that cannot induce a fluid force acting on a general type of articulated link.

In addition, many studies have been conducted on the hydrodynamic forces acting on rigid bodies in the water, and theories have been established. However, there are relatively few studies on the case where a link with multiple joints, such as a robot arm or leg, moves underwater. .

An object of the present invention is to provide a fluid resistance for a multi-moveable multi-sea subsea robot that operates on an articulated link that is induced to be applicable to a motion equation based on the LE (Lagrange-Euler) method for intuitively expressing closed-type motion. It provides an approximate modeling method of torque.

It is another object of the present invention to provide an approximate modeling method of a fluid resistance torque acting on a multi-moveable multi-sea subsea robot that operates on a general articulated link applicable to a pitch, ureter, and roll joint.

Approximate modeling method of fluid resistance torque acting on the multi-joint seabed robot capable of complex movement acting on the articulated link according to an embodiment of the present invention for achieving the above object,

A first step of estimating a fluid force coefficient applicable to the articulated link cross-sectional shape in the water and the articulated link cross-sectional shape of the subsea robot swimming or walking underwater according to the Reynolds number;

A second step of calculating a fluid force acting on a virtual disk piece by dividing each link of the articulated submarine robot into pieces using a fluid force calculation algorithm;

Calculate the fluid force torque acting on the i-coordinate system by integrating the fluid force acting on the disk piece on the j link with respect to the link length, that is, the fluid force acting on the joint coordinate system through the fluid force acting on the articulated link. Calculating a torque;

calculating a generalized fluid force torque by converting the fluid force torque acting on the i-coordinate system to the fluid force torque acting on the i-joint axis and adding up the fluid force torques by the link after the i-joint, i.e., the joint coordinate system And a fourth step of converting the fluid force torque acting on the fluid force torque acting on the joint, and calculating the fluid force torque caused by the articulated link.

Wherein the first step comprises: calculating a Reynolds number using a Reynolds number calculation algorithm; When the robot is moving within a range of Reynolds number range, it is preferable to include the step of estimating the fluid force coefficient according to the cross-sectional shape of each underwater link.

And, the second step, the fluid force calculation step acting on the disk piece of the link, calculating the velocity vector component of the disk piece on the j-th link with respect to the joint angle and the velocity of the fluid through a velocity component calculation algorithm Wow; calculating a projection matrix defined in the i coordinate through a projection matrix calculation algorithm in a plane perpendicular to the j link defined in the i coordinate system (yz plane); calculating a velocity component vector of the disk fragment perpendicular to the j-th link using the projection vector and the velocity vector of the disk fragment on the j-th link defined in the i-coordinate system; Calculating a fluid force acting on a disc piece on the j-th link through a fluid force calculation algorithm.

In addition, the third step, the calculation of the fluid force torque for the link, the step of calculating the position vector of one disk piece on the j link with respect to the i coordinate system; And calculating a hydrodynamic torque acting on the i-coordinate system.

In addition, the fourth step, the generalized fluid force torque calculation step, the step of calculating the fluid force torque acting on the i joint by projecting the fluid force torque acting on the i coordinate system to the i joint axis, and the process It is preferable to repeat the step of calculating all the fluid force torque acting on the i coordinate system by the fluid force acting on the j link in the i-link and sum them to calculate the fluid force torque for the link after the i joint .

According to the present invention, the fluid force acting on the articulated articulated link and the fluid force torque induced therefrom can be modeled in a closed form and applied directly to the LE motion equation. Has one effect.

In addition, the present invention has an effect that can be easily applied to a variety of fields, such as step planning or swimming motion development of the articulated robot moving in the fluid.

In addition, the present invention has the effect of verifying the validity of the present invention by performing a simulation applied to a simple three-section Scara robot that can intuitively estimate the fluid force.

1 is a schematic conceptual diagram of a subsea exploration system using a multi-movement multi-sea subsea robot according to the present invention.
Figure 2 is a perspective view schematically showing a multi-movement multi-sea subsea robot according to an embodiment of the present invention.
3 is an internal block diagram of a multi-moveable multi-sea subsea robot according to the present invention.
Figure 4 is a detailed view showing the joint portion of the robot leg of the articulated subsea robot according to a preferred embodiment of the present invention.
5 is a partial side cross-sectional view of a pressure-resistant waterproof joint structure consisting of an electric motor and a harmonic reducer of a multi-joint subsea robot according to a preferred embodiment of the present invention.
Figure 6 is a detailed view showing the joint portion of the robot arm combined leg according to a preferred embodiment of the present invention.
7 is a view showing the kinematic structure of the robot leg and robot arm combined leg according to a preferred embodiment of the present invention.
8 is a diagram illustrating an algorithm used in an approximate modeling method of a generalized fluid force torque acting on an articulated link according to the present invention.
FIG. 9 is a view illustrating FIG. 8 in detail.
FIG. 10 is a diagram illustrating a vector and a link coordinate system of an underwater articulated link of an articulated manual robot capable of multiple movements in the approximate modeling method of generalized hydraulic force torque acting on the articulated link according to the present invention.
FIG. 11 is a view similar to that of FIG. 10, showing a disk piece of the articulated link and its velocity vector.
12 is a view showing the coordinate system and link parameters of a section 3 link robot used to confirm the approximate modeling method of the generalized fluid resistance torque acting on the articulated link according to the present invention.
13 to 15 are graphs showing the fluid torque of each joint with respect to the joint angle change of joint 3 when joints 3, 2, and 1 of the third link robot of FIG. 12 each have a unit speed.
16 to 18 are graphs schematically showing the fluid torque of each joint with respect to the joint angle when joints 3, 2, and 1 of the third link robot of FIG. 12 each have a unit speed.

Advantages and features of the present invention and methods for achieving them will be apparent with reference to the embodiments described below in detail with the accompanying drawings. It should be understood, however, that the invention is not limited to the disclosed embodiments, but is capable of many different forms and should not be construed as limited to the embodiments set forth herein. Rather, these embodiments are provided so that this disclosure will be thorough and complete, To fully disclose the scope of the invention to those skilled in the art, and the invention is only defined by the scope of the claims. Like reference numerals refer to like elements throughout the specification.

Hereinafter, an approximate modeling method of a fluid resistance torque acting on a multi-joint subsea robot capable of moving in accordance with a preferred embodiment of the present invention will be described in detail with reference to the accompanying drawings.

When walking or swimming with multi-joint multi-foot in water with velocity, the path planning and control of the joint considering the fluid force is necessary. For this purpose, the modeling of the fluid force acting on the bridge link is essential.

The present invention focuses on this, and proposes a numerical model method of fluid force for the articulated link that must be preceded in order to actively utilize the fluid force using the articulated leg in water.

In the present invention, first, by dividing the link into pieces and estimating the fluid force acting on each piece, the fluid force acting on the link is expressed as a function of joint angle and joint velocity by integrating it according to the elongated body theory. The microtorque was calculated by considering the distance vector from each joint to the link fragments and numerically integrated to obtain the generalized fluid resistance torque. In order to verify the validity of the proposed modeling method, a simple three-section SCARA robot is simulated and the results are discussed.

On the other hand, the present invention intends to overcome the existing limitations with a subsea robot of a new concept different from the existing propeller type submersible, for this purpose it is disclosed a multi-joint subsea robot capable of a complex movement as shown in FIG. The existing limitations or problems mentioned in the prior art are overcome by the following concept.

First of all, in terms of safety issues, submarine robots are used instead of divers in environments where it is dangerous for divers to work directly.

On working time issues, the diver's diving time limit is overcome by using a subsea robot.

Regarding the algae problem, the robot overcomes the algae by maintaining a posture in which the grounding force is increased by being in close contact with the seabed, and by placing the buffer 200 between the subsea robot 100 and the mothership 300, the algae force applied to the cable is a submarine robot ( Reduce the impact on

Regarding the clock problem, various ultrasonic imaging apparatuses, which are relatively less affected by turbidity, are utilized, and optical cameras are used for proximity checking.

Regarding obstacles and irregular undersea terrain problems, use a multi-legged landing on the sea floor to maintain static stability so as not to be entangled with obstacles.

Regarding the problem of environmental interference, move and work in the way of seabed walking to minimize the disturbance of the seabed.

We define four core technologies for developing multi-moveable multi-sea subsea robots according to the present invention, and propose an approach for technology development. Unlike the existing submarine robot, which propels the thrust, the newly proposed submarine robot provides a new concept of submarine robot that moves and walks and walks close to the sea floor using legs consisting of several joints.

The concept of undersea robots is similar to the way crabs and lobsters move and work on the bottom of the sea, so the robot is named 'Crabster'.

The subsea robot according to the present invention performs a sunken ship exploration and marine science survey in the seabed up to 200m deep offshore in Korea (also performs marine science survey in the seabed up to 6000m depth). In particular, it can work in the environment of the west coast where the tidal current is strong and visibility is poor, and it has a swimming and walking function without disturbing the environment in the sedimented soil.

1A and 1B are schematic conceptual views of a seabed exploration system using a multi-joint seabed robot capable of moving in accordance with the present invention.

Referring to FIG. 1A, the sea floor exploration system 1000 using the multi-joint seabed robot capable of complex movement according to the present invention shows a state in which the multi-joint seabed robot 100 capable of complex movement reaches and reaches 200 m below the sea floor. The articulated subsea robot 100 is connected to the depressor 200 by a secondary cable 240, and the shock absorber 200 is connected to the bus bar 300 by a primary cable 220. The resistance of the primary cable 220 takes up to the shock absorber 200 and is not transmitted to the subsea robot 100.

The subsea exploration system 1000 using the 200 m multi-role subsea robot 100 capable of moving complex is a depressor 200 to minimize the influence of the fluid force acting on the tether cable to the robot in the heavy current environment. It is a concept to put and operate). The subsea exploration system 1000 has two tasks as follows.

Observation of submarine structures or sinking ships

It moves close to the seabed in the stress environment up to 2 knots to approach the seabed structures and sinking ships, and to investigate the structures existing in the dark clock undersea environment using optical and acoustic equipment.

Robotic arms are used to cut, grind and drill wires, which are necessary for the observation and observation of subsea structures and sinking ships.

Cheonhae Marine Science Research

By moving to a multi-pedestrian walk within 200m of the seabed, it acquires scientific research data necessary for research on marine physics, chemistry, biology and geology while minimizing disturbance of the seabed.

Samples of organisms, soil, and seawater needed for scientific investigations are taken within 200 meters of the seabed.

Referring to FIG. 1B, another embodiment of the present invention shows a state in which a deep sea submarine exploration system 1000-1 capable of exploring by complex movement reaches and swims and walks at 6000 m under the sea, and the articulated seabed The robot 100-1 is connected by a cable to the depressor 200, and the shock absorber 200 is connected by a cable to the bus bar 300. The shock absorber 200 and the articulated subsea robot 100-1 are capable of wired communication or wireless communication.

The subsea exploration system 1000 using the 6,000 m exploration articulated subsea robot 100 that is capable of combined movement was designed to assume a deep sea environment with little algae, but to minimize the effect of the weight of the tether cable on the robot. It is a concept of operating by operating a depressor (200). Deep articulated subsea robots have a buoyancy control function to minimize disturbance to deep sea sediment and prevent the robot's foot from falling into the sea soil. The subsea exploration system 1000 has two tasks as follows.

Deep Sea Marine Science Research

Acquire scientific research data necessary for research of marine physics, chemistry, biology and geology while minimizing sea disturbance in the deep subsea environment of soft ground consisting of sedimentary soil.

Samples of organisms, soil, and seawater needed for scientific research are taken from up to 6,000 meters of seabed.

Long-term Precision Subsea Survey

Investigate close-up precision of irregular seabed topography such as subsea thermal receiving image.

In the wireless autonomous control mode, it operates alone without a buffer and observes a long-term view of a fixed area with minimal energy.

Table 1 shows schematic specifications for FIGS. 1A and 1B, which are examples of the multi-joint seabed robot capable of moving in accordance with the present invention, respectively.

 [Table 1]

As shown in Table 1, the number of legs is four walking legs and two robot arm combined legs.

In addition, the subsea robot according to the present invention is provided with a device capable of detecting a bad clock on the sea floor. The basic specifications (when the legs are folded) are 2.2m in length, 1m in width, 1.1m in height, maximum weight 300kg (including load capacity), 0.5m above ground level, 4 feet of walking legs, 4 DOF legs, 6 DOF legs Two, the maximum specification is a maximum walking speed of 0.5m / sec (1.8km / h), a maximum operating depth of 200m, a maximum bimodulation speed of 2 knots, and a maximum power consumption of 20kW or less. The ability to overcome sea conditions is the maximum working condition Sea state 3 and the maximum survival condition Sea state 4. The bad watch detection capability can be performed in two types, a detection distance of 100m or more and a 10m or more. In other words, it is equipped with a front scanning sonar that can scan the front from the sea floor with a maximum detection distance of more than 100m and an ultrasonic camera that provides a real-time sonar image with a maximum detection distance of more than 10m. The control method is wired remote control method, and the power supply uses a tether cable.

The function of the subsea robot capable of combined movement is once again summarized.

function

-Adjust the posture of the body with multi-joint multi-legs by walking on the sea floor and moving the gait.

-Equipped with two robotic arms for working on the sea floor.

-Equipped with ultrasonic imaging equipment to overcome the bad clock.

-Built in turbidity, dissolved oxygen, conductivity, temperature, depth and pH measurement sensor.

-All information of the submarine robot is remotely monitored in real time.

-Posture stabilization and footstep correction function for overturning risk due to disturbance such as irregular terrain, bird, etc.

Pressure tight watertight method

-Structurally stable pressure and watertight performance at a depth of 200m.

-In case of watertight water tightness such as rotating shaft system, guarantee operation in insulating oil.

-Anticorrosive function against corrosion by sea water and salt.

Toughness

-Operation in Sea State 3, Survive in Sea State 4.

-Move and work in 2 knots of current, survive in 3 knots of current.

-Normal operation in temperatures from minus 10 degrees to 40 degrees and survives from minus 30 degrees to 75 degrees.

responsibility

-Can be used continuously for 24 hours underwater and at sea.

-Scientific research data maintain internationally recognized credibility.

Operational Convenience

-Launching is possible at sea level 3 or lower.

-User graphic interface for operator convenience.

-Reduced operator burden by providing some automatic functions.

Maintainability

-The submarine robot and its supporting devices are easy to disassemble, assemble and replace.

-Modular production, sufficient spare parts.

-Various buses can be used, easy to pack, move and install.

Scalability

-Secure communication channel and power line of extra channel for additional equipment.

-Robot arm replacement of underwater work tools.

Emergency response function

-When the mechanical connection between the submarine robot and the remote system is broken, the submarine robot uses its own power for more than 3 days to transmit its underwater position by ultrasound.

-If the submarine robot is overturned underwater due to excessive seabed steepness, instantaneous current flow or operation mistake, secure the ability to recover its posture by itself or with the help of a remote support device.

The 6,000m exploration submarine robot according to the present invention is similar to the 200m exploration submarine robot, but has little effect of algae and aims to carry out scientific research in a stable deep sea environment with a good watch, and further has a built-in buoyancy control function. By having a swimming function, disturbance of sediment soil is minimized. In addition, wireless communication and autonomous control were added to expand the type and method of exploration.

Details of the approach to the development of underwater joint mechanism of the subsea robot according to the present invention are summarized in Table 2 below.

[Table 2]

According to Table 2, as the main demanding function of the underwater joint mechanism, first, pressure / watertight is required in the mechanical field, and a motor / gear / bearing integrated waterproof joint module was developed. Perform development. In the anticorrosion method, corrosion resistant materials such as aluminum and stainless steel were applied, and oil repellent design of the insulating oil filling method was applied, and the anticorrosive structure was installed by installing a sacrificial anode. In addition, it adopts harmonic drive reducer to achieve zero backlash, performs structural analysis based optimal design, and uses lightweight high strength material.

In the electric field, to provide a submarine robot with a small, lightweight, high-power joint, a low-speed, high-torque BDC motor is adopted, a heat dissipation structure is designed using sea water and filling oil, and a hole center type for joint position feedback. A proximity limit sensor and an electric absolute position encoder are applied. In the field of control, compliance controller design is applied.

The structure of the articulated subsea robot according to the present invention will be described in more detail with reference to FIGS. 2 and 3.

First, Figure 2 is a perspective view schematically showing a multi-joint subsea robot according to an embodiment of the present invention. The articulated subsea robot of FIG. 2 is merely an embodiment, and its appearance is deformable.

2, the articulated subsea robot 100 is a streamlined body (110); A multi-jointed walking leg having a plurality of pairs mounted on the left and right sides of the body and composed of a plurality of joints; Control means mounted in the body and controlling a walking state and a swimming state in the water through the articulated walking leg; Walking leg driving means controlled by the control means for generating a driving signal for driving the articulated walking leg; Sensing means mounted in the body to sense a posture of the body and contact with an external object; And a buoyancy sensing means for detecting buoyancy of the body and communication means for transmitting / receiving a wired / wireless signal with the external device.

The buoyancy sensing means has a buoyancy sensor for providing a buoyancy sensing function, and provides a function to adjust the buoyancy of the body according to the sense signal detected by the buoyancy sensor.

The sensing means is characterized in that it comprises a posture and motion measurement sensor 42, the underwater position tracking device 50, and a force / moment sensor 43 installed on the bottom of the body.

It is mounted on the front of the body includes a photographing means for photographing the underwater image, wherein the photographing means comprises an ultrasonic camera 20 and the pan / tilt function underwater camera 22 and the lighting device (22a, not shown) It is done.

The communication means is characterized in that it comprises an optical communication modem (60).

The communication means is characterized in that connected to the shock absorber through the optical fiber and the power cable built-in secondary cable 240.

The body is characterized in that made of lightweight high strength composite fiber material.

In addition, the sensing means is characterized in that it comprises a moment sensor is installed on the two front front legs of the subsea robot to perform the ground detection.

A plurality of articulated walking legs 121, 122, 123 (not shown), 124, 125 (not shown), and 126 are provided on the side of the body portion 110 of the subsea robot 100-1, two on each side. It is provided (123, 124, 125, 126), and two (121, 122) is provided on the front side. Two articulated walking legs (121, 122) attached to the double front side is a robot arm combined legs to perform the functions of the legs and arms. Each articulated walking leg 121, 122, 123, 124, 125, 126 is composed of a plurality of joints (for example, 121a, 121b, 122a, 122b, etc.).

The multi-joint subsea robot 100 according to the present invention can walk on the seabed in a group of 6 or 4, and two front legs can also be used as robot arms. The four legs 123, 124, 125 and 126 have four joint structures actively controlled by the electric motor, and the front two legs have six joints and one gripper. This concept is based on lobster robots, which focus on biomechanical simulation, and a technique in which each leg consists of a joint and a pedal [Christina, G., Meyer, N., Martin, B., "Simulation of an underwater hexapod robot," Ocean Engineering, Vol 36, pp 39-47, 2009.]. In addition, it is a new submarine robot that actively controls posture in response to fluid force.

The structure of the leg of the articulated subsea robot is described in more detail below with reference to FIGS. 4 to 7. When the submarine robot moves, it is possible to walk quickly while securing posture stability using six legs. When working or moving things using the robot arm combined legs, support the body or walk with four legs. When the submarine robot moves on four legs, walking stability and speed are relatively lower than when moving on six legs, but all the necessary work and moving functions can be achieved underwater.

The multi-moveable multi-sea subsea robot according to the present invention has a streamlined body and a leg shape of a multi-joint structure to be suitable for working in a stress-based environment, and detects disturbance caused by fluid force and minimizes the effects thereof. Has the function of controlling the posture of the legs.

Next, Figure 3 is a block diagram of a multi-joint subsea robot capable of moving in accordance with the present invention.

Referring to Figure 3, the control system 10 for controlling the swimming and walking process of the multi-joint seabed robot 100 that can move complex,

Front-scanning sonar 20 to shoot up to 100m ahead with ultrasound

Ultrasonic camera 20a for capturing a front image up to 10m with ultrasound in real time,

Pan / tilting function underwater camera 22 and lighting device (22a, not shown) that can shoot underwater and rotate and switch angles,

Data storage unit 30 for storing the sensed data and the captured image data during the swimming and walking process,

Posture and motion measurement sensor 42 for detecting the posture of the subsea robot and measuring the state of movement,

Force / moment sensor 43 for sensing the force and moment acting on the walking leg of the subsea robot,

Proximity sensor (44) for detecting the limit of the joint angle,

Speed sensor 48 for sensing the speed and flow rate of the robot,

Underwater position tracking device for tracking and sensing the underwater position of the performing robot in real time (50),

Optical communication modem 60, which handles the signal transmission and reception with the buffer,

A motor driving unit 70 for generating a motor driving signal,

First to Nth electric motors 72-1, ..., 72-N operating according to the signal of the motor driver;

First to N-th reduction gears 74-1, ..., 74-N, which are operated according to the electric motor and connected to the joint mechanism to transmit the motion of the motor,

A control system 10 for transmitting and receiving signals to and from a buffer and a ground bus through an optical communication modem, and controlling a function of transmitting data obtained when swimming and walking the submarine robot; And

Power supply unit 80 for supplying power,

It includes.

Each other leg end is equipped with a force sensor or a sensing sensor for ground sensing (not shown).

Figure 4 is a detailed view showing the joint portion of the robot leg of the articulated subsea robot according to a preferred embodiment of the present invention, Figure 5 is an electric motor and harmonic reducer of the articulated sea robot according to a preferred embodiment of the present invention Partial cross-sectional side view of the pressure-resistant waterproof joint structure, Figure 6 is a detailed view showing the joint portion of the robot arm combined leg according to a preferred embodiment of the present invention, Figure 7 is a robot leg and robot arm according to a preferred embodiment of the present invention It is a figure which shows the kinematic structure of a combined leg.

4, the joint portion of the robot leg of the multi-joint subsea robot capable of swimming underwater according to a preferred embodiment of the present invention is the first joint (125a), the second joint (125b), the third joint (125c) and It consists of the 4th joint 125d. The robot leg 124a is connected to the end of the fourth joint 125d, and the robot leg 124b is connected between the third joint 125c and the fourth joint 125d.

The first joint 125a, the second joint 125b, and the third joint 125c are waterproof assembled by the pressure-resistant waterproof joint structure (see FIG. 5).

Referring to FIG. 5, the first joint 125a, the second joint 125b, and the third joint 125c are waterproof assembled by the pressure-resistant waterproof joint structure, specifically, the first waterproof body 410. , The second waterproof body 420 and the third waterproof body 430, and the first waterproof body 410 is frameless BLDC motor 72-1 is wrapped by the waterproof O-ring 414, pressure-resistant waterproof housing Inscribed to 418 is mounted via the bearing 412. The speed reducer 74-1 for reducing the driving force of the frameless BLDC motor 72-1 is rotatably connected to the waterproof housing 418 through a bearing 412.

6, the joint portion of the robot arm combined leg according to a preferred embodiment of the present invention is the first joint 125a, the second joint 125b, the third joint 125c, the fourth joint 124d, It consists of the 5th joint 125e and the 6th joint 125f. A gripper 122a-1 is connected to an end of the sixth joint 125f, a robot leg 121c is connected between the third joint 125c and the fourth joint 125d, and a fourth joint 125d. And a robot leg 121b is connected between the fifth joint 125e and a robot leg 121a is connected between the fifth joint 125e and the sixth joint 125f.

The first joint 125a, the second joint 125b, and the third joint 125c are waterproof assembled by the pressure-resistant waterproof joint structure (see FIG. 5). Other joints are also assembled in a pressure-resistant waterproof structure. Feedback of each joint may be detected through a limit sensor installed in the joint, and the limit sensor may be a hall sensor (not shown).

Referring to Figure 7, looking at the kinematic structure of the robot leg and the robot arm combined leg according to a preferred embodiment of the present invention, four robot legs are connected to the subsea robot body 110, of the subsea robot body 110 Two robotic arms are connected to the front. Roll, pitch and yaw rotations are rotated around X, Y and Z axes, respectively.

The articulated subsea robot 100 according to a preferred embodiment of the present invention is a structure that actively performs subsea walking with 28 joints on a total of six legs. Each joint is driven by the first to Nth electric motors 74-1, ..., 74-N. The technique of mechanically and electrically designing and controlling the joints of the submarine robot is defined as the underwater mechanism technology. The articulation mechanisms applied on land have been extended or redesigned to apply in seawater where water pressure exists.

The joint mechanism refers to a joint mechanism composed of each of the six legs of the articulated link subsea robot according to the present invention, as shown in Figure 2, each leg is connected to four joints, the front two legs are 6 Connected to the joints of the dog. Joints connected to the two anterior legs each serve as a robot arm.

Each joint mechanism consists of a joint drive motor, harmonic reducer, joint angle sensor, and joint limit sensor. The joint drive motor was designed and mounted in a pressure resistant waterproof housing using a frameless BLDC motor to obtain a small, lightweight, low speed, high torque. The pressure-resistant waterproof housing was watertight using an O-ring. The harmonic drive reducer is adopted to minimize the backlash of the joint and to obtain the proper reduction ratio. In addition, the absolute angle of the joint can be obtained by attaching an absolute encoder to the joint to the reducer output. For safety, the joint angle limit is equipped with a magnetic proximity switch.

The multi-movement multi-joint subsea robot according to the present invention is installed on the sea floor and is connected to the buffer medium and connected through the ground bus and the shock absorber. The ground bus receives and stores the photographed image information of the seabed topography through the seabed robot, and transmits a movement command signal to search for a specific area.

Submarine robots move along the sea floor to a specific area and can walk or swim when moving.

8 is a diagram illustrating an algorithm used in the approximate modeling method of the generalized fluid resistance torque acting on the articulated link according to the present invention.

을 계산하는 것으로 다음과 같은 알고리즘을 포함하고 있다.Referring to FIG. 8, the approximate modeling method of the generalized fluid resistance torque acting on the articulated link according to the present invention is based on the equation of motion of the articulated articulated link (see Equation 1 below).

Calculate the following algorithm.

First, an algorithm (10) for estimating a fluid force coefficient applicable to the cross-sectional shape of an articulated link of a subsea robot swimming or walking underwater according to the cross-sectional shape of the articulated articulated link and the Reynolds number (see Equation 4),

A fluid force calculation algorithm 20 including a plurality of algorithms (see Equations 7 to 18 below) for calculating a fluid force acting on each link of the articulated subsea robot through a fluid force calculation algorithm,

a fluid force torque calculation algorithm 30 including a plurality of algorithms (see Equations 19 to 21 below) for calculating a fluid force torque acting on the i-coordinate system by the fluid force acting on the j-link, and

A plurality of algorithms (Equations 22 to Equations) for converting the fluid force torque of the i-coordinate system from i to j links into the fluid force torque of the i-joint, and adding them for all the links to calculate the fluid force torque (resistance torque) Fluid force torque calculation algorithm 40, including the reference numeral 24).

FIG. 9 is a view illustrating FIG. 8 in detail.

추정 과정이 진행된다.n Freedom of articulated link robot motion equation (refer to Equation 1), and then fluid resistance and lift

The estimation process proceeds.

First, the Reynolds number is calculated (see Equation 4), it is determined whether it is within an application range of the fluid coefficient (S10), and the fluid force coefficient is estimated according to the shape of the link cross section (S20).

Thereafter, the fluid force calculation algorithm acting on the link is performed (S200).

First, a process of calculating a velocity vector of a disk fragment on a link j (see Equations 10 to 12) is performed (S222). Thereafter, a process of calculating a projection matrix algorithm (Equation 9) in a plane perpendicular to the j-link defined in the i-coordinate system is performed (S224). Subsequently, a process of calculating a velocity component vector of a disk piece perpendicular to the j-link (see Equation 8 and Equations 13 to 14) is performed (S226). Subsequently, an algorithm (see Equation 7) for calculating a fluid force acting on a disk piece on j-link is performed (S228).

Subsequently, the processing process of the fluid force torque calculation algorithm acting on the i-coordinate system by the fluid force of j-link includes the following detailed process (S300).

First, a process of calculating a position vector of a disc on a j-link for an i-coordinate system (see Equation 21) is performed (S30). Thereafter, a processing algorithm (see Equation 20) for calculating the torque of the fluid force acting on the i-coordinate system is performed (S32).

 Then, the generalized fluid force torque calculation algorithm processing by the link from i to j includes the following detailed process (S400).

First, an algorithm (see Equation 22) for calculating the fluid force torque acting on the i joint by projecting the fluid force torque acting on the i coordinate system to the i joint axis is performed (S42). Subsequently, a process of an algorithm (see Equation 24) for calculating the final fluid force torque acting on the i joint by adding the fluid force torques for all the links after the i joint from the i link to the j link is performed (S44).

FIG. 10 is a diagram showing a vector and a link coordinate system of an underwater multi-joint link of a multi-joint underwater robot capable of complex movement in the approximate modeling method of a generalized fluid resistance torque acting on a multi-joint link according to the present invention.

FIG. 11 is a view similar to that of FIG. 10, showing a disk piece of the articulated link and its velocity vector.

Approximate Modeling of Fluid Resistance

Kinetic Equation for Underwater Articulated Links

When the n-degree of freedom articulated link robot moves in the underwater environment, the motion equation of the robot can be expressed as Equation 1 below.

[Equation 1]

,

,

은 부가질량을 포함하는 관성행렬이고,

는 강체와 부가질량에 의한 코리올리와 구심력,

는 유체저항 및 양력항,

는 부력, 중력, 그리고 유체가속도항이다.

는 로봇의 관절변수,

는 관절토크벡터이다. [수학식 1]의 각 항 중에서 유체저항력에 의한 항

을 다음절에서 근사적으로 추정한다.here

Is an inertial matrix containing additional mass,

Is the Coriolis and centripetal force due to the rigid body and the added mass,

Is the fluid resistance and lift term,

Are the buoyancy, gravity, and fluid acceleration terms.

Is the joint variable of the robot,

Is the joint torque vector. In each term of [Equation 1], the term due to fluid resistance

Is approximated in the next section.

Fluid

When an articulated link moves in a viscous fluid, the link is subject to resistance and lift, which can be expressed as a function of the fluid force coefficient associated with the cross-sectional shape and the relative velocity of the link's fluid.

&Quot; (2) "

&Quot; (3) "

,

,

와

는 각각 마찰저항계수와 압력저항계수이다.

은 링크의 양력계수,

,

및

는 각각 링크의 침수표면적, 횡단면적 및 평면형상의 면적이다.

는 유체의 속도에 대한 강체의 상대속도이다. 저항력 및 양력계수는 링크의 앙각(angle of attack)

와 다음 [수학식 4]로 정의되는 레이놀즈수에 의해 결정된다.Where fD is the resistive force and the relative velocity and direction of the link and fluid are opposite. FL is the lift and acts in a direction perpendicular to the relative velocity of the link and fluid.

Wow

Are the frictional resistance coefficient and the pressure resistance coefficient, respectively.

Is the lift coefficient of the link,

,

And

Are the submerged surface area, cross sectional area and planar area of the link, respectively.

Is the relative velocity of the body to the velocity of the fluid. Resistance and lift factors are the angle of attack

And Reynolds number defined by Equation 4 below.

&Quot; (4) "

는 유체의 점성계수이고 는 몰수체의 길이이다.

는

로 정의되는 동점성 계수이다. 20℃의 청수인 경우 동점성 계수는

이다. 몰수체의 저항 및 유체력 계수는 몰수체의 표면과 물 사이의 경계조건에 따라 다른 특성을 가진다. 경계층의 조건은 몸체의 형상, 표면거칠기 및 레이놀즈수에 의해 정의되므로, 해석적으로 정확한 계수를 유도하는 것은 거의 불가능하다. 저항계수와 양력계수를 결정하는 한가지 방법은 기하학적으로 유사한 모델에 대해 실험적으로 구하는 것이다.here,

Is the viscosity of the fluid Is the length of the condensate.

The

The kinematic viscosity defined by For fresh water at 20 ° C, the kinematic viscosity

to be. The resistivity and fluid force coefficient of the condensate have different characteristics depending on the boundary condition between the surface of the condensate and the water. Since the condition of the boundary layer is defined by the shape of the body, the surface roughness and the Reynolds number, it is almost impossible to derive an analytically accurate coefficient. One way to determine the resistance and lift coefficients is to obtain experimental results for geometrically similar models.

의 레이놀즈수 범위내에서 움직인다고 가정하고, 실험적으로 얻어진 저항 및 양력계수를 사용한다고 가정하면, 상기 [수학식2] 및 [수학식3]은 다음과 같이 쓸 수 있다.If the robot underwater

Assuming that it is moved within the Reynolds number range, and using the experimentally obtained resistance and lift coefficient, [Equation 2] and [Equation 3] can be written as follows.

[Equation 5]

&Quot; (6) "

Fluid resistance to the link

The generalized fluid and lift torques (D term in [Equation 1]) acting on the articulated link robot are represented as a function of the coefficients of fluid force determined by joint angle, angular velocity, fluid velocity and link shape. Assuming that the j-th link is divided into small disk pieces having a micro-thickness dl in the link coordinate system of the n degrees of freedom and the vector diagram as shown in FIG. 10, the resistance applied to the disk pieces can be written as follows for the i coordinate system.

[Equation 7]

,

,

는 i좌표계에서 표현된 j번째 링크상의 한 원반조각에 작용하는 저항력이고,

는 앙각

의 함수로 표현되는 j번째 링크의 2차원저항계수이고, 앙각

는 유체속도벡터

와 원반조각의 속도벡터

사이의 각도이다.

는

에 직각인 평면에 투영된 원반의 투영길이이다.

는 j번째 링크에 직각인 방향의 속도의 성분이다. 도6으로 부터,

는 유체에 대한 원반조각의 속도를(

)평면으로 투영하여 다음과 같이 얻어진다.
here,

Is the resistance acting on a disk piece on the jth link expressed in the i coordinate system,

Elevation

2D resistance coefficient of the jth link expressed as a function of

Is the fluid velocity vector

Velocity vector

Angle between.

The

Projection length of the disc, projected on a plane perpendicular to.

Is a component of velocity in the direction perpendicular to the jth link. 6,

Is the speed of the disk piece relative to the fluid (

Projected onto a plane, it is obtained as follows.

[Equation 8]

,

,

는 i좌표계에서 표현된 j번째 링크의 속도이고,

는 i좌표계에서 정의된(

)평면으로의 투영행렬로 다음과 같이 정의된다.
here,

Is the speed of the jth link expressed in the i coordinate system,

Is defined in i

The projection matrix onto the plane is defined as

&Quot; (9) "

,

,

는 i좌표계에서 j좌표계로의 회전행렬이다.

와

는 각각 i좌표계에서 표현된 y축과 z축의 단위벡터이고,

와

는 j좌표계에서 표현된 단위벡터이다.here,

Is the rotation matrix from the i coordinate system to the j coordinate system.

Wow

Are unit vectors of y-axis and z-axis respectively expressed in i-coordinate system,

Wow

Is the unit vector expressed in the j coordinate system.

In order to express the resistance acting on the (i + 1) th joint as a function of the joint variable and its first derivative, the velocity of one point fixed to the jth link is derived with respect to the i coordinate system. The speed of j link expressed in i coordinate system is obtained as follows.

&Quot; (10) "

.

.

는

로 정의되는 직교좌표계 벡터로부터 동차 좌표계 벡터로의 변환이다.

는 동차좌표변환행렬이다.

는

의

에 대한 편미분이다.here,

The

Is a transformation from a rectangular coordinate system vector defined in the equation to a homogeneous coordinate system vector.

Is a homogeneous coordinate transformation matrix.

The

of

Partial differential for.

Introducing a new notation, as shown in Equation 11 below,

&Quot; (11) "

,

,

Equation 10 may be written in a simplified form as follows.

[Equation 12]

.

.

는 관절변수와 그 1차 미분의 함수로 다음과 같이 유도된다.Substituting Equation 12 into Equation 8,

Is a function of the joint variable and its first derivative as

&Quot; (13) "

.

.

는

로 정의되는

의 역변환이다. [수학식 13]의

와

는 관절변수

의 함수이고

는 j좌표계의 원점에서 j링크에 위치한 원반조각까지의 위치벡터이다. j좌표계는 j번째링크에 고정되어 있으므로,

는 다음과 같이 표현된다.

The

Defined as

Is the inverse of. Of Equation 13

Wow

Is a joint variable

Is a function of

Is the position vector from the origin of j coordinate system to the disk piece located at j link. Since the j coordinate system is fixed to the jth link,

Is expressed as follows.

&Quot; (14) "

,

,

Where x is the distance from the j coordinate system to the disk piece.

When the structure is sufficiently thin and the fluid velocity changes significantly over the length of the structure, the force per unit length of the structure is acted by the local fluid velocity, which corresponds to the local reaction force on the moving structure in integer, which is the theory).

According to the elongated body theory, the resistive force acting on the j-th link is the integral of the fluid force acting on the disk [Equation 7].

&Quot; (15) "

.

.

Substituting [Equation 13] into [Equation 15], the following [Equation 16] is obtained.

&Quot; (16) "

.

.

Here, assuming that the link is divided into s pieces as shown in FIG. 10, the static integral of Equation 16 may be approximated by a numerical integral as in Equation 17. FIG.

&Quot; (17) "

&Quot; (18) "

,

,

Generalized Fluid Resistance Torque

Next, the fluid force torque acting on the i-coordinate axis by the resistance of the j-th link can be written as Equation 19 below.

&Quot; (19) "

는 i좌표계에서 j좌표계로의 위치벡터이다. [수학식 17]과 같은 방법으로 [수학식 19]는 다음과 같이 근사화된다(도 11 참조).here,

Is the position vector from the i coordinate system to the j coordinate system. In the same manner as in Equation 17, Equation 19 is approximated as follows (see FIG. 11).

&Quot; (20) "

&Quot; (21) "

)좌표계의

축과 일치하므로, j번째 링크에 의해 i번째 관절에 작용하는 유체력 토크는

을

축으로 투영함으로써 다음과 같이 얻어진다.The i joint of the articulated link is (

Of the coordinate system

Coincident with the axis, the fluid force torque acting on the i-th joint by the j-th link is

of

By projecting on the axis, it is obtained as follows.

&Quot; (22) "

,

,

here,

&Quot; (23) "

는 아래 [수학시 24]와 같이 얻을 수 있다.Finally, the hydrodynamic torque acting on the i-th joint by all links

Can be obtained as shown below.

&Quot; (24) "

,

,

In the same way, the fluid lift applied to the i-th joint can be obtained. It is omitted here because of space.

12 is a view showing the coordinate system and link parameters of a section 3 link robot used to confirm the approximate modeling method of the generalized fluid resistance torque acting on the articulated link according to the present invention.

13 to 15 are graphs schematically showing the fluid torque of each joint with respect to the joint angle of joint 3 of the third link robot of FIG. 12.

16 to 18 are graphs schematically showing the fluid torque of each joint with respect to the joint angle of the second joint robot of FIG. 12.

Simulation examples and considerations

Numerical simulation is performed using SCARA-type three-section link robot to identify the induced fluid resistance model and the results are discussed. The robot used in the simulation is a three-section link robot having a coordinate system and a DH parameter as shown in FIG. The link of the robot is assumed to be a cylinder of 0.1m in diameter with a unit length. The two-dimensional resistance coefficient of each link was 1.1, and the number of disc pieces per link (see FIGS. 10 and 11) was 20, and the simulation was performed.

FIG. 13 is a result showing the fluid fluid force torque of a joint that appears as an interaction according to the angular velocity of each joint when the joint angle 3 changes between 0 degrees and 360 degrees. Fig. 13 shows the result when joint 3 has a unit speed. Regardless of the angle of joint 3, joint 3 always receives a constant fluid torque. However, the fluid fluid torque applied to joints 1 and 2 is greatest at 0 degrees with the arm fully extended, and the largest torque is applied to joint 1, where the distance between the resistance vector and the joint axis is farthest. The direction of the torque is the torque due to the fluid resistance force that is opposite to the rotational speed of joint 3, so the direction is reversed and negative. At 90 degrees and 270 degrees, the fluid force vector on link 3 and the distance between each joint axis are equal, so all of the same force torque is applied. Joint torques 1 and 2 become 0 at the angle of joint 3 (112 degrees and 137 degrees) where the distance between the fluid force vector and the joint axis becomes zero. At 180 degrees, the torque is the maximum value in the opposite direction, but the distance between the fluid force vector and the joint is short, so the magnitude is smaller than 0 degrees.

When joints 2 and 3 each have a unit velocity, the fluid resistance torques of the joints are shown in FIGS. 14 and 15, respectively. When joint 3 is 0 degrees, the largest torque is applied to all joints, and the size thereof is increased compared to the case of FIG. 13 in which joint 3 has a speed. When the joint angle of joint 3 is 130 degrees, 115 degrees, and 110 degrees, the absolute magnitude of the fluid force applied to joints 3 and 2 is minimized, respectively, and this can be seen as the optimal position of joint 3 in terms of fluid force. . As the angle increases beyond the optimal position of joint 3, the torque on joint 3 is reversed, and the torque on joints 1 and 2 increases again.

When joint 1 has a unit angular velocity, the direction of torque of joint 3 at about 110 degrees is reversed, and the absolute magnitudes of the torques of joints 1 and 2 at 102 degrees and 108 degrees are minimized, respectively. It can be said to be a kind of fluid force optimum under given conditions. In the case where the joint 1 has a unit angular velocity, as the linear velocity of the link 2 and 3 increases relatively, the fluid torque is also shown to be much larger than in FIGS. 13 and 14.

16 is a result showing the fluid fluid force torque of the joints appearing in interaction according to the angular velocity of each joint when the second joint angle is changed between 0 degrees and 360 degrees. In FIG. 16, in which joint 3 has a unit angular velocity, the relative positions of links 2 and 3 are constant, so torques applied to joints 2 and 3 are both constant. Joint torque 1 is the minimum from 0 degrees to the maximum 180 degrees. This is because the distance between the fluid force acting on the joint 1 and the link 3 in this position becomes the maximum minimum respectively. In the case of FIG. 17 in which the second joint has a unit angular velocity, the same situation as in FIG. 16 is obtained. However, the absolute value of the joint torque is larger than in FIG. 16 due to the increase in the linear velocity of the link. In the case of FIG. 18 where joint 3 has a unit angular velocity, torques of joints 1 and 3 become minimum at 180 degrees, and torque applied to joint 2 is changed at 127 degrees.

In the hydrodynamic torque simulation results performed using the SCARA robot, we can confirm that the previously modeled hydrodynamic force model agrees well with the intuitively inferred result.

In the present invention, the fluid force acting on the articulated articulated link and the fluid force torque induced therefrom are modeled approximately. The proposed model is derived in a closed form and can be directly applied to the L-E equation and is easy to use for various analysis or design. In order to verify the proposed model, the validity of the proposed model is investigated by applying it to a simple three-section SCARA robot that can intuitively estimate the fluid force. This is expected to be applicable to various fields such as step planning and swimming motion development of articulated robots moving in fluid.

Although the preferred embodiments of the present invention have been disclosed for illustrative purposes, those skilled in the art will appreciate that various modifications, additions and substitutions are possible, without departing from the scope and spirit of the invention as disclosed in the accompanying claims. Such changes and modifications can be said to belong to the present invention without departing from the scope of the technical idea provided by the present invention. Therefore, the scope of the present invention will be determined by the claims described below.

100: submarine robot
110: body
200: shock absorber
300: Mothership

Claims (5)

A first step of determining an application range of the fluid force coefficient according to the cross-section of the articulated link of the subsea robot swimming or walking underwater;
A second step of approximating a fluid force acting on the articulated link moving in the water;
Calculating a fluid force torque acting on the joint coordinate system through the fluid force acting on the articulated link; And
A fourth step of converting the fluid force torque acting on the joint coordinate system into the fluid force torque acting on the joint, and calculating the fluid force torque caused by the articulated link;
Including,
The first step includes: calculating a Reynolds number using a Reynolds number calculation algorithm; Estimating a fluid force coefficient according to the cross-sectional shape of each underwater link when the robot moves within a range of Reynolds numbers.
The second step includes: dividing the link into a plurality of disk pieces through a fluid force calculation algorithm, and calculating a velocity component vector of one disk piece on j links in the i coordinate system; Calculating a projection matrix onto a plane perpendicular to j-link defined in the i-coordinate system through a projection matrix calculation algorithm; calculating a velocity component vector of the disk piece perpendicular to the j-link; And calculating a fluid force acting on a disc piece on j-links. Approximate modeling method of fluid resistance torque acting on a multi-moveable multi-sea subsea robot, comprising:
delete delete The method of claim 1,
In the third step,
Calculating a position vector of a disk piece on j link with respect to the i coordinate system; And
Calculating a fluid force torque acting on the i-coordinate system;
Approximate modeling method of fluid resistance torque acting on a multi-moveable multi-sea subsea robot, comprising a.
The method of claim 4, wherein
The fourth step,
Converting the fluid force torque acting on the i coordinate system to the fluid force torque acting on the i joint; And
calculating a fluid force torque acting on the i-joint on the i-link and j-link;
Approximate modeling method of fluid resistance torque acting on a multi-moveable multi-sea subsea robot, comprising a.

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