CN115070771B - Elastic double-ring synchronous control method for rope traction parallel robot - Google Patents
Elastic double-ring synchronous control method for rope traction parallel robot Download PDFInfo
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- CN115070771B CN115070771B CN202210848877.0A CN202210848877A CN115070771B CN 115070771 B CN115070771 B CN 115070771B CN 202210848877 A CN202210848877 A CN 202210848877A CN 115070771 B CN115070771 B CN 115070771B
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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
- B25J9/16—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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- 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
- B25J9/1615—Programme controls characterised by special kind of manipulator, e.g. planar, scara, gantry, cantilever, space, closed chain, passive/active joints and tendon driven manipulators
- B25J9/1623—Parallel manipulator, Stewart platform, links are attached to a common base and to a common platform, plate which is moved parallel to the base
Abstract
The invention discloses a rope traction parallel robot elastic double-ring synchronous control method, which comprises the following steps: step 1, establishing an elasticity equation, a dynamic equation of a movable platform and a dynamic equation of a winding drum end according to a kinematic equation and a motor rotation equation of a rope traction parallel robot; step 2, setting a pose combination error vector and a pose sliding mode vector according to a kinematic equation of the moving platform; step 3, setting an outer ring reference tension control law and an inner ring motor synchronous control law of the rope traction parallel robot according to the pose combination error vector and the pose sliding mode vector in combination with a dynamic equation, an elastic equation and a motor rotation equation of the movable platform; and 4, synchronously controlling motors for driving the winding drums of the rope traction parallel robot according to the outer ring reference tension control law and the inner ring motor synchronous control law. The method can process the problem of elastic deformation of the ropes while ensuring synchronous control of multiple ropes, and effectively improves the control performance and precision.
Description
Technical Field
The invention relates to the field of rope traction parallel robot control, in particular to an elastic double-ring synchronous control method for a rope traction parallel robot.
Background
The rope traction parallel robot achieves the purpose of controlling the brake platform to move in the working space by changing the length of the rope wound on the winding drum. Although the rope is light and can be conveniently wound and unwound in a large range, the introduction of the rope brings expansion of a working space, reduction of motion inertia and enhancement of load capacity to the rope traction parallel robot, the rope has inevitable elasticity, and certain elastic deformation can be generated under the action of rope tension, so that the control precision of the rope traction parallel robot is seriously influenced. Meanwhile, the motion of the movable platform in the working space is acted by a plurality of ropes connected to the movable platform, so that the synchronous winding and unwinding characteristics of the ropes also influence the control precision of the rope traction parallel robot. Therefore, aiming at the rope elasticity problem of the rope traction parallel robot and the synchronous winding and unwinding characteristics of a plurality of ropes, a control method capable of realizing rope elasticity compensation while ensuring synchronous winding and unwinding of the plurality of ropes is urgently needed, so that the control performance of the rope traction parallel robot is comprehensively improved.
At present, the elasticity of a rope is often ignored in the dynamic control of the existing rope traction parallel robot, and the rope is modeled into an inelastic connecting rod. However, as the application of rope-towed parallel robots diversifies, it is not practical to ignore the elasticity of the rope in some scenarios. In addition, the dynamics control strategy of the existing rope traction parallel robot rarely analyzes the characteristic of synchronous winding and unwinding of a plurality of ropes. Therefore, how to start from two aspects of rope elasticity and multi-rope synchronization, the problem of elastic deformation of the rope is solved while multi-rope synchronous control is ensured, and therefore the control precision of the rope traction parallel robot in the track tracking task is effectively improved.
In view of the above, the present invention is particularly proposed.
Disclosure of Invention
The invention aims to provide a rope traction parallel robot elastic double-ring synchronous control method which can process the elastic deformation problem of ropes while ensuring multi-rope synchronous control, thereby effectively improving the control precision of the rope traction parallel robot in a track tracking task and further solving the technical problems in the prior art.
The purpose of the invention is realized by the following technical scheme:
the embodiment of the invention provides an elastic double-ring synchronous control method for a rope traction parallel robot, which comprises the following steps:
and 4, synchronously controlling motors for driving the winding drums by the rope traction parallel robot according to the outer ring reference tension control law and the inner ring motor synchronous control law set in the step 3, changing the length of the rope wound on the winding drums, and enabling the movable platform connected with the rope to move along a set expected track.
Compared with the prior art, the elastic double-ring synchronous control method for the rope traction parallel robot has the beneficial effects that:
the elasticity of the rope is considered in the modeling process of the rope traction parallel robot and a corresponding modeling elasticity equation is adopted, the rope is regarded as a linear axial spring without mass, and the compensation of the elasticity of the rope is realized by designing an outer ring reference tension control scheme; in addition, the method analyzes the synchronous traction characteristic of the tensioned rope, defines the synchronous error of the length of the tensioned rope, and synchronously converts the length of the tensioned rope into motor synchronization through a reference tension control scheme of an outer ring, so that an inner ring motor synchronization control scheme is designed on the basis. According to the method, the outer ring reference tension control and the inner ring motor synchronous control are combined to form an elastic double-ring synchronous control law considering rope elasticity, the elastic deformation problem of the rope can be processed while multi-rope synchronous control is guaranteed, the control performance of the rope traction parallel robot in a track tracking task is effectively improved, and the problems of rope elasticity influence and insufficient control precision of the existing rope traction parallel robot are solved.
Drawings
In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings needed to be used in the description of the embodiments are briefly introduced below, and it is obvious that the drawings in the following description are only some embodiments of the present invention, and it is obvious for those skilled in the art to obtain other drawings based on the drawings without creative efforts.
Fig. 1 is a flowchart of an elastic double-ring synchronous control method for a rope-traction parallel robot according to an embodiment of the present invention.
Fig. 2 is a structural diagram of a rope-towed parallel robot according to an embodiment of the present invention.
Fig. 3 is a control block diagram of an elastic double-ring synchronous control method for a rope traction parallel robot according to an embodiment of the present invention.
Fig. 4 is a diagram of a desired trajectory set by a rope-towed parallel robotic mobile platform according to an embodiment of the present invention.
Detailed Description
The technical scheme in the embodiment of the invention is clearly and completely described in combination with the specific content of the invention; it is to be understood that the described embodiments are merely exemplary of the invention, and are not intended to limit the invention to the particular forms disclosed. All other embodiments, which can be derived by a person skilled in the art from the embodiments of the present invention without making any creative effort, shall fall within the protection scope of the present invention.
The terms that may be used herein are first described as follows:
the term "and/or" means that either or both can be achieved, for example, X and/or Y means that both cases include "X" or "Y" as well as "X and Y".
The terms "comprising," "including," "containing," "having," or other similar terms of meaning should be construed as non-exclusive inclusions. For example: including a feature (e.g., material, component, ingredient, carrier, formulation, material, dimension, part, component, mechanism, device, process, procedure, method, reaction condition, processing condition, parameter, algorithm, signal, data, product, or article of manufacture), is to be construed as including not only the particular feature explicitly listed but also other features not explicitly listed as such which are known in the art.
The term "consisting of 823070 \8230composition" means to exclude any technical characteristic elements not explicitly listed. If used in a claim, the term shall render the claim closed except for the usual impurities associated therewith which do not include the technical features other than those explicitly listed. If the term occurs in only one clause of the claims, it is defined only to the elements explicitly recited in that clause, and elements recited in other clauses are not excluded from the overall claims.
Unless expressly stated or limited otherwise, the terms "mounted," "connected," and "secured," etc., are to be construed broadly, as for example: can be fixedly connected, can also be detachably connected or integrally connected; can be mechanically or electrically connected; they may be connected directly or indirectly through intervening media, or they may be interconnected between two elements. The specific meaning of the above terms herein can be understood by those of ordinary skill in the art as appropriate.
The terms "central," "longitudinal," "lateral," "length," "width," "thickness," "upper," "lower," "front," "rear," "left," "right," "vertical," "horizontal," "top," "bottom," "inner," "outer," "clockwise," "counterclockwise," and the like are used in an orientation or positional relationship that is indicated based on the orientation or positional relationship shown in the drawings for ease of description and simplicity of description only, and are not meant to imply or imply that the device or element so referred to must have a particular orientation, be constructed in a particular orientation, and be operated in a particular manner and therefore are not to be construed as limiting herein.
The following describes in detail an elastic double-ring synchronous control method for a rope traction parallel robot provided by the invention. Details which are not described in detail in the embodiments of the invention belong to the prior art which is known to the person skilled in the art. The examples of the present invention, in which specific conditions are not specified, were carried out according to the conventional conditions in the art or conditions suggested by the manufacturer. The reagents or instruments used in the examples of the present invention are not specified by manufacturers, and are all conventional products available by commercial purchase.
As shown in fig. 1, an embodiment of the present invention provides a rope-traction parallel robot elastic double-ring synchronization control method, including:
and 4, synchronously controlling motors for driving the winding drums by the rope traction parallel robot according to the outer ring reference tension control law and the inner ring motor synchronous control law set in the step 3, changing the length of the rope wound on the winding drums, and enabling the movable platform connected with the rope to move along a set expected track.
In the method, the controlled rope pulls the parallel robot through drivingmMotor to connect the motorsmThe drum being rotated to change the winding on the drummThe length of the rope controlling the moving platform in the working spacenFreedom degree movement; wherein, the first and the second end of the pipe are connected with each other,mandnis a positive integer which is a multiple of,mis greater thann；
The base coordinate of the controlled rope traction parallel robot isO-xyzIts originOOn the base of the rope-drawn parallel robot fixed to the ground, the base beingO-xyzThe coordinate system is a fixed coordinate system and does not change along with the movement of the platform;
coordinate system of moving platform of controlled rope traction parallel robotP-xyzIts originPAt the center of mass of the moving platform, the moving platform coordinate systemP-xyzThe moving coordinate system is changed along with the movement of the moving platform;
at the initial state, the base coordinate systemO-xyzAnd the moving platform coordinate systemP-xyzAre parallel to each other.
In step 1 of the method, an elasticity equation of the rope traction parallel robot is established according to a kinematic equation and a motor rotation equation of the rope traction parallel robot in the following manner, and the elasticity equation comprises the following steps:
setting the length vector of the rope after tensioning to
Solving the kinematic equation of the rope traction parallel robot according to the following method to obtain theiLength of rope after tensioning of rope
：
In the above-mentioned formula (1),
is shown asiThe length of the rope after the rope is tensioned,i=1,2,...,m；
representing the modular length of the vector;
representing the origin of a coordinate system of a moving platformPIn the basic coordinate systemO-xyzThe lower position vector is obtained by measuring through a camera;
showing the connection point of the rope to the moving platformP i On-moving platform coordinate systemP-xyzA lower position vector;
indicating the point of connection of the rope to the drumB i In the basic coordinate systemO-xyzA lower position vector;
representing a moving platform coordinate systemP-xyzAnd base coordinate systemO-xyzThe rotation matrix is obtained by measuring through a camera;
setting the length vector of the rope before tensioning to
Solving the rotation equation of the motor of the rope traction parallel robot to obtain the secondiLength of rope before tensioning
：
In the above-mentioned formula (2),
denotes the firstiLength of the rope before tensioning;
is shown asiAn initial length of the root rope;
representing the gear ratio of the mechanism;
representing the motor rotation angle, the rope length vector before tensioning is represented in the form:
in the above-mentioned formula (3),
represents the rope length vector before tensioning;
representing an initial rope length vector;
a drive matrix representing a reel mechanism;
representing a motor rotation angle vector;
establishing an elastic equation of the rope traction parallel robot according to the elastic modulus of the rope, wherein the elastic equation comprises the following steps:
in the above-mentioned formula (4),
representing a tension vector of the rope;
is the length vector of the rope after tensioning;
is the rope length vector before tensioning;
representing the stiffness matrix of the rope, obtained by equation (5) as follows:
in the above-mentioned formula (5),Erepresenting the modulus of elasticity of the rope;Arepresenting the cross-sectional area of the rope;diag -1 (L 2 ) Representing diagonal elements asL 2 The inverse of the diagonal matrix of (a),
is the rope length vector before tensioning;
in step 1 of the method, a platform dynamics equation of the rope traction parallel robot is established according to the elastic equation in the following way, and the method comprises the following steps:
defining the difference between the kinetic energy and the potential energy of the rope traction parallel robot as a Lagrange function, and obtaining an initial moving platform kinetic equation of the rope traction parallel robot according to the Lagrange function as follows:
in the above-mentioned formula (6),
indicating moving platform in base coordinate systemO-xyzA lower pose vector;
indicating moving platform in base coordinate systemO-xyzA lower velocity vector;
indicating moving platform in base coordinate systemO-xyzIs as followsAn acceleration vector;
representing a mass and inertia matrix of the moving platform;
a coriolis matrix representing a moving platform;
representing a gravity vector of the moving platform;
representing a Jacobian matrix corresponding to the rope traction parallel robot;
representing the tension vector of the rope;
elastic equation for pulling rope to parallel robot
And combining the dynamic equation of the initial moving platform to obtain the final moving platform dynamic equation of the rope traction parallel robot, wherein the final moving platform dynamic equation is as follows:
in step 1 of the method, a drum end kinetic equation of the rope traction parallel robot is established according to an elastic equation in the following way, and the method comprises the following steps:
in the above-mentioned formula (8),
a matrix of inertia representing the web;
a matrix representing the viscous friction coefficient of the spool;
a matrix representing the coulomb friction coefficients of the spool;
a velocity vector representing a motor rotation angle;
an acceleration vector representing a motor rotation angle;
representing a symbolic function;
representing the torque vector of the motor.
In step 2 of the method, a rope length tracking error vector, a rope length synchronization error vector and a rope length coupling error vector after the rope traction parallel robot is tensioned are set according to a moving platform kinematics equation of the rope traction parallel robot in the following manner, and a pose combination error vector and a pose sliding mode vector of the rope traction parallel robot are set according to the set rope length coupling error vector, and the method comprises the following steps:
rope length tracking error vector after rope traction parallel robot tensioning is set
Comprises the following steps:
in the above-mentioned formula (9),
representing a desired tensioned rope length vector;
representing the actual tensioned rope length vector;
tracking error vector in conjunction with set tensioned rope length
Setting the synchronous error vector of the length of the rope after tensioning
Comprises the following steps:
in the above-mentioned formula (10),
the number of ropes;
representing a desired tensioned rope length vector
To (1) aiA component;
desired post-tensioning rope length vector
To (1) ajA component;
representing a rope length tracking error vector after tensioning
To (1) aiA component;
representing a rope length tracking error vector after tensioning
To (1) ajA component;
tracking error vector in conjunction with set tensioned rope length
Synchronous error vector with length of rope after tensioning
Setting the rope length coupling error vector after tensioning
Comprises the following steps:
in the above-mentioned formula (11),
representing a rope length synchronization error vector after tensioning;
is a constant greater than zero;
representing an integral variable, varying from 0 to
；
The integral time is represented, namely the total time of the control method of the current rope traction parallel robot;
setting upCombined error vector of tensioned rope lengths
Comprises the following steps:
in the above-mentioned formula (12),
representing coupling error velocity vector, coupling error vector by rope length
Obtaining a first derivative;
combined error vector in combination with set post-tensioning rope length
Setting the pose combination error vector of the rope traction parallel robot
Comprises the following steps:
in the above-mentioned formula (13),
representing a Jacobian matrix
A pseudo-inverse matrix of (d);
combined set pose combined error vector
Setting the integral error vector
Comprises the following steps:
in the above-mentioned formula (14),
is a constant greater than zero;
integrating error vector in conjunction with settings
Setting a pose sliding mode vector of the rope traction parallel robot
Comprises the following steps:
in the above-mentioned formula (15),
representing integral error velocity vector by summing the integral error vector
Obtaining a first derivative;
is a constant greater than zero.
In step 3 of the method, an outer ring reference tension control law and an inner ring motor synchronous control law of the rope traction parallel robot are set according to the pose combination error vector and the pose sliding mode vector of the rope traction parallel robot set in the step 2 in the following manner by combining the dynamic platform kinetic equation, the elastic equation and the motor rotation equation of the rope traction parallel robot set in the step 1, and the method comprises the following steps:
combining the obtained pose with the error vector
Sum pose sliding mode vector
And combining a dynamic platform equation of the rope traction parallel robot, and setting an outer ring reference tension control law of the rope traction parallel robot as follows:
in the above-mentioned formula (16),
representing an outer ring reference tension control law;
representation matrix
The pseudo-inverse matrix of (c);
combining the error velocity vectors for pose by aligning the pose
Obtaining a first-order derivation;
representing the sliding mode velocity vector by aligning the attitude sliding mode vector
Obtaining a first-order derivation;
、
are all constants greater than zero;
is a matrix
For ensuring that the reference rope tension vector is positive; s represents a pose sliding mode vector of the rope traction parallel robot;
indicating moving platform in base coordinate systemO-xyzA lower pose vector;
indicating moving platform in base coordinate systemO-xyzA lower velocity vector;
representing a mass and inertia matrix of the moving platform;
representing a gravity vector of the moving platform;
representing a symbolic function;
representing an integral variable, varying from 0 to
；
Expressing integral time, namely the total time acted by the current rope traction parallel robot control method;λ 1 、λ 2 is a constant greater than zero;
dynamic platform in base coordinate system for indicating settingO-xyzThe following reference acceleration vector is obtained by the following equation:
in the above-mentioned formula (17),
indicating moving platform in base coordinate systemO-xyzA lower actual acceleration vector;
combining the set outer ring reference tension control law of the rope traction parallel robot with the elastic equation of the rope traction parallel robot to obtain a reference rope length vector before the rope traction parallel robot is tensioned as follows:
in the above-mentioned formula (18),
representing a reference rope length vector before tensioning;
representing an identity matrix;
representing a rope length vector after tensioning;
combining the reference rope length vector before tensioning with the motor rotation equation of the rope traction parallel robot to obtain a reference motor rotation angle vector
Comprises the following steps:
and setting the inner ring motor synchronous control law of the rope traction parallel robot as follows according to the obtained reference motor rotation angle vector:
in the above-mentioned formula (20),
and
are positive definite diagonal constant matrixes;
representing an actual motor rotation angle vector;
representing an actual motor angular velocity vector;
a motor rotation angle vector representing a reference;
a motor angular velocity vector representing a reference;
representing the control torque vector of the motor.
In summary, the control method according to the embodiment of the invention starts with rope elasticity of the rope traction parallel robot, analyzes a kinematics and dynamics model of the rope traction parallel robot, sets a rope length tracking error vector, a rope length synchronization error vector and a rope length coupling error vector after tensioning by combining a multi-rope structure, further sets a pose combination error vector and a pose sliding mode vector of the rope traction parallel robot, then designs an outer loop reference tension control law and an inner loop motor synchronization control law respectively by combining the dynamics model of the rope traction parallel robot, and finally combines the two control laws to form a rope traction parallel robot double-loop synchronization control law considering rope elasticity, and synchronously controls motors of the rope traction parallel robot driving winding drums according to the control laws, thereby changing the rope length wound on the winding drums, and further enabling a movable platform connected with each rope to move along a set expected track.
In order to more clearly show the technical solutions and the technical effects provided by the present invention, the following describes in detail an elastic dual-ring synchronization control method of a rope-traction parallel robot provided by an embodiment of the present invention with specific embodiments.
Example 1
The embodiment provides an elastic double-ring synchronous control method for a rope traction parallel robot. The rope traction parallel robot controlled by the method has a structure as shown in figure 2, and the robot is driven by a drivemA motor to connect the motorsmThe individual reels being rotated to change the winding on the reelsmThe length of the rope, and thus of the brake platform, being controlled in the working spacenFreedom degree movement;mandnis a positive integer which is a multiple of,mis greater thann(ii) a The base coordinate of the controlled rope traction parallel robot isO-xyzIts originOThe rope traction parallel robot is positioned on a base of the rope traction parallel robot fixed on the ground; coordinate system of moving platform of controlled rope traction parallel robotP-xyzIts originPThe mass center of the movable platform is positioned; base coordinate systemO-xyzThe fixed coordinate system does not change along with the movement of the movable platform; moving platform coordinate systemP-xyzThe moving coordinate system can change along with the movement of the moving platform; at the initial state, the base coordinate systemO-xyzAnd moving platform coordinate systemP-xyzAre parallel to each other.
The control method comprises the following steps:
due to the elasticity, the length of the rope before and after tensioning changes to a certain extent. Setting the length vector of the rope after tensioning to
The following kinematic equation can be solved:
in the above-mentioned formula (1),
denotes the firstiThe length of the rope after the rope is tensioned,i=1,2,...,m；
representing the modular length of the vector;
representing the origin of the coordinate system of the moving platformPIn the basic coordinate systemO-xyzThe lower position vector can be obtained by measuring through a camera;
indicating the point of attachment of a rope to a moving platformP i On-moving platform coordinate systemP-xyzA lower position vector;
indicating the point of connection of the rope to the drumB i In the basic coordinate systemO-xyzA lower position vector;
representing a moving platform coordinate systemP-xyzAnd base coordinate systemO-xyzThe rotation matrix in between can be measured by a camera.
Setting the length vector of the rope before tensioning to
The motor rotation equation can be solved according to the following motor rotation equation:
in the above-mentioned formula (2),
is shown asiLength of the rope before tensioning;
is shown asiAn initial length of the root rope;
representing the gear ratio of the mechanism;
indicating the motor rotation angle. The rope length vector, which expresses the rope length before tensioning as a vector, is:
in the above-mentioned formula (3),
representing a rope length vector prior to tensioning;
representing an initial rope length vector;
representing a mechanism drive matrix;
representing a motor rotation angle vector.
The elasticity equation of the rope traction parallel robot can be obtained according to the elasticity of the rope:
in the above-mentioned formula (4),
representing the stiffness matrix of the rope, which can be found by the following equation:
in the above-mentioned formula (5),Erepresenting the modulus of elasticity of the rope;Arepresenting the cross-sectional area of the rope;diag -1 (L 2 ) Representing diagonal elements asL 2 The inverse of the diagonal matrix of (a),
is the rope length vector before tensioning.
Defining the difference between the kinetic energy and the potential energy of the rope traction parallel robot as a Lagrange function, and obtaining an initial moving platform kinetic equation of the rope traction parallel robot according to the Lagrange function as follows:
in the above-mentioned formula (6),
indicating moving platform in base coordinate systemO-xyzA lower pose vector;
indicating moving platform in base coordinate systemO-xyzA lower velocity vector;
indicating moving platform in base coordinate systemO-xyzA lower acceleration vector;
representing a mass and inertia matrix of the moving platform;
a coriolis matrix representing a moving platform;
representing a gravity vector of the moving platform;
a jacobian matrix representing a rope-towed parallel robot;
representing the tension vector of the rope.
Combining an elastic equation of the rope traction parallel robot with a dynamic equation of the movable platform to obtain a final dynamic equation of the movable platform of the rope traction parallel robot, wherein the final dynamic equation of the movable platform of the rope traction parallel robot is as follows:
the dynamic equation of the reel end of the rope traction parallel robot can be established as follows:
in the above-mentioned formula (8),
a matrix of inertia representing the web;
a matrix representing the viscous friction coefficient of the spool;
a matrix representing the coulomb friction coefficients of the spool;
a velocity vector representing a motor rotation angle;
an acceleration vector representing a motor rotation angle;
representing a symbolic function;
representing the torque vector of the motor.
And 2, setting a rope length tracking error vector, a rope length synchronous error vector and a rope length coupling error vector after the rope traction parallel robot is tensioned according to a moving platform kinematics equation of the rope traction parallel robot, and setting a pose combination error vector and a pose sliding mode vector of the rope traction parallel robot according to the set rope length coupling error vector. The method comprises the following specific steps:
rope length tracking error vector after rope traction parallel robot tensioning is set
Comprises the following steps:
in the above-mentioned formula (9),
represents a desired post-tensioning rope length vector;
representing the actual, tensioned rope length vector.
Setting a synchronous error vector of the length of the tensioned rope in combination with the set tracking error vector of the length of the tensioned rope
Comprises the following steps:
in the above-mentioned formula (10),
the number of ropes;
representing a desired tensioned rope length vector
To (1) aiA component;
indicating desired rope length vector after tensioning
To (1) ajA component;
representing a rope length tracking error vector after tensioning
To (1) aiA component;
representing a rope length tracking error vector after tensioning
To (1) ajAnd (4) a component.
Tracking error vector in conjunction with set tensioned rope length
Synchronous error vector with length of rope after tensioning
Defining the length coupling error vector of the rope after tensioning
Comprises the following steps:
in the above-mentioned formula (11),
representing a rope length synchronization error vector after tensioning;
is a constant greater than zero;
representing an integral variable;
representing the integration time.
Setting a combined error vector for a tensioned rope length
Comprises the following steps:
in the above-mentioned formula (12),
representing the coupling error velocity vector.
Combined error vector in combination with set post-tensioning rope length
Setting pose combination error vector
Comprises the following steps:
in the above-mentioned formula (13),
representing a Jacobian matrix
The pseudo-inverse matrix of (2).
Combined set pose combined error vector
Further, the following integral error vector is set
Comprises the following steps:
in the above-mentioned formula (14),
is a constant greater than zero.
Integrating error vector in conjunction with settings
Setting the following pose sliding mode vector
Comprises the following steps:
in the above-mentioned formula (15),
representing an integral error velocity vector;
is a constant greater than zero.
And 3, setting an outer ring reference tension control law and an inner ring motor synchronous control law of the rope traction parallel robot according to the pose combination error vector and the pose sliding mode vector of the rope traction parallel robot set in the step 2 and by combining the dynamic equation, the elastic equation and the motor rotation equation of the movable platform of the rope traction parallel robot set in the step 1. The method comprises the following specific steps:
combining the obtained pose with the error vector
Sum pose sliding mode vector
And combining a dynamic equation of a movable platform of the rope traction parallel robot, and setting an initial outer ring reference tension control law of the rope traction parallel robot as follows:
in the above-mentioned formula (16),
representing an outer ring reference tension control law;
representation matrix
A pseudo-inverse matrix of (d);
a pose combination error velocity vector is obtained;
representing a sliding mode velocity vector;
、
are all constants greater than zero;
is composed of
The null-space vector of (a) to ensure that the referenced rope tension vector is positive; s represents a pose sliding mode vector of the rope traction parallel robot;
indicating moving platform in base coordinate systemO-xyzA lower pose vector;
indicating moving platform in base coordinate systemO-xyzA lower velocity vector;
representing a mass and inertia matrix of the moving platform;
representing a gravity vector of the moving platform;
representing a symbolic function;
representing an integral variable, varying from 0 to
；
The integral time is represented, namely the total time of the control method of the current rope traction parallel robot;λ 1 、λ 2 is a constant greater than zero;
dynamic platform in base coordinate system for indicating settingO-xyzThe following reference acceleration vector can be obtained by the following equation:
in the above-mentioned formula (17),
indicating moving platform in base coordinate systemO-xyzThe actual acceleration vector of.
Combining the set outer ring reference tension control law of the rope traction parallel robot with the elastic equation of the rope traction parallel robot to obtain a reference rope length vector before the rope traction parallel robot is tensioned as follows:
in the above-mentioned formula (18),
representing a reference rope length vector before tensioning;
representing an identity matrix;
representing a rope length vector after tensioning;
combining the reference rope length vector before tensioning with the motor rotation equation of the rope traction parallel robot to obtain the reference motor rotation angle vector
Comprises the following steps:
and setting the inner ring motor synchronous control law of the rope traction parallel robot as follows according to the obtained reference motor rotation angle vector:
in the above-mentioned formula (20),
and
are positive definite diagonal constant matrixes;
representing an actual motor rotation angle vector;
representing an actual motor angular velocity vector;
a motor rotation angle vector representing a reference;
a motor angular velocity vector representing a reference;
representing the control torque vector of the motor.
And 4, synchronously controlling motors for driving the winding drums by the rope traction parallel robot according to the rope traction parallel robot elastic double-ring synchronous control law considering the rope elasticity, so that the length of the rope wound on the winding drums is changed, and further, the movable platforms connected with the ropes move along a set expected track.
The rope traction parallel robot elastic double-ring synchronous control block diagram is shown in figure 3. The embodiment pulls the motor torque vector of the parallel robot by the control rope
Thereby controlling the movable platform to perform high-precision motion along the set expected track as shown in figure 4.
In summary, the method provided by the embodiment of the invention starts with rope elasticity of the rope traction parallel robot, analyzes a kinematics and dynamics model of the rope traction parallel robot, sets a rope length tracking error vector, a rope length synchronization error vector and a rope length coupling error vector after tensioning by combining a multi-rope structure, further sets a pose combination error vector and a pose sliding mode vector of the rope traction parallel robot, then respectively designs an outer ring reference tension control law and an inner ring motor synchronization control law by combining the dynamics model of the rope traction parallel robot, and finally combines the two control laws to form a rope traction parallel robot elasticity double-ring synchronization control law considering the rope elasticity. Compared with the prior art, the elastic double-ring synchronous control method considering rope elasticity provided by the embodiment of the invention at least has the following beneficial effects:
(1) The rope is regarded as a linear axial spring without mass, and a perfect motion model of the rope traction parallel robot is established, wherein the perfect motion model comprises a kinematic equation, a motor rotation equation, a dynamic platform equation, an elastic equation and a drum end dynamic equation.
(2) Based on the multi-rope traction characteristic, the length synchronization error of the tensioned rope is defined and converted into the synchronization characteristic of the motor, and the inner ring motor synchronization control law is designed on the basis, so that the multi-rope synchronization control performance of the rope traction parallel robot is effectively improved.
(3) Aiming at the elasticity problem of the rope, an outer ring reference tension control law containing rope elasticity compensation is designed based on the synchronous error of the length of the tensioned rope, and a double-ring synchronous control law is constructed by combining the outer ring reference tension control law with an inner ring motor synchronous control law, so that the motion precision of the rope traction parallel robot is finally improved under the action of the double-ring synchronous control.
Those of ordinary skill in the art will understand that: all or part of the processes of the methods according to the embodiments may be implemented by a program, which may be stored in a computer-readable storage medium, and when executed, may include the processes according to the embodiments of the methods described above. The storage medium may be a magnetic disk, an optical disk, a Read-Only Memory (ROM), a Random Access Memory (RAM), or the like.
The above description is only for the preferred embodiment of the present invention, but the scope of the present invention is not limited thereto, and any changes or substitutions that can be easily conceived by those skilled in the art within the technical scope of the present invention are included in the scope of the present invention. Therefore, the protection scope of the present invention shall be subject to the protection scope of the claims. The information disclosed in this background section is only for enhancement of understanding of the general background of the invention and should not be taken as an acknowledgement or any form of suggestion that this information forms the prior art already known to a person skilled in the art.
The above description is only for the preferred embodiment of the present invention, but the scope of the present invention is not limited thereto, and any changes or substitutions that can be easily conceived by those skilled in the art within the technical scope of the present invention are included in the scope of the present invention. Therefore, the protection scope of the present invention should be subject to the protection scope of the claims. The information disclosed in this background section is only for enhancement of understanding of the general background of the invention and should not be taken as an acknowledgement or any form of suggestion that this information forms the prior art already known to a person skilled in the art.
Claims (7)
1. An elastic double-ring synchronous control method for a rope traction parallel robot is characterized by comprising the following steps:
step 1, establishing an elastic equation of the rope traction parallel robot according to a kinematic equation and a motor rotation equation of the rope traction parallel robot, and establishing a dynamic equation of a movable platform and a dynamic equation of a winding drum end of the rope traction parallel robot according to the elastic equation;
step 2, setting a rope length tracking error vector, a rope length synchronous error vector and a rope length coupling error vector after the rope traction parallel robot is tensioned according to a moving platform kinematics equation of the rope traction parallel robot, and setting a pose combination error vector and a pose sliding mode vector of the rope traction parallel robot according to the set rope length coupling error vector;
step 3, setting an outer ring reference tension control law and an inner ring motor synchronous control law of the rope traction parallel robot according to the pose combination error vector and the pose sliding mode vector of the rope traction parallel robot set in the step 2 and by combining the dynamic equation, the elastic equation and the motor rotation equation of the movable platform of the rope traction parallel robot set in the step 1;
and 4, synchronously controlling motors for driving the winding drums by the rope traction parallel robot according to the outer ring reference tension control law and the inner ring motor synchronous control law set in the step 3, changing the length of the rope wound on the winding drums, and enabling the movable platform connected with the rope to move along a set expected track.
2. The rope traction parallel robot elastic double-ring synchronous control method according to claim 1, characterized in that in the method, the rope traction parallel robot to be controlled drivesmMotor to connect the motorsmThe reel being rotated to change the winding thereofmThe length of the rope controlling the movement of the platform in the working spacenFreedom degree movement; wherein the content of the first and second substances,mandnis a positive integer and is a non-zero integer,mis greater thann；
The base coordinate of the controlled rope traction parallel robot isO-xyzIts originOOn the base of the rope-drawn parallel robot fixed to the ground, the base coordinate systemO-xyzThe coordinate system is a fixed coordinate system and does not change along with the movement of the platform;
coordinate system of movable platform of controlled rope traction parallel robotP-xyzIts originPAt the center of mass of the moving platform, the moving platform coordinate systemP-xyzThe moving coordinate system is changed along with the movement of the moving platform;
at the initial state, the base coordinate systemO-xyzAnd the moving platform coordinate systemP-xyzAre parallel to each other.
3. The rope traction parallel robot elastic double-ring synchronous control method according to claim 1 or 2, wherein in the step 1, an elastic equation of the rope traction parallel robot is established according to a kinematic equation and a motor rotation equation of the rope traction parallel robot in the following manner, and the method comprises the following steps:
setting the length vector of the rope after tensioning to
Solving the kinematic equation of the rope traction parallel robot according to the following method to obtain theiLength of rope after tensioning of rope
：
In the above-mentioned formula (1),
is shown asiThe length of the rope after the rope is tensioned,i=1,2,...,m；
representing the modular length of the vector;
representing the origin of the coordinate system of the moving platformPIn the basic coordinate systemO-xyzThe lower position vector is obtained by measuring through a camera;
indicating the point of attachment of a rope to a moving platformP i On-moving platform coordinate systemP-xyzA lower position vector;
indicating the point of connection of the rope to the drumB i In the basic coordinate systemO-xyzA lower position vector;
representing a moving platform coordinate systemP-xyzAnd base coordinate systemO-xyzThe rotation matrix is obtained by camera measurement;
setting the length vector of the rope before tensioning to
Solving the motor rotation equation of the parallel robot based on the rope tractioniLength of rope before tensioning
：
In the above-mentioned formula (2),
is shown asiLength of the rope before tensioning;
is shown asiAn initial length of the root rope;
representing the gear ratio of the mechanism;
representing the motor rotation angle, the rope length vector before tensioning is represented in the form:
in the above-mentioned formula (3),
represents the rope length vector before tensioning;
representing initial rope length vectors；
A drive matrix representing a reel mechanism;
representing a motor rotation angle vector;
establishing an elastic equation of the rope traction parallel robot according to the elastic modulus of the rope, wherein the elastic equation comprises the following steps:
in the above-mentioned formula (4),
representing the tension vector of the rope;
is the length vector of the rope after tensioning;
is the rope length vector before tensioning;
representing the stiffness matrix of the rope, obtained by equation (5) as follows:
in the above-mentioned formula (5),Erepresenting the modulus of elasticity of the rope;Arepresenting the cross-sectional area of the rope; diag -1 (L 2 ) Representing diagonal elements as L 2 The inverse of the diagonal matrix of (a),
is the rope length vector before tensioning.
4. The elastic double-ring synchronous control method for the rope traction parallel robot as claimed in claim 3, wherein in the step 1, the platform dynamics equation of the rope traction parallel robot is established according to the elastic equation in the following way, comprising:
defining the difference between the kinetic energy and the potential energy of the rope traction parallel robot as a Lagrange function, and obtaining an initial moving platform kinetic equation of the rope traction parallel robot according to the Lagrange function as follows:
in the above-mentioned formula (6),
indicating moving platform in base coordinate systemO-xyzA lower pose vector;
indicating moving platform in base coordinate systemO-xyzA lower velocity vector;
indicating moving platform in base coordinate systemO-xyzA lower acceleration vector;
representing a mass and inertia matrix of the moving platform;
a coriolis matrix representing a moving platform;
representing a gravity vector of the moving platform;
representing a Jacobian matrix corresponding to the rope traction parallel robot;
representing the tension vector of the rope;
elastic equation for pulling rope to parallel robot
And combining the dynamic equation of the initial moving platform to obtain the final moving platform dynamic equation of the rope traction parallel robot, wherein the final moving platform dynamic equation is as follows:
5. the elastic double-ring synchronous control method for the rope traction parallel robot as claimed in claim 3, wherein in the step 1, a drum end kinetic equation of the rope traction parallel robot is established according to the elastic equation in the following way, comprising:
in the above-mentioned formula (8),
a matrix of inertia representing the web;
a matrix representing the viscous friction coefficient of the spool;
a matrix of coulomb friction coefficients representing the spool;
a velocity vector representing a motor rotation angle;
an acceleration vector representing a motor rotation angle;
representing a symbolic function;
representing the torque vector of the motor.
6. The rope pulling parallel robot elastic double-ring synchronous control method according to claim 3, wherein in the step 2, the rope length tracking error vector, the rope length synchronization error vector and the rope length coupling error vector after the rope pulling parallel robot is tensioned are set according to the moving platform kinematics equation of the rope pulling parallel robot, and the pose combination error vector and the pose sliding mode vector of the rope pulling parallel robot are set according to the set rope length coupling error vector, and the method comprises the following steps:
rope length tracking error vector after rope traction parallel robot tensioning is set
Comprises the following steps:
in the above-mentioned formula (9),
representing a desired tensioned rope length vector;
representing the actual tensioned rope length vector;
tracking error vector in conjunction with set tensioned rope length
Setting the synchronous error vector of the length of the rope after tensioning
Comprises the following steps:
in the above-mentioned formula (10),
is the number of ropes;
representing a desired post-tensioning rope length vector
To (1) aiA component;
desired post-tensioning rope length vector
To (1) ajA component;
representing a rope length tracking error vector after tensioning
To (1) aiA component;
representing a rope length tracking error vector after tensioning
To (1)jA component;
tracking error vector in conjunction with set tensioned rope length
Synchronous error vector with length of rope after tensioning
Setting the rope length after tensioning coupling error vector
Comprises the following steps:
in the above-mentioned formula (11),
representing a rope length synchronization error vector after tensioning;
is a constant greater than zero;
representing an integral variable, varying from 0 to
；
The integral time is represented, namely the total time of the control method of the current rope traction parallel robot;
setting a combined error vector for a tensioned rope length
Comprises the following steps:
in the above-mentioned formula (12),
representing the coupling error velocity vector, the coupling error vector by rope length
Obtaining a first-order derivation;
combined error vector in combination with set post-tensioning rope length
Setting the pose combination error vector of the rope-traction parallel robot
Comprises the following steps:
in the above-mentioned formula (13),
representing a Jacobian matrix
A pseudo-inverse matrix of (d);
pose combination error vector in conjunction with settings
Setting the integral error vector
Comprises the following steps:
in the above-mentioned formula (14),
is a constant greater than zero;
integrating error vector in conjunction with settings
Setting a pose sliding mode vector of the rope traction parallel robot
Comprises the following steps:
in the above-mentioned formula (15),
representing integral error velocity vector by summing the integral error vector
Obtaining a first-order derivation;
a constant greater than zero.
7. The method for controlling the rope-traction parallel robot through the elastic double-ring synchronization according to claim 6, wherein in the step 3, the outer-ring reference tension control law and the inner-ring motor synchronization control law of the rope-traction parallel robot are set according to the pose combination error vector and the pose sliding-mode vector of the rope-traction parallel robot set in the step 2 by combining the dynamic equation of the rope-traction parallel robot moving platform, the elastic equation and the motor rotation equation set in the step 1, and the method comprises the following steps:
combining the obtained pose with an error vector
Sum pose sliding mode vector
And combining a dynamic platform equation of the rope traction parallel robot, and setting an initial outer ring reference tension control law of the rope traction parallel robot as follows:
in the above-mentioned formula (16),
representing an outer ring reference tension control law;
representation matrix
A pseudo-inverse matrix of (d);
combining error velocity directions for poseMeasure, combine error vectors by aligning pose
Obtaining a first derivative;
representing the sliding mode velocity vector by aligning the attitude sliding mode vector
Obtaining a first-order derivation;
、
are all constants greater than zero;
is a matrix
The null-space vector of (a) to ensure that the referenced rope tension vector is positive; s represents a pose sliding mode vector of the rope traction parallel robot;
indicating moving platform in base coordinate systemO-xyzA lower pose vector;
indicating moving platform in base coordinate systemO-xyzA lower velocity vector;
representing a mass and inertia matrix of the moving platform;
representing a gravity vector of the moving platform;
representing a symbolic function;
representing an integral variable, varying from 0 to
；
The integral time is represented, namely the total time of the control method of the current rope traction parallel robot;λ 1 、λ 2 is a constant greater than zero;
indicating set moving platform in base coordinate systemO-xyzThe following reference acceleration vector is obtained by the following equation:
in the above-mentioned formula (17),
indicating moving platform in base coordinate systemO-xyzA lower actual acceleration vector;
combining the set outer ring reference tension control law of the rope traction parallel robot with the elastic equation of the rope traction parallel robot to obtain a reference rope length vector before the rope traction parallel robot is tensioned as follows:
in the above-mentioned formula (18),
representing a reference rope length vector before tensioning;
representing an identity matrix;
representing a rope length vector after tensioning;
combining the reference rope length vector before tensioning to the motor rotation equation of the rope traction parallel robot to obtain a reference motor rotation angle vector
Comprises the following steps:
and setting the inner ring motor synchronous control law of the rope traction parallel robot as follows according to the obtained reference motor rotation angle vector:
in the above-mentioned formula (20),
and
are positive definite diagonal constant matrixes;
representing an actual motor rotation angle vector;
representing an actual motor angular velocity vector;
a motor rotation angle vector representing a reference;
a motor angular velocity vector representing a reference;
representing the control torque vector of the motor.
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Citations (5)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN105974797A (en) * | 2016-07-01 | 2016-09-28 | 厦门大学 | Rope-driven parallel robot motion control method in consideration of elasticity effect and compensation |
| CN107122568A (en) * | 2017-05-24 | 2017-09-01 | 西安科技大学 | A kind of flexible cable traction dirt extraction robot kinetic stability evaluation method |
| CN110216685A (en) * | 2019-03-12 | 2019-09-10 | 汕头大学 | A kind of cable parallel robot and control method for the detection of coal bunker inner wall defect |
| CN111409069A (en) * | 2020-03-18 | 2020-07-14 | 中国科学技术大学 | Method for solving kinematic speed of rope traction parallel robot with variable structure |
| CN112975912A (en) * | 2021-03-09 | 2021-06-18 | 西安工业大学 | Flight type rope traction parallel robot complete rigidity model and rigidity characteristic analysis method |
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| EP3700716A1 (en) * | 2017-10-24 | 2020-09-02 | Ludban, Neil | Hybrid delta robot |
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Patent Citations (5)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN105974797A (en) * | 2016-07-01 | 2016-09-28 | 厦门大学 | Rope-driven parallel robot motion control method in consideration of elasticity effect and compensation |
| CN107122568A (en) * | 2017-05-24 | 2017-09-01 | 西安科技大学 | A kind of flexible cable traction dirt extraction robot kinetic stability evaluation method |
| CN110216685A (en) * | 2019-03-12 | 2019-09-10 | 汕头大学 | A kind of cable parallel robot and control method for the detection of coal bunker inner wall defect |
| CN111409069A (en) * | 2020-03-18 | 2020-07-14 | 中国科学技术大学 | Method for solving kinematic speed of rope traction parallel robot with variable structure |
| CN112975912A (en) * | 2021-03-09 | 2021-06-18 | 西安工业大学 | Flight type rope traction parallel robot complete rigidity model and rigidity characteristic analysis method |
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