Method for end compensation of underwater manipulator based on gaussian process

Abstract

The application relates to the technical field of underwater mechanical arms, in particular to a method for compensating the tail end of an underwater mechanical arm based on a Gaussian process, which successfully establishes a model for the deviation distance of an end effector in underwater space control of the end effector by means of the Gaussian process, reduces a large number of correction points collected compared with the method adopting DART or (HG-) Dagger in the prior art, alleviates the long calculation time and low work efficiency existing in the prior art, and improves the underwater work reliability of the mechanical arm.

Description

Technical Field

[0001] This invention relates to the field of underwater robotic arm technology, and in particular to a method for end-effector compensation of an underwater robotic arm based on Gaussian processes. Background Technology

[0002] With the continuous advancement of robotic arm technology, they have been widely used to perform various repetitive or simple tasks, improving production efficiency and reducing labor costs. However, a key challenge of modern robotics is enabling robotic arms to work effectively in complex and unknown underwater environments, such as marine resource exploration, seabed surveys, and the repair and maintenance of underwater equipment. The unique characteristics of the underwater environment, such as high pressure, low temperature, and low visibility, bring additional difficulties to the operation of robotic arms. Therefore, research on how to improve the operating efficiency and accuracy of underwater robotic arms while reducing operational complexity has become a research hotspot.

[0003] In existing technologies, such as DART or (HG-)DAgger, noise has been injected into the execution of supervised strategies to guide robots into unvisited areas and collect databases in a larger environment.

[0004] However, the above method requires the collection of a large number of correction points for judgment during the end-effector compensation process, which takes a long time and is inefficient. Therefore, further solutions are needed to address the aforementioned technical problems. Summary of the Invention

[0005] The purpose of this invention is to provide a method for end-effector compensation of an underwater robotic arm based on Gaussian processes, so as to alleviate the technical problems in the prior art that require the collection of a large number of correction points for judgment during the end-effector compensation process, resulting in long calculation time and low work efficiency.

[0006] To address the aforementioned technical problems, the embodiments of the present invention provide the following technical solutions:

[0007] The first aspect of the present invention provides a method for end-effector compensation of an underwater robotic arm based on a Gaussian process, comprising a binocular camera, a control unit, and a robotic arm, wherein the binocular camera and the robotic arm are both electrically connected to the control unit;

[0008] A binocular camera is installed at the end of the robotic arm to collect underwater environmental information and motion information of each joint of the robotic arm; the control unit is used to control the movement of each joint of the robotic arm and to calculate the collected motion information of each joint. The steps are as follows:

[0009] S10. Obtain the motion trajectory of each joint of the robotic arm through the control unit, and train the motion trajectory using the Gaussian process algorithm combined with kinematic data to obtain the expected motion model of the current task;

[0010] The motion model is used to provide a probability distribution of the expected Cartesian trajectory of the robotic arm in the current environment; and to calculate the mean and variance of the probability distribution;

[0011] S20. When the end effector of the robotic arm is guided to fall into the high confidence region with minimum variance by adding a gravity term to the manifold of the variance of the desired motion model;

[0012] When there is no interference, the end effector of the robotic arm moves within a high-confidence region with minimal variance;

[0013] When interference occurs, the movement trajectory of the robotic arm's end effector is changed until the interference is eliminated and the robotic arm returns to the high-confidence region.

[0014] In some modified embodiments of the first aspect of the present invention, step S10 includes the following steps:

[0015] S11. Obtain the mathematical characteristics of the motion trajectory, including Gaussian noise E, input state ξ = [x, y, z], and output state. The expression is:

[0016]

[0017] S12. Train the motion trajectory using kinematic instances to obtain the desired motion model;

[0018] The kinematic instance expression is:

[0019]

[0020] N is the number of position points of the Cartesian trajectory of the robotic arm's end effector, ξ i Let i be the end position of the i-th trajectory point. The output is the given trajectory data resampled and calculated by difference, where each element is the difference between two arrays at the corresponding position.

[0021] Substituting the kinematic instance expression into the expression for the motion trajectory, we obtain the desired motion model as follows:

[0022]

[0023] Ξ=[ξ1,ξ2,…,ξ N The input variable matrix in the kinematic example; m(Ξ) is the mean, and K(Ξ,Ξ) is the covariance matrix. Each element in K(Ξ,Ξ) is Ker(ξ). i ,ξ j ) is ξ i and ξ j covariance,

[0024] Ker(*,*) is the kernel function for a Gaussian process, and its expression is as follows:

[0025]

[0026] k(x i ,x j ): indicates the input point x i and x j Kernel function values ​​between

[0027] ||x i -x j || 2 It is point x i and x j The square of the Euclidean distance between them

[0028] l is a hyperparameter of the Gaussian kernel;

[0029] S13. Calculate the mean and variance of the Gaussian distribution among adjacent data points at the end of the robotic arm. The expression is:

[0030]

[0031]

[0032] Where ξ is the variance of k individual evaluation points, and k * Let ξ be the covariance between the training input Ξ and K be the covariance matrix of the training input. Let y be the variance of the Gaussian noise at the training points, and y be the training output; k and k * Both K and K are functions of the kernel function and its hyperparameters.

[0033] In some modified embodiments of the first aspect of the present invention, step 20 includes the following steps;

[0034] S21. Calculate the kernel matrix between the current end-effector position and the input features of the training data based on the kernel function, and calculate the variance of the kernel matrix.

[0035] The gradient vector is multiplied by the inverse of the kernel matrix to obtain the gradient of the variance with respect to the input features. For the input point (ξ = [x1, x2, x3]), the gradient of the output is calculated. Its expression is:

[0036]

[0037] α is a constant based on the maximum permissible automatic modulation, where ξ is the evaluation point, g(ξ) is the correction vector, and I is the inertia matrix; Let k be the variance of the Gaussian noise at the training points. * Let ξ be the covariance between ξ and the training input Ξ.

[0038] S22. Before the robotic arm moves its current position at the end effector, calculate the required aggregation directions f and K. l The expression for the aggregated vector representing the difference between *Δz* is: The expression for the aggregated vector is:

[0039] f = K l Δx+g(ξ);

[0040] Where Δx is the predicted distance that each axis at the end is to move based on the current position, Δx = f / K l The distance K required to move to the region of minimum variance l Δz is the modulation constant, representing the maximum offset distance along each axis;

[0041] S23. Combine the aggregation vectors f and K l *Δz is compared;

[0042] When the aggregation vector f is greater than K l At *Δz, the end effector of the robotic arm will move Δz along each axis according to its current position by the maximum offset distance.

[0043] When the aggregation vector f is less than K l At *Δz, the end effector of the robotic arm will offset along each axis by Δx+g(ξ) / K according to its current position. l .

[0044] Compared to existing technologies, this new method utilizes a binocular camera and control unit. The binocular camera is positioned at the end of the robotic arm to collect underwater environmental information and motion information from each joint of the robotic arm. The control unit controls the movement of each joint of the robotic arm and performs calculations based on the collected motion information. The steps are as follows:

[0045] S10. Obtain the motion trajectory of each joint of the robotic arm through the control unit, and train the motion trajectory using the Gaussian process algorithm combined with kinematic data to obtain the expected motion model of the current task;

[0046] The motion model is used to provide a probability distribution of the expected Cartesian trajectory of the robotic arm in the current environment; and to calculate the mean and variance of the probability distribution;

[0047] The above steps are based on the imitation learning stage of Gaussian processes. First, the working trajectory is modeled, and then the Gaussian process algorithm is used in combination with kinematic data to train these trajectories, thereby obtaining the desired motion model adapted to the current task. This model represents the probability distribution of the desired Cartesian trajectory, providing a basis for the control of the robotic arm.

[0048] S20. When the end effector of the robotic arm is guided to fall into the high confidence region with minimum variance by adding a gravity term to the manifold of the variance of the desired motion model;

[0049] When there is no interference, the end effector of the robotic arm moves within a high-confidence region with minimal variance;

[0050] When interference occurs, the movement trajectory of the robotic arm's end effector is changed until the interference is eliminated and the robotic arm returns to the high confidence area.

[0051] In the compensation phase of the robotic arm's end effector, when the robotic arm encounters an obstacle, its trajectory needs to be adjusted to avoid entering previously unvisited workspace areas with high uncertainty. End effector offsets in these areas may cause dangerous or undesirable dynamic behaviors in the robotic arm. Under normal circumstances, the end effector of the robotic arm will be located in the region of minimum variance and move along the normal taught trajectory. When trajectory adjustment is required, the end effector can be manually adjusted to avoid interference. Once the interference is eliminated, the robotic arm returns to the predicted region with higher confidence and continues to move along the taught trajectory. The above process can be achieved by adding a gravity term to the variance manifold, similar to the principle that a marble on a track will automatically return to the track after being disturbed by a collision.

[0052] Therefore, by implementing the technical solution of this invention, compared with the existing technology that uses DART or (HG-)Dagger, this invention successfully establishes a model of the offset distance of the end effector in underwater space by using Gaussian processes. Therefore, it reduces the collection of a large number of correction points, alleviates the long calculation time and low work efficiency of the existing technology, and improves the reliability of the robotic arm in underwater operation. Attached Figure Description

[0053] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the accompanying drawings used in the embodiments will be briefly described below.

[0054] Figure 1 A logic flowchart of the method for end-effector compensation of an underwater robotic arm based on a Gaussian process provided in an embodiment of the present invention;

[0055] Figure 2 The trajectory diagram of the target object being transferred from point a to point b by the robotic arm in the method of underwater robotic arm end-effector compensation based on Gaussian process provided in the embodiment of the present invention;

[0056] Figure 3 This is an experimental scenario diagram showing the end effector of an underwater robotic arm and the target object at point a in the method for end effector compensation based on Gaussian process provided in an embodiment of the present invention.

[0057] Figure 4 This is an experimental scenario diagram of the underwater robotic arm's end-effector transferring the target object to point b in the method for compensation of the underwater robotic arm based on Gaussian process provided in an embodiment of the present invention.

[0058] Figure 5 The trajectory diagram of the periodic test of the movement trajectory of the underwater manipulator in the method of Gaussian process-based underwater manipulator end-effector compensation provided in the embodiment of the present invention;

[0059] Figure 6 This is an experimental scenario diagram of the periodic testing of the movement trajectory of an underwater robotic arm in the method for end-effector compensation based on Gaussian process provided in an embodiment of the present invention.

[0060] Wherein: 10 - binocular camera; 20 - control components. Detailed Implementation

[0061] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0062] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, the technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings of the embodiments of the present invention.

[0063] like Figure 1 As shown, this embodiment provides a method for end-effector compensation of an underwater robotic arm based on a Gaussian process, including a binocular camera 10, a control unit 20, and a robotic arm. Both the binocular camera 10 and the robotic arm are electrically connected to the control unit 20. The control unit 20 can be controlled using computer-related algorithm software.

[0064] A binocular camera 10 is installed at the end of the robotic arm and is used to collect underwater environmental information and motion information of each joint of the robotic arm; the control unit 20 is used to control the motion of each joint of the robotic arm and to calculate the collected motion information of each joint of the robotic arm. The steps are as follows:

[0065] S10. The motion trajectory of each joint of the robotic arm is obtained through the control unit 20, and the motion trajectory is trained using the Gaussian process algorithm combined with kinematic data to obtain the expected motion model of the current task.

[0066] The motion model is used to provide a probability distribution of the expected Cartesian trajectory of the robotic arm in the current environment; and to calculate the mean and variance of the probability distribution;

[0067] S20. When the end effector of the robotic arm is guided to fall into the high confidence region with minimum variance by adding a gravity term to the manifold of the variance of the desired motion model;

[0068] When there is no interference, the end effector of the robotic arm moves within a high-confidence region with minimal variance;

[0069] When interference occurs, the movement trajectory of the robotic arm's end effector is changed until the interference is eliminated and the robotic arm returns to the high-confidence region.

[0070] This embodiment is based on a kinematic imitation learning strategy, which records the learning process through manual instruction and uses a controller to complete the task of teaching the trajectory. This strategy mainly consists of two stages:

[0071] Phase 1: Imitation learning based on Gaussian processes, i.e., step S10:

[0072] In this stage, the movement trajectory of the robotic arm is first modeled, and then these trajectories are trained using the Gaussian process algorithm combined with kinematic data to obtain the desired motion model adapted to the current task, i.e., the taught trajectory. This model represents the probability distribution of the desired Cartesian trajectory, providing a foundation for the control of the robotic arm.

[0073] Phase Two: End-of-line compensation, i.e., step S20:

[0074] When a robotic arm encounters an obstacle, it may need to adjust its trajectory to avoid entering previously unvisited, high-uncertainty workspace areas. End-effector offsets in these areas can cause dangerous or undesirable dynamic behaviors in the robotic arm; it then moves along the normal taught trajectory. When trajectory adjustments are needed, the end effector can be manually manipulated to adjust its position to avoid interference. Once the disturbance is eliminated, the robotic arm returns to the predicted area with higher confidence and continues moving along the taught trajectory. This process can be achieved by adding a gravitational term to the variance manifold, similar to how a marble on a track automatically returns to its track after a collision.

[0075] Furthermore, S10 includes the following steps:

[0076] S11. The expression for obtaining the motion trajectory is:

[0077]

[0078] in, A continuous and differentiable nonlinear differential equation, where The noise representing a dynamic system, in this paper mainly refers to the noise measured by sensors, and is assumed to be Gaussian noise with the form E ~ N(0,σ). 2 I), where The output state variable (ξ can be the joint angle, end pose, and end velocity of the robotic arm, etc.), and the input state ξ = [x, y, z].

[0079] In the process of imitation learning, the first step is to model the working trajectory of the robotic arm. According to the theory of dynamic systems, the task trajectory should be modeled as a first-order autonomous ordinary differential equation. This modeling method can maintain the high robustness of the model when dealing with spatial disturbances.

[0080] S12. Train the motion trajectory using kinematic instances to obtain the desired motion model;

[0081] The kinematic instance expression is:

[0082]

[0083] N is the number of position points of the Cartesian trajectory of the robotic arm's end effector, ξ i Let i be the end position of the i-th trajectory point. The output is calculated by resampling the given trajectory data through difference, where each element is the difference between two arrays at the corresponding position.

[0084] Substituting the kinematic instance expression into the expression for the motion trajectory, we obtain the desired motion model as follows:

[0085]

[0086] Ξ=[ξ1,ξ2,…,ξ N The input variable matrix in the kinematic example; m(Ξ) is the mean, and K(Ξ,Ξ) is the covariance matrix. Each element in K(Ξ,Ξ) is Ker(ξ). i ,ξ j ) is ξ i and ξ j The covariance of the process is the gravitational term mentioned above; Ker(*,*) is the kernel function of the Gaussian process, expressed as follows:

[0087]

[0088] k(x i ,x j ): indicates the input point x i and x j Kernel function values ​​between

[0089] ||x i -x j ||2 It is point x i and x j The square of the Euclidean distance between them

[0090] l: Hyperparameters of the Gaussian kernel;

[0091] S13. Calculate the mean and variance of the Gaussian distribution among adjacent data points at the end of the robotic arm. The expression is:

[0092]

[0093]

[0094] Where ξ is the variance of k individual evaluation points, and k * Let ξ be the covariance between the training input Ξ and K be the covariance matrix of the training input. Let y be the variance of the Gaussian noise at the training points, and y be the training output; k and k * Both K and K are functions of the kernel function and its hyperparameters.

[0095] As can be seen from the expression of the motion trajectory, the motion model mainly describes the relationship between the positions of the robotic arm in the current task. The change between adjacent data points between these positions can be obtained through Gaussian process regression: the result is the mean and variance of the Gaussian distribution, and μ(x) and Σ are the mean and variance of the Gaussian distribution, respectively.

[0096] Imitation learning strategies based on Gaussian processes are implemented due to their strong environmental adaptability, autonomously generating corresponding Cartesian task distributions that reflect the state of the robotic arm and its environment. However, the generated trajectory distribution is based on the operator's kinematic instances, a process that may be constrained by human physiological characteristics, resulting in potentially less smooth kinematic instances. Especially after prolonged work, the operator may experience muscle fatigue, further affecting the smoothness of the trajectory.

[0097] Compared to traditional trajectory planning, the Gaussian process-based imitation learning strategy uses Gaussian process algorithms to construct action models. This strategy utilizes Gaussian process regression to predict the Cartesian trajectory distribution under specific task conditions, producing not only the expected trajectory but also a probabilistic model. This probabilistic model provides possibilities for subsequent optimization processes.

[0098] Furthermore, the goal of this embodiment is for the robotic arm's end effector to complete the target task regardless of its position. The primary task is to progressively correct the end effector as its position changes. When the end effector enters previously unexplored areas of the workspace, the desired position may have high uncertainty, leading to dangerous and undesirable dynamics for the robot. This problem is known as covariate transfer and is common when applying behavior cloning. Some solutions, such as DART or (HG-)DAgger, have investigated injecting noise into the execution of supervised policies to guide the robot into unexplored areas and collect a database within a larger environment. This technique can also be applied to interactive correction, but collecting many correction points can be very time-consuming and data-inefficient.

[0099] As an alternative, this embodiment utilizes information about the model variance and its continuous differentiability to model how to correct the end effector position, i.e., prevent further entry into the positional region. Intuitively, the taught motion trajectory can be likened to a road, and the end effector of the robotic arm to a car. Without external interference, the car will drive normally, and the end effector will be located in the region of minimum variance and move inward. When the end effector changes direction, it's like the car's direction shifting, potentially causing the car to enter a dangerous area. The car should return to its original path, just as the robotic arm should return to the region of higher confidence. This is similar to adding a gravity term to the variance manifold, inducing the end effector to always "fall into" the region of minimum variance, just as a marble automatically returns to the bottom of a pipe when its trajectory deviates. The realization of the stable prior is proportional to the gradient of the variance manifold.

[0100] Based on the above ideas, step 20 includes the following steps;

[0101] S21. Calculate the kernel matrix between the current end-effector position and the input features of the training data based on the kernel function, and calculate the variance of the kernel matrix.

[0102] The gradient vector is multiplied by the inverse of the kernel matrix to obtain the gradient of the variance with respect to the input features. For the input point (ξ = [x1, x2, x3]), the gradient of the output is calculated. Its expression is:

[0103]

[0104] α is a constant based on the maximum permissible automatic modulation, where ξ is the evaluation point, g(ξ) is the correction vector, and I is the inertia matrix; Let k be the variance of the Gaussian noise at the training points. * Let ξ be the covariance between ξ and the training input Ξ.

[0105] The kernel matrix is ​​calculated based on the current terminal position and the input features of the training data using the kernel function. The variance is then calculated. Finally, the gradient vector is multiplied by the inverse of the kernel matrix to obtain the gradient of the variance with respect to the input features. For the input point (ξ = [x1, x2, x3]), the gradient of the output is calculated. This is obtained by calculating the partial derivative of the kernel function, where the length scale is (l). Specifically, the gradient calculation formula is: Finally, we obtain...

[0106]

[0107] Finally, before the robotic arm performs the end effector movement, it is necessary to ensure that the end effector has a modulation effect for diffusion and end effector constraints. During the process of modifying the end effector, the required end effector position offset after modification is crucial. Therefore, it is necessary to calculate the difference between the required aggregation vector and the correction vector.

[0108] S22. Before the robotic arm moves its current position at the end effector, calculate the required aggregation directions f and K. l The expression for the aggregated vector representing the difference between *Δz* is: The expression for the aggregated vector is:

[0109] f = K l Δx+g(ξ);

[0110] Where Δx is the predicted distance that each axis at the end is to move based on the current position, Δx = f / K l The distance K required to move to the region of minimum variance l Δz is the modulation constant, representing the maximum offset distance along each axis;

[0111] S23. Combine the aggregation vectors f and K l *Δz is compared;

[0112] When the aggregation vector f is greater than K l At *Δz, the end effector of the robotic arm will move Δz along each axis according to its current position by the maximum offset distance.

[0113] When the aggregation vector f is less than K l At *Δz, the end effector of the robotic arm will offset along each axis by Δx+g(ξ) / K according to its current position. l .

[0114] Furthermore, to verify the feasibility of this embodiment, a five-DOF robotic arm of the reachminialpha5 was selected to verify the technical effects of the above content. The Denavit-Hartenberg (DH) parameters of the five-DOF robotic arm are shown in Table 1.

[0115] Table 1 Parameters of a Five-DOF Robotic Arm

[0116] 0 46.2 <![CDATA[θ0+π]]> 20 π / 2 1 0 <![CDATA[θ1-θ a ]]> 150.71 π 2 0 <![CDATA[θ2-θ a ]]> 20 -π / 2 3 -180 <![CDATA[θ3+π / 2]]> 0 π / 2 4 0 -π / 2 0 0

[0117] The inertial parameters of the five-free robotic arm are shown in Table 2:

[0118] Table 2. Inertial parameters of a five-DOF robotic arm

[0119]

[0120]

[0121] In this context, inertia is measured relative to the center of mass, and the position of the center of mass is measured relative to the DH coordinate system. To simplify calculations, the dexterous hand and the end effector of the robotic arm are treated as a single unit when calculating the inertia parameters. To verify the method of this embodiment, experiments were conducted using two different operational tasks, each with its own variations.

[0122] like Figure 2-4 As shown, the purpose of the experiment was to use a robotic arm to carry the target object to a designated location in water. Specifically, in... Figure 2 In the diagram, point a represents the initial position of the robotic arm's end effector, point b represents the target position of the robotic arm's end effector, the black curve represents the teaching trajectory, and the red and blue curves represent the trajectory formed by the robotic arm's end effector at different initial positions. It can be seen that after performing imitation learning in step S10 and end effector compensation in step S20, the robotic arm's end effector can accurately reach the target position b even at different initial positions a.

[0123] like Figure 5 and Figure 6 As shown, the second method analyzes the periodic permanent motion scenario of an underwater pipe, where the target object is placed in a specific position. Among these, Figure 5 The black lines in the diagram represent the teaching trajectory, and the red lines represent the reproduction trajectory.

[0124] In the above experiment, a single trajectory was taught to place the target object within a fixed circle. After teaching, the trajectory was reproduced. Before reproduction, two disturbance scenarios were arranged. The first scenario involved teaching the robotic arm to place it in a designated position. Before reproduction, two different initial positions and different end-effector heights were used to place the target. The main focus was on achieving the target at the designated position and within a tolerance of 3 cm.

[0125] At the start of the experiment, the robotic arm's end effector had already grasped the target object, such as... Figure 2The operator controls the robotic arm's joint movements via keyboard keys to complete the task and records the end-effector trajectory. Training using an imitation learning strategy is required, and the robotic arm successfully completes the task for both variations. The time spent on robotic arm control is as follows: teaching time 12.3s, first position reproduction time 13.1s, second position reproduction time 13.5s. Under stable prior conditions, the error between the first reproduced target position and the taught target position is 0.5cm, and the error between the second reproduced target position and the taught target position is 0.41cm.

[0126] Therefore, it is highly desirable for the robot to return to the same joint configuration at the end of each operational cycle; this property is known as the "cyclicity" of motion. For redundant robots, it is possible for the end effector to return to the same task space position, but the robot is in a completely different joint configuration. This mechanism helps users focus solely on the motion of the end effector during kinematic demonstrations, and guarantees the cyclicity of the computation during policy execution. However, since the primary focus is not on learning null space constraints, further details and investigation will be added in future work.

[0127] The task is considered successful if the required domains of different cross-sections of the pipe are cleaned after each cycle and the movement continues for at least 7 cycles. The teaching cycle time is 15.7 seconds, and the maximum error time between each reproduction cycle and the teaching cycle does not exceed 3 seconds.

[0128] In terms of quantity, the robot not only successfully completed seven cycles, but also maintained a high degree of consistency in its movements.

[0129] A Gaussian process model was successfully established to model the offset distance of the end effector in underwater space. Using the learned model parameters, two additional safety features can be established. First, if the robot arm is too far from the demonstration area, based on existing stability priors, it helps guide the robot back to the nearest low-variance region, thus enabling it to return to the demonstration area.

[0130] Furthermore, a stable prior can infer that its effect should decrease in the region between demonstrations, allowing the robot more freedom of movement in these regions. However, in the case of desired multimodal behavior, such as obstacle avoidance, this can be achieved by constraining the maximum length scale of the kernel used. This is equivalent to generating multiple independent variance grooves, rather than a wider one.

[0131] Further investigation shows that it can be used for underwater target guidance and periodic motion. When used in conjunction with null space control, cyclicity can be achieved, resulting in high consistency of motion.

[0132] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the technical scope disclosed in the present invention should be included within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be determined by the scope of the claims.

Claims

1. A method for end-effector compensation of an underwater robotic arm based on Gaussian processes, characterized in that, It includes a binocular camera, a control unit, and a robotic arm, with both the binocular camera and the robotic arm electrically connected to the control unit; The binocular camera is used to collect underwater environmental information and motion information of each joint of the robotic arm; the control unit is used to control the motion of each joint of the robotic arm and to perform calculations on the collected motion information of each joint of the robotic arm. The steps are as follows: S10. Obtain the motion trajectory of each joint of the robotic arm through the control unit, and train the motion trajectory using the Gaussian process algorithm combined with kinematic data to obtain the expected motion model of the current task; The motion model is used to provide a probability distribution of the expected Cartesian trajectory of the robotic arm in the current environment; and to calculate the mean and variance of the probability distribution; S20. When the end effector of the robotic arm is guided to fall into the high confidence region with minimum variance by adding a gravity term to the manifold of the variance of the desired motion model; When there is no interference, the end effector of the robotic arm moves within a high-confidence region with minimal variance; When interference occurs, the movement trajectory of the robotic arm's end effector is changed until the interference is eliminated and the robotic arm returns to the high confidence area. S10 includes the following steps: S11. Obtain the mathematical features of the motion trajectory, including Gaussian noise E and input state. and output status The expression is: ; S12. Train the motion trajectory using kinematic instances to obtain the desired motion model; The kinematic instance expression is: ; N is the number of position points of the Cartesian trajectory of the robotic arm's end effector. Given the end position of the i-th trajectory point, the output is the resampled trajectory data calculated by difference, where each element is the difference between two arrays at the corresponding position; Substituting the kinematic instance expression into the expression for the motion trajectory, we obtain the desired motion model as follows: ; Input variable matrix in a kinematic instance; The mean, Let be the covariance matrix. Each element for and covariance, Let be the kernel function of the Gaussian process, expressed as follows: ; : indicates an input point and Kernel function values ​​between; It is a point and The square of the Euclidean distance between them; represents the hyperparameters of the Gaussian kernel; S13. Calculate the mean and variance of the Gaussian distribution among adjacent data points at the end of the robotic arm. The expression is: ； ； Among them Single evaluation point variance for With training input Covariance between To train the input covariance matrix, Let y be the variance of the Gaussian noise at the training points, and y be the training output. and as well as They are all functions of the kernel function and its hyperparameters.

2. The method for end-effector compensation of an underwater robotic arm based on a Gaussian process according to claim 1, characterized in that, Step 20 includes the following steps; S21. Calculate the kernel matrix between the current end-effector position and the input features of the training data based on the kernel function, and calculate the variance of the kernel matrix and add a gravity term. By multiplying the gradient vector by the inverse of the kernel matrix, we obtain the gradient of the variance with respect to the input features for the input point. Calculate the gradient of the output Its expression is: ； α is a constant based on the maximum permissible automatic modulation, where As evaluation points, For the correction vector; I The inertia matrix; The variance of the Gaussian noise at the training points. for With training input Covariance between them; S22. Before the robotic arm's end effector moves to its current position, calculate the required aggregation direction. and The difference between them, the expression for the aggregate vector is: ； in, This refers to the predicted distance that each axis at the end of the device needs to move based on its current position. The distance required to move to the region of minimum variance. The modulation constant is Maximum offset distance along each axis; S23. Aggregate vectors and Perform a comparison; When aggregate vector Greater than At that time, the end effector of the robotic arm will move along the maximum offset distance of each axis according to its current position. ; When aggregate vector Less than At that time, the end effector of the robotic arm will offset along each axis according to its current position by an amount of [missing information]. .

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