CN114367964B - Reconstruction planning method for rope traction parallel robot - Google Patents
Reconstruction planning method for rope traction parallel robot Download PDFInfo
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- B—PERFORMING OPERATIONS; TRANSPORTING
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Abstract
The invention discloses a reconstruction planning method for a rope traction parallel robot, which comprises the following steps: step 1, setting a coordinate system and parameters of a rope traction parallel robot, and respectively establishing a dynamic equation of a movable platform and a single rope leading-out device; step 2, establishing a mathematical model corresponding to the force feasible working space according to the parameters; step 3, planning a track of the movable platform and dispersing the track into a path point set of the movable platform, and combining a mathematical model corresponding to the feasible working space to determine the relation between the feasible working space of the current configuration and the path of the movable platform; step 4, judging whether an optimal configuration exists; and 5, setting an objective function which minimizes the number of the moving rope leading-out points in the continuous reconstruction, and solving a rope leading-out point position sequence in the continuous reconstruction, namely finishing the reconstruction planning of the rope traction parallel robot. The method carries out planning reconstruction by adjusting to the optimal configuration and implementing a continuous reconstruction mode, and the number of the moving rope leading-out points is minimum, thereby saving energy.
Description
Technical Field
The invention relates to the field of rope traction parallel robots, in particular to a reconstruction planning method of a rope traction parallel robot.
Background
The rope traction parallel robot has the advantages of large working space, high load-weight ratio, easiness in assembly and layout and the like, but the fixed configuration of the rope traction parallel robot restricts the performance of the robot and is difficult to adapt to requirements of different tasks. Therefore, researchers have designed reconfigurable rope-towed parallel robots that increase mission flexibility by changing the location of the rope-to-fixed frame attachment points (referred to as rope exit points). At present, after a target configuration is obtained through optimization, reconstruction is achieved through manual operation before a task is executed, and the mode of offline assembly again hinders the execution of the task and the improvement of production efficiency.
Although the chinese patent application 202010192426.7 and CN202010191743.7 disclose a kinematics optimization solution method for a rope traction parallel robot with a variable structure, the problem of reconstruction planning of the robot cannot be solved. The Chinese patent application 201910523043.0 discloses a self-reconfiguration planning method of a heterogeneous modular robot based on a reinforcement learning algorithm, but a rope traction parallel robot adopts rope drive, and the tension of the rope is unidirectional, so that the reconfiguration planning suitable for the modular robot cannot be applied to the rope traction parallel robot. In addition, the positions of all rope leading-out points need to be adjusted continuously in the continuous reconstruction process, so that not only is the energy consumption increased, but also the risk of collision with an obstacle is increased, therefore, under the condition of meeting the task requirements, the problem of how to minimize the number of the rope leading-out points needing to be moved in the continuous reconstruction process is also a concern, but the effective rope traction parallel robot reconstruction planning method is lacked at present.
In view of the above, the present invention is particularly proposed.
Disclosure of Invention
The invention aims to provide a reconstruction planning method for a rope traction parallel robot, which can plan the positions of rope leading-out points to realize the reconstruction of the rope traction parallel robot and minimize the number of the rope leading-out points needing to be moved in the continuous reconstruction process, thereby 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 a reconstruction planning method for a rope traction parallel robot, which comprises the following steps:
step 2, establishing a mathematical model corresponding to the feasible working space of the force of the rope-traction parallel robot according to the parameters of the rope-traction parallel robot;
step 3, planning a track of the movable platform and dispersing the track into a set of path points of the movable platform, determining the relation between the force feasible working space of the current configuration of the rope traction parallel robot and the path of the movable platform by combining a mathematical model corresponding to the force feasible working space, judging whether the force feasible working space of the current configuration completely comprises the path of the movable platform according to the mathematical model corresponding to the force feasible working space, if so, determining that the configuration does not need to be adjusted, and finishing the planning; if not, determining to trigger reconstruction, and executing the step 4;
step 4, judging whether the rope traction parallel robot has an optimal configuration, if so, finishing planning; if not, executing the step 5;
and 5, setting an objective function which minimizes the number of the moving rope leading-out points in the continuous reconstruction, solving a rope leading-out point position sequence of the rope traction parallel robot in the continuous reconstruction, and finishing the reconstruction planning of the rope traction parallel robot.
Compared with the prior art, the rope traction parallel robot reconfiguration planning method provided by the invention has the beneficial effects that:
by determining the relationship between the force feasible working space of the rope traction parallel robot and the movable platform path, the force feasible working space of the current configuration cannot completely contain the movable platform path as a trigger condition for the reconstruction of the rope traction parallel robot; when the reconfiguration is triggered, the method preferentially searches for an optimal configuration, the rope leading-out point can be automatically moved to an optimal position without disassembly and assembly, and then a driving motor of the rope leading-out point is in a locked state when the movable platform moves, so that no extra energy is consumed; when the optimal configuration can not meet the task, continuous reconstruction is carried out, the configuration reconstruction is automatically completed when the movable platform moves, the range of the feasible working space of force is dynamically adjusted, the path of the movable platform is always positioned in the feasible working space of force, and in the continuous reconstruction process, the number of the moved rope leading-out points can be minimized and the corresponding moving distance can be calculated by the method, so that the energy is saved.
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In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings required to be used in the description of the embodiments are briefly introduced below, and it is obvious that the drawings in the description below are only some embodiments of the present invention, and it is obvious for those skilled in the art that other drawings can be obtained according to the drawings without creative efforts.
Fig. 1 is a flowchart of a rope-traction parallel robot reconfiguration planning method according to an embodiment of the present invention.
Fig. 2 is a specific flowchart of a rope-traction parallel robot reconfiguration planning method according to an embodiment of the present invention.
Fig. 3 is a schematic structural diagram of a rope traction parallel robot according to an embodiment of the present invention.
Fig. 4 is a schematic view of a linear task path scene of a moving platform of a rope-traction parallel robot according to an embodiment of the present invention.
The part names corresponding to the marks in the figure are as follows: 11-a fixed frame; 12-rope take-off, 121-guide pulley, 122-slider; 13-a rope; 14-moving the platform; 15-a motor driving the lead screw; 16-a motor driving the drum; 17-a reel; 18-vertical lead screw.
Detailed Description
The technical scheme in the embodiment of the invention is clearly and completely described below by combining 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 three cases including "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, step, process, method, reaction condition, processing condition, parameter, algorithm, signal, data, product, or article, etc.) that is not specifically recited, should be interpreted to include not only the specifically recited feature but also other features not specifically recited and known in the art.
The term "consisting of … …" is meant to exclude any technical feature 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 as specifically listed in that clause, and elements recited in other clauses are not excluded from the overall claims.
Unless otherwise expressly stated or limited, the terms "mounted," "connected," "secured," and the like 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.
When concentrations, temperatures, pressures, dimensions, or other parameters are expressed as ranges of values, the ranges of values should be understood to specifically disclose all ranges formed by any pair of upper values, lower values, or preferred values within the range, regardless of whether the ranges are explicitly recited; for example, if a numerical range of "2 ~ 8" is recited, then the numerical range should be interpreted to include ranges of "2 ~ 7", "2 ~ 6", "5 ~ 7", "3 ~ 4 and 6 ~ 7", "3 ~ 5 and 7", "2 and 5 ~ 7", and the like. Unless otherwise indicated, the numerical ranges recited herein include both the endpoints thereof and all integers and fractions within the numerical range.
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 rope traction parallel robot reconfiguration planning method provided by the invention is described in detail below. Details which are not described in detail in the embodiments of the invention belong to the prior art which is known to a person skilled in the art. Those not specifically mentioned in the examples of the present invention 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 reconstruction planning method for a rope-towed parallel robot, where planning a position of a rope leading-out point to implement reconstruction of the rope-towed parallel robot includes:
step 2, establishing a mathematical model corresponding to the feasible working space of the force of the rope-traction parallel robot according to the parameters of the rope-traction parallel robot;
step 3, planning a track of the movable platform and dispersing the track into a set of path points of the movable platform, determining the relation between the force feasible working space of the current configuration of the rope traction parallel robot and the path of the movable platform by combining a mathematical model corresponding to the force feasible working space, judging whether the force feasible working space of the current configuration completely comprises the path of the movable platform according to the mathematical model corresponding to the force feasible working space, if so, determining that the configuration does not need to be adjusted, and finishing the planning; if not, determining to trigger reconstruction, and executing the step 4;
step 4, judging whether the rope traction parallel robot has an optimal configuration, if so, finishing planning; if not, executing the step 5;
and 5, setting an objective function which minimizes the number of the moving rope leading-out points in the continuous reconstruction, solving a rope leading-out point position sequence of the rope traction parallel robot in the continuous reconstruction, and finishing the reconstruction planning of the rope traction parallel robot.
In step 1 of the method, a coordinate system and parameters of the rope traction parallel robot to be reconstructed and planned are set according to the following modes, and a dynamic equation of a movable platform of the rope traction parallel robot and a dynamic equation of a single rope leading-out device are respectively established according to the set coordinate system and parameters, wherein the dynamic equation comprises the following steps:
setting global coordinate system of rope-traction parallel robot
Of (2)
A rope leading-out point which is positioned on the ground of the fixed frame of the rope-traction parallel robot and leads the rope to the parallel robot
For position vector of
It is shown that the process of the present invention,
，
the number of the leading-out points of the ropes and the number of the ropes are used for the position vector of the movable platform of the rope traction parallel robot
Showing that the ropes pull the ropes of the parallel robots
Is a direction vector of
Establishing a dynamic equation of a movable platform of the rope traction parallel robot and a dynamic equation of a single rope leading-out device;
the dynamic equation of the movable platform is as follows:
（1）；
in the formula (1), the reaction mixture is,
a structural matrix corresponding to the parallel robot is towed by the rope,
；
a rope tension vector for the rope-towed parallel robot;
the mass of a moving platform for the rope traction parallel robot;
a moving platform acceleration for the rope-towed parallel robot;
，
is the acceleration of gravity;
the kinetic equation for the single rope lead-out device is:
（2）；
in the formula (2), the reaction mixture is,
an axial driving force of a rope pulling-out device for pulling the parallel robot for the rope;
a rope tension for said rope pulling parallel robots;
；
the weight of a rope take-off device that pulls the parallel robot for the rope;
is the acceleration of gravity;
acceleration of a rope lead-out device of the parallel robot is pulled for the rope.
In step 2 of the above method, the mathematical model established is:
in the formula (3), the reaction mixture is,
a structural matrix corresponding to the parallel robot is towed by the rope,
；
rope for pulling parallel robots for said ropeA tension vector;
the rope pulls the dynamic platform of the parallel robot to bear the resultant external force;
the lower limit of the rope tension vector is set to be 10N;
the components are set to 200N for the upper limit of the rope tension vector.
In step 3 of the method, a movable platform track is planned and dispersed into a movable platform path point set in the following way, and a mathematical model corresponding to a binding force feasible working space determines the relation between the force feasible working space of the current configuration of the rope traction parallel robot and the movable platform path, including:
at the time of
Planning the path of the moving platform by adopting a track planning algorithm to obtain the track
，
The trajectory is
，
According to a given time step
Discretization into a set of moving platform waypoints
，
，
Is composed of
Integer multiples of;
converting the mathematical model formula (3) corresponding to the force feasible working space into an inequality by adopting a moving hyperplane method:
（4）；
in the above formula (4), matrix
Sum vector
Drawing a corresponding structural matrix of the parallel robot according to the rope by a moving hyperplane method
Upper limit of rope tension vector
Lower limit of rope tension vector
Obtaining;
judging whether the force feasible working space of the current configuration of the rope-traction parallel robot completely contains a moving platform path according to the mathematical model corresponding to the force feasible working space in the following way, including:
determining a set of moving platform waypoints
Whether each of the waypoints in the set is fullIf the inequality (4) is satisfied, determining that the feasible working space of the force of the current configuration of the rope-traction parallel robot completely contains a moving platform path without adjusting the configuration; and if not, determining that the force feasible working space of the current configuration of the rope traction parallel robot cannot completely contain the moving platform path, and triggering reconfiguration.
In step 4 of the method, whether the rope-traction parallel robot has an optimal configuration is judged according to the following modes, including:
setting the position of a rope leading-out point of the rope-traction parallel robot
Between the upper and lower limits of position:
in the above formula (5), lower limit of position
(ii) a Upper limit of position
；
Setting the first objective function as:
（6）；
in the formula (6), the reaction mixture is,
capacity margin indexes for keeping the mobile platform away from the boundary of the power feasible working space;
-setting said inequality (4) and said inequality (5) as a first penalty function by means of a penalty function:
in the formula (7), the reaction mixture is,
is a penalty factor;
is constrained by all inequalities;
the number of inequality constraints;
adding the first penalty function of the formula (7) and the first objective function of the formula (6) to form a new objective function, solving the new objective function by adopting a competitive particle swarm algorithm to obtain an optimal configuration, determining that the rope traction parallel robot can be adjusted to a fixed optimal configuration if the optimal configuration has a solution, and finishing planning; if the optimization is solution-free, it is determined that there is no optimal configuration.
In step 4 of the above-described method,
is set as
；
The search space dimension of the competitive particle swarm algorithm is
。
In step 5 of the above method, an objective function for minimizing the number of moving rope leading-out points in continuous reconstruction is set in the following manner, and a rope leading-out point position sequence of the rope traction parallel robot in continuous reconstruction is solved, including:
step 51, constructing the total displacement of the rope leading-out points into an indefinite linear equation set;
step 52, setting a rope leading-out point physical constraint condition and a second objective function which minimizes the number of the moved rope leading-out points in continuous reconstruction;
and 54, filtering the solved speed sequence of the rope leading-out points and smoothing to obtain a position sequence of the rope leading-out points.
In the step 51, the total rope leading-out point displacement is constructed into an indefinite linear equation set according to the following mode, which includes:
by using
Representing and moving platform path point set
In (1)
Rope leading-out point corresponding to position of moving platform
The initial position of the cord exit point
The method is obtained by measuring the actually planned rope traction parallel robot;
by using
，
Representing the change in position of the cord exit point; by using
Is shown in time
Inner position
And
the speed of (d) in between; by using
，
Representing and moving platform path point set
Corresponding rope leading-out point
The speed sequence of (a);
the rope leading-out point of the rope traction parallel robot is at the total time
Total displacement of internal movement
Comprises the following steps:
in the formula (8), the reaction mixture is,
is one
Vector of (2), solution in equation (8)
Is not unique;
is one
A constant vector of (2);
in step 52, the setting of the physical constraint conditions for the rope exit points and the second objective function for minimizing the number of the moved rope exit points in the continuous reconstruction includes:
setting a rope leading-out point
In the position of
Speed, velocity
Acceleration of the object
Satisfy respective upper and lower limits:
in the formula (9), the reaction mixture is,
；
；
；
(ii) a Setting a second objective function for minimizing the number of rope exit points moved in successive reconstructions as:
in the formula (10), the reaction mixture is,
the value range is 0 to 1 for weight;
the number of the rope leading-out points is the number of the rope leading-out points;
is a speed sequence of rope leading-out points;
the number of the path points of the movable platform is;
capacity margin indexes for moving the power platform away from the boundary of the power feasible working space;
in the step 53, solving a speed sequence of rope index points in the continuous reconstruction by using a second objective function which minimizes the number of the moving rope lead-out points in the continuous reconstruction includes:
-setting the inequality of said equation (4) and said equation (9) as a second penalty function by means of a penalty function, adding the second penalty function to a second objective function of said equation (10) as an overall objective function, the corresponding sequence of rope exit point positions being represented during the optimization iteration as:
in the above-mentioned formula (11),
for the initial known position of each rope leading-out point, solving a speed sequence of the rope leading-out points in the continuous reconstruction process by adopting a competitive particle swarm algorithm;
in step 54, the solved speed sequence of the rope leading-out points is filtered and smoothed to obtain a position sequence of the rope leading-out points, which includes:
setting a speed sequence for the exit point of a rope
The filtration condition of each element in (1) is completely 0:
in the above-mentioned formula (12),
to obtain
Then obtaining the position sequence of the rope leading-out points through the formula (11); and smoothing by adopting a spline curve to obtain a position sequence of the rope leading-out points.
In the above-mentioned method, the first step of the method,
in the step 52, the process is carried out,
set to 0.995;
in said step 53, in a second penalty function
Is set as
；
In the step 53, the search space dimension of the competitive particle swarm optimization is
。
In the above method, the reconstructed planned rope-towed parallel robot includes:
fixingA frame,
A rope leading-out device,
A vertical screw rod,
A motor,
A winding drum,
A rope and a movable platform, wherein the rope is arranged on the movable platform,
is a positive integer; wherein,
each rope leading-out device consists of a sliding block and a guide pulley, and the guide pulley is connected and arranged on the sliding block and can synchronously move along with the sliding block;
the other end of each rope is connected with the movable platform after sequentially passing around a guide pulley of a rope leading-out device above the rope, and each rope suspends the movable platform in the fixed frame.
In step 3 of the method, the trajectory planning algorithm adopts any one of a trapezoidal trajectory planning algorithm and a sigmoid trajectory planning algorithm. Other conventional trajectory planning algorithms may also be employed.
In step 4 of the method, the optimal configuration of the rope traction parallel robot is a fixed configuration, the position of the rope leading-out point is adjusted before the movable platform moves, the optimal configuration is adjusted, and the position of the rope leading-out point is not changed any more when the movable platform moves.
In step 5 of the method, the continuous reconstruction is that the position of the rope leading-out point is automatically adjusted according to the change of the path of the movable platform in the moving process of the movable platform.
In summary, according to the method provided by the embodiment of the invention, by analyzing the relationship between the force feasible working space of the rope-towed parallel robot and the movable platform path, the force feasible working space of the current configuration cannot completely contain the movable platform path as the trigger condition for reconstructing the rope-towed parallel robot. When the reconfiguration is triggered, the method preferentially searches for the optimal configuration, the rope leading-out point can be automatically moved to the optimal position without disassembly and assembly, and then a driving motor of the rope leading-out point is in a locked state when the movable platform moves, so that extra energy is not consumed. When the optimal configuration can not meet the task, continuous reconstruction is carried out, configuration reconstruction is automatically completed when the movable platform moves, the range of the feasible working space of force is dynamically adjusted, the path of the movable platform is always positioned in the feasible working space of force, and in the continuous reconstruction process, the number of the moved rope leading-out points can be minimized and the corresponding moving distance can be calculated by the method, so that the energy is saved.
In order to more clearly show the technical solutions and the technical effects provided by the present invention, the reconfiguration planning method for a rope-traction parallel robot provided by the embodiment of the present invention is described in detail with specific embodiments below.
Example 1
The embodiment provides a reconstruction planning method for a rope traction parallel robotThe rope traction parallel robot structure reconstructed and planned by the method is shown in fig. 3 and comprises the following steps: a fixed frame,
A rope leading-out device,
A vertical screw rod,
A rope is arranged,
An electric motor: (
A motor for driving the screw rod and
a motor for driving the drum),
A winding drum and a movable platform, wherein the winding drum is arranged on the movable platform,
is a positive integer; the rope leading-out device mainly comprises a sliding block and a rope guide pulley;
the motor drives each vertical screw rod distributed in the fixed frame to rotate, so that a sliding block of the rope leading-out device is driven to move up and down, the position of a guide pulley arranged on the sliding block is changed, and the rope pulls the parallel robot to reconstruct; in addition, the
The motors are connected with and distributed on the ground winding drums in the fixed frame, and one winding drum is arranged below each vertical screw rod and used for winding and unwinding the ropeRope; global coordinate system
Of (2)
The fixed frame is positioned on the ground; the rope from the reel end is connected with the movable platform after passing through the guide pulley
The radius of the guide pulley is small relative to the total working space and can be reduced to a point, whereby the rope is considered to be drawn off from the rope exit point
（
) At the point of exit, the cord
In that
The position of the direction is fixed, and the direction is fixed,
the change of the direction position represents the change of the configuration of the rope traction parallel robot.
The specific steps of the reconstruction planning method are shown in fig. 2, and include:
in the above-mentioned formula (1),
a corresponding structural matrix for the rope-towing parallel robot, wherein,
；
a rope tension vector for the rope-towed parallel robot;
the mass of the moving platform for the rope traction parallel robot;
a moving platform acceleration of the rope-towed parallel robot;
，
is the acceleration of gravity;
the kinetic equation for a single rope takeoff is:
in the above-mentioned formula (2),
,
、
and
respectively representing the axial driving force, weight and acceleration of the rope lead-out means,
is the rope tension.
Step 2, establishing a mathematical model of the force feasible working space: according to the parameters in the step 1, the mathematical model of the force feasible working space of the rope traction parallel robot is as follows:
in the above-mentioned formula (3),
a structural matrix corresponding to the parallel robot is towed by the rope,
；
is the rope tension vector;
the lower limit of the tension vector is set to be 10N;
the upper limit of the tension vector is set as 200N;
the movable platform is stressed by external force;
step 3, planning a track of the movable platform, dispersing the track into a set of path points of the movable platform, and analyzing the relation between the feasible working space of the current configuration and the path of the movable platform: at the time of
Planning the path of the movable platform shown in FIG. 4 by using conventional trajectory planning algorithm (such as trapezoidal and S-shaped) to obtain trajectory
(
) According to a given time step
Discretization into a set of moving platform waypoints
，
，
Is composed of
Integer multiples of; converting the mathematical model formula (3) into an inequality by adopting a mobile hyperplane method:
in the above formula (4), matrix
Sum vector
Can be obtained according to the mobile hyperplane method, both of which are related to the rope-traction parallel robot configuration. Determining a set of moving platform waypoints
Whether each path point meets an inequality (4) or not is judged, if yes, the feasible working space of the current configuration completely contains the path of the movable platform, the configuration does not need to be adjusted, and planning is finished; if not, determining that the force feasible working space of the current configuration cannot completely contain the moving platform path (namely, the reconstruction triggering condition is met), triggering reconstruction, and continuing to perform the step 4.
Step 4, judging whether an optimal configuration exists: setting the position of the cord exit point
Between the upper and lower limits of position:
in the above-mentioned formula (5),
，
(ii) a To ensure the robustness of the force balance, the first objective function is set as:
in the above-mentioned formula (6),
moving the platform away from the boundary of the power feasible working space for capacity margin; -setting said inequality (4) and said inequality (5) as a first penalty function by means of a penalty function: :
in the above-mentioned formula (7),
in order to be a penalty factor,
for the purpose of all the inequality constraints,
the number of inequality constraints; adding said first penalty function (7) to the first objective function (6)
Forming a new objective function
Solving the optimal configuration by adopting a competitive particle swarm algorithm;
is set as
The search space dimension of the competitive particle swarm algorithm is equal to
If the optimization has a solution, determining that the robot can be adjusted to a fixed optimal configuration, and finishing planning; if there is no solution, step 5 is started.
Step 5, setting an objective function which minimizes the number of moving rope leading-out points in continuous reconstruction, solving a rope leading-out point position sequence of the rope traction parallel robot in the continuous reconstruction, namely completing reconstruction planning of the rope traction parallel robot, wherein the step 5 comprises the following steps:
and step 51, expressing the total displacement of the rope leading-out points into the form of an indefinite linear equation set:
by using
，
Representing and moving platform path point set
In
Rope leading-out point corresponding to position of moving platform
The initial position vector of the rope exit point
The method is obtained by measuring the actually planned rope traction parallel robot;
by using
，
Indicating a change in the position of the cord exit point;
by using
，
Representing and moving platform path point set
Corresponding rope leading-out point
The speed sequence of (a);
rope exit point in total time
Total displacement of internal movement
The corresponding system of indefinite linear equations is:
in the above-mentioned formula (8),
is one
The vector of (a);
is one
A constant vector of (2); because of the fact that
Solution in formula (8)
Is not unique;
step 52, setting a rope leading-out point physical constraint condition and a second objective function which minimizes the number of the moved rope leading-out points in the continuous reconstruction: setting a rope leading-out point
In the position of
Speed of the motor
Acceleration of the vehicle
Satisfy respective upper and lower limits:
in the above-mentioned formula (9),
；
；
；
(ii) a In order to reduce the number of rope leading-out points moving in the continuous reconstruction process of the robot, a second objective function for continuous reconstruction is set as follows:
in the above-mentioned formula (10),
the value range is 0 to 1 for weight;
the number of the rope leading-out points is the number of the rope leading-out points;
is a speed sequence of rope leading-out points;
the number of the path points of the movable platform is;
capacity margin indexes for moving the power platform away from the boundary of the power feasible working space;
the larger the value is,
the more the number of the middle zero elements is,
the value is finely adjusted according to different tracks of the movable platform, wherein
Set to 0.995; the first term in the second objective function is normalized by the norm L1
The medium elements are characterized by sparsity and the like,
the number of the non-zero elements is the least, so that the number of the zero elements is the most, and the number of the movable rope leading-out points is ensured to be the least; second term by adding capacity margin indicator
The dynamic platform is far away from the boundary of the feasible working space of the force, so that the robustness of the force balance is ensured;
in the above-mentioned formula (11),
for each rope exit point an initial known location; because the competitive particle swarm algorithm is suitable for solving the global optimization problem of the high-dimensional search space, the competitive particle swarm algorithm is adopted to solve the overall objective function, so that the rope of the robot is pulledThe number of rope leading-out points moving in the continuous reconstruction process of the parallel robot is minimum; in a second penalty function
Is set as
(ii) a The search space dimension of the competitive particle swarm algorithm is
。
Step 54, filtering the rope leading-out point speed sequence and smoothing the rope leading-out point position sequence: the L1 norm would be
The medium elements present sparsity but are optimized
Some of the element values are not completely 0 but infinitely inclined to 0, and in order to make the sparse characteristic more thoroughly appear, the following filtering conditions are set so that the sparse characteristic is more thoroughly expressed
Wherein the elements are all 0:
in the above-mentioned formula (12),
(ii) a To obtain
Then obtaining the position sequence of the rope leading-out points through the formula (11); due to the fact that
And
the set value is small, and the influence on the sequence of the rope leading-out point positions is negligible; and smoothing by adopting a spline curve to obtain a position sequence, namely finishing the reconstruction planning of the rope traction parallel robot.
In summary, compared with the prior art, the reconstruction planning method of the embodiment of the present invention at least has the following beneficial effects:
(1) by analyzing the relation between the feasible working space of the rope traction parallel robot and the task path of the movable platform, the feasible working space of the current configuration force cannot completely contain the path of the movable platform as a trigger condition for reconstructing the rope traction parallel robot, and the reconstruction motion of the rope traction parallel robot is planned by combining the physical constraints of the position, the speed, the acceleration and the like of a rope leading-out point and the rope tension constraint.
(2) The optimal configuration is selected preferentially, the rope leading-out point can be automatically moved to the optimal position without disassembly and assembly, and the driving motor of the rope leading-out point is located in a locked state when the movable platform moves, so that the rope leading-out point is not required to be additionally controlled, and extra energy is not consumed.
(3) When the optimal configuration of the rope-traction parallel robot is detected to be incapable of meeting the task, continuous reconfiguration planning is started, configuration reconfiguration is automatically completed when the movable platform moves, the range of the force-feasible working space is dynamically adjusted, and the path of the movable platform is always positioned in the force-feasible working space.
(4) The number of the moving rope leading-out points can be minimized in the continuous reconstruction process, the moving distance of the rope leading-out points can be calculated, the rope leading-out points stop moving after being moved to a proper position, and energy is greatly saved.
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 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 that is already known to a person skilled in the art.
Claims (10)
1. A reconstruction planning method for a rope traction parallel robot is characterized by comprising the following steps:
step 1, setting a coordinate system and parameters of a rope traction parallel robot to be reconstructed and planned, and respectively establishing a dynamic equation of a movable platform of the rope traction parallel robot and a dynamic equation of a single rope leading-out device according to the set coordinate system and parameters;
step 2, establishing a mathematical model corresponding to the feasible working space of the force of the rope-traction parallel robot according to the parameters of the rope-traction parallel robot;
step 3, planning a track of the movable platform and dispersing the track into a set of path points of the movable platform, determining the relation between the force feasible working space of the current configuration of the rope traction parallel robot and the path of the movable platform by combining a mathematical model corresponding to the force feasible working space, judging whether the force feasible working space of the current configuration completely comprises the path of the movable platform according to the mathematical model corresponding to the force feasible working space, if so, determining that the configuration does not need to be adjusted, and finishing the planning; if not, determining to trigger reconstruction, and executing the step 4;
step 4, judging whether the rope traction parallel robot has the optimal configuration, if so, finishing planning; if not, executing the step 5;
and 5, setting an objective function which minimizes the number of the moving rope leading-out points in the continuous reconstruction, solving a rope leading-out point position sequence of the rope traction parallel robot in the continuous reconstruction, and finishing the reconstruction planning of the rope traction parallel robot.
2. The rope-towed parallel robot reconfiguration planning method according to claim 1, wherein in said step 1, the coordinate system and parameters of the rope-towed parallel robot reconfigured are set in the following manner, and the kinetic equation of the moving platform of the rope-towed parallel robot and the kinetic equation of the single rope lead-out device are respectively established according to the set coordinate system and parameters, including:
setting a global coordinate system of a rope-towed parallel robot for a plan to be reconstructed
Origin of (2)
On the ground of the fixed frame of the rope-drawn parallel robot, a rope leading-out point for the rope-drawn parallel robot
For the position vector of
It is shown that,
，
the number of the leading-out points of the ropes and the number of the ropes are used for the position vector of the movable platform of the rope traction parallel robot
Showing that the ropes pull the ropes of the parallel robots
Has a direction vector of
Establishing a dynamic equation of a movable platform of the rope traction parallel robot and a dynamic equation of a single rope leading-out device;
the dynamic equation of the movable platform is as follows:
（1）；
in the formula (1), the reaction mixture is,
a corresponding structural matrix of the parallel robot is drawn for the rope,
；
a rope tension vector for the rope-towed parallel robot;
the mass of the moving platform for the rope traction parallel robot;
a moving platform acceleration of the rope-towed parallel robot;
，
is the acceleration of gravity;
the dynamic equation of the single rope leading-out device is as follows:
（2）；
in the formula (2), the reaction mixture is,
an axial driving force of a rope pulling-out device for pulling the parallel robot for the rope;
a rope tension for said rope pulling parallel robots;
；
the weight of a rope take-off device that pulls the parallel robot for the rope;
is the acceleration of gravity;
acceleration of a rope lead-out device of the parallel robot is pulled for the rope.
3. The rope-towed parallel robot reconfiguration planning method according to claim 2, wherein in said step 2, the mathematical model established is:
in the formula (3), the reaction mixture is,
a corresponding structural matrix of the parallel robot is drawn for the rope,
；
a rope tension vector for the rope-towed parallel robot;
the rope pulls the dynamic platform of the parallel robot to bear the resultant external force;
the lower limit of the rope tension vector is set to be 10N;
the upper limit of the rope tension vector is set to 200N.
4. The rope-towed parallel robot reconfiguration planning method according to claim 3, wherein in said step 3, a moving platform trajectory is planned and discretized into a moving platform path in the following manner, and a mathematical model corresponding to a force feasible working space is combined to determine a relationship between a force feasible working space of a current configuration of said rope-towed parallel robot and a moving platform path, including:
at the time of
Planning the path of the moving platform by adopting a track planning algorithm to obtain a track
，
Connecting the track
，
According to a given time step
Discretization into a set of moving platform waypoints
，
，
Is composed of
Integer multiples of;
converting the mathematical model formula (3) corresponding to the force feasible working space into an inequality by adopting a moving hyperplane method:
（4）；
in the above formula (4), matrix
Sum vector
Drawing a corresponding structural matrix of the parallel robot according to the rope by a moving hyperplane method
Upper limit of rope tension vector
Lower limit of rope tension vector
Obtaining;
judging whether the force feasible working space of the current configuration of the rope-traction parallel robot completely contains a moving platform path according to the mathematical model corresponding to the force feasible working space in the following way, including:
determining a set of moving platform waypoints
Whether each path point meets the inequality (4) or not is judged, if yes, the feasible working space of the current configuration of the parallel robot drawn by the rope completely contains the path of the movable platform without adjusting the configuration; and if not, determining that the force feasible working space of the current configuration of the rope traction parallel robot cannot completely contain the moving platform path, and triggering reconstruction.
5. The reconfiguration planning method for a rope-drawn parallel robot according to claim 4, wherein in the step 4, determining whether the rope-drawn parallel robot has an optimal configuration comprises:
setting the position of a rope leading-out point of the rope-traction parallel robot
Between the upper and lower limits of position:
the formula (A) is5) Middle, lower limit of position
(ii) a Upper limit of position
；
Setting the first objective function as:
（6）；
in the above-mentioned formula (6),
capacity margin indexes for moving the power platform away from the boundary of the power feasible working space;
-setting said inequalities (4) and (5) as a first penalty function by means of a penalty function:
in the formula (7), the reaction mixture is,
is a penalty factor;
is constrained for all inequalities;
the number of inequality constraints;
adding the first penalty function of the formula (7) and the first objective function of the formula (6) to form a new objective function, solving the optimal configuration of the new objective function by adopting a competitive particle swarm algorithm, if the optimal configuration has a solution, determining that the rope traction parallel robot can be adjusted to a fixed optimal configuration, and finishing planning; if the optimization is not solved, it is determined that there is no optimal configuration.
6. Rope-towed parallel robot reconfiguration planning method according to claim 5, characterized in that in said step 4,
is set as
；
The search space dimension of the competitive particle swarm algorithm is
。
7. The reconstruction planning method for rope-drawn parallel robot according to claim 5, wherein in the step 5, an objective function for minimizing the number of moving rope leading-out points in the continuous reconstruction is set in the following manner, and the rope leading-out point position sequence of the rope-drawn parallel robot in the continuous reconstruction is solved, including:
step 51, constructing the total displacement of the rope leading-out points into an indefinite linear equation set;
step 52, setting a physical constraint condition of the rope leading-out points and a second objective function which minimizes the number of the moved rope leading-out points in continuous reconstruction;
step 53, solving a speed sequence of rope index out-points in continuous reconstruction through a second objective function which minimizes the number of the moved rope out-points in the continuous reconstruction;
and 54, filtering the solved speed sequence of the rope leading-out points and smoothing to obtain a position sequence of the rope leading-out points.
8. The rope-towed parallel robot reconfiguration planning method according to claim 7, wherein in said step 51, the rope pull-out point total displacement is constructed as an indeterminate linear equation set in the following manner, including:
by using
Representing and moving platform path point set
In (1)
Rope leading-out point corresponding to position of moving platform
The initial position of the cord exit point
The method is obtained by measuring the actually planned rope traction parallel robot;
by using
，
Indicating a change in the position of the cord exit point; by using
Is shown in time
Inner position
And
the speed of the motor; by using
，
Representing and moving platform path point set
Corresponding rope leading-out point
The speed sequence of (a);
the rope leading-out point of the rope traction parallel robot is in the total time
Total displacement of internal movement
Comprises the following steps:
in the formula (8), the reaction mixture is,
is one
Vector of (3), solution in equation (8)
Is not unique;
is one
A constant vector of (2);
in step 52, the setting of the physical constraint conditions for the rope exit points and the second objective function for minimizing the number of the moved rope exit points in the continuous reconstruction includes:
setting a rope leading-out point
Position of
Speed, velocity
Acceleration of the object
Satisfy respective upper and lower limits:
in the formula (9), the reaction mixture is,
；
；
；
(ii) a Setting a second objective function for minimizing the number of rope exit points moved in the continuous reconstruction as:
in the formula (10), the reaction mixture is,
the value range is 0 to 1 for weight;
the number of the rope leading-out points is the number of the rope leading-out points;
is a speed sequence of rope leading-out points;
the number of the path points of the movable platform is;
capacity margin indexes for moving the power platform away from the boundary of the power feasible working space;
in the step 53, solving a speed sequence of rope index exit points in continuous reconstruction by using a second objective function that minimizes the number of moving rope exit points in continuous reconstruction includes:
-setting the inequality of said equation (4) and said equation (9) as a second penalty function by means of a penalty function, adding the second penalty function to a second objective function of said equation (10) as an overall objective function, the corresponding sequence of rope exit point positions being represented during the optimization iteration as:
in the above-mentioned formula (11),
solving the ropes in the continuous reconstruction process by adopting a competitive particle swarm algorithm for the initial known position of each rope leading-out pointIndexing a velocity sequence of points;
in the step 54, the solved speed sequence of the rope leading-out points is filtered and smoothed to obtain a position sequence of the rope leading-out points, which includes:
setting a speed sequence for the exit point of a rope
The filtration condition of each element in (1) is completely 0:
in the above-mentioned formula (12),
to obtain
Then obtaining the position sequence of the rope leading-out points through the formula (11); and smoothing by adopting a spline curve to obtain a position sequence of the rope leading-out points.
9. The rope-towed parallel robot reconfiguration planning method according to claim 8,
in the step 52, the process is carried out,
set to 0.995;
in said step 53, in a second penalty function
Is set as
；
In the step 53, the search space dimension of the competitive particle swarm optimization is
。
10. Rope-towed parallel robot reconfiguration planning method according to any one of claims 1 to 8, characterized in that in said method, said reconfigured planned rope-towed parallel robot comprises:
a fixed frame,
A rope leading-out device,
A vertical screw rod,
A motor,
A winding drum,
A rope and a movable platform, wherein the rope is arranged on the movable platform,
is a positive integer; wherein,
each rope leading-out device consists of a sliding block and a guide pulley, and the guide pulley is connected and arranged on the sliding block and can synchronously move along with the sliding block;
the other end of each rope is connected with the movable platform after sequentially passing around a guide pulley of a rope leading-out device above the rope, and each rope suspends the movable platform in the fixed frame.
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