Motion prediction method of robot under time-varying and time-delay conditions

Abstract

The invention discloses a motion prediction method of a robot under time-varying and time-delay conditions. The number of secondary predictors and gain parameters are determined according to the maximum value of time delay, the initial joint position of the robot and the initial joint speed; determining a time-varying prediction interval of each secondary predictor according to the time delay changing along with time; dividing the state of the robot from the time-lag motion to the current motion interval into motion sub-states with the same number as the secondary predictors; constructing secondary predictors of which the number is the same as that of the motion sub-states; the secondary predictors are connected in series one by one, the time-varying and time-delay robot joint position and joint speed signals serve as the input of the first secondary predictor, and the predicted value output by the previous secondary predictor serves as the input of the next secondary predictor; the robot joint position and speed prediction method is high in prediction precision, wide in application range, easy to apply and popularize in engineering, and beneficial to promoting development of the robot technology.

Description

Technical Field

[0001] The present invention relates to the field of robot sensing and control, and in particular to a method for predicting robot motion under time-varying delay conditions. Background Art

[0002] Robotics plays an increasingly important role in many fields. From industrial manufacturing to medical care, from scientific exploration to home services, the application scenarios of robots are constantly expanding. With the increasing application of robots, the precise control and prediction of their movements have become key issues. In practical applications, robots often face complex working environments, among which time-varying delay is a challenge that cannot be ignored. Time-varying delay may be caused by many factors, such as the instability of the communication network, the delay of sensor data transmission, and the change of processing time of the control system. This time-varying delay will have many adverse effects on the robot's motion control. In traditional robot motion control, it is usually assumed that the delay is fixed or negligible. However, in reality, the existence of time-varying delay causes a deviation between the actual movement of the robot and the expected movement, reducing the accuracy and stability of the movement. Time-varying delay may cause the robot's action to lag and fail to respond to control instructions in time, thereby affecting the quality and efficiency of the robot's task execution. In some fields with high safety requirements, such as medical surgical robots and unmanned robots, time-varying delay may cause serious safety issues. If the robot cannot accurately predict and adapt to the change of delay, it may cause harm to patients or pedestrians. However, when faced with time-varying delays, traditional prediction methods are unable to timely and effectively adjust and optimize prediction strategies, which results in a large deviation between the prediction results and the actual robot motion state. Therefore, it is necessary to study a prediction method that can effectively adapt to time-varying delays. Summary of the invention

[0003] The purpose of the present invention is to provide a method for predicting the motion of a robot under time-varying delay conditions. Under the condition that the delay is known, the prediction intervals of predictors at each level are determined so that the robot's current actual joint position and joint velocity can be predicted in real time based on the robot's joint position and joint velocity signals whose delay size varies with time.

[0004] In order to solve the above technical problems, the technical solution of the present invention is: a motion prediction method of a robot under time-varying delay conditions, comprising the following steps:

[0005] S1: Based on the nonlinear dynamic model of the n-DOF robot, according to the maximum value of the delay τ max , robot initial joint position q 10 and the robot's initial joint velocity q 20 , determine the number m of secondary predictors and the gain parameter K of the secondary predictors;

[0006] S2: Determine the time-varying prediction interval Δ of each secondary predictor based on the number m of secondary predictors and the time delay size τ(t) that varies with time i (t);

[0007] S3: Time-varying prediction interval Δ according to each secondary predictor i (t) Divide the robot's state from the time-delay motion to the current motion interval into m motion sub-states, the same number as the secondary predictors;

[0008] S4: According to the m motion sub-states divided in step S3, construct m secondary predictors, which are the same in number as the motion sub-states, to predict the corresponding motion sub-states;

[0009] S5: Connect the corresponding m secondary predictors in series according to the order of motion sub-states, use the time-varying and delayed robot joint position and joint velocity signals as the input of the first secondary predictor, and use the predicted value output by the previous secondary predictor as the input of the next secondary predictor. The last secondary predictor outputs the predicted value of the robot's actual joint position and actual joint velocity, which is used to predict the robot's current actual joint position and joint velocity in real time.

[0010] Preferably, in step S1, according to the robot's initial joint position q 10 and the robot's initial joint velocity q 20 , determine the gain parameter K of the secondary predictor, and the calculation formula is as follows:

[0011]

[0012] Among them, q 10 is the initial joint position of the robot, q 20 is the initial joint velocity of the robot.

[0013] Preferably, in step S1, according to the maximum value τ of the delay max Determine the number of secondary predictors m, calculated as follows:

[0014]

[0015] Where K is the gain parameter of the secondary predictor.

[0016] Preferably, in step S2, the time-varying prediction interval Δ of the secondary predictor i (t), the calculation formula is as follows:

[0017]

[0018] Among them, T i(t) is an auxiliary variable, τ(t) is the time delay that varies with time, t is a time variable, m is the number of secondary predictors, i = 1, 2, ..., m.

[0019] Preferably, in step S3, by x τ i (t) = [x 1i (t)x 2i (t)] represents the m motion sub-states, and the element x in each motion sub-state 1i (t) and x 2i (t), the expression is as follows:

[0020]

[0021] Among them, x1(t) is the joint position of the multi-degree-of-freedom robot, x2(t) is the joint velocity of the multi-degree-of-freedom robot, i=1,2,…,m represents the number of the motion sub-state, τ(t) is the time delay size that changes with time, Δ i (t) is the time-varying prediction interval of the secondary predictor, and t is the time variable.

[0022] Preferably, in step S4, the secondary predictor is constructed by a prediction algorithm represented by a set of m equations, and the expression is as follows:

[0023]

[0024] in, is an auxiliary variable with no specific meaning, K is the gain parameter of the secondary predictor, t is the time variable, and Represents the prediction result of the robot's motion sub-state. The prediction results of the robot's actual joint position and actual joint velocity are output by the last secondary predictor, that is, and f(.) is the robot dynamics equation function, u is the robot control input, r i (t) is the error calibration term.

[0025] Preferably, the error calibration term r i (t), the calculation formula is as follows:

[0026]

[0027] Where α is another gain parameter of the secondary predictor, and its value range is 0.5<α<1.5; Δ i (t) is the time-varying prediction interval of the secondary predictor; y 1i (t) and y 2i (t) input joint position and joint velocity signals to the secondary predictor;

[0028] When i=1, y 1i =x1(t-τ),y 2i =x2(t-τ), which is the robot joint position and joint velocity signals with time-varying delay;

[0029] When i=2,…,m, That is, the previous secondary predictor outputs prediction signals of the robot's joint positions and joint velocities.

[0030] Compared with the prior art, the present invention has the following beneficial effects: (1) by determining the time-varying prediction interval of the secondary prediction, the same series structure as that under the fixed delay condition is adopted under the time-varying delay condition, thereby overcoming the problem that the fixed delay algorithm is not applicable under the time-varying delay condition. Compared with the traditional method, the present invention significantly improves the adaptability of the algorithm; (2) by reasonably dividing the time-varying prediction interval and constructing the secondary predictor, each secondary predictor only performs relatively simple calculations within its specific time-varying prediction interval, which can effectively improve the prediction efficiency; the present invention has a certain robustness to the change of the delay, that is, when the delay changes significantly, since the prediction interval of the secondary predictor can be adaptively adjusted, the robot's motion state can still be accurately predicted. This robustness is of great significance in the complex and changeable actual working environment and helps to promote the development of robot technology. BRIEF DESCRIPTION OF THE DRAWINGS

[0031] In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the accompanying drawings required for use in the description of the embodiments of the present invention will be briefly introduced below. Obviously, the accompanying drawings in the following description are only some embodiments of the present invention. For ordinary technicians in this field, other accompanying drawings can be obtained based on these accompanying drawings without paying creative work.

[0032] Figure 1 It is a schematic diagram of the overall system of the robot motion prediction method of the present invention;

[0033] Figure 2 It is a schematic diagram of the time-varying prediction interval of the secondary predictor in the present invention;

[0034] Figure 3 This is a schematic diagram of the construction principle of a single secondary predictor in the present invention whose prediction interval changes with time. DETAILED DESCRIPTION

[0035] The following is a further detailed description of the present invention in conjunction with the accompanying drawings. The terminal technical solution of the embodiment of the present invention is clearly and completely described. Obviously, the described embodiment is a part of the embodiment of the present invention, not all of the embodiments. Based on the embodiment of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0036] The present invention is dedicated to solving the problem of delayed transmission of robot motion state information due to time-varying communication delay. Based on the nonlinear dynamic model of the n-DOF robot, a prediction method for the joint position and joint velocity during robot motion is designed. The present invention redefines the time-varying prediction interval for each secondary predictor to cope with the time-varying delay. Based on the robot joint position and joint velocity signals with time-varying delay, the actual joint position and joint velocity of the robot can be predicted in real time and accurately.

[0037] like Figure 1 As shown, the present invention discloses a method for predicting the motion of a robot under time-varying delay conditions, comprising the following steps:

[0038] S1: Based on the nonlinear dynamic model of the n-DOF robot, according to the maximum value of the delay τ max , robot initial joint position q 10 and the robot's initial joint velocity q 20 , determine the number m of secondary predictors and the gain parameter K of the secondary predictors.

[0039] The nonlinear dynamic model of the n-DOF robot is expressed as follows:

[0040]

[0041] Where x1∈R n , x2∈R n Respectively represent the joint position and joint velocity of the n-DOF robot, M(x1)∈R n×n is the inertia matrix of the n-DOF robot, C(x1,x2)∈R n×n is the centrifugal force and Coriolis force matrix, u∈R n is the control input of the robot, d∈R n For unknown dynamics and disturbances.

[0042] The model is further rewritten as the following expression:

[0043]

[0044] Define the robot dynamics equation function f(x1,x2,u)=M -1(x1)[u(t)-C(x1,x2)x2(t)].

[0045] According to the robot's initial joint position q 10 and the robot's initial joint velocity q 20 , determine the gain parameter K of the secondary predictor in the robot motion prediction system, and the calculation formula is as follows:

[0046]

[0047] Among them, q 10 is the initial joint position of the robot, q 20 is the initial joint velocity of the robot.

[0048] Generally speaking, a suitable K value helps improve the stability of the robot motion prediction system. If K is too large or too small, the robot motion prediction system will become unstable or the prediction effect will deteriorate. When the value of K is too large, the robot motion prediction system will respond too strongly to the error, resulting in oscillation or even instability. When the value of K is too small, the robot motion prediction system will have insufficient error correction ability, slow response, and unable to effectively predict the desired trajectory.

[0049] According to the preset maximum delay value τ max Determine the number m of secondary predictors required in the robot motion prediction system, and the calculation formula is as follows:

[0050]

[0051] Where K is the gain parameter of the secondary predictor. The minimum number of required secondary predictors can be obtained through the above inequality.

[0052] S2: Determine the time-varying prediction interval Δ of each secondary predictor based on the number m of secondary predictors and the time delay size τ(t) that varies with time i (t), the specific calculation formula is as follows:

[0053]

[0054] Among them, T i (t) is an auxiliary variable, τ(t) is the time delay that varies with time, t is a time variable, m is the number of secondary predictors, i = 1, 2, ..., m.

[0055] The time-varying prediction interval of each secondary predictor can be easily obtained through the above two calculation formulas, such as Figure 2 As shown, it should be noted that the time delay size τ(t) that varies with time must be used as the input of the time-varying prediction interval generation module in order to calculate the time-varying prediction interval of each secondary predictor.

[0056] S3: Time-varying prediction interval Δ according to each secondary predictor i (t) Divide the robot's state from the time-delay motion to the current motion interval into m motion sub-states, the same number as the secondary predictors.

[0057] By x τ i (t) = [x 1i (t)x 2i (t)] represents the m motion sub-states, and the element x in each motion sub-state 1i (t) and x 2i (t), the expression is as follows:

[0058]

[0059] Among them, x1(t) is the joint position of the multi-degree-of-freedom robot, x2(t) is the joint velocity of the multi-degree-of-freedom robot, i=1,2,…,m represents the number of the motion sub-state, τ(t) is the time delay size that changes with time, Δ i (t) is the time-varying prediction interval of the secondary predictor, and t is the time variable. It should be noted that the above two expressions represent the physical meaning of each motion sub-state, rather than the calculation method. After the motion sub-state is established, it is not necessary to calculate its value.

[0060] S4: According to the m motion sub-states divided in step S3, construct m secondary predictors which are the same in number as the motion sub-states, for predicting the corresponding motion sub-states.

[0061] The secondary predictor is constructed by a prediction algorithm represented by a set of m equations, as follows:

[0062]

[0063] in, is the auxiliary variable, K is the gain parameter of the secondary predictor, t is the time variable, and Represents the prediction result of the robot's motion sub-state. The prediction results of the robot's actual joint position and actual joint velocity are output by the last secondary predictor, that is, and f(.) is the robot dynamics equation function, u is the robot control input, r i (t) is the error calibration term.

[0064] Preferably, the error calibration term r i (t), the calculation formula is as follows:

[0065]

[0066] Where α is another gain parameter of the secondary predictor, and its value range is 0.5<α<1.5; Δ i (t) is the time-varying prediction interval of the secondary predictor; y 1i (t) and y 2i (t) input joint position and joint velocity signals to each secondary predictor;

[0067] When i=1, y 1i =x1(t-τ),y 2i =x2(t-τ), which is the robot joint position and joint velocity signals with time-varying delay;

[0068] When i=2,…,m, That is, the previous secondary predictor outputs prediction signals of the robot's joint positions and joint velocities.

[0069] As can be seen from the above formula, each secondary predictor has the same structure except for the input signal and the time-varying prediction interval. The input of the first secondary predictor is the delayed robot joint position and joint velocity signal, while the subsequent secondary predictor uses the output of the previous secondary predictor as input. According to the above algorithm, the construction principle of the secondary predictor is as follows: Figure 3 As shown in the figure, building a secondary predictor requires: gain module, integral module, differential module, summation (difference) module, multiplication (division) module, constant input module and delay module.

[0070] Then, the measured time delay size τ(t) that varies with time is used as the input of the time-varying prediction interval generation module to determine the time-varying prediction interval Δ of each secondary predictor. i (t), thus, the prediction range of each secondary predictor can accurately follow the time-varying delay.

[0071] S5: Connect the corresponding m secondary predictors in series according to the order of the motion sub-states, use the time-varying and delayed robot joint position and joint velocity signals as the input of the first secondary predictor, and the next secondary predictor uses the predicted value output by the previous secondary predictor as the input, and the last secondary predictor outputs the predicted value of the actual joint position and actual joint velocity of the robot, thereby forming a series predictor, such as Figure 1 As shown in Figure 2. It is used to predict the actual joint position and joint velocity of the robot in real time.

[0072] The parts not involved in the present invention are the same as the prior art or are implemented by using the prior art.

[0073] The above contents are further detailed descriptions of the present invention in combination with specific implementation methods, and it cannot be determined that the specific implementation of the present invention is limited to these descriptions. For ordinary technicians in the technical field of the present invention, several simple deductions or substitutions can be made without departing from the concept of the present invention, which should be regarded as falling within the scope of protection of the present invention.

Claims

1. A method for predicting robot motion under time-varying delay conditions, characterized in that: The steps include: S1: Based on the nonlinear dynamic model of the n-DOF robot, according to the maximum value of the delay τ max , robot initial joint position q 10 and the robot's initial joint velocity q 20 , determine the number m of secondary predictors and the gain parameter K of the secondary predictors; S2: Determine the time-varying prediction interval Δ of each secondary predictor based on the number m of secondary predictors and the time delay size τ(t) that varies with time i (t); S3: Time-varying prediction interval Δ according to each secondary predictor i (t) Divide the robot's state from the time-delay motion to the current motion interval into m motion sub-states, the same number as the secondary predictors; S4: According to the m motion sub-states divided in step S3, construct m secondary predictors, which are the same in number as the motion sub-states, to predict the corresponding motion sub-states; S5: Connect the corresponding m secondary predictors in series according to the order of motion sub-states, use the time-varying and delayed robot joint position and joint velocity signals as the input of the first secondary predictor, and use the predicted value output by the previous secondary predictor as the input of the next secondary predictor. The last secondary predictor outputs the predicted value of the robot's actual joint position and actual joint velocity, which is used to predict the robot's current actual joint position and joint velocity in real time.

2. The method for predicting robot motion under time-varying delay conditions according to claim 1, characterized in that: In step S1, according to the robot's initial joint position q 10 and the robot's initial joint velocity q 20 , determine the gain parameter K of the secondary predictor, and the calculation formula is as follows: Among them, q 10 is the initial joint position of the robot, q 20 is the initial joint velocity of the robot.

3. The method for predicting robot motion under time-varying delay conditions according to claim 1, characterized in that: In step S1, according to the maximum value of the delay τ max Determine the number of secondary predictors m, calculated as follows: Where K is the gain parameter of the secondary predictor.

4. The method for predicting robot motion under time-varying delay conditions according to claim 1, characterized in that: In step S2, the time-varying prediction interval Δ of the secondary predictor i (t), the calculation formula is as follows: Among them, T i (t) is an auxiliary variable, τ(t) is the time delay that varies with time, t is a time variable, m is the number of secondary predictors, i = 1, 2, ..., m.

5. The method for predicting robot motion under time-varying delay conditions according to claim 1, characterized in that: In step S3, by x τ i (t) = [x 1i (t)x 2i (t)] represents the m motion sub-states, and the element x in each motion sub-state 1i (t) and x 2i (t), the expression is as follows: Among them, x1(t) is the joint position of the multi-degree-of-freedom robot, x2(t) is the joint velocity of the multi-degree-of-freedom robot, i=1,2,…,m represents the number of the motion sub-state, τ(t) is the time delay size that changes with time, Δ i (t) is the time-varying prediction interval of the secondary predictor, and t is the time variable.

6. The method for predicting robot motion under time-varying delay conditions according to claim 1, characterized in that: In step S4, the secondary predictor is constructed by a prediction algorithm represented by a set of m equations, which is expressed as follows: in, is an auxiliary variable with no specific meaning, K is the gain parameter of the secondary predictor, t is the time variable, and Represents the prediction result of the robot's motion sub-state. The prediction results of the robot's actual joint position and actual joint velocity are output by the last secondary predictor, that is, and f(.) is the robot dynamics equation function, u is the robot control input, r i (t) is the error calibration term.

7. The method for predicting robot motion under time-varying delay conditions according to claim 6, characterized in that: The error calibration term r i (t), the calculation formula is as follows: Where α is another gain parameter of the secondary predictor, and its value range is 0.5<α<1.5; Δ i (t) is the time-varying prediction interval of the secondary predictor; y 1i (t) and y 2i (t) input joint position and joint velocity signals to the secondary predictor; When i=1, y 1i =x1(t-τ),y 2i =x2(t-τ), which is the robot joint position and joint velocity signals with time-varying delay; When i=2,…,m, That is, the previous secondary predictor outputs prediction signals of the robot's joint positions and joint velocities.

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