Dynamic trajectory planning method for cable-parallel robots with parallel cable constraints

Abstract

This application discloses a dynamic trajectory planning method for a cable-parallel robot constrained by parallel ropes. The method includes: establishing a kinematic and dynamic model of the cable-parallel robot based on a preset configuration of the robot constrained by parallel ropes; simplifying the kinematic and dynamic model of the robot based on the principle that rope forces in the same direction can be combined; obtaining performance evaluation indicators for evaluating the torsional resistance of the moving platform based on the force equivalent model and torque analysis of the parallel ropes; and establishing a trajectory equation based on the trajectory model for the gate-shaped dynamic trajectory required for palletizing tasks, and optimizing the dynamic trajectory according to the constraint conditions with the comprehensive index of trajectory power consumption and torsional performance as the optimization objective, thereby achieving control over the gate-shaped characteristics of the trajectory. This solves the problem that related technologies have limitations in enriching the configuration and degree of freedom of cable-parallel robots, reducing the constraint capacity of the ropes, and failing to meet the usage requirements of cable-parallel robots.

Description

Technical Field

[0001] This application relates to the field of dynamic trajectory planning technology, and in particular to a dynamic trajectory planning method for a cable-parallel robot with parallel cable constraints. Background Technology

[0002] With the continuous development of cable-driven parallel robot technology, it has been widely used in aerospace, warehousing and logistics, motion simulation and other fields, and has fully demonstrated its outstanding advantages such as large working space, strong load-bearing capacity, good power performance, light weight and low cost.

[0003] In related technologies, dynamic trajectories can be planned for suspended cable-driven parallel robots to achieve a larger range of motion in a controllable and stable state, thus expanding the application scenarios of cable-driven parallel robots.

[0004] However, the existing technologies are limited in terms of the configuration and degree of freedom of cable-parallel robots, which reduces the constraint capacity of the ropes and fails to meet the usage requirements of cable-parallel robots, thus requiring urgent improvement. Summary of the Invention

[0005] This application provides a dynamic trajectory planning method for cable-parallel robots with parallel rope constraints, in order to solve the problems in related technologies, such as the difficulty in enriching the configuration and degree of freedom of cable-parallel robots, certain limitations, reduced rope constraint capacity, and inability to meet the usage requirements of cable-parallel robots.

[0006] The first aspect of this application provides a method for dynamic trajectory planning of a cable-parallel robot constrained by parallel ropes, comprising the following steps: establishing a kinematic and dynamic model of the cable-parallel robot based on a preset configuration of the cable-parallel robot constrained by parallel ropes; simplifying the kinematic and dynamic model of the cable-parallel robot based on the principle that rope forces in the same direction can be combined, to obtain the final kinematic and dynamic model of the cable-parallel robot; obtaining performance evaluation indicators for evaluating the torsional resistance of the moving platform based on the force equivalent model and torque analysis of the parallel ropes; and, based on the final kinematic and dynamic model, establishing a trajectory equation based on a preset trajectory model for the gate-shaped dynamic trajectory required for the palletizing task, and using the comprehensive index of trajectory power consumption and torsional performance obtained from the performance evaluation indicators as the optimization target, optimizing and solving the gate-shaped dynamic trajectory of the cable-parallel robot according to preset constraints to achieve control of the gate-shaped characteristics of the trajectory.

[0007] Optionally, in one embodiment of this application, the final kinematic and dynamic model is:

[0008]

[0009] M k +Mq +M0=0,

[0010] Where F1 and F2 are the resultant forces of parallel cables or the forces of a single cable, e1 and e2 are the direction vectors of the cables, m is the mass of the moving platform and the load, and g is the acceleration due to gravity. To accelerate the moving platform, M k M is the torsional moment of the parallel cable. q This refers to the tilting moment of the mechanism.

[0011] Optionally, in one embodiment of this application, the performance evaluation index for evaluating the torsional resistance of the moving platform includes a torsional resistance index and a torsional equilibrium index, wherein,

[0012] The torsional resistance index is defined as follows:

[0013] TRAI=||M km || / ||M g ||,

[0014] Among them, M g This is the reference torque for the load.

[0015] The torsional equilibrium index is defined as follows:

[0016] TRBI = ||M q || / ||M km ||,

[0017] Among them, M q This refers to the tilting moment of the mechanism.

[0018] Optionally, in one embodiment of this application, the comprehensive index of trajectory power consumption and torsional performance is defined as:

[0019]

[0020] Where W represents the power consumption of the entire dynamic trajectory.

[0021] Optionally, in one embodiment of this application, the step of establishing a trajectory equation based on a preset trajectory model and optimizing the dynamic trajectory of the cable-parallel robot according to preset constraints, with the comprehensive index of trajectory power consumption and torsional performance obtained from the performance evaluation index as the optimization target, includes: when the trajectory model is a Fourier series model, selecting the order of the Fourier series according to the preset constraints, differentiating the trajectory model to obtain the first velocity and first acceleration at each point of the trajectory, analyzing the velocity constraints at the endpoints of the trajectory to simplify the model, solving the coefficient parameters of the Fourier series according to the position and acceleration constraints at the endpoints, and optimizing the frequency of the dynamic trajectory with the minimum TPTI as the optimization target.

[0022] Optionally, in one embodiment of this application, the step of establishing a trajectory equation based on a preset trajectory model and optimizing the dynamic trajectory of the cable-parallel robot according to preset constraints, with the comprehensive index of trajectory power consumption and torsional performance obtained from the performance evaluation index as the optimization target, includes: when the trajectory model is a polynomial function model, selecting the order of the polynomial function according to the preset constraints, differentiating the trajectory model to obtain the second velocity and second acceleration at each point of the trajectory, analyzing the velocity constraints at the trajectory endpoints to simplify the model, optimizing the time and horizontal acceleration at the endpoint of each dynamic trajectory segment with the minimum TPTI as the optimization target, and solving the polynomial coefficient parameters according to the position and acceleration constraints at the endpoints.

[0023] A second aspect of this application provides a dynamic trajectory planning device for a cable-parallel robot constrained by parallel ropes, comprising: a modeling module for establishing a kinematic and dynamic model of the cable-parallel robot based on a preset configuration of the cable-parallel robot constrained by parallel ropes; a processing module for simplifying the kinematic and dynamic model of the cable-parallel robot based on the principle that the rope forces in the same direction can be combined, to obtain a final kinematic and dynamic model of the cable-parallel robot; an acquisition module for acquiring performance evaluation indicators for evaluating the torsional resistance of the moving platform based on the force equivalent model and torque analysis of the parallel ropes; and a control module for establishing a trajectory equation based on a preset trajectory model for the gate-shaped dynamic trajectory required by the palletizing task based on the final kinematic and dynamic model, and using the comprehensive index of trajectory power consumption and torsional performance obtained from the performance evaluation indicators as the optimization target, optimizing and solving the gate-shaped dynamic trajectory of the cable-parallel robot according to preset constraints, thereby realizing the control of the gate-shaped characteristics of the trajectory.

[0024] Optionally, in one embodiment of this application, the final kinematic and dynamic model is:

[0025]

[0026] M k +M q +M0=0,

[0027] Where F1 and F2 are the resultant forces of parallel cables or the forces of a single cable, e1 and e2 are the direction vectors of the cables, m is the mass of the moving platform and the load, and g is the acceleration due to gravity. To accelerate the moving platform, M k M is the torsional moment of the parallel cable. q This refers to the tilting moment of the mechanism.

[0028] Optionally, in one embodiment of this application, the performance evaluation index for evaluating the torsional resistance of the moving platform includes a torsional resistance index and a torsional equilibrium index, wherein,

[0029] The torsional resistance index is defined as follows:

[0030] TRAI=||M km || / ||M g ||,

[0031] Among them, M g This is the reference torque for the load.

[0032] The torsional equilibrium index is defined as follows:

[0033] TRBI = ||M q || / ||M km ||,

[0034] Among them, M q This refers to the tilting moment of the mechanism.

[0035] Optionally, in one embodiment of this application, the comprehensive index of trajectory power consumption and torsional performance is defined as:

[0036]

[0037] Where W represents the power consumption of the entire dynamic trajectory.

[0038] Optionally, in one embodiment of this application, the control module is further configured to, when the trajectory model is a Fourier series model, select the order of the Fourier series according to the preset constraints, differentiate the trajectory model to obtain the first velocity and the first acceleration at each point of the trajectory, analyze the velocity constraints at the trajectory endpoints to simplify the model, solve the coefficient parameters of the Fourier series according to the position and acceleration constraints at the endpoints, and optimize the frequency of the dynamic trajectory with the minimum TPTI as the optimization objective.

[0039] Optionally, in one embodiment of this application, the control module is further configured to, when the trajectory model is a polynomial function model, select the order of the polynomial function according to the preset constraints, differentiate the trajectory model to obtain the second velocity and second acceleration at each point of the trajectory, analyze the velocity constraints at the trajectory endpoints to simplify the model, optimize the time and horizontal acceleration at the endpoint of each dynamic trajectory with the minimum TPTI as the optimization objective, and solve the polynomial coefficient parameters according to the position and acceleration constraints at the endpoints.

[0040] A third aspect of this application provides an electronic device, including: a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the program to implement the dynamic trajectory planning method for a cable-parallel robot with parallel cable constraints as described in the above embodiments.

[0041] A fourth aspect of this application provides a computer-readable storage medium storing a computer program that, when executed by a processor, implements the above-described dynamic trajectory planning method for a cable-parallel robot with parallel cable constraints.

[0042] This application embodiment can establish a kinematic and dynamic model of a cable-parallel robot based on a preset parallel rope constraint configuration. Based on the principle that rope forces in the same direction can be combined, the kinematic and dynamic model of the cable-parallel robot is simplified. Based on the force equivalence model and torque analysis of parallel ropes, performance evaluation indicators are obtained to assess the torsional resistance of the moving platform. For the gate-shaped dynamic trajectory required for palletizing tasks, trajectory equations can be established based on the trajectory model, and the comprehensive index of trajectory power consumption and torsional performance can be used as the optimization objective. Thus, the gate-shaped dynamic trajectory can be obtained by optimizing the solution according to the constraint conditions, realizing the control of the trajectory gate-shaped characteristics. This enriches the configuration and degree of freedom of the cable-parallel robot, effectively improving the constraint capacity of the ropes and meeting the usage requirements of the cable-parallel robot. Therefore, it solves the problems in related technologies, such as the difficulty in enriching the configuration and degree of freedom of cable-parallel robots, certain limitations, reduced rope constraint capacity, and inability to meet the usage requirements of cable-parallel robots.

[0043] Additional aspects and advantages of this application will be set forth in part in the description which follows, and in part will be obvious from the description, or may be learned by practice of this application. Attached Figure Description

[0044] The above and / or additional aspects and advantages of this application will become apparent and readily understood from the following description of the embodiments taken in conjunction with the accompanying drawings, wherein:

[0045] Figure 1 This is a flowchart illustrating a dynamic trajectory planning method for a cable-parallel robot with parallel cable constraints, according to an embodiment of this application.

[0046] Figure 2 A schematic diagram of a planar two-degree-of-freedom translational cable parallel robot structure constrained by a single-sided parallel cable according to a specific embodiment of this application;

[0047] Figure 3 This is a schematic diagram of a point-to-point gate-type dynamic trajectory based on a Fourier series model, according to a specific embodiment of this application.

[0048] Figure 4 This is a schematic diagram of a point-to-point gate-type dynamic trajectory based on a polynomial function model, according to a specific embodiment of this application.

[0049] Figure 5This is a schematic diagram of the structure of a dynamic trajectory planning device for a cable-parallel robot with parallel cable constraints according to an embodiment of this application;

[0050] Figure 6 This is a schematic diagram of the structure of an electronic device according to an embodiment of this application. Detailed Implementation

[0051] The embodiments of this application are described in detail below. Examples of these embodiments are shown in the accompanying drawings, wherein the same or similar reference numerals denote the same or similar elements or elements having the same or similar functions throughout. The embodiments described below with reference to the accompanying drawings are exemplary and intended to explain this application, and should not be construed as limiting this application.

[0052] The following describes a dynamic trajectory planning method for a cable-parallel robot with parallel rope constraints, based on embodiments of this application, with reference to the accompanying drawings. Addressing the limitations of the related technologies mentioned in the background section, which restrict the variety of configurations and degrees of freedom for cable-parallel robots, reduce rope constraint capacity, and fail to meet the usage requirements of cable-parallel robots, this application provides a dynamic trajectory planning method for a cable-parallel robot with parallel rope constraints. In this method, a kinematic and dynamic model of the cable-parallel robot is established based on a preset configuration of the parallel rope-constrained robot. Based on the principle that rope forces in the same direction can be combined, the kinematic and dynamic model of the cable-parallel robot is simplified. Based on the force equivalent model and torque analysis of the parallel ropes, performance evaluation indicators are obtained to assess the torsional resistance of the moving platform. For the gate-shaped dynamic trajectory required for palletizing tasks, a trajectory equation is established based on the trajectory model, and the comprehensive index of trajectory power consumption and torsional performance is used as the optimization objective. Thus, the gate-shaped dynamic trajectory can be obtained by optimizing the solution according to the constraint conditions, achieving control over the gate-shaped characteristics of the trajectory. This enriches the configuration and degrees of freedom of the cable-parallel robot, effectively improves the rope constraint capacity, and meets the usage requirements of the cable-parallel robot. This solves the problems in related technologies, such as the difficulty in enriching the configuration and degree of freedom of cable-parallel robots, the limitations, the reduced constraint capacity of the ropes, and the inability to meet the usage requirements of cable-parallel robots.

[0053] Specifically, Figure 1 This is a flowchart illustrating a dynamic trajectory planning method for a cable-parallel robot with parallel cable constraints, provided in an embodiment of this application.

[0054] like Figure 1 As shown, the dynamic trajectory planning method for a cable-parallel robot with parallel cable constraints includes the following steps:

[0055] In step S101, the kinematic and dynamic model of the cable parallel robot is established according to the preset parallel cable-constrained cable parallel robot configuration.

[0056] It is understood that the embodiments of this application can be based on the configuration of a parallel cable-coupled robot constrained by parallel cables, and kinematic and dynamic modeling of the parallel cable-coupled robot can be performed, thereby enabling the parallel cable-coupled robot to achieve a dynamic range of motion beyond the static workspace, so as to improve the range of motion of the parallel cable-coupled robot.

[0057] For example, such as Figure 2 As shown, a planar 2-DOF non-mass point cable parallel robot with a single set of parallel cable constraints is shown. It includes a set of parallel cables A1B1, A2B2 and A3B3, where A1 to A3 are the connection points between the cables and the moving platform, and B1 to B3 are the cable exit points of the stationary platform, and A1B1 = A2B2.

[0058] Furthermore, the parallel ropes constrain the in-plane rotation of the moving platform, ensuring that A1B1 remains parallel to B1B2. Additionally, the parallel ropes can be driven by a single actuator to achieve synchronous motion, meaning this cable-parallel robot requires only two actuators.

[0059] In step S102, based on the principle that cable forces in the same direction can be combined, the kinematic and dynamic model of the cable parallel robot is simplified to obtain the final kinematic and dynamic model of the cable parallel robot.

[0060] It is understood that, based on the principle that the parallel cable forces in the same direction can be merged, the parallel cable forces of the parallel cable robot can be merged to the origin of the follower coordinate system, and the kinematic and dynamic model of the cable parallel robot can be simplified to obtain the final kinematic and dynamic model of the cable parallel robot in the following steps, thereby improving the feasibility of dynamic trajectory planning of the cable parallel robot constrained by parallel cables.

[0061] In one embodiment of this application, the final kinematic and dynamic model is as follows:

[0062]

[0063] M k +M q +M0=0,

[0064] Where F1 and F2 are the resultant forces of parallel cables or the forces of a single cable, e1 and e2 are the direction vectors of the cables, m is the mass of the moving platform and the load, and g is the acceleration due to gravity. To accelerate the moving platform, M k M is the torsional moment of the parallel cable. q This refers to the tilting moment of the mechanism.

[0065] Among them, M k The torsional moment of the parallel cable is:

[0066] M k =r0×Δfe1

[0067] Where r0 is the radius of the parallel cable spacing, and Δf is the difference in force between the parallel cables.

[0068] M q Let the tilting moment of the mechanism be:

[0069] M q =r1×F1e1+r2×F2e2

[0070] Where r1 and r2 are the equivalent cable force arm vectors.

[0071] In step S103, based on the force equivalent model and torque analysis of the parallel cable, performance evaluation indicators are obtained to evaluate the torsional resistance of the dynamic platform.

[0072] It is understood that the embodiments of this application can be based on the force equivalent model and torque analysis of the parallel cable, and obtain the performance evaluation index used to evaluate the torsional resistance of the moving platform in the following steps, so that the parallel cable can be used for driving, the constraint capacity of the cable can be improved, and the torsional resistance of the parallel cable can be effectively improved.

[0073] Optionally, in one embodiment of this application, the performance evaluation index for evaluating the torsional resistance of the moving platform includes a torsional resistance index and a torsional equilibrium index.

[0074] Among them, the torsional resistance index TRAI can be used as a dimensionless local index to measure the maximum torsional resistance of a moving platform under a specific orientation. That is, the torsional resistance index is defined as:

[0075] TRAI=||M km || / ||M g ||,

[0076] Among them, M g This is the reference torque for the load.

[0077] but:

[0078] M g =r0×mg

[0079] By finding the minimum TRAI value on the trajectory (recorded as 0 when TRAI is less than 0), the torsional resistance index of the trajectory cable (TTRAI) can be defined as follows:

[0080]

[0081] Among them, W T Given a dynamic trajectory, this is the set of poses and motion states.

[0082] Among them, the Torsional Resilience Index (TRBI) is a dimensionless local index used to measure the resistance of a mechanism to torsion in both forward and reverse directions under a specific orientation. The Torsional Resilience Index is defined as follows:

[0083] TRBI = ||M q || / ||M km ||,

[0084] Among them, M q This refers to the tilting moment of the mechanism.

[0085] The maximum value of TRBI is obtained on the trajectory (when TRBI is greater than 1, it is recorded as 1), and the trajectory cable torsional equilibrium index (TTRBI) is defined as follows:

[0086]

[0087] In step S104, based on the final kinematics and dynamics model, for the gate-shaped dynamic trajectory required by the palletizing task, the trajectory equation is established based on the preset trajectory model, and the comprehensive index of trajectory power consumption and torsional performance obtained from the performance evaluation index is used as the optimization target. The gate-shaped dynamic trajectory of the cable-parallel robot is optimized and solved according to the preset constraints to realize the control of the trajectory gate-shaped characteristics.

[0088] It is understood that the embodiments of this application can establish trajectory equations based on the trajectory model, such as Fourier series models and polynomial function models, for the gate-shaped dynamic trajectory required by the palletizing task, based on the final kinematic and dynamic model. The trajectory power consumption and torsional performance comprehensive index obtained from the performance evaluation index are used as the optimization target. The gate-shaped dynamic trajectory of the cable parallel robot is obtained by optimizing and solving according to the constraint conditions, and the control of the trajectory gate-shaped characteristics is realized. In this way, the parallel cable parallel robot can realize the dynamic movement range beyond the static workspace, improve the constraint capacity of the rope, and effectively improve the anti-torsion performance of the parallel rope.

[0089] In one embodiment of this application, the comprehensive index of trajectory power consumption and torsional performance is used to comprehensively measure trajectory anti-torsional performance and trajectory power consumption performance, that is, the comprehensive index of trajectory power consumption and torsional performance is defined as follows:

[0090]

[0091] Where W represents the power consumption of the entire dynamic trajectory.

[0092] Optionally, in one embodiment of this application, a trajectory equation is established based on a preset trajectory model, and the trajectory power consumption and torsional performance comprehensive index obtained from the performance evaluation index are used as the optimization target. The dynamic trajectory of the cable-parallel robot is optimized and solved according to preset constraints. This includes: when the trajectory model is a Fourier series model, the order of the Fourier series is selected according to the preset constraints, the derivative of the trajectory model is obtained, the first velocity and the first acceleration at each point of the trajectory are obtained, the velocity constraint conditions at the endpoints of the trajectory are analyzed to simplify the model, the coefficient parameters of the Fourier series are solved according to the position and acceleration constraints at the endpoints, and the frequency of the dynamic trajectory is optimized and solved with the minimum TPTI as the optimization target.

[0093] For example, such as Figure 3 As shown, Figure 3 This is a schematic diagram of a simulation example and an experimental example of a point-to-point gate-type dynamic trajectory based on a Fourier series model.

[0094] The following section describes point-to-point gate-type dynamic trajectory planning based on the Fourier series model. The robot platform sequentially executes a series of point-to-point dynamic trajectories passing through the target point.

[0095] Two adjacent target points p i With p i+1 The trajectory of the connection is denoted as H. i (t), the gantry-type dynamic trajectory requires the instantaneous velocity of the moving platform at each material pick-up and drop-off target point to be equal to 0 while the acceleration is not equal to 0. Therefore, the i-th segment of the trajectory H i The constraint conditions at the endpoints of (t) are:

[0096] H i (t i ) = p i H i (t i+1 ) = p i+1 ,

[0097]

[0098]

[0099] Furthermore, in embodiments of this application where there are no explicit requirements for endpoint acceleration, the trajectory is guaranteed to meet the constraint condition of acceleration continuity, and trajectory H... i The constraints at the endpoints of (t) are simplified to:

[0100] H i (t i ) = p i H i (t i+1 ) = p i+1 ,

[0101]

[0102]

[0103] Generally, H i (t) n The dynamic trajectory model of the Fourier series is as follows:

[0104]

[0105]

[0106] Among them, T i Let be the motion time of the i-th dynamic trajectory segment.

[0107] but:

[0108] T i =π / ω i .

[0109] Furthermore, the i-th order Fourier series trajectory model has 2i+1 parameters. Based on the constraint number of 5, the trajectory model based on the second order Fourier series is selected. The Fourier coefficients can be directly determined through constraint solving, which helps to simplify the trajectory planning process and improve the solution efficiency.

[0110] The trajectory model of the second-order Fourier series is as follows:

[0111] x(t)=a i,x0 +a i,x1 cos(ω i t)+b i,x1 sin(ω i t)+a i,x2 cos(2ω i t)+b i,x2 sin(2ω i t), t∈[0,T i ),

[0112] y(t)=a i,y0 +a i,y1 cos(ω i t)+b i,y1 sin(ω i t)+a i,y2 cos(2ω i t)+b i,y2 sin(2ω i t), t∈[0,T i ).

[0113] To simplify the Fourier series trajectory model, the trajectory model can be analyzed based on the velocity constraints at the endpoints of each trajectory segment, and irrelevant terms in the model can be removed.

[0114] Therefore, the velocity equation of the trajectory is:

[0115] x′(t)=ω i (-a i,x1 cos(ω i t)+b i,x1 sin(ω i t)-2a i,x2 cos(2ω i t)+2b i,x2 sin(2ω i t), t∈[0,T i ),

[0116] y′(t)=ω i (-a i,y1 cos(ω i t)+b i,y1 sin(ω i t)-2a i,y2 cos(2ω i t)+2b i,y2 sin(2ω i t), t∈[0,T i ).

[0117] Based on the constraint that the velocity at the endpoint is 0, we can obtain b. i,x1 =b i,x2 =b i,y1 =b i,y2 =0.

[0118] The dynamic trajectory model based on the second-order Fourier series can be simplified as follows:

[0119] x(t)=A x +B x cos(ω i t)+C x cos(2ω i t), t∈[0,T i ),

[0120] y(t)=A y +B y cos(ω i t)+C y cos(2ω i t), t∈[0,T i ).

[0121] Based on the position and acceleration constraints at the endpoints, the parameters are further solved as follows:

[0122]

[0123]

[0124]

[0125]

[0126]

[0127]

[0128] in, and For the i-th target point p i The acceleration components in the horizontal and vertical directions can be obtained from the (i-1)th segment of the trajectory, and the initial acceleration of the first target point is 0.

[0129] The frequency ω of the dynamic trajectory is measured using TPTI as an indicator. i To optimize, namely:

[0130]

[0131] Where, ω i,g Let be the natural frequency of the robot on the i-th trajectory segment, and k be a constraint on the lowest frequency.

[0132] In the above formula, k = 0.8 is used to prevent production efficiency from being too low and to meet efficiency requirements.

[0133] Optionally, in one embodiment of this application, a trajectory equation is established based on a preset trajectory model, and the trajectory power consumption and torsional performance comprehensive index obtained from the performance evaluation index are used as the optimization target. The dynamic trajectory of the cable-parallel robot is optimized and solved according to preset constraints. This includes: when the trajectory model is a polynomial function model, selecting the order of the polynomial function according to preset constraints, differentiating the trajectory model to obtain the second velocity and second acceleration at each point of the trajectory, analyzing the velocity constraint conditions at the trajectory endpoints to simplify the model, optimizing and solving the time and horizontal acceleration at the termination point of each segment of the dynamic trajectory with the minimum TPTI as the optimization target, and solving the polynomial coefficient parameters according to the position and acceleration constraints at the endpoints.

[0134] For example, such as Figure 4 As shown, Figure 4 This is a schematic diagram of a simulation example and an experimental example of a point-to-point gate-type dynamic trajectory based on a polynomial function model.

[0135] The following section describes point-to-point gate-type dynamic trajectory planning based on a polynomial function model. The robot platform sequentially executes a series of point-to-point dynamic trajectories passing through the target point.

[0136] Two adjacent target points p i With p i+1 The trajectory of the connection is denoted as H. i (t), the gantry-type dynamic trajectory requires the instantaneous velocity of the moving platform at each material pick-up and drop-off target point to be equal to 0 while the acceleration is not equal to 0. Therefore, the i-th segment of the trajectory H i The constraint conditions at the endpoints of (t) are:

[0137] H i (t i ) = p i H i (t i+1 ) = p i+1 ,

[0138]

[0139]

[0140] Optionally, when there are no explicit requirements for the endpoint acceleration, the trajectory must satisfy the constraint condition of acceleration continuity, and the trajectory H... i The constraints at the endpoints of (t) are simplified to:

[0141] H i (t i ) = p i H i (t i+1 ) = p i+1 ,

[0142]

[0143]

[0144] Generally, H i (t) n The dynamic trajectory model of the Fourier series is as follows:

[0145] x i (t)=s x0 +s x1 τ+s x2 τ 2 +s x3 τ 3 +s x4 τ 4 +s x5 τ 5 ,τ∈[0,T i ),

[0146] y i (t)=s y0 +s y1 τ+s y2 τ 2 +s y3 τ 3 +s y4 τ 4 +s y5 τ 5 ,τ∈[0,T i ).

[0147] Therefore, a system of linear equations [A] is established. s A v A a ] T s = [b s b v b a ] T ,in,

[0148] s = [s x0 s x1 s x2 s x3 s x4 s x5 s y0 s y1 s y2 s y3 s y4 s y5 ] T ,

[0149]

[0150]

[0151]

[0152] b s =[x i x i+1 y i y i+1 ],

[0153] b v =[0 0 0 0],

[0154]

[0155] Optionally, applying different vertical accelerations to the endpoints of the polynomial function model trajectory can achieve control of the trajectory gate characteristics.

[0156] The acceleration at the end point of each dynamic trajectory segment and the trajectory running time are optimized using TPTI as the metric:

[0157]

[0158] Among them, T i,g Let k be the motion time calculated based on the natural frequency on the i-th segment of the dynamic trajectory. T To constrain the longest motion time, k a This is a constraint on the maximum endpoint acceleration.

[0159] To prevent excessively low production efficiency, k is taken in the above formula. T =1.2, k a =2

[0160] The dynamic trajectory planning method for a cable-parallel robot with parallel rope constraints proposed in this application can establish a kinematic and dynamic model of the cable-parallel robot based on a preset configuration of the robot with parallel rope constraints. Based on the principle that rope forces in the same direction can be combined, the kinematic and dynamic model of the cable-parallel robot is simplified. Based on the force equivalent model and torque analysis of the parallel ropes, performance evaluation indicators for evaluating the torsional resistance of the moving platform are obtained. For the gate-shaped dynamic trajectory required for palletizing tasks, trajectory equations can be established based on the trajectory model, and the comprehensive index of trajectory power consumption and torsional performance can be used as the optimization objective. Thus, the gate-shaped dynamic trajectory can be obtained by optimizing the solution according to the constraint conditions, realizing the control of the trajectory gate-shaped characteristics. This enriches the configuration and degree of freedom of the cable-parallel robot, effectively improving the constraint capacity of the ropes and meeting the usage requirements of the cable-parallel robot. Therefore, it solves the problems in related technologies, such as the difficulty in enriching the configuration and degree of freedom of cable-parallel robots, certain limitations, reduced rope constraint capacity, and inability to meet the usage requirements of cable-parallel robots.

[0161] Next, referring to the accompanying drawings, a dynamic trajectory planning device for a cable-parallel robot with parallel cable constraints is described according to an embodiment of this application.

[0162] Figure 5 This is a block diagram of a dynamic trajectory planning device for a cable-parallel robot with parallel rope constraints, according to an embodiment of this application.

[0163] like Figure 5 As shown, the dynamic trajectory planning device 10 for parallel rope-constrained cable-parallel robot includes: a setup module 100, a processing module 200, an acquisition module 300, and a control module 400.

[0164] Specifically, module 100 is established to build the kinematic and dynamic model of the cable-parallel robot based on the preset configuration of the cable-parallel robot constrained by parallel ropes.

[0165] The processing module 200 is used to simplify the kinematic and dynamic model of the cable parallel robot based on the principle that cable forces in the same direction can be combined, so as to obtain the final kinematic and dynamic model of the cable parallel robot.

[0166] The acquisition module 300 is used to acquire performance evaluation indicators for evaluating the torsional resistance of the dynamic platform based on the force equivalent model and torque analysis of the parallel cable.

[0167] The control module 400 is used to establish trajectory equations based on a preset trajectory model for the gate-shaped dynamic trajectory required by the palletizing task, based on the final kinematic and dynamic model. It optimizes the dynamic trajectory of the cable-parallel robot according to preset constraints, using the comprehensive index of trajectory power consumption and torsional performance obtained from the performance evaluation index as the optimization target, thereby realizing the control of the trajectory gate-shaped characteristics.

[0168] Optionally, in one embodiment of this application, the final kinematic and dynamic model is:

[0169]

[0170] M k +M q +M0=0,

[0171] Where F1 and F2 are the resultant forces of parallel cables or the forces of a single cable, e1 and e2 are the direction vectors of the cables, m is the mass of the moving platform and the load, and g is the acceleration due to gravity. To accelerate the moving platform, M k M is the torsional moment of the parallel cable. q This refers to the tilting moment of the mechanism.

[0172] Optionally, in one embodiment of this application, the performance evaluation indicators for evaluating the torsional resistance of the moving platform include a torsional resistance indicator and a torsional equilibrium indicator, wherein...

[0173] Torsional resistance index is defined as:

[0174] TRAI=||M km || / ||M g ||,

[0175] Among them, M g This is the reference torque for the load.

[0176] The torsional equilibrium index is defined as follows:

[0177] TRBI = ||M q || / ||M km ||,

[0178] Among them, M qThis refers to the tilting moment of the mechanism.

[0179] Optionally, in one embodiment of this application, the comprehensive index of trajectory power consumption and torsional performance is defined as:

[0180]

[0181] Where W represents the power consumption of the entire dynamic trajectory.

[0182] Optionally, in one embodiment of this application, the control module 400 is further configured to select the order of the Fourier series according to preset constraints when the trajectory model is a Fourier series model, differentiate the trajectory model to obtain the first velocity and first acceleration at each point of the trajectory, analyze the velocity constraint conditions at the trajectory endpoints to simplify the model, solve the coefficient parameters of the Fourier series according to the position and acceleration constraints at the endpoints, and optimize the frequency of the dynamic trajectory with the minimum TPTI as the optimization objective.

[0183] Optionally, in one embodiment of this application, the control module 400 is further configured to select the order of the polynomial function according to preset constraints when the trajectory model is a polynomial function model, differentiate the trajectory model to obtain the second velocity and second acceleration at each point of the trajectory, analyze the velocity constraint conditions at the trajectory endpoints to simplify the model, optimize the time and horizontal acceleration at the endpoint of each dynamic trajectory with the minimum TPTI as the optimization objective, and solve the polynomial coefficient parameters according to the position and acceleration constraints at the endpoints.

[0184] It should be noted that the foregoing explanation of the embodiment of the dynamic trajectory planning method for cable-parallel robots with parallel rope constraints also applies to the dynamic trajectory planning device for cable-parallel robots with parallel rope constraints in this embodiment, and will not be repeated here.

[0185] The dynamic trajectory planning device for a parallel-rope constrained cable-parallel robot proposed in this application can establish a kinematic and dynamic model of the cable-parallel robot based on a preset configuration of the parallel-rope constrained cable-parallel robot. Based on the principle that cable forces in the same direction can be combined, the kinematic and dynamic model of the cable-parallel robot is simplified. Based on the force equivalent model and torque analysis of the parallel cables, performance evaluation indicators for evaluating the torsional resistance of the moving platform are obtained. For the gate-shaped dynamic trajectory required for palletizing tasks, trajectory equations can be established based on the trajectory model, and the comprehensive index of trajectory power consumption and torsional performance can be used as the optimization objective. Thus, the gate-shaped dynamic trajectory can be obtained by optimizing the solution according to the constraint conditions, realizing the control of the trajectory gate-shaped characteristics. This enriches the configuration and degree of freedom of the cable-parallel robot, effectively improving the constraint capacity of the ropes and meeting the usage requirements of the cable-parallel robot. Therefore, it solves the problems in related technologies, such as the difficulty in enriching the configuration and degree of freedom of the cable-parallel robot, its limitations, reduced rope constraint capacity, and inability to meet the usage requirements of the cable-parallel robot.

[0186] Figure 6 A schematic diagram of the structure of an electronic device provided in an embodiment of this application. The electronic device may include:

[0187] The memory 601, the processor 602, and the computer program stored on the memory 601 and capable of running on the processor 602.

[0188] When the processor 602 executes the program, it implements the dynamic trajectory planning method for cable-parallel robots with parallel cable constraints provided in the above embodiments.

[0189] Furthermore, electronic devices also include:

[0190] Communication interface 603 is used for communication between memory 601 and processor 602.

[0191] The memory 601 is used to store computer programs that can run on the processor 602.

[0192] The memory 601 may include high-speed RAM memory, and may also include non-volatile memory, such as at least one disk storage device.

[0193] If the memory 601, processor 602, and communication interface 603 are implemented independently, then the communication interface 603, memory 601, and processor 602 can be interconnected via a bus to complete communication between them. The bus can be an Industry Standard Architecture (ISA) bus, a Peripheral Component Interconnect (PCI) bus, or an Extended Industry Standard Architecture (EISA) bus, etc. Buses can be categorized as address buses, data buses, control buses, etc. For ease of representation, Figure 6 The bus is represented by a single thick line, but this does not mean that there is only one bus or one type of bus.

[0194] Optionally, in a specific implementation, if the memory 601, processor 602, and communication interface 603 are integrated on a single chip, then the memory 601, processor 602, and communication interface 603 can communicate with each other through an internal interface.

[0195] The processor 602 may be a central processing unit (CPU), an application specific integrated circuit (ASIC), or one or more integrated circuits configured to implement the embodiments of this application.

[0196] This application also provides a computer-readable storage medium storing a computer program that, when executed by a processor, implements the above-described dynamic trajectory planning method for a cable-parallel robot with parallel cable constraints.

[0197] In the description of this specification, the references to terms such as "one embodiment," "some embodiments," "example," "specific example," or "some examples," etc., indicate that a specific feature, structure, material, or characteristic described in connection with that embodiment or example is included in at least one embodiment or example of this application. In this specification, the illustrative expressions of the above terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in one or more embodiments or examples. Moreover, without contradiction, those skilled in the art can combine and integrate the different embodiments or examples described in this specification, as well as the features of different embodiments or examples.

[0198] Furthermore, the terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of technical features indicated. Thus, a feature defined as "first" or "second" may explicitly or implicitly include at least one of that feature. In the description of this application, "N" means at least two, such as two, three, etc., unless otherwise explicitly specified.

[0199] Any process or method described in the flowchart or otherwise herein can be understood as representing a module, segment, or portion of code comprising one or N executable instructions for implementing custom logic functions or processes, and the scope of the preferred embodiments of this application includes additional implementations in which functions may be performed not in the order shown or discussed, including substantially simultaneously or in reverse order depending on the functions involved, as should be understood by those skilled in the art to which embodiments of this application pertain.

[0200] The logic and / or steps represented in the flowchart or otherwise described herein, for example, can be considered as a sequenced list of executable instructions for implementing logical functions, and can be embodied in any computer-readable medium for use by, or in conjunction with, an instruction execution system, apparatus, or device (such as a computer-based system, a processor-included system, or other system that can fetch and execute instructions from, an instruction execution system, apparatus, or device). For the purposes of this specification, "computer-readable medium" can be any means that can contain, store, communicate, propagate, or transmit programs for use by, or in conjunction with, an instruction execution system, apparatus, or device. More specific examples (a non-exhaustive list) of computer-readable media include: an electrical connection having one or more wires (electronic device), a portable computer disk drive (magnetic device), random access memory (RAM), read-only memory (ROM), erasable and editable read-only memory (EPROM or flash memory), fiber optic devices, and portable optical disc read-only memory (CDROM). Alternatively, the computer-readable medium may be paper or other suitable media on which the program can be printed, since the program can be obtained electronically by optically scanning the paper or other medium, followed by editing, interpreting, or otherwise processing as necessary, and then stored in a computer memory.

[0201] It should be understood that the various parts of this application can be implemented using hardware, software, firmware, or a combination thereof. In the above embodiments, the N steps or methods can be implemented using software or firmware stored in memory and executed by a suitable instruction execution system. If implemented in hardware, as in another embodiment, it can be implemented using any one or a combination of the following techniques known in the art: discrete logic circuits having logic gates for implementing logical functions on data signals, application-specific integrated circuits (ASICs) having suitable combinational logic gates, programmable gate arrays (PGAs), field-programmable gate arrays (FPGAs), etc.

[0202] Those skilled in the art will understand that all or part of the steps of the methods in the above embodiments can be implemented by a program instructing related hardware. The program can be stored in a computer-readable storage medium, and when executed, the program includes one or a combination of the steps of the method embodiments.

[0203] Furthermore, the functional units in the various embodiments of this application can be integrated into a processing module, or each unit can exist physically separately, or two or more units can be integrated into a module. The integrated module can be implemented in hardware or as a software functional module. If the integrated module is implemented as a software functional module and sold or used as an independent product, it can also be stored in a computer-readable storage medium.

[0204] The storage medium mentioned above can be a read-only memory, a disk, or an optical disk, etc. Although embodiments of this application have been shown and described above, it is understood that the above embodiments are exemplary and should not be construed as limiting this application. Those skilled in the art can make changes, modifications, substitutions, and variations to the above embodiments within the scope of this application.

Claims

1. A dynamic trajectory planning method for parallel cable-constrained cable parallel robots, characterized in that, Includes the following steps: Based on the pre-defined configuration of the cable-parallel robot constrained by parallel ropes, a kinematic and dynamic model of the cable-parallel robot is established. Based on the principle that cable forces in the same direction can be combined, the kinematic and dynamic model of the cable-parallel robot is simplified to obtain the final kinematic and dynamic model of the cable-parallel robot, wherein the final kinematic and dynamic model is as follows: ， ， wherein, with is the parallel cable resultant or single cable force, with is the cable direction vector, is the moving platform and payload mass, is the gravitational acceleration, is the moving platform acceleration, is the parallel cable torsional moment, is the mechanism self-tilting moment; Based on the force equivalent model and torque analysis of parallel cables, performance evaluation indicators for assessing the torsional resistance of the dynamic platform are obtained. These indicators include a torsional resistance index and a torsional equilibrium index. The torsional resistance index TRAI is defined as follows: ， in, The load reference torque; The torsional equilibrium index TRBI is defined as follows: ， in, For the tilting moment of the mechanism; and Based on the final kinematics and dynamics model, for the gate-shaped dynamic trajectory required by the palletizing task, a trajectory equation is established based on a preset trajectory model. Using the trajectory power consumption and torsional performance comprehensive index (TPTI) obtained from the performance evaluation index as the optimization objective, the gate-shaped dynamic trajectory of the cable-parallel robot is optimized and solved according to preset constraints, thereby achieving control over the trajectory gate-shaped characteristics. The trajectory power consumption and torsional performance comprehensive index (TPTI) is defined as follows: ， in, TTRBI represents the power consumption of the entire dynamic trajectory, TTRAI represents the trajectory cable force torsional balance index, and TTRAI represents the trajectory cable force torsional resistance index.

2. The method according to claim 1, characterized in that, The process involves establishing a trajectory equation based on a preset trajectory model, and using the comprehensive index of trajectory power consumption and torsional performance obtained from the performance evaluation index as the optimization objective. The process then optimizes and solves the portal dynamic trajectory of the cable-parallel robot according to preset constraints, including: When the trajectory model is a Fourier series model, the order of the Fourier series is selected according to the preset constraints. The derivative of the trajectory model is obtained to get the first velocity and the first acceleration at each point of the trajectory. The velocity constraint at the endpoint of the trajectory is analyzed to simplify the model. The coefficient parameters of the Fourier series are solved according to the position and acceleration constraints at the endpoint. The frequency of the dynamic trajectory is optimized with the minimum TPTI as the optimization objective.

3. The method according to claim 1, characterized in that, The process involves establishing a trajectory equation based on a preset trajectory model, and using the comprehensive index of trajectory power consumption and torsional performance obtained from the performance evaluation index as the optimization objective. The process then optimizes and solves the portal dynamic trajectory of the cable-parallel robot according to preset constraints, including: When the trajectory model is a polynomial function model, the order of the polynomial function is selected according to the preset constraints. The derivative of the trajectory model is obtained to obtain the second velocity and second acceleration at each point of the trajectory. The velocity constraint conditions at the trajectory endpoints are analyzed to simplify the model. The time and horizontal acceleration at the endpoint of each dynamic trajectory are optimized with the minimum TPTI as the optimization objective. The polynomial coefficient parameters are solved according to the position and acceleration constraints at the endpoints.

4. A dynamic trajectory planning device for a cable-parallel robot with parallel cable constraints, characterized in that, include: A module is established to build the kinematic and dynamic model of the cable-parallel robot based on a preset configuration of the cable-parallel robot constrained by parallel ropes. The processing module is used to simplify the kinematic and dynamic model of the cable-parallel robot based on the principle that cable forces in the same direction can be combined, to obtain the final kinematic and dynamic model of the cable-parallel robot, wherein the final kinematic and dynamic model is as follows: ， ， in, and It can be the resultant force of parallel cables or the force of a single cable. and Let the direction vector of the rope be . For dynamic platform and load quality, It is the acceleration due to gravity. To accelerate the platform, For the torsional moment of the parallel cable, The self-tilting moment of the mechanism; The acquisition module is used to acquire performance evaluation indicators for assessing the torsional resistance of the dynamic platform based on the force equivalent model and torque analysis of the parallel cables. These performance evaluation indicators include a torsional resistance indicator and a torsional equilibrium indicator. The torsional resistance indicator TRAI is defined as follows: ， in, The load reference torque; The torsional equilibrium index TRBI is defined as follows: ， in, For the tilting moment of the mechanism; and The control module is used to establish trajectory equations based on a preset trajectory model, targeting the gate-shaped dynamic trajectory required for the palletizing task, based on the final kinematics and dynamics model. Using the trajectory power consumption and torsional performance comprehensive index (TPTI) obtained from the performance evaluation index as the optimization objective, it optimizes and solves the gate-shaped dynamic trajectory of the cable-parallel robot according to preset constraints, thereby achieving control over the gate-shaped trajectory characteristics. The trajectory power consumption and torsional performance comprehensive index (TPTI) is defined as follows: ， in, TTRBI represents the power consumption of the entire dynamic trajectory, TTRAI represents the trajectory cable force torsional balance index, and TTRAI represents the trajectory cable force torsional resistance index.

5. The apparatus according to claim 4, characterized in that, The control module is further configured to, when the trajectory model is a Fourier series model, select the order of the Fourier series according to the preset constraints, differentiate the trajectory model to obtain the first velocity and first acceleration at each point of the trajectory, analyze the velocity constraints at the trajectory endpoints to simplify the model, solve the coefficient parameters of the Fourier series according to the position and acceleration constraints at the endpoints, and optimize the frequency of the dynamic trajectory with the minimum TPTI as the optimization objective.

6. The apparatus according to claim 4, characterized in that, The control module is further configured to, when the trajectory model is a polynomial function model, select the order of the polynomial function according to the preset constraints, differentiate the trajectory model to obtain the second velocity and second acceleration at each point of the trajectory, analyze the velocity constraints at the trajectory endpoints to simplify the model, optimize the time and horizontal acceleration at the endpoint of each dynamic trajectory with the minimum TPTI as the optimization objective, and solve the polynomial coefficient parameters according to the position and acceleration constraints at the endpoints.

7. An electronic device, characterized in that, include: The system includes a memory, a processor, and a computer program stored in the memory and executable on the processor, the processor executing the program to implement the dynamic trajectory planning method for a cable-parallel robot with parallel cable constraints as described in any one of claims 1-3.

8. A computer-readable storage medium having a computer program stored thereon, characterized in that, The program is executed by the processor to implement the dynamic trajectory planning method for cable-parallel robots with parallel cable constraints as described in any one of claims 1-3.

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