A robot motion prediction method under time-varying delay conditions

Abstract

This invention discloses a method for predicting robot motion under time-varying delay conditions. The method determines the number of secondary predictors and their gain parameters based on the maximum time delay, the robot's initial joint position, and the initial joint velocity. The time-varying prediction interval of each secondary predictor is determined by the time-varying delay magnitude. The robot's state from time-delayed motion to the current motion interval is divided into motion sub-states, the same number as the number of secondary predictors. Secondary predictors are constructed, the same number as the number of motion sub-states. The secondary predictors are connected in series, with the time-varying delay robot joint position and velocity signals as input to the first secondary predictor, and the predicted values ​​output by the previous secondary predictor as input to each subsequent secondary predictor. The last secondary predictor outputs the predicted values ​​of the robot's actual joint position and actual joint velocity. This invention offers high prediction accuracy, wide applicability, ease of engineering application and promotion, and contributes to the development of robotics technology.

Description

Technical Field

[0001] This invention relates to the field of robot sensing and control, and more particularly to a method for predicting the motion of a robot under time-varying and time-delay conditions. Background Technology

[0002] Robotics is playing an increasingly important role in numerous fields, from industrial manufacturing to healthcare, from scientific exploration to home services, with its application scenarios constantly expanding. As robot applications become more widespread, precise control and prediction of their motion have become crucial issues. In practical applications, robots often face complex working environments, among which time-varying latency is a significant challenge. Time-varying latency can be caused by various factors, such as unstable communication networks, delays in sensor data transmission, and variations in control system processing time. This time-varying latency can have many adverse effects on robot motion control. In traditional robot motion control, it is usually assumed that the latency is fixed or negligible. However, in reality, the existence of time-varying latency causes a deviation between the robot's actual and expected motion, reducing the accuracy and stability of the motion. Time-varying latency may cause the robot's actions to lag, failing to respond to control commands in a timely manner, thus affecting the quality and efficiency of robot task execution. In some fields with high safety requirements, such as medical surgical robots and autonomous robots, time-varying latency can lead to serious safety problems. If the robot cannot accurately predict and adapt to changes in latency, it may cause harm to patients or pedestrians. However, traditional prediction methods cannot adjust and optimize prediction strategies in a timely and effective manner when faced with time-varying delays, leading to significant deviations between the predicted results and the actual motion state of the robot. Therefore, it is necessary to study a prediction method that can effectively adapt to time-varying delay variations. Summary of the Invention

[0003] The purpose of this invention is to provide a motion prediction method for robots under time-varying delay conditions. Under the condition that the delay is known, the prediction interval of each level of predictor is determined so that it can predict the current actual joint position and joint speed of the robot in real time based on the robot joint position and joint speed signals that the delay magnitude changes with time.

[0004] To solve the above technical problems, the technical solution of the present invention is: a method for predicting the motion of a robot under time-varying and time-delay conditions, comprising the following steps:

[0005] S1: A nonlinear dynamic model based on an n-degree-of-freedom robot, using the maximum time delay τ. max The initial joint position q of the robot 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: Based on the number of secondary predictors m and the time delay τ(t) that varies with time, determine the time-varying prediction interval Δ of each secondary predictor. i (t);

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

[0008] S4: Based on the m motion sub-states divided in step S3, construct m secondary predictors, the same number as the number of 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 the kinematic sub-states. Use the time-varying and time-delayed robot joint position and joint velocity signals as the input of the first secondary predictor. 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, based on the robot's initial joint position q 10 And the robot's initial joint velocity q 20 The gain parameter K of the secondary predictor is determined by the following formula:

[0011]

[0012] Where, q 10 Let q be the initial joint position of the robot. 20 This represents the initial joint velocity of the robot.

[0013] Preferably, in step S1, based on the maximum value τ of the time delay... max The number of secondary predictors, m, is determined using the following formula:

[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, through 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 is... 1i (t) and x 2i (t), the expression is as follows:

[0020]

[0021] Where x1(t) represents the joint position of the multi-degree-of-freedom robot, x2(t) represents the joint velocity of the multi-degree-of-freedom robot, i = 1, 2, ..., m represents the label of the kinematic sub-state, τ(t) represents the time delay that varies with time, and Δ i (t) represents the time-varying prediction interval of the secondary predictor, where t is the time variable.

[0022] Preferably, in step S4, the secondary predictor is constructed using a prediction algorithm represented by a system of m equations, as shown below:

[0023]

[0024] in, The auxiliary variable has no specific meaning; K is the gain parameter of the secondary predictor; and t is the time variable. and The predicted results of the robot's motion sub-states, the predicted results of the robot's actual joint positions and actual joint velocities are output by the last secondary predictor, i.e. and f(.) is the robot's dynamic equation function, u is the robot's control input, and r i (t) represents the error calibration term.

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

[0026]

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

[0029] When i = 2, ..., m That is, the previous secondary predictor outputs the predicted signals of the robot's joint position and joint velocity.

[0030] Compared with the prior art, the beneficial effects of the present invention are as follows: (1) By determining the time-varying prediction interval of the secondary prediction, it adopts the same series structure under time-varying delay conditions as under fixed delay conditions, thus overcoming the problem that the fixed delay algorithm is not applicable under time-varying delay conditions. 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 performs relatively simple calculations only 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 time delay, that is, when the time delay changes significantly, the prediction interval of the secondary predictor can be adaptively adjusted, and the robot's motion state can still be accurately predicted. This robustness is of great significance in complex and ever-changing actual working environments and helps to promote the development of robot technology. Attached Figure Description

[0031] To more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings used in the description of the embodiments of the present invention will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0032] Figure 1 This is a schematic diagram of the overall system of the robot motion prediction method in this invention;

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

[0034] Figure 3 This is a schematic diagram illustrating the construction principle of a single secondary predictor that predicts the time-varying interval in this invention. Detailed Implementation

[0035] The present invention will now be described in further detail with reference to the accompanying drawings. The terminal technical solutions of the embodiments of the present invention will be clearly and completely described. Obviously, the described embodiments are only some, not all, of the embodiments of the present invention. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without creative effort are within the scope of protection of the present invention.

[0036] This invention addresses the problem of delayed robot motion state information transmission caused by time-varying communication delays. Based on a nonlinear dynamics model of an n-degree-of-freedom robot, a prediction method for joint positions and velocities during robot motion is designed. This invention redefines the time-varying prediction interval for each secondary predictor to cope with time-varying delays. Based on the time-varying joint position and velocity signals, it can predict the robot's current actual joint position and velocity in real time and with high accuracy.

[0037] like Figure 1 As shown, this invention discloses a motion prediction method for robots under time-varying and time-delay conditions, comprising the following steps:

[0038] S1: A nonlinear dynamic model based on an n-degree-of-freedom robot, using the maximum time delay τ. max The initial joint position q of the robot 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-degree-of-freedom robot is expressed as follows:

[0040]

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

[0042] The model is further rewritten as follows:

[0043]

[0044] Define the robot's dynamic equation function as f(x1,x2,u)=M -1(x1)[u(t)-C(x1,x2)x2(t)].

[0045] Based on the robot's initial joint position q 10 And the robot's initial joint velocity q 20 The gain parameter K of the secondary predictor in the robot motion prediction system is determined by the following formula:

[0046]

[0047] Where, q 10 Let q be the initial joint position of the robot. 20 This represents the initial joint velocity of the robot.

[0048] Generally, a suitable value for K helps improve the stability of a robot motion prediction system. If K is too large or too small, the robot motion prediction system will become unstable or its prediction performance will deteriorate. When K is too large, the robot motion prediction system will respond too strongly to errors, leading to oscillations or even instability. When K is too small, the robot motion prediction system will lack the ability to correct errors, respond slowly, and be unable to effectively predict the desired trajectory.

[0049] Based on the preset maximum delay τ max The number m of secondary predictors required in the robot motion prediction system is determined by the following formula:

[0050]

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

[0052] S2: Based on the number of secondary predictors m and the time delay τ(t) that varies with time, determine the time-varying prediction interval Δ of each secondary predictor. 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 using the two calculation formulas above, such as... Figure 2 As shown, it should be noted that the time delay magnitude 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: Based on the time-varying prediction interval Δ of each secondary predictor i (t) Divide the robot's state from time-delayed motion to the current motion interval into m motion sub-states, the same number as the secondary predictors.

[0057] Through 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 is... 1i (t) and x 2i (t), the expression is as follows:

[0058]

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

[0060] S4: Based on the m motion sub-states divided in step S3, construct m secondary predictors, the same number as the number of motion sub-states, to predict the corresponding motion sub-states.

[0061] The secondary predictor is constructed using a prediction algorithm represented by a system of m equations, as shown below:

[0062]

[0063] in, K is the gain parameter of the secondary predictor, and t is the time variable. and The predicted results of the robot's motion sub-states, the predicted results of the robot's actual joint positions and actual joint velocities are output by the last secondary predictor, i.e. and f(.) is the robot's dynamic equation function, u is the robot's control input, and r i (t) represents the error calibration term.

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

[0065]

[0066] Where α is another gain parameter of the secondary predictor, with a value range of 0.5 < α < 1.5; Δ i (t) represents the time-varying prediction interval of the secondary predictor; y 1i (t) and y 2i (t) provides the joint position and joint velocity signals as inputs 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 signal with time-varying delay;

[0068] When i = 2, ..., m That is, the previous secondary predictor outputs the predicted signals of the robot's joint position and joint velocity.

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

[0070] Next, the measured time delay τ(t) is used as the input to 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 kinematic sub-states. Use the time-varying and time-delayed robot joint position and velocity signals as the input to the first secondary predictor. Each subsequent secondary predictor uses the predicted value output by the previous one as its input. The last secondary predictor outputs the predicted values ​​of the robot's actual joint position and velocity, thus forming a series predictor. Figure 1 As shown. This is used to predict the robot's current actual joint position and joint velocity in real time.

[0072] All parts not covered in this invention are the same as or implemented using existing technologies.

[0073] The above description, in conjunction with specific embodiments, provides a further detailed explanation of the present invention. It should not be construed that the specific implementation of the present invention is limited to these descriptions. For those skilled in the art, various simple deductions or substitutions can be made without departing from the concept of the present invention, and all such modifications and substitutions should be considered within the scope of protection of the present invention.

Claims

1. A method for predicting the motion of a robot under time-varying delay conditions, characterized in that: Includes the following steps: S1: Based on The nonlinear dynamics model of a degree-of-freedom robot, based on the maximum value of the time delay. Initial joint positions of the robot and robot initial joint velocity Determine the number of secondary predictors and the gain parameters of the secondary predictor ; S2: Based on the number of secondary predictors and the magnitude of time delay Determine the time-varying prediction interval of each secondary predictor. ; S3: Based on the time-varying prediction intervals of each secondary predictor The robot's states from time-delayed motion to its current motion range are divided into the same number as the number of secondary predictors. One motion sub-state; S4: Based on the division in step S3 There are 10 motion sub-states, and the same number of motion sub-states are constructed. Each secondary predictor is used to predict the corresponding motion sub-state; S5: Based on the order of the moving sub-states, the corresponding... The system consists of several secondary predictors connected in series. The time-varying and time-delayed robot joint position and joint velocity signals are used as the input of the first secondary predictor. The subsequent secondary predictor uses the predicted value output by the previous secondary predictor as its input. 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. In step S1, based on the robot's initial joint positions... and robot initial joint velocity Determine the gain parameters of the secondary predictor. The calculation formula is as follows: ； in, The initial joint positions of the robot, The initial joint velocities of the robot; In step S1, based on the maximum value of the delay Determine the number of secondary predictors The calculation formula is as follows: ； in, This is the gain parameter of the secondary predictor; In step S2, the time-varying prediction interval of the secondary predictor The calculation formula is as follows: ； ； in, As an auxiliary variable, The time delay varies over time. For time variables, The number of secondary predictors. .

2. The motion prediction method for a robot under time-varying delay conditions according to claim 1, characterized in that: In step S3, through Indicates the Each motion substate contains elements. and The expression is as follows: ； ； in, For the joint positions of a multi-degree-of-freedom robot, For the joint velocities of a multi-degree-of-freedom robot, The label indicating the sub-state of motion. The time delay varies over time. The time-varying prediction interval of the secondary predictor. It is a time variable.

3. The motion prediction method for a robot under time-varying delay conditions according to claim 1, characterized in that: In step S4, the secondary predictor passes through The prediction algorithm is constructed using a system of equations, expressed as follows: ； in, As an auxiliary variable, it has no specific meaning. This refers to the gain parameter of the secondary predictor. For time variables, and The predicted results of the robot's motion sub-states, the predicted results of the robot's actual joint positions and actual joint velocities are output by the last secondary predictor, i.e. and , For the robot's dynamic equations, For the control input of the robot, This is an error calibration item.

4. The motion prediction method for a robot under time-varying delay conditions according to claim 3, characterized in that: The error calibration item The calculation formula is as follows: ； in, This is another gain parameter for the secondary predictor, with a value range of [value range missing]. ; This represents the time-varying prediction interval of the secondary predictor. and Input the joint position and joint velocity signals to the secondary predictor; when hour, , Instantaneous variable-delay robot joint position and joint velocity signals; when hour, , That is, the previous secondary predictor outputs the predicted signals of the robot's joint position and joint velocity.

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