CN120422252B - Real-time solving reconstruction planning method for man-machine interaction rope traction parallel robot - Google Patents

Abstract

The present invention discloses a real-time solution and reconfiguration planning method for a rope-pulled parallel robot with human-machine interaction, belonging to the field of robot configuration planning. The method comprises the following steps: 1. constructing a kinematic and dynamic model based on the positional relationship between the rope index point and the moving platform, and establishing an admittance model; 2. using the hyperplane movement method based on the dynamic and admittance models to express the force feasibility condition, and setting the optimization problem objective function according to the force feasibility condition; 3. constraining the rope index point solution problem to be expressed as a nonlinear optimization problem, approximating the nonlinear optimization problem to a linear optimization problem through linear approximation, and solving the approximate optimal solution of the linear optimization problem; and 4. correcting the approximate optimal solution based on an artificial potential field set according to the dynamic characteristics, while ensuring solution speed and ensuring that the obtained rope index point position does not lie at the boundary of the solution space, thereby completing the reconfiguration planning of the robot's real-time solution of the rope index point. This method can ensure real-time solution performance and human-machine interaction stability.

Description

Real-time solution and reconfiguration planning method for a rope-pulled parallel robot with human-robot interaction

Technical Field

The present invention relates to the technical field of configuration planning of a rope-pulled parallel robot, and in particular to a real-time solution reconstruction planning method of a rope-pulled parallel robot for physical human-machine interaction.

Background Art

Rope-pulled parallel robots have been widely used in numerous fields due to their large workspace, large payload, and rope-driven nature. Furthermore, because they use flexible ropes instead of rigid links, they offer inherent safety advantages when applied to human-robot interaction. Furthermore, leveraging the robot's ease of reconfiguration, researchers have designed a reconfigurable rope-pulled parallel robot with real-time rope indexing points to enhance human-robot interaction performance. However, determining the optimal rope indexing point location is a nonlinear optimization problem. For robots with millisecond control cycles, the solution time for this nonlinear optimization problem in practical systems is significantly longer than the robot's control cycle, making it difficult to apply to human-robot interaction tasks. Furthermore, due to the physical properties of the rope, which can only provide tension but not thrust, the rope-pulled parallel robot must be kept taut during operation, making it challenging for human-robot interaction tasks with their inherent randomness.

Chinese invention patent CN202210478153.1 discloses a freely connected reconfigurable robot, but its reconstruction method cannot be applied to rope-pulled parallel robots, and cannot be reconfigured in real time for human-computer interaction tasks.

In view of this, the present invention is proposed.

Summary of the Invention

The purpose of the present invention is to provide a reconstruction planning method for real-time solution of a rope-pulled parallel robot with human-machine interaction, which reduces the complexity of problem solving through linear approximation, ensures real-time performance, and combines the artificial potential field method to ensure the stability of human-machine interaction, thereby solving the above-mentioned technical problems existing in the prior art.

The purpose of the present invention is achieved through the following technical solutions:

A real-time solution reconstruction planning method for a rope-pulled parallel robot with human-machine interaction, comprising:

Step 1: Based on the spatial relationship between the rope index extraction point and the moving platform of the rope-pulled parallel robot, a kinematic model of the rope-pulled parallel robot and a dynamic model of the moving platform are constructed, and an admittance model is established to enable the moving platform to follow the movement of the operator's arm.

Step 2: Based on the dynamic model and admittance model obtained in step 1 and the human-machine interaction characteristics, the hyperplane movement method is used to express the force feasibility conditions of the rope-pulled parallel robot, and the objective function of the optimization problem is set according to the force feasibility conditions and the interaction force.

Step 3: Based on the objective function of the optimization problem obtained in step 2, the rope index point solution problem is expressed as a nonlinear optimization problem through constraints, the nonlinear optimization problem is approximated as a linear optimization problem through linear approximation, and the approximate optimal solution of the linear optimization problem is solved by the dual simplex method;

In step 4, the artificial potential field is set according to the human-computer interaction characteristics and the dynamic characteristics of the rope-pulled parallel robot, and the approximate optimal solution of the linear optimization problem obtained in step 3 is corrected. While ensuring the solution speed, the position of the rope index release point is not located at the boundary of the solution space. In other words, the reconstruction plan for the real-time solution of the rope index release point of the rope-pulled parallel robot is completed.

Compared with the prior art, the real-time solution and reconstruction planning method of the human-machine interactive rope-pulled parallel robot provided by the present invention has the following beneficial effects:

By approximating the nonlinear objective function and nonlinear force feasible constraint in the original nonlinear optimization problem into a linear optimization problem, it is possible to complete the solution of the linear optimization problem within a shorter control cycle, ensuring the solution speed while also ensuring that a usable solution can be obtained stably; by setting up an artificial potential field, the problem that the solutions of the linear optimization problem are all located on the boundary of the solution space is corrected, avoiding the problem that the rope-traction parallel robot cannot stably complete the task during the human-computer interaction process.

BRIEF DESCRIPTION OF THE DRAWINGS

In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the following briefly introduces the drawings required for use in the description of the embodiments. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative work.

FIG1 is a flow chart of a method for real-time reconfiguration planning of a rope-pulled parallel robot applicable to physical human-machine interaction tasks, provided by an embodiment of the present invention.

FIG2 is a flow chart of setting an artificial potential field to correct a solution to a linear optimization problem according to an embodiment of the present invention.

FIG3 is a schematic structural diagram of a rope-pulled parallel robot suitable for physical human-machine interaction tasks provided by an embodiment of the present invention.

DETAILED DESCRIPTION

The following is a clear and complete description of the technical solutions in the embodiments of the present invention in conjunction with the specific content of the present invention. Obviously, the embodiments described are only some embodiments of the present invention, not all embodiments, and do not constitute a limitation of the present invention. All other embodiments obtained by ordinary technicians in this field based on the embodiments of the present invention without making any creative efforts shall fall within the scope of protection of the present invention.

First, the following terms may be used in this article:

The term “and/or” means that either or both of them can be realized at the same time. For example, X and/or Y includes both “X” or “Y” and “X and Y”.

The terms "include," "comprises," "contains," "has," or other similar expressions should be interpreted as non-exclusive. For example, "including certain technical features (such as raw materials, components, ingredients, carriers, dosage forms, materials, dimensions, parts, components, mechanisms, devices, steps, procedures, methods, reaction conditions, processing conditions, parameters, algorithms, signals, data, products, or manufactured articles)" should be interpreted as including not only the technical features explicitly listed, but also other technical features known in the art that are not explicitly listed.

The term "consisting of" excludes any technical features not explicitly listed. If used in a claim, this term renders the claim closed, excluding any technical features other than those explicitly listed, except for conventional impurities associated with them. If this term appears only in a clause of a claim, it limits only the elements explicitly listed in that clause; elements listed in other clauses are not excluded from the claim as a whole.

Unless otherwise specified or limited, the terms "mounted," "connected," "connect," and "fixed" should be interpreted broadly. For example, they can refer to fixed, detachable, or integral connections; mechanical or electrical connections; direct or indirect connections through an intermediary; and internal communication between two components. Those skilled in the art will understand the specific meanings of the above terms in this document based on specific circumstances.

When concentration, temperature, pressure, size or other parameters are expressed in the form of a numerical range, the numerical range should be understood to specifically disclose all ranges formed by the pairing of any upper limit, lower limit, or preferred value within the numerical range, regardless of whether the range is explicitly stated. For example, if a numerical range of "2 to 8" is stated, the numerical range should be interpreted as including ranges of "2 to 7," "2 to 6," "5 to 7," "3 to 4 and 6 to 7," "3 to 5 and 7," "2 and 5 to 7," etc. Unless otherwise specified, the numerical ranges stated herein include both their endpoints and all integers and fractions within the numerical range.

The terms "center", "longitudinal", "lateral", "length", "width", "thickness", "up", "down", "front", "back", "left", "right", "vertical", "horizontal", "top", "bottom", "inside", "outside", "clockwise", "counterclockwise", etc., indicating the orientation or position relationship, are based on the orientation or position relationship shown in the accompanying drawings and are only for the convenience and simplification of description, and do not explicitly or implicitly indicate that the device or element referred to must have a specific orientation, be constructed and operate in a specific orientation, and therefore should not be understood as a limitation to this document.

The scheme provided by the present invention is described in detail below. The contents not described in detail in the examples of the present invention belong to the prior art known to professionals in this field. If specific conditions are not specified in the examples of the present invention, they are carried out according to conventional conditions in the field or conditions recommended by the manufacturer. If the manufacturer of the reagents or instruments used in the examples of the present invention is not specified, they are all conventional products that can be purchased commercially.

As shown in FIG1 , an embodiment of the present invention provides a real-time solution reconstruction planning method for a rope-pulled parallel robot in human-machine interaction. The method uses an artificial potential field method to correct the approximate optimal solution of a linear optimization problem obtained by linear approximation, thereby improving the workspace and freedom during human-machine interaction. The method includes:

Step 1: Based on the spatial position relationship between the rope index extraction point and the moving platform of the rope-pulled parallel robot, a kinematic model of the rope-pulled parallel robot and a dynamic model of the moving platform are constructed, and the model is used to implement an admittance model for the moving platform to follow the movement of the operator's arm.

Step 2: Based on the dynamic model and admittance model obtained in step 1 and the human-machine interaction characteristics, the hyperplane movement method is used to express the force feasibility conditions of the rope-pulled parallel robot, and the objective function of the optimization problem is set according to the force feasibility conditions and the interaction force.

Step 3: Based on the objective function of the optimization problem obtained in step 2, the rope index point solution problem is expressed as a nonlinear optimization problem through constraints, the nonlinear optimization problem is approximated as a linear optimization problem through linear approximation, and the approximate optimal solution of the linear optimization problem is solved by the dual simplex method;

In step 4, the artificial potential field is set according to the human-computer interaction characteristics and the dynamic characteristics of the rope-pulled parallel robot, and the approximate optimal solution of the linear optimization problem obtained in step 3 is corrected. While ensuring the solution speed, the position of the rope index release point is not located at the boundary of the solution space. In other words, the reconstruction plan for the real-time solution of the rope index release point of the rope-pulled parallel robot is completed.

Preferably, in the above method, the rope-pulled parallel robot is a rope-pulled parallel robot with continuous reconfiguration planning, comprising:

Fixed frame, 4 rope indexing devices, 4 vertical screws, 8 motors, 4 drums, 4 ropes and a moving platform; among them,

Each rope indexing device is composed of a slider and a guide pulley, wherein the guide pulley is arranged on the slider and can move synchronously with the slider;

Four vertical screws are respectively provided at the four corners of the fixed frame, and a slider and a guide pulley of a rope indexing device are provided on each vertical screw. One end of each vertical screw is connected to a motor, which can rotate under the drive of the motor and drive the slider and the guide pulley to move up and down;

Four drums are arranged on the ground in the fixed frame, one drum is arranged below each vertical screw, a rope is wound around each drum, and each drum is connected to a motor and can be rotated by the motor to retract and release the connected rope;

The other end of each rope is passed through the guide pulley of the rope indexing device above it in turn and then connected to the movable platform, and each rope suspends the movable platform in the fixed frame;

The position of the rope index extraction point and the rope length of the rope of the rope-pulled parallel robot can be changed simultaneously and continuously to achieve continuous reconstruction.

Preferably, in the above method, in the rope-pulled parallel robot, the rope index extraction point is regarded as a fixed point on the slider.

Preferably, in step 1 of the above method, a kinematic model of the rope-pulled parallel robot is constructed according to the spatial positional relationship between the rope index extraction point and the moving platform of the rope-pulled parallel robot in the following manner, including:

The kinematic model of the rope-pulled parallel robot is established as follows: The static coordinate system in which the moving platform of the rope-pulled parallel robot remains relatively stationary with the ground is defined as , select a point on the ground as the origin of the coordinate system; the moving platform of the rope-pulled parallel robot has three translational degrees of freedom, and is provided with an upward pulling force by four ropes to form a suspended configuration. The position of the moving platform in the static coordinate system is expressed as , _Px is the x-axis coordinate of the center of mass of the moving platform, _Py is the y-axis coordinate of the center of mass of the moving platform, _Pz is the z-axis coordinate of the center of mass of the moving platform, the superscript T represents the transpose of the matrix, the position of the rope index point in the static coordinate system is expressed as , ,in and are constants, determined by the installation position of the vertical screw. The height of the rope index point, the height of each rope index point is expressed in vector form ; Based on the definitions of the above points in the static coordinate system, The vector of the rope pointing from the moving platform to the rope index point is expressed as:

(1);

No. The length of a rope is expressed as , the length of each rope is expressed as a vector , No. The unit vector of the direction of the cable tension exerted by the rope on the moving platform is expressed as ,in, Indicates the The projection of the unit vector of the cable tension force exerted by the rope on the moving platform along the x-axis direction, Indicates the The projection of the unit vector of the cable tension force exerted by the rope on the moving platform along the y-axis direction, Indicates the The projection of the unit vector of the cable tension exerted by the rope on the moving platform along the z-axis.

Preferably, in step 1 of the above method, a dynamic model of the moving platform of the rope-pulled parallel robot is constructed according to the spatial positional relationship between the rope index extraction point and the moving platform of the rope-pulled parallel robot in the following manner, including:

The established dynamic model of the moving platform is expressed by the Newton-Euler equation:

(2);

In the formula (2), is the mass matrix of the rope-pulled parallel robot, where For the quality of the dynamic platform, is the identity matrix, is the gravity vector of the rope-pulled parallel robot, where is the acceleration due to gravity; is the acceleration of the moving platform of the rope-pulled parallel robot; is the Jacobian matrix between the joint space and the Cartesian space of the rope-pulled parallel robot; is the rope tension vector of the rope-pulled parallel robot; The interactive force exerted by humans on the moving platform during human-computer interaction.

Preferably, in step 1 of the above method, an admittance model for enabling the moving platform to follow the movement of the operator's arm is established in the following manner, including:

A virtual mass damping model is set between the moving platform and the operator's arm as an admittance model to ensure the stability of human-computer interaction while allowing the moving platform to follow the operator's arm during human-computer interaction. The admittance model is:

(3);

In the formula (3), and are the inertia term and damping term in the admittance model respectively; 、 are the expected acceleration and expected velocity of the moving platform of the rope-pulled parallel robot respectively;

The interaction force is measured by the sensor installed on the dynamic platform Then, the reference trajectory that conforms to the admittance model is obtained by solving the admittance model of Equation (3). The reference trajectory is input as the desired trajectory into the position controller of the rope-pulled parallel robot for tracking to achieve follow-up control. No stiffness term is set in the admittance model, which can ensure that when the interaction force is removed during the following process, the moving platform remains in the current position.

Preferably, in step 2 of the above method, the force feasibility condition of the rope-pulled parallel robot is expressed using a hyperplane movement method based on the dynamic model and admittance model obtained in step 1, combined with the human-machine interaction characteristics, and a corresponding objective function is set according to the force feasibility condition and the interaction force, including:

The force feasibility condition of the rope-pulled parallel robot is expressed as follows: when the rope tension has upper and lower limit constraints, there exists a set of rope tensions that satisfy the constraints. , so that the dynamic model of the moving platform in formula (2) is established, is the lower limit of the rope tension vector, and its components are all set to 10N; is the upper limit of the rope tension vector. According to the property that the set of the resultant forces of all ropes on the moving platform is a convex hull, the force feasibility condition of the rope-pulled parallel robot is expressed by the hyperplane movement method. The force feasibility condition is:

(4);

In the formula (4), is the resultant force of the rope tension on the moving platform of the parallel robot; the matrix and vector They are respectively the Jacobian matrices corresponding to the rope-pulled parallel robot using the hyperplane moving method , the lower limit of the rope tension vector , the upper limit of the rope tension vector Get, where the matrix Elements in Expressed as:

(5);

In the formula (5), is the unit normal vector of the hyperplane, as well as represents the rope vector used to construct the hyperplane, where is the number of normal vectors corresponding to the hyperplane, , , is the subscript of the rope vector that constitutes the hyperplane; vector Elements in Expressed as:

(6);

In the formula (6), is the tension value provided by each rope when calculating in the hyperplane moving method, As the basis for judging the value of tension, For the The transpose of the unit vector of the cable tension applied by the rope on the moving platform, i=1,2,3,4, provides the upper limit of the cable tension if the angle between the normal vector of the hyperplane and the unit vector of the cable tension applied by the rope on the moving platform is acute, otherwise it provides the lower limit of the cable tension. is the projection of the unit vector of the cable tension force exerted by the cable on the moving platform onto the normal vector of the hyperplane, 、 、 、 are the transposes of the unit vectors of the cable tension directions exerted by the first, second, third and fourth ropes on the moving platform respectively;

According to the above hyperplane movement method, the objective function of the optimization problem is set by combining the relationship between the interaction force direction and the operator's intention. for:

(7);

In the formula (7), is the normalized weight coefficient set according to the angle between the interaction force and the normal vector; For the rope along the The margin of the resultant force that the normal vector of the hyperplane can provide, .

Preferably, in step 3 of the above method, the rope index point solution problem is expressed as a nonlinear optimization problem through constraints based on the objective function of the optimization problem obtained in step 2, the nonlinear optimization problem is approximated as a linear optimization problem through linear approximation, and an approximate solution to the linear optimization problem is solved using the dual simplex method in the following manner, including:

According to the objective function of the optimization problem of formula (7) and the force feasibility condition of formula (4), the upper and lower limits of the position, velocity and acceleration when the rope index point changes are set as follows:

(8);

In the formula (8), the position of the moving platform is set Upper limit 2.4m, lower limit 0.1m above the moving platform, the speed The absolute value is less than 0.1m/s, the acceleration The absolute value is less than 0.02m/ ^s2 ; the above formula (4) and formula (7) are both nonlinear functions of the rope index point position, and can be approximated as linear functions through linear approximation;

The control period of the rope-pulled parallel robot is set to The upper limit of the rope index output point speed is 0.1m/s. In each control cycle, the maximum moving distance of the rope index output point is ; Since the expected rope index output point position is calculated at the beginning of each control cycle, the actual position of the moving platform at the end of the control cycle cannot be accurately predicted, and the actual position of the moving platform The distance moved in each control cycle is also very small, so when solving the rope index point, it is assumed that the actual position of the moving platform is is a constant; according to the definition of rope length and the matrix of formula (5) Elements , in each control cycle the rope length vector and the normal vector of the hyperplane Approximately a constant value; when When it is much greater than 0, according to the definition is a fixed value, and When close to 0, ignore Change for Therefore, it can be approximately considered that is a constant; according to the objective function of the optimization problem of formula (7) and is considered a constant, the coefficient It can also be regarded as a constant value in each control cycle;

Based on this, the constraints and objective functions are organized into linear functions of the optimization variables, and the dual simplex method is used to solve the linear function. The approximate optimal solution is expressed as , the approximate optimal solution The change relative to the start of the control cycle is expressed as .

Preferably, in step 4 of the above method, since human behavior during human-machine interaction is unpredictable, a dynamic buffer space needs to be reserved at the boundary in terms of the constraint conditions to ensure the stability of the system. Although the coefficients have been set in the process of setting the objective function of formula (7) to keep the rope-pulled parallel robot away from the boundary area of the force feasible condition, if it has already approached the boundary of the force feasible condition during the human-machine interaction process, a strategy with a faster adjustment speed is required to keep it away from the boundary. According to the artificial potential field set according to the above human-machine interaction characteristics and the dynamic characteristics of the rope-pulled parallel robot, the approximate solution to the linear optimization problem solved in step 3 is corrected. At the same time, considering that the setting of the artificial potential field cannot strictly guarantee the satisfaction of the constraints set in the linear optimization problem, it is also necessary to scale the rope index point position change obtained by solving the artificial potential field so that it strictly satisfies the rope index point position, velocity and acceleration constraints. Finally, by setting the activation function, the artificial potential field is made effective at the boundary conditions, and the linear optimization solution is mainly used to adjust the rope index point position at non-boundary conditions.

Referring to FIG. 2 , specifically, in the above step 4, the approximate optimal solution of the linear optimization problem obtained in step 3 is corrected by setting an artificial potential field according to the human-machine interaction characteristics and the dynamic characteristics of the rope-pulled parallel robot in the following manner, including:

Step 41, setting artificial potential field: according to the direction of the interaction force and the dynamic characteristics of the rope-pulled parallel robot obtained by the hyperplane moving method, set the artificial potential field for:

(9);

In the formula (9), Indicates the direction of the interaction force, from the expected force distance to the hyperplane; is the gravitational constant of the artificial potential field;

Step 42, calculate the change of the rope index extraction point based on the potential field force of the artificial potential field: take the derivative of the distance on both sides of the artificial potential field of equation (9) to obtain the potential field force of the artificial potential field The expression is:

(10);

The potential force of the artificial potential field The resultant force is used as the distance of the rope index output point adjustment in each control cycle for:

(11);

Step 43, check by box constraint: when the position and velocity at the start of any control cycle are known, the box constraints of the position, velocity and acceleration of the rope index point are unified into one box constraint , The lower bound of the rope index point position, The upper bound of the rope index point position is obtained through the box constraint Check whether the adjustment of the rope index extraction point based on the distance of formula (11) satisfies the constraint;

make is the final change of the rope index point under the artificial potential field. If the constraint is satisfied, then If the constraints are not satisfied, then ,in is the scaling factor, which makes the final change of the rope index point under the artificial potential field after adjustment Satisfy box constraints;

In step 44, the activation function is used to fuse the artificial potential field and the approximate optimal solution of the linear optimization problem to obtain a corrected approximate optimal solution.

In the above step 44, the approximate optimal solution of the artificial potential field and the linear optimization problem is fused by the following activation function:

(12);

in, is the natural logarithm; is the coefficient for scaling the activation function; is the minimum value of the margin of the desired force to each hyperplane, that is, the minimum margin; is the expected value of the minimum margin. When the actual minimum margin is less than the expected value of the minimum margin When the artificial potential field plays a leading role in adjusting the rope index point, the actual minimum margin is greater than the expected value of the minimum margin. The approximate optimal solution of the linear optimization problem plays a dominant role in the adjustment of the rope index output point.

In summary, the method in this embodiment of the present invention, by designing a linear approximation method for a rope-pulled parallel robot, simplifies the nonlinear optimization problem into a linear optimization problem. This significantly reduces solution complexity, improves computational efficiency, and enables real-time solution during human-robot interaction. Considering that the optimal solution to a linear optimization problem lies at the boundary of the solution space, but the boundary conditions of the robot used for human-robot interaction are unstable, an artificial potential field is designed to correct the solution to the linear optimization problem, ensuring system stability.

In order to more clearly demonstrate the technical solution and technical effects provided by the present invention, the solution provided by the embodiment of the present invention is described in detail with reference to specific embodiments below.

Example 1

This embodiment provides a real-time solution reconstruction planning method for a rope-pulled parallel robot suitable for physical human-machine interaction. The method is performed in the following steps (see FIG1 ):

Step 1: Construct a kinematic model of the rope-pulled parallel robot according to the spatial position relationship between the rope, the rope index extraction point, and the moving platform of the rope-pulled parallel robot in the following manner, obtain the dynamic model of the moving platform based on the Newton-Euler equations, and design an admittance model according to the needs of the physical human-computer interaction task.

As shown in Figure 3, in the above step 1, the kinematic model established is: the static coordinate system in which the moving platform and the ground remain relatively stationary is defined as , select a point on the ground as the origin of the coordinate system. The end moving platform of the rope-pulled parallel robot has three translational degrees of freedom, and is provided with an upward pulling force by four ropes, forming a suspended configuration, where the position of the moving platform can be expressed in the static coordinate system as , _Px is the x-axis coordinate of the center of mass of the moving platform, _Py is the y-axis coordinate of the center of mass of the moving platform, _Pz is the z-axis coordinate of the center of mass of the moving platform, the superscript T represents the transpose of the matrix, and the position of the rope index point in the static coordinate system can be expressed as , ,in and are all constants, determined by the installation position of the vertical screw. is the height of the rope index point. The height of each rope index point can be expressed as a vector ; Based on the definitions of the above points in the static coordinate system, it means The vector of the rope from the moving platform to the rope index point can be expressed as:

(1);

From this The length of a rope can be expressed as , the length of each rope can be expressed as a vector , No. The unit vector of the cable tension force applied by the cable to the moving platform can be expressed as , where e _ix represents the The projection of the unit vector of the cable tension force applied by the rope to the moving platform along the x-axis, e _iy represents the The projection of the unit vector of the cable tension force applied by the rope to the moving platform along the y-axis, e _iz represents the The projection of the unit vector of the cable tension force exerted by the rope on the moving platform along the z-axis;

The established dynamic equation of the moving platform can be expressed by the Newton-Euler equation as follows:

(2);

In the formula (2), is the mass matrix of the rope-pulled parallel robot, where For the quality of the dynamic platform, is the identity matrix, is the gravity vector of the rope-pulling parallel robot, where is the acceleration due to gravity; is the acceleration of the moving platform of the rope-pulled parallel robot; The Jacobian matrix between the joint space and the Cartesian space of the rope-pulled parallel robot; is the rope tension vector of the rope-pulling parallel robot; The interaction force exerted by humans on the moving platform during human-machine interaction is then set up. An admittance model is then set up between the moving platform and the human, and a virtual mass damping model is set up between the moving platform and the human hand. This is an admittance model that not only allows the moving platform to follow the operator's movement during human-machine interaction but also ensures the stability of the human-machine interaction. The admittance model is:

(3);

In the formula (3), and are the inertia term and damping term in the admittance model respectively; 、 They are the expected acceleration and expected velocity of the moving platform of the rope-pulled parallel robot; the interaction force is measured by the sensor installed on the moving platform The reference trajectory that conforms to the admittance model can then be obtained by solving Equation (3). This trajectory can be input into the position controller as the desired trajectory for tracking, thus achieving the following control effect. Since the platform remains in its current position when the interaction force is removed during the following process, no stiffness term is set in the admittance model.

Step 2: Based on the robot model obtained in step 1 and the characteristics of human-machine interaction, a hyperplane movement method is used to represent the force feasibility conditions of the rope-pulled parallel robot, and a corresponding objective function is set according to the force feasibility conditions and the interaction force.

In the above step 2, the force feasibility condition of the rope pulling parallel robot can be expressed as: when the rope tension has upper and lower limit constraints, there exists a set of rope tensions that satisfy the constraints. So that the formula (2) is established, is the lower limit of the rope tension vector, and its components are all set to 10N; is the upper limit of the rope tension vector, and its components are all set to 200N; but due to the Jacobian matrix in formula (2) There is a one-dimensional null space, and it is rather difficult to determine whether there is a set of cable forces that can satisfy the constraints. Considering that the set of the resultant forces that all cables can exert on the moving platform is a convex hull, the hyperplane movement method can be used to express the force feasibility condition of the cable-pulled parallel robot. The force feasibility condition can be expressed as:

(4);

In the formula (4), is the resultant force of the rope pulling force on the moving platform of the parallel robot; matrix and vector The hyperplane moving method is used according to the Jacobian matrix corresponding to the rope-pulling parallel robot , the lower limit of the rope tension vector , the upper limit of the rope tension vector Get, where the matrix The elements in can be represented as:

(5);

In the formula (5), is the unit normal vector of the hyperplane, as well as represents the rope vector used to construct the hyperplane, where is the number of normal vectors corresponding to the hyperplane, , , is the subscript of the rope vector that forms the hyperplane; vector The elements in can be represented as:

(6);

In the formula (6), is the tension value provided by each rope when calculating in the hyperplane moving method, As the basis for judging the value of tension, For the The transpose of the unit vector of the cable tension applied by the rope on the moving platform, i=1,2,3,4, provides the upper limit of the cable tension if the angle between the normal vector of the hyperplane and the unit vector of the cable tension applied by the rope on the moving platform is acute, otherwise it provides the lower limit of the cable tension. is the projection of the unit vector of the cable tension force exerted by the cable on the moving platform onto the normal vector of the hyperplane, 、 、 、 are the transposes of the unit vectors of the cable tension directions applied by the first, second, third and fourth ropes on the moving platform respectively;

According to the above hyperplane movement method, the objective function of the optimization problem is set based on the relationship between the interaction force direction and human intention. for:

(7);

in, is the resultant force of the rope tension that the moving platform of the parallel robot is expected to receive; is the normalized weight coefficient set according to the angle between the interaction force and the normal vector; For along the The normal vector of the hyperplane, the margin of the net force that the rope can provide, .

Step 3: Based on the objective function obtained in step 2, the rope index point solution problem can be expressed as a nonlinear optimization problem after considering the constraints. The nonlinear optimization problem can be approximated as a linear optimization problem through linear approximation, and the dual simplex method can be used to solve this linear optimization problem.

In step 3 above, the equation (7) is used as the objective function of the optimization problem, the force feasibility condition in equation (4) is considered, and the position, velocity, and acceleration of the rope index output point when it changes are set to meet the upper and lower limits:

(8);

In the formula (8), the upper limit of the position is set to 2.4m, the lower limit is set to 0.1m above the moving platform, the absolute value of the speed is less than 0.1m/s, and the absolute value of the acceleration is less than 0.02m/ ^s2 ; the formulas (4) and (7) are both nonlinear functions of the rope index point position, and can be approximated to linear functions through linear approximation;

The control period of the rope-pulled parallel robot is set to The upper limit of the rope index output point speed is 0.1m/s, so the maximum moving distance of the rope index output point in each control cycle is ; Since the expected rope index output point position is calculated at the beginning of each control cycle, the actual position of the moving platform at the end of the control cycle cannot be accurately predicted, and the position of the moving platform The distance moved in each control cycle is also very small, so when solving the rope index point, it is assumed that is a constant value; according to the definition of rope length and formula (5), the rope length vector in each control cycle and the normal vector of the hyperplane Can be approximated as a constant; when When it is much greater than 0, according to the definition is a fixed value, and Near 0 o'clock, Change for The influence of can be ignored, so it can be approximately considered that is a constant; according to the objective function of the optimization problem of formula (7) and is considered a constant, the coefficient It can also be regarded as a constant in each control cycle. In this way, the constraints and objective functions can be organized into linear functions of the optimization variables. The dual simplex method can be used to solve this linear optimization problem, and the optimal solution can be expressed as , the change of the optimal solution relative to the start time of the control cycle can be expressed as .

Step 4: Based on the approximate solution of the linear optimization problem obtained in step 3, the approximate solution of the linear optimization problem is corrected by setting an artificial potential field according to the human-computer interaction characteristics and the dynamic characteristics of the rope-pulled parallel robot. While ensuring the solution speed, the problem of the position of the rope index output point being located at the boundary of the solution space is avoided as much as possible, thereby completing the real-time solution of the rope index output point of the rope-pulled parallel robot.

As shown in Figure 2, in step 4 above, the linear approximate solution is corrected using an artificial potential field, which mainly includes:

Step 41, setting an artificial potential field: considering the direction of the interaction force and the dynamic characteristics of the rope-pulled parallel robot obtained by the hyperplane movement method, setting an artificial potential field:

(9);

In the formula (9), Indicates the direction of the interaction force, from the expected force The distance to the hyperplane, is the gravitational constant of the potential field set;

Step 42, calculate the change in the rope index extraction point obtained based on the potential field force: By simultaneously taking the derivative of the distance on both sides of the equation (9), the expression for the potential field force can be obtained:

(10);

The resultant force of the potential field is used as the distance of the rope index point adjustment in each control cycle:

(11);

Step 43, check by box constraint: When the position and velocity at the start of any control cycle are known, the box constraints of the position, velocity and acceleration of the rope index point can be unified into one box constraint , The lower bound of the rope index point position, is the upper bound of the rope index point position, but the adjustment of the rope index point by formula (11) may not strictly guarantee the satisfaction of the constraint, so it is tested; let is the final change of the rope index point under the artificial potential field. If the constraint is satisfied, then If the constraints are not satisfied, then ,in is the scaling factor, which can make the adjusted Satisfy box constraints;

Step 44: Use the activation function (i.e., Sigmoid function) to fuse the optimal solution of the artificial potential field and the linear optimization problem: Since the artificial potential field is used to move the rope index point away from the boundary of the solution space, it is hoped that it will only work at the boundary. The solutions of the two methods can be combined through the activation function:

(12);

in, is the natural logarithm; is the coefficient for scaling the activation function; is the minimum value of the margin of the desired force to each hyperplane, called the minimum margin, is the expected value of the minimum margin. When the actual minimum margin is less than When the artificial potential field plays a leading role in adjusting the rope index point, the minimum margin is greater than Time-linear optimization plays a leading role in adjusting the rope index output point.

In summary, the real-time solution and reconstruction planning method for a rope-pulled parallel robot applicable to physical human-machine interaction tasks according to the embodiment of the present invention has at least the following advantages compared to the prior art:

(1) An interaction index suitable for completing human-robot interaction tasks on a rope-pulled parallel robot is set up, which can be used to quantitatively evaluate the quality of human-robot interaction or robot configuration;

(2) Simplifying the nonlinear optimization problem into a linear optimization problem greatly reduces the complexity of the solution and improves the computational efficiency, so that it can be solved in real time during the human-computer interaction process.

(3) After obtaining the simplified linear optimization problem, the dual simplex method is used to replace the sampling-based or gradient iteration-based nonlinear optimization problem solving method to ensure the convergence of the solution.

(4) Considering that the optimal solution of the linear optimization problem lies on the boundary of the solution space, but the robot used for human-computer interaction is unstable at the boundary conditions, an artificial potential field is designed to correct the solution of the linear optimization problem, thereby ensuring the stability of the system.

Those skilled in the art will appreciate that all or part of the processes in the above-described method embodiments can be implemented by instructing related hardware through a program. The program can be stored in a computer-readable storage medium. When executed, the program can include the processes in the above-described method embodiments. The storage medium can be a magnetic disk, an optical disk, a read-only memory (ROM), or a random access memory (RAM).

The above description is only a preferred embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any changes or substitutions that can be easily thought of by any person skilled in the art within the technical scope disclosed in the present invention should be included in the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be based on the scope of protection of the claims. The information disclosed in the background technology section of this article is only intended to deepen the understanding of the overall background technology of the present invention, and should not be regarded as an admission or any form of implication that the information constitutes prior art already known to those skilled in the art.

Claims (10)

1. A reconstruction planning method for real-time solving of man-machine interaction rope traction parallel robots is characterized by comprising the following steps:

step 1, constructing a kinematic model of the rope traction parallel robot and a dynamic model of the movable platform according to the spatial position relation between a rope leading-out point of the rope traction parallel robot and the movable platform, and constructing an admittance model for realizing that the movable platform moves along with an arm of an operator;

step 2, representing the force feasible conditions of the rope traction parallel robot by using a hyperplane movement method according to the dynamic model and the admittance model obtained in the step 1 and combining with the human-computer interaction characteristics, and setting an objective function of the optimization problem according to the force feasible conditions and the interaction force;

Step 3, according to the objective function of the optimization problem obtained in the step 2, the problem of solving the rope leading-out point is expressed as a nonlinear optimization problem through constraint, the nonlinear optimization problem is approximated as a linear optimization problem through linear approximation, and the approximate optimal solution of the linear optimization problem is solved by a dual simplex method;

And 4, correcting the approximate optimal solution of the linear optimization problem obtained in the step 3 according to the man-machine interaction characteristic and the artificial potential field set by the dynamics characteristic of the rope traction parallel robot, ensuring the solving speed and enabling the position of the solved rope leading-out point not to be located at the boundary of the solving space, thus finishing the reconstruction planning of the real-time solving of the rope leading-out point of the rope traction parallel robot.

2. The reconstruction planning method for real-time solution of man-machine interaction rope traction parallel robots according to claim 1, wherein the rope traction parallel robots are rope traction parallel robots for continuous reconstruction planning, comprising:

The device comprises a fixed frame, 4 rope leading-out devices, 4 vertical screw rods, 8 motors, 4 reels, 4 ropes and a movable platform, wherein,

Each rope leading-out device consists of a sliding block and a guide pulley, and the guide pulley is arranged on the sliding block and can synchronously move along with the sliding block;

the four corners of the fixed frame are respectively provided with 4 vertical lead screws, each vertical lead screw is provided with a sliding block and a guide pulley of a rope leading-out device, one end of each vertical lead screw is connected with a motor, and the sliding block and the guide pulley can be driven by the motor to rotate and move up and down;

4 reels are arranged on the ground in the fixed frame in a surrounding mode, a reel is arranged below each vertical screw rod, a rope is wound on each reel, each reel is connected with a motor, and the reels can rotate under the driving of the motor to retract and release the connected rope;

The other end of each rope sequentially winds around a guide pulley of the rope leading-out device above the rope and then is connected with the movable platform, and each rope suspends the movable platform in the fixed frame;

the position of a rope leading-out point of the rope traction parallel robot and the rope length of the rope can be continuously changed at the same time, so that continuous reconstruction is realized.

3. The reconstruction planning method for real-time solution of man-machine interaction rope traction parallel robot according to claim 2, wherein in the rope traction parallel robot, a rope leading-out point is regarded as a fixed point on a sliding block.

4. The reconstruction planning method for real-time solution of a rope traction parallel robot with man-machine interaction according to any one of claims 1 to 3, wherein in the step 1, a kinematic model of the rope traction parallel robot is constructed according to a spatial position relationship between a rope leading-out point of the rope traction parallel robot and a movable platform in the following manner, and the method comprises the following steps:

Definition the static coordinate system that the moving platform of the rope traction parallel robot keeps relatively static with the ground is The movable platform of the rope-pulled parallel robot has 3 translational degrees of freedom, 4 ropes provide upward pulling force for the movable platform to form a suspension configuration, and the position of the movable platform is expressed as a static coordinate systemP _x is the x-axis coordinate of the moving platform centroid, P _y is the y-axis coordinate of the moving platform centroid, P _z is the z-axis coordinate of the moving platform centroid, the superscript T represents the transpose of the matrix, and the position of the rope leading-out point is represented in the static coordinate system as,WhereinAndAre all constant and are determined by the installation position of the vertical screw rod,The height of each rope leading-out point is expressed as a vector formBased on definition of each point in the static coordinate systemVector of the root rope from the movable platform to the rope leading-out pointExpressed as:

(1);

First, the The length of the root rope is expressed asThe rope length of each rope is expressed in vector formFirst, theThe unit vector of the direction of the cable force and the pull force exerted by the root rope on the movable platform is expressed as, wherein,Represent the firstThe projection of the unit vector of the cable force and the pulling force applied to the movable platform by the cable along the x-axis direction,Represent the firstThe projection of the unit vector of the cable force and the pulling force applied to the movable platform by the cable along the y-axis direction,Represent the firstAnd the projection of the unit vector of the cable force and tension direction applied to the movable platform by the cable along the z-axis direction.

5. The reconstruction planning method for real-time solution of rope-drawn parallel robot with man-machine interaction according to claim 4, wherein in the step 1, a dynamic model of a moving platform of the rope-drawn parallel robot is constructed according to a spatial position relationship between a rope leading-out point of the rope-drawn parallel robot and the moving platform in the following manner, and the method comprises the following steps:

The established dynamic model of the dynamic platform is expressed as a Newton Euler equation:

(2);

In the above-mentioned formula (2), Mass matrix for a rope-drawing parallel robot, whereinIs the mass of the movable platform and is characterized in that,Is a matrix of units which is a matrix of units,A gravity vector for a rope-drawn parallel robot, whereinGravitational acceleration; the acceleration of the parallel robot movable platform is pulled by the rope; A jacobian matrix between the joint space and the Cartesian space of the parallel robot is pulled for the rope; a rope tension vector of the parallel robot is pulled for the rope; And in the human-computer interaction process, the human applies interaction force on the movable platform.

6. The reconstruction planning method for real-time solution of man-machine interaction rope traction parallel robot according to claim 5, wherein in step 1, an admittance model for realizing that the moving platform follows the arm movement of the operator is established in the following manner, comprising:

Virtual mass damping models are arranged between the movable platform and the arms of the operators and used as admittance models for guaranteeing the stability of human-computer interaction while the movable platform moves along with the arms of the operators in the human-computer interaction, and the admittance models are as follows:

(3);

in the above-mentioned formula (3), AndRespectively an inertia term and a damping term in the admittance model;、 the method comprises the steps that the expected acceleration and the expected speed of a movable platform of the parallel robot are respectively pulled by a rope;

The interaction force is measured by a sensor arranged on the movable platform And obtaining a reference track conforming to the admittance model by solving the admittance model in the formula (3), and inputting the reference track as an expected track to a position controller of the rope traction parallel robot for tracking to realize follow-up control, wherein a rigidity item is not arranged in the admittance model, so that the movable platform can be kept at the current position when the interaction force is removed in the follow-up process.

7. The reconstruction planning method for real-time solution of rope-drawn parallel robots with man-machine interaction according to claim 6, wherein in the step 2, according to the dynamics model and admittance model obtained in the step 1, by combining man-machine interaction characteristics, the force feasible condition of the rope-drawn parallel robots is represented by a hyperplane movement method, and according to the force feasible condition and interaction force, a corresponding objective function is set, comprising:

The force feasible condition of the rope traction parallel robot is expressed as that when the rope tension has upper and lower limit constraint, a group of rope tension meeting the constraint exists So that the dynamic model of the moving platform of the formula (2) is established,The lower limit of the rope tension vector is set to 10N; as the upper limit of the rope tension vector, according to the characteristic that the combination of all ropes and the movable platform is a convex hull, the super-plane movement method is used for representing the feasible force conditions of the rope traction parallel robot, and the feasible force conditions are as follows:

(4);

In the above-mentioned formula (4), For the resultant force of rope pulling force applied to the movable platform of the expected rope pulling parallel robotSum vectorJacobian matrix corresponding to parallel robot pulled by rope through hyperplane movement methodLower limit of rope tension vectorUpper limit of rope tension vectorObtaining, wherein, a matrixElements of (a)Expressed as:

(5);

In the above-mentioned formula (5), Is a unit normal vector of the hyperplane,AndRepresenting a rope vector for constituting a hyperplane, whereinIs the number of normal vectors corresponding to the hyperplane,,,Subscript of rope vector for forming hyperplaneElements of (a)Expressed as:

(6);

In the above-mentioned formula (6), For the tension value provided by each rope when calculated in the hyperplane movement method,In order to judge the basis of the magnitude of the tension value,Is the firstThe transpose of the unit vector of the rope force pulling force direction applied by the root rope to the movable platform, i=1, 2,3,4, if the included angle between the normal vector of the hyperplane and the unit vector of the rope force pulling force direction applied by the rope to the movable platform is an acute angle, providing the upper limit value of the rope pulling force, otherwise providing the lower limit value of the rope pulling force,The projection of the unit vector of the rope force and tension direction applied to the movable platform by the rope to the hyperplane normal vector,、、、The unit vectors of the 1 st rope, the 2 nd rope, the 3 rd rope and the 4 th rope are respectively transposed in the direction of the cable force pulling force applied to the movable platform;

Setting an objective function of the optimization problem according to the representation of the hyperplane movement method and combining the relation between the interactive force direction and the intention of the operator The method comprises the following steps:

(7);

In the above-mentioned formula (7), The normalized weight coefficient is set according to the included angle between the interaction force and the normal vector; Along the first line The margin of the resultant force that can be provided by the normal vector of the hyperplane,。

8. The reconstruction planning method for real-time solution of man-machine interaction rope traction parallel robot according to claim 7, wherein in the step 3, the solution problem of the rope leading-out point is represented as a nonlinear optimization problem by constraint according to the objective function of the optimization problem obtained in the step 2, the nonlinear optimization problem is approximated as a linear optimization problem by linear approximation, and the approximation solution of the linear optimization problem is solved by a dual simplex method, comprising:

Setting, according to the objective function of the optimization problem of the formula (7) and the force feasible condition of the formula (4), the upper and lower limits that the position, the speed and the acceleration of the rope when the rope leading-out point is changed respectively meet are as follows:

(8);

in the formula (8), the position of the movable platform is set Upper limit of (2)Is 2.4m, lower limitIs 0.1m higher than the movable platform, the speed isAbsolute value is less than 0.1m/s, accelerationThe absolute value is smaller than 0.02m/s ², the formula (4) and the formula (7) are nonlinear functions of the positions of the rope leading-out points, and can be approximated to be linear functions through linear approximation;

the control period of the rope traction parallel robot is set as follows The upper limit of the speed of the rope leading-out point is 0.1m/s, and the maximum moving distance of the rope leading-out point in each control period isWhen the expected rope leading-out point position is calculated at the starting moment of each control period, the actual position of the movable platform at the end of the control period cannot be accurately predicted, and the actual position of the movable platformThe distance moved in each control cycle is likewise small, so that the actual position of the mobile platform is assumed when solving the rope take-off pointIs of a constant value, according to the definition of the length of the rope and the matrix of the formula (5)Elements of (2)Rope length vector in each control periodNormal vector of hyperplaneApproximately constant value whenFar greater than 0, by definitionIs of a constant valueNear 0, ignoreChange of the pairAnd thus can be approximated asIs constant, an objective function of an optimization problem according to the formula (7) and is to beIs regarded as constant, coefficientCan also be considered a constant value in each control period;

according to the method, constraint and objective functions are both arranged into linear functions of optimized variables, the linear functions are solved by a dual simplex method, and the obtained approximate optimal solution is expressed as The approximately optimal solutionThe amount of change with respect to the start time of the control period is expressed as。

9. The reconstruction planning method for real-time solution of rope traction parallel robot with man-machine interaction according to claim 8, wherein in the step 4, the correction of the near-optimal solution of the linear optimization problem obtained in the step 3 is performed according to the man-machine interaction characteristic and the artificial potential field set by the dynamics characteristic of the rope traction parallel robot, comprising:

Step 41, setting an artificial potential field according to the interaction force direction and the dynamics characteristics of the rope traction parallel robot obtained by the hyperplane movement method The method comprises the following steps:

(9);

In the above-mentioned formula (9), Representing the direction of the interaction force from the desired forceDistance to the hyperplane; a gravitational constant for the set artificial potential field;

step 42, calculating the potential field force according to the set artificial potential field Obtaining the variation of the rope leading-out point by simultaneously deriving the distance from two sides of the artificial potential field of the formula (9) to obtain the potential force of the artificial potential fieldThe expression of (2) is:

(10);

Potential field force of artificial potential field As the distance of adjustment of the rope take-off point per control periodThe method comprises the following steps:

(11);

Step 43, by means of box constraint detection, the box constraints of position, speed and acceleration of the rope exit point are unified into one box constraint when the position speed at the beginning of any control period is known ,Is the lower boundary of the position of the rope leading-out point,Is restricted by the box for the upper limit of the position of the rope leading-out pointDetecting whether the adjustment of the distance of the formula (11) to the rope exit point satisfies a constraint;

Order the For the final variation of the rope lead-out point under artificial potential field, if the constraint is satisfiedIf the constraint is not satisfied, thenWhereinTo scale the scale factor, the final variation of the rope leading-out point under the artificial potential field after adjustmentSatisfying the box constraint;

and step 44, fusing the artificial potential field and the approximate optimal solution of the linear optimization problem by using the activation function to obtain a corrected approximate optimal solution.

10. The method for reconstructing and planning the real-time solution of the man-machine interaction rope traction parallel robot according to claim 9, wherein in the step 44, the approximate optimal solution of the artificial potential field and the linear optimization problem is fused by the following activation function, which is:

(12);

wherein, the Is natural logarithm; scaling the activation function; a minimum value for the desired force to the respective hyperplane margin, i.e., a minimum margin; is the expected value of the minimum margin, when the actual minimum margin is smaller than the expected value of the minimum margin When the artificial potential field dominates the adjustment of the rope take-off point, when the actual minimum margin is larger than the expected value of the minimum marginThe near optimal solution of the time-linear optimization problem dominates the adjustment of the rope take-off point.