CN112405497B - Hybrid mechanism system based on passive compensation and motion decomposition method thereof - Google Patents

Hybrid mechanism system based on passive compensation and motion decomposition method thereof Download PDF

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CN112405497B
CN112405497B CN202010978080.3A CN202010978080A CN112405497B CN 112405497 B CN112405497 B CN 112405497B CN 202010978080 A CN202010978080 A CN 202010978080A CN 112405497 B CN112405497 B CN 112405497B
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CN112405497A (en
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魏延辉
樊雅妮
郭彤旭
谢吉顺
于恬
付敬恒
邵红
王玥玥
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Harbin Engineering University
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    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B25—HAND TOOLS; PORTABLE POWER-DRIVEN TOOLS; MANIPULATORS
    • B25J—MANIPULATORS; CHAMBERS PROVIDED WITH MANIPULATION DEVICES
    • B25J9/00—Programme-controlled manipulators
    • B25J9/003—Programme-controlled manipulators having parallel kinematics
    • B25J9/0072—Programme-controlled manipulators having parallel kinematics of the hybrid type, i.e. having different kinematics chains
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B25—HAND TOOLS; PORTABLE POWER-DRIVEN TOOLS; MANIPULATORS
    • B25J—MANIPULATORS; CHAMBERS PROVIDED WITH MANIPULATION DEVICES
    • B25J9/00—Programme-controlled manipulators
    • B25J9/16—Programme controls
    • B25J9/1656—Programme controls characterised by programming, planning systems for manipulators
    • B25J9/1664—Programme controls characterised by programming, planning systems for manipulators characterised by motion, path, trajectory planning

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Abstract

The invention provides a hybrid mechanism system based on passive compensation, which comprises a hybrid mechanism, a pressure sensor array at the tail end of the hybrid mechanism, a motion distributor for wave passive compensation and a hybrid mechanism hydraulic system. The hybrid structure comprises a six-degree-of-freedom parallel mechanism, a three-degree-of-freedom series mechanism and a mounting base; the six-degree-of-freedom parallel mechanism consists of six hydraulic cylinders and an upper platform, the three-degree-of-freedom serial mechanism consists of a swing mechanism, a pitching mechanism and a telescopic mechanism, the mounting base is used for fixing the parallel mechanism on a deck of the operation and maintenance ship, and the three-degree-of-freedom serial mechanism and the six-degree-of-freedom parallel mechanism are formed by hinged supports. The passive compensation method can realize the passive compensation of the offshore operation and maintenance ship under the condition of high sea condition, and ensure the normal operation and maintenance of the offshore platform under severe weather. Compared with an active sea wave compensation system, the sea wave compensation system has the advantages of low energy consumption and low cost, is suitable for short-time and quick operation and maintenance requirements on the sea, and has strong practicability.

Description

Hybrid mechanism system based on passive compensation and motion decomposition method thereof
Technical Field
The invention relates to a series-parallel mechanism system and a motion decomposition method thereof, in particular to a series-parallel mechanism system based on passive compensation and a motion decomposition method thereof, and belongs to the technical field of ocean engineering.
Background
With the concept of sustainable development, people pay more attention to the development and use of clean energy and green energy due to the current situation that the traditional energy has high energy consumption, high pollution and high emission and causes irreversible damage to the environment. Based on this, the development and the use of offshore wind energy enter the visual field of each country, the installation quantity of wind turbines is greatly increased, and each country looks at the most important component part in a new energy strategy. The country highly pays attention to the development of offshore wind power, and some guidance documents and regulations are continuously gone out to promote the steady development of offshore wind power. However, the vigorous development of offshore wind resources has also met with some problems. Wind turbine platforms often require maintenance and repair, however, offshore storm conditions can cause personnel to be very dangerous to the platform from ship, and offshore compensation platforms are highly required to safely transport personnel and equipment from ship to wind turbine platform. In order to maintain stability of the gallery bridge and thus personnel safety, research into a hybrid-based wave compensation system becomes important.
In the research on the offshore operation compensation system, the heave motion compensation of the offshore operation system is firstly researched and is also researched most, and the problem of offshore supply is mainly solved, wherein the research on a heave compensation crane, a robot arm and a winch is mainly used. On the research of the wave compensation platform, a great deal of research work is carried out by savoury leaf, excellent, wanghoujiao and the like, and on the basis of completing the research of the ancient sunken ship salvage platform test of south China sea I, the research idea of the wave compensation platform is further provided. The wave compensation platform is researched from designing, building a test platform to mathematical modeling, computer simulation, control algorithm design and realizing effective control of the whole system process, and the feasibility of the wave compensation platform is verified through a solid model test. The Lishizhong adopts a multi-sensor technology to construct a wave compensation stable platform system with a wave compensation function, so that motion compensation opposite to the motion direction of the ship is realized, and a relatively stable platform is constructed.
The passive compensation of the hydraulic system actuator is realized by using the hydraulic accumulator of the hybrid mechanism by referring to the research experience of other methods, and the short-time, quick and stable effective compensation of the hybrid mechanism on the sea operation and maintenance ship under the interference of sea waves received by the sea operation and maintenance ship under complex sea conditions is met.
Disclosure of Invention
Aiming at the defects in the prior art, the invention aims to provide the wave compensation system of the series-parallel mechanism with good stability and low energy consumption, which can be used for maintenance personnel to safely and smoothly walk onto a fan platform, and can realize the passive compensation of the boarding system by utilizing the energy accumulator of the hydraulic system of the boarding system according to the requirement of the wave compensation system.
The purpose of the invention is realized by the following steps:
a hybrid mechanism system based on passive compensation comprises a hybrid mechanism, a pressure sensor array at the tail end of the hybrid mechanism, a motion distributor for wave passive compensation and a hybrid mechanism hydraulic system.
The invention also includes such features:
the hybrid structure comprises a six-degree-of-freedom parallel mechanism, a three-degree-of-freedom series mechanism and a mounting base; the six-degree-of-freedom parallel mechanism consists of six hydraulic cylinders and an upper platform, the three-degree-of-freedom serial mechanism consists of a swing mechanism, a pitching mechanism and a telescopic mechanism, a mounting base is used for fixing the parallel mechanism on a deck of the operation and maintenance ship, and the three-degree-of-freedom serial mechanism and the six-degree-of-freedom parallel mechanism consist of hinged supports;
the pressure sensor array at the tail end of the hybrid mechanism is arranged in two directions, uniformly distributed at intervals of 5 degrees in the horizontal direction according to the semicircular tail end of the hybrid mechanism, and used for detecting the contact force change condition of the advancing direction of the tail end of the hybrid mechanism and the offshore platform; the device is arranged at the lower end of the tail end of the hybrid mechanism in the vertical direction, is uniformly distributed in a semicircular mode at intervals of every 5 degrees, and detects the stress change condition of the lap joint of the tail end of the hybrid mechanism and the offshore platform;
the motion distributor for wave passive compensation analyzes and decomposes motion according to pressure information detected by a pressure sensor array at the tail end of the hybrid mechanism, forms motion instructions of each execution part of the series of hybrid mechanisms, and drives each hydraulic cylinder and each hydraulic motor of the corresponding hybrid mechanism to move by using the capacity stored by an energy accumulator of a hydraulic system, so that the tail end of the hybrid mechanism is ensured to be in effective contact with an offshore platform, and the compensation of the wave motion of a ship is realized, the motion amplitude of the hybrid mechanism of a boarding system is greatly reduced compared with that of the ship, the boarding platform is reliably butted with the offshore platform under a high sea condition, and the safe transportation of personnel is guaranteed;
the hydraulic system of the parallel-serial mechanism consists of a power source, an energy accumulator, an execution hydraulic cylinder of a six-degree-of-freedom parallel mechanism, a hydraulic execution element of a three-degree-of-freedom serial mechanism and an oil tank, wherein the power source consists of a motor, a hydraulic pump, an overflow valve and a filter; the energy accumulator is provided with a plurality of groups of energy accumulator units according to the system compensation requirement; the actuating element of the six-degree-of-freedom parallel mechanism consists of six hydraulic cylinders; when the hybrid mechanism is butted with an offshore platform, a person manually controls the tail end of the hybrid mechanism to be lapped on the offshore platform, and after passive compensation is carried out, pressure energy accumulated by a system energy accumulator is respectively supplied according to the requirements of each executing hydraulic element, so that passive compensation is realized;
a motion decomposition method of a series-parallel mechanism system based on passive compensation comprises the steps of firstly, respectively establishing a motion coordinate system for each mechanism position of a parallel platform and a series gangway ladder, and solving a homogeneous transformation matrix according to joint motion characteristics; pushing down and deriving Jacobian matrixes of the parallel platform and the series gangway ladder in a Cartesian space, and fusing the Jacobian matrixes and the series gangway ladder to obtain a kinematic model of the parallel mechanism in a task space; then, the Jacobian matrix pseudo-inverse method is utilized to carry out basic distribution on the motion quantity of each joint of the parallel platform and the serial gangway ladder, a weight coefficient matrix and a null space item are added into the original Jacobian matrix by combining the limit position of each joint, and then the avoidance of the singular configuration of the gangway ladder is completed by combining the projection gradient method, and the method specifically comprises the following steps:
step 1: establishing a kinematic model of a series-parallel mechanism;
and 2, step: and setting a motion planning method based on the kinematic model of the hybrid mechanism.
The step 1 specifically comprises the following steps:
(1) establishing an integral model of a series-parallel connection mechanism
Setting three attitude angles of the upper platform relative to the base coordinate as alpha, beta and gamma, respectively, and the position vector of the center of the upper platform in the base coordinate system as
Figure BDA0002686549440000031
Then the parallel Stewart platform transforms the matrix into
Figure BDA0002686549440000032
Figure BDA0002686549440000033
The rotation angle of the first joint of the series gangway ladder is set as theta1The second joint rotation angle is theta2The third joint expansion amount is d3A homogeneous transformation matrix of the series gangway ladder according to the D-H method is
Figure BDA0002686549440000034
(2) Establishing a series Gangtai Jacobian matrix
Under the base coordinate system, the motion equation of the gangway ladder with three degrees of freedom in series is
Figure BDA0002686549440000035
Figure BDA0002686549440000036
Wherein
Figure BDA0002686549440000037
The pose vector of the gangway ladder under the base coordinate system is shown, and the q is the rotation angle or displacement vector of three joints of the gangway ladder under the joint coordinate system. J is a unit ofsThe joint space movement speed is converted into the movement speed of a Cartesian space, and the pose quantity of the Cartesian space is converted into the speed quantity of the joint space through the joint space movement speed.
(3) Establishing parallel platform Jacobian matrix
The coordinates of the hinge points of the supporting legs connected with the platform in the corresponding coordinate system can be obtained according to the geometric structures of the movable platform and the static platform, and the coordinates of the hinge points of the upper platform in the movable coordinate system areAA, coordinates of each hinge point of the lower platform under a static coordinate system areBB, coordinates of each hinge point of the movable platform under the static coordinate system are as follows:
Figure BDA0002686549440000041
the vector of each leg under the static coordinate system is expressed as:
BL＝[BL1 BL2 BL3 BL4 BL5 BL6]
BL＝BA-BB
in order to calculate the working speed of each supporting leg, the derivatives of the two ends of the upper formula are calculated, and the speed vectors of each hinge point of the upper platform are obtained as follows:
Figure BDA0002686549440000042
let q ═ x y z α β γ]TGeneralized coordinates representing the motion of the upper platform are:
Figure BDA0002686549440000043
Figure BDA0002686549440000044
(4) establishing a Jacobian matrix of a hybrid mechanism under a task space
Defining the speed of each joint of the hybrid mechanism under a motion coordinate system as xi ═ x y z alpha theta gamma theta1 θ2 d3]TThe pose vector of the tail end of the manipulator under the inertial coordinate system is
Figure BDA0002686549440000045
A homogeneous transformation matrix of the gangway terminal transformed from the motion coordinate system to the inertia coordinate system is
Figure BDA0002686549440000046
Wherein the position matrix and the attitude matrix of the gangway end are included.
The derivation of the position of the ramp end in the inertial coordinate system can be obtained
Figure BDA0002686549440000047
Wherein
Figure BDA0002686549440000048
[iwv×]Is a diagonally symmetric matrix, i.e. foriwv＝[wx wy wz]TIs provided with
Figure BDA0002686549440000049
Two algorithms of x y x and x y x are used in the derivation, x and y being matrices.
Derivation of attitude matrix of accommodation ladder terminal under inertial coordinate system
Figure BDA00026865494400000410
Whereiniwe＝iwv+iRv vwe。
And combining the position matrix and the derivative of the attitude matrix to obtain a kinematic model of the hybrid mechanism:
Figure BDA0002686549440000051
wherein JtaskIs the Jacobian matrix of the hybrid mechanism under the task space.
The step 2 specifically comprises the following steps:
(1) pseudo inverse solution of Jacobi matrix
According to the kinematic equation under the task space of the hybrid mechanism, the inverse of the kinematic equation can be obtained:
Figure BDA0002686549440000052
wherein
Figure BDA0002686549440000053
Is the plus inverse of the jacobian matrix, also known as the pseudo-inverse or the mole-pennissl inverse,
Figure BDA0002686549440000054
is the desired velocity trajectory at the end of the gangway, i.e. the amount of compensation for wave disturbances.
Adding a weighted norm matrix to each joint speed of the series-parallel mechanism to obtain a weighted Jacobian matrix plus inverse:
Figure BDA0002686549440000055
(2) the multitask priority method comprises the following steps:
least square solution of minimum norm of kinematic model under task space of hybrid mechanism
Figure BDA0002686549440000056
Wherein N is the degree of freedom of the whole series-parallel mechanism,
Figure BDA0002686549440000057
is the velocity and angular velocity vector of any one mechanism or joint,
Figure BDA0002686549440000058
is a joint vector term in the Jacobian matrix null space. Will be provided with
Figure BDA0002686549440000059
The form-representational-wise-Jacobian-matrix multi-task priority planning algorithm is:
Figure BDA00026865494400000510
wherein k is the number of secondary tasks;
Figure BDA00026865494400000511
represents a series of secondary tasks;
Figure BDA00026865494400000512
is the Jacobian matrix in the corresponding secondary mission motion equation.
Numerical drift problems may arise when integrating the position obtained for each joint velocity, so a closed loop of error between the desired and planned values is introduced:
Figure BDA00026865494400000513
and the secondary task I is set as joint limit constraint, three joints are constraint objects for the gangway ladder in series connection, and the moving platform pose of the parallel platform is taken as a constraint object. First, an objective optimization function is defined
Figure BDA0002686549440000061
Wherein C isi0 is a constant coefficient used for defining the limiting effect strength of the ith joint; q. q ofi、qimaxAnd q isiminThe angle (position), maximum rotation (movement) boundary value, and minimum rotation (movement) boundary value of the i-th joint, respectively.
Secondly, defining the weight coefficient of the serial gangway ladder part as follows:
Figure BDA0002686549440000062
Figure BDA0002686549440000063
and the secondary task II is set as singular configuration constraint, and the singularity of the parallel platform is distributed in the whole working space, and the great singularity can be avoided only by joint limitation, so that the singular configuration of the gangway ladder is avoided by adopting a method for limiting the operability of the serial mechanism. The degree of operability is used for describing the distance of the mechanism from a singular configuration state, and is defined as
Figure BDA0002686549440000064
Where J is the Jacobian matrix of the corresponding mechanism.
For the avoidance of singular configuration of the gangway ladder in series, the gradient of the operability of the gangway ladder is calculated by taking the angle (position) of each joint as a variable
Figure BDA0002686549440000065
Figure BDA0002686549440000066
Figure BDA0002686549440000067
(3) Multi-task weighted minimum norm solution based on projection gradient method
The planning method finally adopted by the invention is determined to be a multi-task weighted minimum norm solution based on the projection gradient method based on the weighted minimum norm method and the projection gradient method, and the specific expression is
Figure BDA0002686549440000068
Wherein
Figure BDA0002686549440000069
Indicating the desired trajectory of the end of the gangway,
Figure BDA00026865494400000610
error value, K, for the desired trajectory and the planned trajectory of the ramp endeIn order to achieve the corresponding gain,
Figure BDA00026865494400000611
represents the jacobian matrix after the constraint of joint constraint is added.
(4) Parallel platform inverse kinematics solution
The motion amount of the parallel-serial mechanism, which is obtained by the motion planning method, is expressed in the form of displacement (rotation) amount of three joints of the series gangway ladder and six-degree-of-freedom position attitude amount at the tail end of the parallel platform, wherein the expansion amount corresponding to six connecting rods is required to be further solved for the parallel platform through inverse kinematics.
Parallel platform inverse kinematics solution, knowing the transformation matrix of the upper platform center relative to the lower platform center
Figure BDA0002686549440000071
The target determines the amount of expansion and contraction of each rod length. In the upper platform coordinate systemArbitrary vector RaCan be transformed into R in the lower platform coordinate system by means of coordinate transformationbP is the origin A of the moving coordinate system in the fixed coordinate system B-xbybzbIs determined.
The homogeneous transformation matrix of the parallel platform is as follows:
Figure BDA0002686549440000072
Figure BDA0002686549440000073
Figure BDA0002686549440000074
in the formula:
Figure BDA0002686549440000075
P＝{Xp Yp Zp}T
Figure BDA0002686549440000076
Figure BDA0002686549440000077
Figure BDA0002686549440000078
Figure BDA0002686549440000079
compared with the prior art, the invention has the beneficial effects that:
(1) the passive compensation method can realize passive compensation of the offshore operation and maintenance ship under the condition of high sea condition, and ensure the normal operation and maintenance of the offshore platform under severe weather.
(2) Compared with an active sea wave compensation system, the sea wave compensation system has the advantages of low energy consumption and low cost, is suitable for short-time and quick operation and maintenance requirements on the sea, and has strong practicability.
(3) Compared with an active sea wave compensation system, the sea wave passive compensation system utilizes the energy accumulator to accumulate energy, can more quickly realize attitude compensation of the offshore operation and maintenance ship, overcomes the defects of sensor noise, active compensation calculation errors and actuating mechanism motion errors, and can more accurately realize sea wave passive compensation.
Drawings
FIG. 1 is a diagram of a passive compensation system for sea waves;
FIG. 2 is a schematic diagram of a series-parallel mechanism of a wave compensation system;
FIGS. 3a-b are diagrams of a series-parallel mechanism end pressure sensor profile, wherein (a) is a top view; (b) a side view;
FIG. 4 is a schematic diagram of a passive compensated motion distributor;
FIG. 5 is a hydraulic system of the series-parallel mechanism;
FIG. 6 is a flow chart of a series-parallel mechanism motion planning;
FIG. 7 is a series-parallel mechanism model diagram of the sea wave compensation system.
Detailed Description
The present invention will be described in further detail with reference to the accompanying drawings and specific embodiments.
The invention provides a hybrid mechanism system based on passive compensation and a motion decomposition method thereof. The principle is that the contact force of the tail end of the on-board hybrid mechanism and the offshore platform on the sea, which is interacted in the automatic compensation stage, is used as reference, the position and posture change of the hybrid mechanism relative to the landing platform, which is caused by the influence of sea waves on the operation and maintenance ship, is indirectly detected, the passive compensation of the hydraulic system executing mechanism is realized through the hydraulic energy accumulator of the hybrid mechanism, and the short-time, quick and stable effective compensation of the hybrid mechanism on the offshore operation and maintenance ship under the interference of the sea waves under the complex sea condition is met.
The passive compensation of the hydraulic system execution mechanism is realized through a hydraulic energy accumulator of the hybrid mechanism, so that the short-time, quick and stable effective compensation of the hybrid mechanism to the offshore operation and maintenance ship under the influence of sea waves under complex sea conditions is met, and the problems that the active compensation of the boarding system consumes more energy of the system and the power supply to the ship is higher can be greatly solved. And has more safety and practicability.
The concrete solving method is as follows:
the passive compensation system of the series-parallel mechanism system consists of a series-parallel mechanism, a pressure sensor array at the tail end of the series-parallel mechanism, a motion distributor for wave passive compensation and a hydraulic system of the series-parallel mechanism.
The series-parallel mechanism mainly comprises a six-degree-of-freedom parallel mechanism, a three-degree-of-freedom series mechanism and a mounting base: the six-degree-of-freedom parallel mechanism consists of six hydraulic cylinders and an upper platform and is mainly used for compensating the three-dimensional attitude (pitching, rolling and course) of the operation and maintenance ship influenced by sea waves; the three-degree-of-freedom series mechanism consists of a swing mechanism, a pitching mechanism and a telescopic mechanism and can compensate three-dimensional direction displacement of the operation and maintenance ship influenced by sea waves; the installation base is used for fixing the hybrid mechanism on the deck of the operation and maintenance ship. The three-freedom-degree series mechanism and the six-freedom-degree parallel mechanism are formed by hinged supports.
The pressure sensor array at the tail end of the hybrid mechanism of the boarding system is arranged in two directions, the pressure sensor array is uniformly distributed at intervals of 5 degrees in the horizontal direction according to the semicircular tail end of the hybrid mechanism, and the contact force change condition of the tail end advancing direction of the hybrid mechanism and the offshore platform is mainly detected; the vertical direction is arranged at the lower end of the tail end of the hybrid mechanism, and the hybrid mechanism is uniformly distributed in a semicircular mode at intervals of every 5 degrees to detect the stress change condition of the lap joint of the tail end of the hybrid mechanism and the offshore platform.
The motion distributor for wave passive compensation analyzes and decomposes motion according to pressure information detected by a pressure sensor array at the tail end of the hybrid mechanism, forms motion instructions of each execution part of the series hybrid mechanism, and drives each part of hydraulic cylinders and hydraulic motors of the corresponding hybrid mechanism to move by using the capacity stored by an energy accumulator of a hydraulic system, so that the tail end of the hybrid mechanism is ensured to be effectively contacted with a marine platform, and the compensation of ship wave motion (rolling, pitching and heaving) is realized, so that the motion amplitude of the hybrid mechanism of the boarding system is greatly reduced compared with that of a ship, the boarding platform is reliably butted with the marine platform under a high sea condition, and the safe transportation of personnel is ensured.
The hydraulic system of the parallel-serial mechanism consists of a power source, an energy accumulator, an execution hydraulic cylinder of the six-degree-of-freedom parallel mechanism, a hydraulic execution element (a hydraulic cylinder and a hydraulic motor) of the three-degree-of-freedom serial mechanism and an oil tank. The power source consists of a motor, a hydraulic pump, an overflow valve and a filter; the energy accumulator is provided with a plurality of groups of energy accumulator units according to the system compensation requirement; the actuating element of the six-degree-of-freedom parallel mechanism consists of six hydraulic cylinders; the hydraulic element of the three-degree-of-freedom series mechanism consists of two high-power hydraulic motors and a hydraulic cylinder. When the hybrid mechanism is in butt joint with the offshore platform, a person manually controls the tail end of the hybrid mechanism to be lapped on the offshore platform, after passive compensation is carried out, pressure energy gathered by the system energy accumulator is respectively supplied according to the requirements of each execution hydraulic element, and passive compensation is realized.
The method comprises the steps of firstly establishing a motion coordinate system aiming at the positions of mechanisms of a parallel platform and a series gangway ladder respectively and solving a homogeneous transformation matrix according to the motion characteristics of joints based on the kinematic distribution of a series-parallel mechanism with contact force change. And (3) pushing down in Cartesian space to derive Jacobian matrixes of the parallel platform and the series gangway ladder, and fusing the Jacobian matrixes and the series gangway ladder to obtain a kinematic model of the parallel-series mechanism in the task space. And then, the motion amount of each joint of the parallel platform and the serial gangway ladder is basically distributed by utilizing a Jacobi matrix pseudo-inverse method. In order to meet the requirements on performance indexes and realize optimization of constraint, the invention combines the limit positions of all joints to add a weight coefficient matrix and a null space item into an original Jacobian matrix, and combines a projection gradient method to complete the avoidance of the strange configuration of the gangway.
Implementation 1: as shown in fig. 1, the passive compensation system of the series-parallel mechanism system is composed of a series-parallel mechanism, a pressure sensor array at the tail end of the series-parallel mechanism, a motion distributor for wave passive compensation, and a hydraulic system of the series-parallel mechanism.
Implementation 2: as shown in fig. 2, the parallel-serial mechanism mainly comprises a six-degree-of-freedom parallel mechanism, a three-degree-of-freedom serial mechanism and an installation base: the six-degree-of-freedom parallel mechanism consists of six hydraulic cylinders and an upper platform and is mainly used for compensating the three-dimensional attitude (pitching, rolling and course) of the operation and maintenance ship influenced by sea waves; the three-degree-of-freedom series mechanism consists of a swing mechanism, a pitching mechanism and a telescopic mechanism and can compensate three-dimensional direction displacement of the operation and maintenance ship influenced by sea waves; the mounting base is used for fixing the hybrid mechanism on the operation and maintenance ship deck. The three-freedom-degree series mechanism and the six-freedom-degree parallel mechanism are formed by a hinged support.
Implementation 3: as shown in the attached figure 3, the pressure sensor array at the tail end of the hybrid mechanism of the boarding system is arranged in two directions, the pressure sensor array is uniformly distributed at intervals of 5 degrees in the horizontal direction according to the semicircular tail end of the hybrid mechanism, and the pressure sensor array is mainly used for detecting the contact force change condition of the advancing direction of the tail end of the hybrid mechanism and an offshore platform; the vertical direction is arranged at the lower end of the tail end of the hybrid mechanism, and the hybrid mechanism is uniformly distributed in a semicircular mode at intervals of every 5 degrees to detect the stress change condition of the lap joint of the tail end of the hybrid mechanism and the offshore platform.
Implementation 4: as shown in fig. 4, the motion distributor for wave passive compensation analyzes and decomposes motion according to pressure information detected by a pressure sensor array at the tail end of the hybrid mechanism, forms motion instructions of each execution component of the series of hybrid mechanisms, and drives each hydraulic cylinder and each hydraulic motor of the corresponding hybrid mechanism to move by using the capacity stored by an energy accumulator of a hydraulic system, so as to ensure that the tail end of the hybrid mechanism is effectively contacted with an offshore platform, and realize the compensation of ship wave motion (rolling, pitching and heaving), thereby greatly reducing the motion amplitude of the hybrid mechanism of the boarding system compared with a ship, and finally realizing the reliable butt joint of the boarding platform and the offshore platform under high sea conditions and ensuring the safe transportation of personnel.
Implementation 5: as shown in fig. 5, the hydraulic system of the parallel-serial mechanism is composed of a power source, an energy accumulator, an actuating hydraulic cylinder of the six-degree-of-freedom parallel mechanism, hydraulic actuating elements (a hydraulic cylinder and a hydraulic motor) of the three-degree-of-freedom serial mechanism, and an oil tank. The power source consists of a motor, a hydraulic pump, an overflow valve and a filter; the energy accumulator is provided with a plurality of groups of energy accumulator units according to the system compensation requirement; the actuating element of the six-degree-of-freedom parallel mechanism consists of six hydraulic cylinders; the hydraulic element of the three-degree-of-freedom series mechanism consists of two high-power hydraulic motors and a hydraulic cylinder. When the hybrid mechanism is in butt joint with the offshore platform, a person manually controls the tail end of the hybrid mechanism to be lapped on the offshore platform, after passive compensation is carried out, pressure energy gathered by the system energy accumulator is respectively supplied according to the requirements of each execution hydraulic element, and passive compensation is realized.
Implementation 6: referring to fig. 6, in the contact force variation-based kinematic distribution of the hybrid mechanism, a motion coordinate system is established for each mechanism position of the parallel platform and the serial gangway ladder, and a homogeneous transformation matrix is solved according to joint motion characteristics. And pushing down and deriving Jacobian matrixes of the parallel platform and the series gangway ladder in the Cartesian space, and fusing the Jacobian matrixes and the series gangway ladder to obtain a kinematic model of the parallel mechanism in the task space. And then, the motion amount of each joint of the parallel platform and the serial gangway ladder is basically distributed by using a Jacobi matrix pseudo-inverse method. In order to meet the requirements on performance indexes and realize optimization of constraint, the invention combines the limit positions of all joints to add a weight coefficient matrix and a null space item into an original Jacobian matrix, and combines a projection gradient method to complete the avoidance of the strange configuration of the gangway.
Step 1: with reference to FIG. 7, a kinematic model of the series-parallel mechanism is established
(1) Establishing an integral model of a series-parallel connection mechanism
Setting three attitude angles of the upper platform relative to the base coordinate as alpha, beta and gamma, respectively, and the position vector of the center of the upper platform in the base coordinate system as
Figure BDA0002686549440000111
Then the parallel Stewart platform transforms the matrix into
Figure BDA0002686549440000112
Figure BDA0002686549440000113
The first joint rotation angle of the series gangway ladder is set as theta1The second joint rotation angle is theta2The third joint has a stretching amount d3A homogeneous transformation matrix of the series gangway ladder according to the D-H method is
Figure BDA0002686549440000114
(2) Establishing a series Gangtai Jacobian matrix
Under the base coordinate system, the equation of motion of the gangway ladder with three degrees of freedom in series is
Figure BDA0002686549440000115
Figure BDA0002686549440000116
Wherein
Figure BDA0002686549440000117
The pose vector of the gangway ladder under the base coordinate system is shown, and the q is the rotation angle or displacement vector of three joints of the gangway ladder under the joint coordinate system. J is a unit ofsThe joint space movement speed is converted into the movement speed of a Cartesian space, and the pose quantity of the Cartesian space is converted into the speed quantity of the joint space through the joint space movement speed.
(3) Establishing parallel platform Jacobian matrix
The coordinates of the hinge points of the supporting legs connected with the platform in the corresponding coordinate system can be obtained according to the geometric structures of the movable platform and the static platform, and the coordinates of the hinge points of the upper platform in the movable coordinate system areAA, coordinates of each hinge point of the lower platform under a static coordinate system areBB, coordinates of each hinge point of the movable platform under the static coordinate system are：
Figure BDA0002686549440000121
The vector of each leg under the static coordinate system is expressed as:
BL＝[BL1 BL2 BL3 BL4 BL5 BL6]
BL＝BA-BB
in order to calculate the working speed of each supporting leg, derivatives are obtained from the two ends of the above formula, and the velocity vector of each hinge point of the upper platform is obtained as follows:
Figure BDA0002686549440000122
let q ═ x y z α β γ]TGeneralized coordinates representing the motion of the upper platform are:
Figure BDA0002686549440000123
Figure BDA0002686549440000124
(4) establishing a Jacobian matrix of a hybrid mechanism under a task space
Defining the speed of each joint of the hybrid mechanism in a motion coordinate system as xi ═ x y z alpha theta gamma theta1 θ2 d3]TThe pose vector of the tail end of the manipulator under the inertial coordinate system is
Figure BDA0002686549440000125
The homogeneous transformation matrix of the gangway terminal transformed from the motion coordinate system to the inertia coordinate system is
Figure BDA0002686549440000126
Including the position matrix and attitude matrix of the ramp ends.
The derivation of the position of the ramp end in the inertial coordinate system can be obtained
Figure BDA0002686549440000127
Wherein
Figure BDA0002686549440000128
[iwv×]Is a diagonally symmetric matrix, i.e. foriwv＝[wx wy wz]TIs provided with
Figure BDA0002686549440000129
Two algorithms of [ x ] y- [ y x ] x and x × y-y × x are used in the derivation, where x and y are matrices.
Derivation of attitude matrix of accommodation ladder terminal under inertial coordinate system
Figure BDA00026865494400001210
Whereiniwe＝iwv+iRv vwe。
And combining the position matrix and the derivative of the attitude matrix to obtain a kinematic model of the hybrid mechanism:
Figure BDA0002686549440000131
wherein JtaskIs the Jacobian matrix of the hybrid mechanism under the task space.
Step 2: kinematic model based on series-parallel mechanism and design motion planning method
(1) Pseudo-inverse solution of Jacobian matrix
According to the kinematic equation under the task space of the hybrid mechanism, the inverse of the kinematic equation can be obtained:
Figure BDA0002686549440000132
wherein
Figure BDA0002686549440000133
Is the plus inverse of the jacobian matrix, also known as the pseudo-inverse or the mole-pennissl inverse,
Figure BDA0002686549440000134
is the desired velocity trajectory at the end of the gangway, i.e. the amount of compensation for wave disturbances.
Adding a weighted norm matrix to each joint speed of the series-parallel mechanism to obtain a weighted Jacobian matrix plus inverse:
Figure BDA0002686549440000135
(2) multitask priority method:
least square solution of minimum norm of kinematic model under task space of hybrid mechanism
Figure BDA0002686549440000136
Wherein N is the degree of freedom of the whole series-parallel mechanism,
Figure BDA0002686549440000137
is the velocity and angular velocity vector of any one mechanism or joint,
Figure BDA0002686549440000138
is a joint vector term in the Jacobian matrix null space. Will be provided with
Figure BDA0002686549440000139
The form of the representation as a Jacobian matrix can be represented as the multi-task priority planning algorithm:
Figure BDA00026865494400001310
wherein k is the number of secondary tasks;
Figure BDA00026865494400001311
represents a series of secondary tasks;
Figure BDA00026865494400001312
is the Jacobian matrix in the equation of motion of the corresponding secondary task.
Numerical drift problems may arise when integrating the position for each joint velocity, so a closed loop of error between the desired and planned values is introduced:
Figure BDA00026865494400001313
and the secondary task I is set as joint limit constraint, three joints are constraint objects for the gangway ladder in series connection, and the moving platform pose of the parallel platform is taken as a constraint object. Firstly, an objective optimization function is defined
Figure BDA0002686549440000141
Wherein Ci0 is a constant coefficient used for defining the limiting effect strength of the ith joint; q. q ofi、qimaxAnd q isiminThe angle (position), maximum rotation (movement) boundary value, and minimum rotation (movement) boundary value of the i-th joint, respectively.
Secondly, defining the weight coefficient of the series gangway part as follows:
Figure BDA0002686549440000142
Figure BDA0002686549440000143
and the secondary task II is set as a singular configuration constraint, and since the singularity of the parallel platform is distributed in the whole working space and can be avoided only by limiting through joints, the singular configuration of the gangway ladder is avoided by adopting a method for limiting the operability of the serial mechanism. The operability is used for describing the distance of the mechanism from a singular configuration state, and is defined as
Figure BDA0002686549440000144
Where J is the Jacobian matrix of the corresponding mechanism.
For the avoidance of singular configuration of the gangway ladder in series, the gradient of the operability degree of the gangway ladder is obtained by taking the angle (position) of each joint as a variable
Figure BDA0002686549440000145
Figure BDA0002686549440000146
Figure BDA0002686549440000147
(3) Multi-task weighted minimum norm solution based on projection gradient method
The planning method finally adopted by the invention is determined to be a multi-task weighted minimum norm solution based on the projection gradient method based on the weighted minimum norm method and the projection gradient method, and the specific expression is
Figure BDA0002686549440000148
Wherein
Figure BDA0002686549440000149
Indicating the desired trajectory of the end of the gangway,
Figure BDA00026865494400001410
error value, K, for the desired trajectory and the planned trajectory of the ramp endeIn order to achieve the corresponding gain,
Figure BDA00026865494400001411
represents the jacobian matrix after the constraint of joint constraint is added.
(4) Parallel platform inverse kinematics solution
The motion amount of the series-parallel mechanism obtained by the motion planning method is represented by displacement (rotation) amounts of three joints of the series gangway ladder and a six-degree-of-freedom position attitude amount at the tail end of the parallel platform, wherein the stretching amount corresponding to six connecting rods is required to be further solved by inverse kinematics on the parallel platform.
Parallel platform inverse kinematics solution, knowing the transformation matrix of the upper platform center relative to the lower platform center
Figure BDA0002686549440000151
The target finds the amount of expansion and contraction of each rod length. Arbitrary vector R in upper platform coordinate systemaCan be transformed into R in the lower platform coordinate system by means of coordinate transformationbP is the origin A of the moving coordinate system in the fixed coordinate system B-xbybzbOf (2).
The homogeneous transformation matrix of the parallel platform is as follows:
Figure BDA0002686549440000152
Figure BDA0002686549440000153
Figure BDA0002686549440000154
in the formula:
Figure BDA0002686549440000155
P＝{Xp Yp Zp}T
Figure BDA0002686549440000156
Figure BDA0002686549440000157
Figure BDA0002686549440000158
Figure BDA0002686549440000159
in conclusion: the invention provides a hybrid mechanism system based on passive compensation and a motion decomposition method thereof. The passive compensation of the hydraulic system executing mechanism is realized through the hydraulic energy accumulator of the hybrid mechanism based on the reference of the contact force of the tail end of the on-board hybrid mechanism and the offshore platform on the sea, which is interacted in the automatic compensation stage, of the operation and maintenance ship, so that the position and posture change of the hybrid mechanism relative to the landing platform caused by the influence of sea waves is indirectly detected, and the short-time, quick and stable effective compensation of the hybrid mechanism on the offshore operation and maintenance ship under the interference of the sea waves under the complex sea conditions is met. The passive compensation system of the series-parallel mechanism system consists of a series-parallel mechanism, a pressure sensor array at the tail end of the series-parallel mechanism, a motion distributor for wave passive compensation and a hydraulic system of the series-parallel mechanism. The invention also provides a motion decomposition method of the passively compensated parallel-serial mechanism. The invention effectively solves the problems that the active compensation of the boarding system has higher energy consumption on the system and higher requirement on the power supply for the ship, can greatly save the cost of system devices, realizes the real-time, quick, effective and stable compensation, and has safety and practicability.

Claims (1)

1. A motion decomposition method of a series-parallel mechanism system based on passive compensation is characterized in that a motion coordinate system is respectively established for the positions of each mechanism of a parallel platform and a series gangway ladder, and a homogeneous transformation matrix is solved according to the motion characteristics of joints; pushing down in Cartesian space to derive Jacobian matrixes of the parallel platform and the series gangway ladder, and fusing the Jacobian matrixes and the series gangway ladder to obtain a kinematic model of the parallel-serial mechanism in the task space; then, the Jacobian matrix pseudo-inverse method is utilized to carry out basic distribution on the motion quantity of each joint of the parallel platform and the serial gangway ladder, a weight coefficient matrix and a null space item are added into the original Jacobian matrix by combining the limit position of each joint, and then the avoidance of the singular configuration of the gangway ladder is completed by combining the projection gradient method, and the method specifically comprises the following steps:
step 1: establishing a kinematic model of a series-parallel mechanism;
and 2, step: designing a motion planning method based on a kinematic model of the series-parallel mechanism;
the step 1 specifically comprises the following steps:
(1.1) establishing an integral model of the series-parallel connection mechanism
Setting three attitude angles of the upper platform relative to the base coordinate as alpha, beta and gamma, respectively, and the position vector of the center of the upper platform in the base coordinate system as
Figure RE-FDA0003648393820000011
Then the parallel Stewart platform transforms the matrix into
Figure RE-FDA0003648393820000012
Figure RE-FDA0003648393820000013
The first joint rotation angle of the series gangway ladder is set as theta1The second joint rotation angle is theta2The third joint expansion amount is d3The homogeneous transformation matrix of the series gangway ladder according to the D-H method is
Figure RE-FDA0003648393820000014
(1.2) establishing a Cassegrain Gangaba matrix
Under the base coordinate system, the motion equation of the gangway ladder with three degrees of freedom in series is
Figure RE-FDA0003648393820000015
Figure RE-FDA0003648393820000021
Wherein
Figure RE-FDA0003648393820000022
The pose vector of the gangway ladder under the base coordinate system is shown, and q is the corner or displacement vector of three joints of the gangway ladder under the joint coordinate system; j is a unit ofsConverting the joint space movement speed into a Cartesian space movement speed, and converting the pose amount of the Cartesian space into a joint space velocity amount through the Cartesian space movement speed;
(1.3) establishing a parallel platform Jacobian matrix
The coordinates of the hinge points of the connecting legs and the platform in the corresponding coordinate system can be obtained according to the geometrical structures of the movable platform and the static platform, and the coordinates of the hinge points of the upper platform in the movable coordinate system areAA, coordinates of each hinge point of the lower platform under a static coordinate system areBB, coordinates of each hinge point of the movable platform under the static coordinate system are as follows:
Figure RE-FDA0003648393820000023
the vector of each leg under the static coordinate system is expressed as:
BL＝[BL1 BL2 BL3 BL4 BL5 BL6]
BL＝BA-BB
in order to calculate the working speed of each supporting leg, derivatives are obtained from the two ends of the above formula, and the velocity vector of each hinge point of the upper platform is obtained as follows:
Figure RE-FDA0003648393820000024
let q ═ x y z α β γ]TGeneralized coordinates representing the motion of the upper platform are:
Figure RE-FDA0003648393820000025
Figure RE-FDA0003648393820000026
(1.4) establishing a Jacobian matrix of the hybrid mechanism under the task space
Defining the speed of each joint of the hybrid mechanism in a motion coordinate system as xi ═ x y z alpha theta gamma theta1 θ2 d3]TThe pose vector of the tail end of the mechanical arm under the inertial coordinate system is
Figure RE-FDA0003648393820000027
A homogeneous transformation matrix of the gangway terminal transformed from the motion coordinate system to the inertia coordinate system is
Figure RE-FDA0003648393820000028
The position matrix and the attitude matrix of the tail end of the gangway are included;
the position of the tail end of the gangway ladder under an inertial coordinate system can be obtained by derivation
Figure RE-FDA0003648393820000031
Wherein
Figure RE-FDA0003648393820000032
[iwv×]Is a diagonally symmetric matrix, i.e. foriwv＝[wx wy wz]TIs provided with
Figure RE-FDA0003648393820000033
Two algorithms of [ x ] y [ yx ] x and x × y [ -yxx ] x are used in the simultaneous derivation, wherein x and y are matrixes;
the attitude matrix of the tail end of the gangway ladder under the inertial coordinate system is derived
Figure RE-FDA0003648393820000034
Whereiniwe＝iwv+iRv vwe；
And combining the position matrix and the derivative of the attitude matrix to obtain a kinematic model of the hybrid mechanism:
Figure RE-FDA0003648393820000035
wherein JtaskFor the series-parallel mechanism to be in the task spaceA lower-middle Jacobian matrix;
the step 2 specifically comprises the following steps:
(2.1) pseudo-inverse solution of Jacobian matrix
According to the kinematic equation under the task space of the hybrid mechanism, the inverse of the kinematic equation can be obtained:
Figure RE-FDA0003648393820000036
wherein
Figure RE-FDA0003648393820000037
Is the plus inverse of the jacobian matrix, also known as the pseudo-inverse or the mole-pennissl inverse,
Figure RE-FDA0003648393820000038
is the desired speed trajectory at the end of the gangway, i.e. the amount of compensation for wave disturbances;
adding a weighted norm matrix to each joint speed of the series-parallel mechanism to obtain a weighted Jacobian matrix plus inverse:
Figure RE-FDA0003648393820000039
(2.2) multitask priority method:
least norm least square solution of kinematic model under task space of hybrid mechanism
Figure RE-FDA0003648393820000041
Wherein N is the degree of freedom of the whole series-parallel mechanism,
Figure RE-FDA0003648393820000042
is the velocity and angular velocity vector of any one mechanism or joint,
Figure RE-FDA0003648393820000043
is a joint vector term in Jacobian matrix null space; will be provided with
Figure RE-FDA0003648393820000044
The form of the representation as a Jacobian matrix can be represented as the multi-task priority planning algorithm:
Figure RE-FDA0003648393820000045
wherein k is the number of secondary tasks;
Figure RE-FDA0003648393820000046
represents a series of secondary tasks;
Figure RE-FDA0003648393820000047
a Jacobian matrix in a corresponding secondary task motion equation is obtained;
numerical drift problems may arise when integrating the position obtained for each joint velocity, so a closed loop of error between the desired and planned values is introduced:
Figure RE-FDA0003648393820000048
the secondary task I is set as joint limit constraint, three joints are constraint objects for the gangway ladder in series connection, and the moving platform pose of the parallel platform is used as a constraint object; firstly, an objective optimization function is defined
Figure RE-FDA0003648393820000049
Wherein Ci0 is a constant coefficient used for defining the limiting effect strength of the ith joint; q. q ofi、qimaxAnd q isiminRespectively the angle of the ith jointDegree or position, maximum rotation boundary value or maximum movement boundary value, minimum rotation boundary value or minimum movement boundary value;
secondly, defining the weight coefficient of the serial gangway ladder part as follows:
Figure RE-FDA00036483938200000410
Figure RE-FDA00036483938200000411
the secondary task II is set as singular configuration constraint, and since the singularity of the parallel platform is distributed in the whole working space and can only avoid larger singularity through joint limitation, the singular configuration of the gangway ladder is avoided by adopting a method for limiting the operability of the serial mechanism; the operability is used for describing the distance of the mechanism from a singular configuration state, and is defined as
Figure RE-FDA0003648393820000051
Wherein J is the Jacobian matrix of the corresponding mechanism;
for the avoidance of singular configuration of the gangway ladder in series, the gradient of the operability of the gangway ladder is calculated by taking the angle or the position of each joint as a variable
Figure RE-FDA0003648393820000052
Figure RE-FDA0003648393820000053
Figure RE-FDA0003648393820000054
(2.3) projection gradient method-based multitask weighted minimum norm solution
The planning method finally adopted by the invention is determined to be a multitask weighted minimum norm solution based on a projection gradient method based on a weighted minimum norm method and a projection gradient method, and the specific expression is
Figure RE-FDA0003648393820000055
Wherein
Figure RE-FDA0003648393820000056
To indicate the desired trajectory of the end of the gangway,
Figure RE-FDA0003648393820000057
error value, K, for the desired trajectory and the planned trajectory of the ramp endeIn order to achieve the corresponding gain,
Figure RE-FDA0003648393820000058
representing a Jacobian matrix after the constraint of joint limit is added;
(2.4) parallel platform inverse kinematics solution
The motion amount of the parallel-serial mechanism is obtained by the motion planning method, and is expressed in the form of displacement or rotation amount of three joints of the series gangway ladder and the attitude amount of six-degree-of-freedom position at the tail end of the parallel platform, wherein the expansion amount corresponding to six connecting rods is required to be further solved for the parallel platform through inverse kinematics;
parallel platform inverse kinematics solution, knowing the transformation matrix of the upper platform center relative to the lower platform center
Figure RE-FDA0003648393820000059
The target calculates the extension and contraction amount of each rod length; arbitrary vector R in upper platform coordinate systemaCan be transformed into R in the lower platform coordinate system by means of coordinate transformationbP is the origin A of the moving coordinate system in the fixed coordinate system B-xbybzbPosition vector ofAn amount;
the homogeneous transformation matrix of the parallel platform is as follows:
Figure RE-FDA00036483938200000510
Figure RE-FDA00036483938200000511
Figure RE-FDA0003648393820000061
in the formula:
Figure RE-FDA0003648393820000062
P＝{Xp Yp Zp}T
Figure RE-FDA0003648393820000063
Figure RE-FDA0003648393820000064
Figure RE-FDA0003648393820000065
Figure RE-FDA0003648393820000066
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