CN116276990A - Two-degree-of-freedom parallel structure kinematics positive solution method based on neural network training - Google Patents

Two-degree-of-freedom parallel structure kinematics positive solution method based on neural network training Download PDF

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CN116276990A
CN116276990A CN202310203492.3A CN202310203492A CN116276990A CN 116276990 A CN116276990 A CN 116276990A CN 202310203492 A CN202310203492 A CN 202310203492A CN 116276990 A CN116276990 A CN 116276990A
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任俊琦
张航
刘凯
庹华
韩峰涛
于文进
韩建欢
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Abstract

The invention provides a two-degree-of-freedom parallel structure kinematics forward solution method based on neural network training, which comprises the following steps: calculating the inverse solution of the two-degree-of-freedom parallel structure of the robot; according to the requirements of the two-degree-of-freedom parallel structure in a task, setting the attitude space of the tail end O point; dividing the gesture space of the tail end O point according to a preset step length to obtain gestures of a plurality of groups of O points, and respectively obtaining corresponding joint angles A1 and A2 according to the inverse kinematics solution obtained in the step S1; setting a neural network for training, and training to obtain a nonlinear mapping relation between the neural network and the training; analyzing the results of the neural network verification set and the test set, and if the errors meet the error requirements, using the nonlinear mapping relation obtained by training as the solution of the kinematic positive solution; and packaging the obtained nonlinear mapping relation and bringing the nonlinear mapping relation into a robot controller.

Description

Two-degree-of-freedom parallel structure kinematics positive solution method based on neural network training
Technical Field
The invention relates to the technical field of industrial robots, in particular to a two-degree-of-freedom parallel structure kinematics positive solution method based on neural network training.
Background
In addition to the serial configuration, the parallel configuration is also relatively common and widely used in the configuration of robots. For example, a legged robot Cassie, moves motors controlling the knees and ankles of the robot to the hips and knees, respectively, by using a two-degree-of-freedom parallel structure. Compared with a serial mechanism, the parallel mechanism has two advantages, namely, the mass in the robot can occupy a larger motor moving position, so that the moment of inertia of the whole mechanism is reduced, and a better control effect is realized; and secondly, the parallel structure has higher bearing capacity and higher reliability.
However, the parallel structure has a more complex structure, so that it is more difficult to solve the forward and reverse solutions of the robot kinematics than the serial structure. Taking a two-degree-of-freedom parallel structure commonly used for a mechanical arm and a legged robot as an example, as shown in fig. 1. Solving the inverse kinematics solution is relatively easy, namely knowing the pose of the end O point, and the angles of the joints A1 and A2 can be solved through the geometric relationship.
The difficulty is to solve the kinematic orthotopic of such structures, i.e. how to know the pose of the terminal O-point, knowing the angles of joints A1 and A2. Solving the analytic solution requires solving a binary nonlinear equation set, the direct solving difficulty is high, and the accurate solution cannot be ensured. Therefore, the existing technical scheme mainly uses a general numerical method to solve: the angles θ1 and θ2 of the joints A1 and A2 are known. Giving an initial attitude value to the terminal O point, and solving a kinematic inverse solution to obtain angles theta 1 'and theta 2' corresponding to the joints A1 and A2. Calculating an error between theta 1 theta 2 and theta 1 'theta 2', and if the error meets the requirement, obtaining a solving result; if the error does not meet the requirement, updating the estimated value of the terminal gesture, and repeating the process until a result meeting the error requirement is obtained.
The main defects and shortcomings of the technical mode are as follows: the time complexity of solving the kinematic positive solution of the two-degree-of-freedom parallel structure by a numerical method is high, and the time for solving the high-precision solution is long. Under the scene with certain requirements on the calculation speed and precision, the effect of the solving mode of the numerical method is limited.
Disclosure of Invention
The object of the present invention is to solve at least one of the technical drawbacks.
Therefore, the invention aims to provide a two-degree-of-freedom parallel structure kinematics positive solution method based on neural network training.
In order to achieve the above object, an embodiment of the present invention provides a two-degree-of-freedom parallel structure kinematic orthometric solution method based on neural network training, including the steps of:
step S1, calculating the inverse solution of a two-degree-of-freedom parallel structure of the robot;
s2, setting the attitude space of the tail end O point according to the requirements of the two-degree-of-freedom parallel structure in a task;
step S3, dividing the gesture space of the tail end O point according to a preset step length to obtain gestures of a plurality of groups of O points, and respectively obtaining corresponding joint angles A1 and A2 according to the inverse kinematics solution obtained in the step S1;
step S4, setting a neural network for training; taking the posture of the 0 point and the joint angles of the corresponding A1 and A2 in the step S3 as basic data sets to be brought into a nerve network, and training to obtain a nonlinear mapping relation between the posture and the joint angles;
s5, analyzing results of a neural network verification set and a test set, wherein errors between the actual gesture of the tail end 0 point and calculation results of the verification set and the test set are mainly concentrated near-0.00768 radians, and the maximum error is 0.01545 radians; if the error meets the requirement on the accuracy of the kinematic positive solution of the parallel structure, the nonlinear mapping relation obtained by training is used for solving the kinematic positive solution; if the error requirement is not met, modifying the neural network, and repeating the operation again until a nonlinear mapping relation meeting the error requirement is obtained;
and S6, packaging the obtained nonlinear mapping relation and bringing the nonlinear mapping relation into a robot controller.
Further, in said step S1, for the structure shown in fig. 1 in the appendix, the following geometrical relationship equation exists:
1 rod ＝||r Bi -r Ci ||
Figure BDA0004109938460000021
Figure BDA0004109938460000022
Figure BDA0004109938460000023
solving the above equation can result in angles θ1 and θ2 of joint angles A1 and A2:
Figure BDA0004109938460000024
wherein:
Figure BDA0004109938460000025
Figure BDA0004109938460000026
Figure BDA0004109938460000027
l bar ＝||r Bi -r Ai ||
l rod ＝||r Bi -r Ci ||
l spacing ＝||r A1 -r A2 ||
r x is the vector from the O point to the X point in the terminal coordinate system, 0 r x the vector from the O point to the X point in the terminal coordinate system when the terminal gesture is 0 under the initial condition is represented, and the X point refers to any point; r is R y (θ i ) Indicating the joint angle theta i A rotation transformation matrix at the time; x is x rot A rotation transformation matrix for the tip pose; i=1, 2; l (L) spacing Is r A1 ,r A2 The 2 nd order norm of the two vectors subtracted, other parameters and so on.
Further, the steps S1 to S5 are offline processes.
According to the two-degree-of-freedom parallel structure kinematic forward solution method based on neural network training, the two-degree-of-freedom parallel structure kinematic forward solution is calculated by using a neural network training mode. Has the following beneficial effects:
1. the neural network training process can be performed offline, and the mapping relation between the two joint angles and the tail end gesture is calculated in advance, so that the time consumption is shorter than that of other methods for solving the kinematics of the two-degree-of-freedom parallel structure (such as a digital solution method) in calculation, and the requirements of different working conditions on the calculation speed of a control algorithm are met.
2. The application is wide, and the operability is strong. Other structures that facilitate solving the inverse kinematics solution but do not change solving the positive kinematics solution can be solved kinematically using the same method.
Additional aspects and advantages of the invention 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 the invention.
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The foregoing and/or additional aspects and advantages of the invention will become apparent and may be better understood from the following description of embodiments taken in conjunction with the accompanying drawings in which:
FIG. 1 is a two degree of freedom parallel block diagram for a robotic arm and legged robot;
fig. 2 is a flowchart of a two-degree-of-freedom parallel structure kinematic forward solution method based on neural network training according to an embodiment of the present invention.
FIG. 3 is an example of accuracy of a training set, validation set, and test set obtained after training of a neural network, with the abscissa being the error value between the end pose and the kinematic positive solution calculated by the neural network; the ordinate represents the number of data in each dataset. The histogram a part represents the training set, the B part represents the validation set, the C part represents the test set, and the D part represents the zero error baseline.
Detailed Description
Embodiments of the present invention are described in detail below, examples of which are illustrated in the accompanying drawings, wherein like or similar reference numerals refer to like or similar elements or elements having like or similar functions throughout. The embodiments described below by referring to the drawings are illustrative and intended to explain the present invention and should not be construed as limiting the invention.
The invention provides a two-degree-of-freedom parallel structure kinematics positive solution method based on neural network training, which adopts a strategy of neural network training to solve the two-degree-of-freedom parallel structure kinematics positive solution.
As shown in fig. 2, the two-degree-of-freedom parallel structure kinematic forward solution method based on neural network training in the embodiment of the invention includes the following steps:
step S1, calculating the inverse solution of the two-degree-of-freedom parallel structure of the robot.
In step S1, for the structure shown in fig. 1 in the appendix, the following geometrical relationship equation exists:
1 rod ＝||r Bi -r Ci ||
Figure BDA0004109938460000041
Figure BDA0004109938460000042
Figure BDA0004109938460000043
solving the above equation can result in angles θ1 and θ2 of joint angles A1 and A2:
Figure BDA0004109938460000044
wherein:
Figure BDA0004109938460000047
Figure BDA0004109938460000045
Figure BDA0004109938460000046
l bar ＝||r Bi -r Ai ||
l rod ＝||r Bi -r Ci ||
l spacing ＝||r A1 -r A2 ||
r x is a vector from 0 point to X point in the terminal coordinate system, 0 r x a vector from 0 point to X point in the terminal coordinate system when the terminal gesture is 0 in the initial condition, wherein X point refers to any point in the figure 1 of the attached book, such as A1, B2, C1 and the like; r is R y (θ i ) Indicating the joint angle theta i A rotation transformation matrix at the time; x is x rot A rotation transformation matrix for the tip pose; i=1, 2; l (L) spacing Is r A1 ，r A2 The 2 nd order norm of the two vectors subtracted, other parameters and so on.
And S2, setting the attitude space of the terminal 0 point according to the requirements of the two-degree-of-freedom parallel structure in the task.
And S3, dividing the gesture space of the terminal 0 point according to a preset step length to obtain a plurality of groups of gestures of the 0 point, and obtaining corresponding joint angles A1 and A2 according to the inverse kinematics solution obtained in the step S1.
Step S4, setting a neural network for training; taking the posture of the O point and the joint angles of the corresponding A1 and A2 in the step S3 as basic data sets to be brought into a nerve network, and training to obtain a nonlinear mapping relation between the O point and the joint angles.
Specifically, the more the number of layers of the neural network, the longer the calculation time and the higher the result accuracy.
Step S5, analyzing the results of the verification set and the test set of the neural network, taking the neural network trained in the figure 3 as an example, wherein errors between the actual posture of the tail end O point and the calculation results of the verification set and the test set are mainly concentrated near-0.00768 radians, and the maximum error is 0.01545 radians; if the error meets the requirement on the accuracy of the kinematic positive solution of the parallel structure, the nonlinear mapping relation obtained by training is used for solving the kinematic positive solution; if the error requirement is not met, modifying the neural network, and repeating the operation again until the nonlinear mapping relation meeting the error requirement is obtained.
And S6, packaging the obtained nonlinear mapping relation and bringing the nonlinear mapping relation into a robot controller.
Specifically, steps S1 to S5 are offline processes. And packaging the obtained mapping relation and putting the mapping relation into a robot controller.
According to the two-degree-of-freedom parallel structure kinematic forward solution method based on neural network training, the two-degree-of-freedom parallel structure kinematic forward solution is calculated by using a neural network training mode. Has the following beneficial effects:
1. the neural network training process can be performed offline, and the mapping relation between the two joint angles and the tail end gesture is calculated in advance, so that the time consumption is shorter than that of other methods for solving the kinematics of the two-degree-of-freedom parallel structure (such as a digital solution method) in calculation, and the requirements of different working conditions on the calculation speed of a control algorithm are met.
2. The application is wide, and the operability is strong. Other structures that facilitate solving the inverse kinematics solution but do not change solving the positive kinematics solution can be solved kinematically using the same method.
In the description of the present specification, a description referring to terms "one embodiment," "some embodiments," "examples," "specific examples," or "some examples," etc., means that a particular feature, structure, material, or characteristic described in connection with the embodiment or example is included in at least one embodiment or example of the present invention. In this specification, schematic representations of the above terms do not necessarily refer to the same embodiments or examples. Furthermore, the particular features, structures, materials, or characteristics described may be combined in any suitable manner in any one or more embodiments or examples.
Although embodiments of the present invention have been shown and described above, it will be understood that the above embodiments are illustrative and not to be construed as limiting the invention, and that variations, modifications, alternatives, and variations may be made in the above embodiments by those skilled in the art without departing from the spirit and principles of the invention. The scope of the invention is defined by the appended claims and equivalents thereof.

Claims (3)

1. The two-degree-of-freedom parallel structure kinematic forward solution method based on neural network training is characterized by comprising the following steps of:
step S1, calculating the inverse solution of a two-degree-of-freedom parallel structure of the robot;
s2, setting the attitude space of the tail end O point according to the requirements of the two-degree-of-freedom parallel structure in a task;
step S3, dividing the gesture space of the tail end O point according to a preset step length to obtain gestures of a plurality of groups of O points, and respectively obtaining corresponding joint angles A1 and A2 according to the inverse kinematics solution obtained in the step S1;
step S4, setting a neural network for training; taking the posture of the O point and the joint angles of the corresponding A1 and A2 in the step S3 as basic data sets to be brought into a nerve network, and training to obtain a nonlinear mapping relation between the O point and the joint angles;
s5, analyzing results of a neural network verification set and a test set, wherein errors between actual postures of the tail end O points and calculation results of the verification set and the test set are mainly concentrated near-0.00768 radians, and the maximum error is 0.01545 radians; if the error meets the requirement on the accuracy of the kinematic positive solution of the parallel structure, the nonlinear mapping relation obtained by training is used for solving the kinematic positive solution; if the error requirement is not met, modifying the neural network, and repeating the steps S1 to S5 again until a nonlinear mapping relation meeting the error requirement is obtained;
and S6, packaging the obtained nonlinear mapping relation and bringing the nonlinear mapping relation into a robot controller.
2. The two-degree-of-freedom parallel structure kinematic orthometric solution based on neural network training of claim 1, wherein in said step S1, the following geometrical relationship equation exists:
l rod ＝||r Bi -r Ci ||
Figure FDA0004109938450000011
Figure FDA0004109938450000012
Figure FDA0004109938450000013
solving the above equation can result in angles θ1 and θ2 of joint angles A1 and A2:
Figure FDA0004109938450000014
wherein:
Figure FDA0004109938450000021
r x is the vector from the O point to the X point in the terminal coordinate system, 0 r x the vector from the O point to the X point in the terminal coordinate system when the terminal gesture is 0 under the initial condition is represented, and the X point refers to any point; r is R y (θ i ) Indicating the joint angle theta i A rotation transformation matrix at the time; x is x rot A rotation transformation matrix for the tip pose; i=1, 2; l (L) spacing Is r A1 ,r A2 The 2 nd order norm of the two vectors subtracted, other parameters and so on.
3. The two-degree-of-freedom parallel structure kinematic forward solution method based on neural network training of claim 1, wherein the steps S1 to S5 are offline processes.
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Cited By (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN117609673A (en) * 2024-01-24 2024-02-27 中南大学 Six-degree-of-freedom parallel mechanism forward solution method based on physical information neural network

Cited By (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN117609673A (en) * 2024-01-24 2024-02-27 中南大学 Six-degree-of-freedom parallel mechanism forward solution method based on physical information neural network
CN117609673B (en) * 2024-01-24 2024-04-09 中南大学 Six-degree-of-freedom parallel mechanism forward solution method based on physical information neural network

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