Full-decoupling identification method for load kinetic parameters of tandem mechanical arms

Abstract

The invention discloses a full-decoupling identification method for load kinetic parameters of tandem mechanical arms. Comprising the following steps: firstly, constructing a load dynamics model of the tandem mechanical arm, and representing the load dynamics model as a linear parameterization form about load dynamics parameters; thirdly, three movement joints of the tandem connection mechanical arm are determined, excitation track experiments corresponding to the three movement joints are conducted respectively, and joint positions and torque data corresponding to the three movement joints are obtained; and then, in combination with a load dynamic model of the tandem mechanical arm, full decoupling identification is carried out on load dynamic parameters of the tandem mechanical arm by utilizing the joint positions of the three movement joints and the torque data, and the identified load dynamic parameters are obtained. According to the method, the torque component corresponding to each parameter is separated through the set excitation track, diagonal terms of a gravity parameter and an inertia tensor parameter can be independently identified, the problem of parameter coupling in a traditional method is solved, and the identification precision is remarkably improved compared with a traditional coupling method.

Description

Technical Field

[0001] This invention relates to a method for identifying dynamic parameters of a multi-degree-of-freedom robotic arm, specifically a fully decoupled identification method for the load dynamic parameters of a serially connected robotic arm. Background Technology

[0002] With the continuous development of modern industrial technology, the requirements for robotic arms in terms of precision, stability, and adaptability are increasing. To achieve efficient and precise operation, robotic arms must possess accurate dynamic modeling, especially in precision control scenarios where accurate dynamic feedforward models are crucial. The dynamic parameters of a robotic arm are generally divided into body parameters and load parameters. Body parameters are usually identified once at the factory and remain unchanged in most applications; however, load parameters change continuously due to task variations and need to be re-identified online or before the task. Since the load is usually installed at the end of the robotic arm, it has a significant impact on the overall dynamics. Accurate identification of its dynamic parameters is key to improving the adaptability and stability of the robotic arm under different working conditions, effectively reducing jitter and vibration caused by load changes or external disturbances, thereby improving the system's precision and stability.

[0003] Typical load dynamics parameters include one mass, three center-of-mass positions, and six inertial tensors (three diagonal terms and three off-diagonal terms). These parameters are strongly coupled; a single parameter may affect multiple joint moments simultaneously, and a single joint moment may be influenced by multiple parameters. Traditional identification methods based on the minimum condition number of harmonic excitation trajectories often rely on a single trajectory. Since this optimization problem is typically non-convex and the parameters are coupled, a single trajectory that optimizes to a local minimum often fails to adequately excite all parameters and is susceptible to non-ideal factors such as joint friction. Especially when the acceleration of the optimized excitation trajectory is relatively low, the useful signal is often submerged in noise caused by frictional uncertainties, resulting in low accuracy in inertial parameter identification. Summary of the Invention

[0004] To address the problems and needs in the background technology, this invention proposes a fully decoupled identification method for the load dynamic parameters of a serial robotic arm.

[0005] The technical solution of the present invention is as follows:

[0006] I. A fully decoupled identification method for load dynamic parameters of a serially connected robotic arm

[0007] Step 1: Construct a load dynamics model for the tandem robotic arms;

[0008] Step 2: Determine the three motion joints of the connected robotic arm, conduct excitation trajectory experiments for the three motion joints respectively, and obtain the joint positions and torque data for the three motion joints.

[0009] Step 3: Combining the load dynamics model of the tandem robotic arm, the load dynamics parameters of the tandem robotic arm are fully decoupled and identified using the joint positions and torque data of the three motion joints, and the identified load dynamics parameters are obtained.

[0010] In the second step, the three motion joints of the connected robotic arm are determined, specifically including:

[0011] The joint connected to the load is designated as one of the motion joints and recorded as the end joint. Among the joints other than the end joint in the tandem robotic arm, two joints are selected. When the unselected joints are all stationary at zero position, the rotation axes of the two selected joints are parallel. The two selected joints are then designated as the other two motion joints, thus obtaining the three motion joints of the tandem robotic arm.

[0012] In the second step of the excitation trajectory experiment, the excitation trajectory is a symmetrical reciprocating S-shaped curve. The reciprocating S-shaped curve consists of two trajectories with opposite directions but symmetrical motion. The positive trajectory includes 7 velocity stages, namely, acceleration stage, uniform acceleration stage, deceleration stage, uniform speed stage, deceleration stage, deceleration-uniform speed stage, and deceleration-acceleration stage.

[0013] In the second step, the excitation trajectory experiment includes the following experiments:

[0014] One joint is designated as the target joint. All other joints in the connected robotic arm are kept at zero position. Excitation trajectory experiments are conducted under both no-load and loaded conditions to obtain the corresponding joint position and torque data of the target joint under no-load and loaded conditions. The other two joints are then designated as target joints and excitation trajectory experiments are conducted to obtain the corresponding joint position and torque data of the other two joints under no-load and loaded conditions.

[0015] The joint closest to the end effector of the other two joints is used as the reference joint. All joints in the tandem manipulator, except for the end effector and the reference joint, are kept at zero position. The end effector is fixed at zero position. The acceleration of the uniform acceleration and deceleration segments in the excitation trajectory is changed, and a series of excitation trajectory experiments with different accelerations are applied to the reference joint to obtain the first joint position and torque data of the reference joint under different accelerations. Similarly, all joints in the tandem manipulator, except for the end effector and the reference joint, are kept at zero position. The end effector is fixed at 90°. The acceleration of the uniform acceleration and deceleration segments in the excitation trajectory is changed, and a series of excitation trajectory experiments with different accelerations are applied to the reference joint to obtain the second joint position and torque data of the reference joint under different accelerations.

[0016] In the tandem robotic arm, all joints except the end effector are kept at zero position. The acceleration of the uniform acceleration segment and the deceleration segment in the excitation trajectory are changed, and a series of excitation trajectory experiments with different accelerations are applied to the end effector to obtain the joint position and torque data of the end effector under different accelerations; thus, the joint position and torque data corresponding to the three motion joints are obtained.

[0017] The third step is specifically as follows:

[0018] For each motion joint, the torque data under no-load and loaded conditions at the uniform speed segment of the excitation trajectory are subtracted to obtain the torque difference data of the uniform speed segment of that motion joint; after traversing and processing the torque data of the three motion joints, the torque difference data of the uniform speed segment of the three motion joints is obtained; combined with the load dynamics model of the serial robotic arm, the gravity parameters of the load are identified using the torque difference data of the uniform speed segment of the three motion joints.

[0019] By using all the first joint positions and torque data of the end joint under different accelerations, the diagonal terms of the inertia tensor parameters are identified, thereby obtaining the identified load dynamic parameters.

[0020] The load dynamic parameters include the load's gravity parameters and the diagonal term of the inertia tensor parameters.

[0021] II. A computer device

[0022] The computer device includes a memory and a processor, the memory storing a computer program, and the processor executing the computer program to implement the steps of the method.

[0023] III. A computer-readable storage medium

[0024] The medium stores a computer program that, when executed by a processor, implements the steps of the method.

[0025] IV. A computer program product

[0026] The product includes a computer program / instructions that, when executed by a processor, implement the steps of the method.

[0027] The beneficial effects of this invention are as follows:

[0028] This invention utilizes a symmetrical reciprocating S-curve trajectory and designs experiments with different excitation trajectories to counteract the influence of specific parameters on joint torque. This extracts the independent motion and torque information corresponding to each parameter, fully stimulating the influence of different parameters on joint torque and achieving parameter decoupling and identification. In other words, this invention separates the torque components corresponding to each parameter through the set excitation trajectory, and can independently identify the diagonal terms of gravity parameters and inertia tensor parameters, solving the parameter coupling problem in traditional methods.

[0029] Experimental verification on an industrial six-axis robotic arm shows that, compared with traditional coupling methods, the method proposed in this invention can significantly improve the identification accuracy under different load conditions. Attached Figure Description

[0030] Figure 1 This is a flowchart of the method of the present invention.

[0031] Figure 2 This is a schematic diagram of the reciprocating S-curve used in this invention; where (a) is a position diagram, (b) is a velocity diagram, (c) is an acceleration diagram, and (d) is a jerk diagram.

[0032] Figure 3 The identification and fitting results for joint 6 are shown; where (a) is the torque diagram of joint 6 and (b) is the torque difference diagram of joint 6.

[0033] Figure 4 The identification and fitting results for joint 5 are shown; where (a) is the torque diagram of joint 5 and (b) is the torque difference diagram of joint 5.

[0034] Figure 5 The results of the identification and fitting of joint 3 are shown; where (a) is the torque diagram of joint 3 and (b) is the torque difference diagram of joint 3.

[0035] Figure 6 The results of load inertia parameter identification are used to identify the diagonal parameters of the inertia tensor; where (a) is the identification of ZZ. L A schematic diagram of the change in torque of joint 6 under load and no load with acceleration. Figure (b) shows the identification of ZZ. L A schematic diagram of the torque difference at joint 6 as a function of acceleration is shown in (c), which is used to identify YY. L A schematic diagram of the change in torque with and without load at joint 5 as a function of acceleration, (d) is used to identify YY. L A schematic diagram of the torque difference at joint 5 as a function of acceleration, (e) is for identifying XX. L Schematic diagram of the change of torque with and without load at joint 5 as a function of acceleration, (f) is for identifying XX L A schematic diagram showing the change of torque difference at joint 5 with acceleration.

[0036] Figure 7The excitation trajectories with the minimum condition number used in the traditional coupling identification method for comparison are shown in (a) for joint 3, (b) for joint 5, and (c) for joint 6. Detailed Implementation

[0037] To enable those skilled in the art to better understand the present invention and to more clearly define the scope of protection of the present invention, the present invention will be described in detail below with reference to certain specific embodiments and accompanying drawings. It should be noted that the following are only some specific embodiments of the present invention, and are merely a part of the embodiments of the present invention. The specific and direct descriptions of related structures are only for the convenience of understanding the present invention, and the specific features do not necessarily or directly limit the scope of the present invention. Conventional selections and substitutions made by those skilled in the art under the guidance of the present invention, as well as reasonable arrangements and combinations of several technical features under the guidance of the present invention, should all be considered within the scope of protection of the present invention.

[0038] like Figure 1 As shown, the fully decoupled identification method for load dynamic parameters of a serial robotic arm proposed in this invention includes the following steps:

[0039] Step 1: Construct a load dynamics model for the tandem robotic arms;

[0040] Step 2: Determine the three motion joints of the connected robotic arm, conduct excitation trajectory experiments for the three motion joints respectively, and obtain the joint positions and torque data for the three motion joints.

[0041] The second step involves determining the three motion joints of the robotic arm, specifically including:

[0042] The joint connected to the load is designated as one of the motion joints and recorded as the end joint. Among the joints other than the end joint in the tandem robotic arm, two joints are selected. When the unselected joints are all stationary at zero position, the rotation axes of the two selected joints are parallel. The two selected joints are then designated as the other two motion joints, thus obtaining the three motion joints of the tandem robotic arm.

[0043] In the excitation trajectory experiment, the excitation trajectory is a symmetrical reciprocating S-shaped curve. This curve consists of two trajectories moving in opposite directions but with symmetrical motion. The positive trajectory includes seven velocity stages: acceleration, uniform acceleration, deceleration, uniform speed, deceleration / constant speed, and deceleration / acceleration. A schematic diagram of the excitation trajectory is shown below. Figure 2 As shown, Figure 2 (a) is a location diagram. Figure 2 (b) is a velocity diagram. Figure 2 (c) is a schematic diagram of acceleration. Figure 2(d) is a schematic diagram of jerk. Figure 2 The red line represents forward motion, and the blue line represents backward motion. The bolded segments of the lines are the data segments used in the parameter identification process of this invention, namely the three pairs of decoupled motion segments: CV1 / CV2, CA1 / CD2, and CA2 / CD1. For the red curve, the bolded segments are, in order, uniform acceleration, uniform velocity, and deceleration. Let T be the duration of segments CVj, CAj, and CDj. v T a T a j = 1, 2. p CV1 (t),v CV1 (t),a CV1 (t) represent the position, velocity, and acceleration at time t in segment CV1, respectively, and and Defined as p CV1 The dual position of (t), i.e., segment T of CV1 v -The position at time t. And so on, all other variables have the same sign. The symmetry of the reciprocating S-curve is as follows: Figure 2 As shown, the reciprocating S-curve has the following properties:

[0044]

[0045] Where, p cv2 (T v -t) indicates CV2 segment T v -t position This represents the dual position of segment CV2 at time t, i.e., segment CV2 T. v -t represents the position at time t, v cv1 (t) represents the velocity v at time t in segment CV1. cv2 (t) represents the velocity at time t in segment CV2, a cv1 (t) represents the acceleration at time t in segment CV1, a cv2 (t) represents the acceleration at time t in segment CV2. ca1 (t) represents the position of segment CA1 at time t, p cd2 (T a -t) indicates that segment T in CD2 is... a -t position This represents the dual position of segment CD2 at time t, i.e., segment CD2 at time T. a The position at time t, a ca1 (t) represents the acceleration at time t in segment CA1, a cd2 (t) represents the acceleration at time t in segment CD2, p cd1 (t) represents the position of segment CD1 at time t, p ca2 (T a -t) indicates CA2 segment T a-t position This represents the dual position of segment CA2 at time t, i.e., segment CA2 at time T. a -t represents the position at time t, v cd1 (t) represents the velocity v at time t in segment CD1. ca2 (T a -t) indicates CA2 segment T a The velocity at time -t This represents the dual velocity at time t in segment CA2, i.e., segment T in segment CA2. a The velocity at time t, a cd1 (t) represents the acceleration at time t in segment CD1, a ca (t) represents the acceleration at time t in segment CA2.

[0046] Maximum speed, acceleration, and acceleration are v m a m and j m It is worth noting that only experimental data from segments CA, CV, and CD were used during parameter identification. For example, CD1 represents the uniformly decelerated segment moving forward, and CA2 represents the uniformly accelerated segment moving backward.

[0047] Before beginning the identification of dynamic parameters, a reasonable assumption is made about the friction model, namely...

[0048]

[0049] Where, q i Represents the velocity along the i-th axis. The velocity of the i-th axis is Joint friction during time, The velocity of the i-th axis is Joint friction during

[0050] The excitation trajectory experiment includes the following experiments:

[0051] One joint is designated as the target joint. All other joints in the connected robotic arm are stationary at zero position. Excitation trajectory experiments are conducted under both no-load and loaded conditions on the connected robotic arm, i.e., running a reciprocating S-shaped curve excitation trajectory from the negative limit to the positive limit, to obtain the corresponding joint position and torque data of the target joint under no-load and loaded conditions. The other two joints are then designated as target joints and excitation trajectory experiments are conducted to obtain the corresponding joint position and torque data of the other two joints under no-load and loaded conditions. The excitation trajectory applied in the excitation trajectory experiments of different joints is the same.

[0052] The joint closest to the end effector joint among the other two motion joints is used as the reference joint. All joints in the tandem manipulator, except for the end effector joint and the reference joint, are kept at zero position. The end effector joint is fixed at zero position. The acceleration of the uniform acceleration and deceleration segments in the excitation trajectory is changed, and a series of excitation trajectory experiments with different accelerations are applied to the reference joint. That is, the acceleration of the uniform acceleration and deceleration segments in different excitation trajectories is different, obtaining the first joint position and torque data of the reference joint under different accelerations. Similarly, all joints in the tandem manipulator, except for the end effector joint and the reference joint, are kept at zero position. The end effector joint is fixed at 90°. The acceleration of the uniform acceleration and deceleration segments in the excitation trajectory is changed, and a series of excitation trajectory experiments with different accelerations are applied to the reference joint. That is, the acceleration of the uniform acceleration and deceleration segments in different excitation trajectories is different, and the acceleration value is the same as the value set when the end effector joint is fixed at zero position, obtaining the second joint position and torque data of the reference joint under different accelerations.

[0053] In the tandem robotic arm, all joints except the end effector are kept at zero position. The acceleration of the uniform acceleration segment and the deceleration segment in the excitation trajectory are changed, and a series of excitation trajectory experiments with different accelerations are applied to the end effector to obtain the joint position and torque data of the end effector under different accelerations; thus, the joint position and torque data corresponding to the three motion joints are obtained.

[0054] Step 3: Combining the load dynamics model of the tandem robotic arm, the load dynamics parameters of the tandem robotic arm are fully decoupled and identified using the joint positions and torque data of the three motion joints, thus obtaining the identified load dynamics parameters. Furthermore, the dynamics of the overall system can be obtained from the identified load dynamics parameters and the known robotic arm body dynamics parameters, which can then be used in model feedforward compensation or force control for motion control.

[0055] The third step is as follows:

[0056] For each motion joint, the torque data under no-load and loaded conditions at the uniform speed segment of the excitation trajectory are subtracted to obtain the torque difference data of the uniform speed segment of that motion joint; after traversing and processing the torque data of the three motion joints, the torque difference data of the uniform speed segment of the three motion joints is obtained; combined with the load dynamics model of the serial robotic arm, the gravity parameters of the load are identified using the torque difference data of the uniform speed segment of the three motion joints.

[0057] By using the joint position and torque data of the end joint under different accelerations, the first joint position and torque data of the reference joint under different accelerations, and the second joint position and torque data of the reference joint under different accelerations (i.e., data of the uniform acceleration segment), the diagonal terms of the inertia tensor parameters are identified, thereby obtaining the identified load dynamic parameters.

[0058] For example, select 3 joints from a series of robotic arms as moving joints, and fix all other joints in the zero position. Renumber the selected joints as joints 1, 2, and 3. This joint selection can be specifically defined as follows: the most distal joint is joint 3, the next distal joint (i.e., the reference joint) is joint 2, and the front joint parallel to joint 2 is joint 1.

[0059] Step 1: Fix joints 1 and 2 at the zero position, apply a reciprocating S-curve excitation trajectory to joint 3, obtain the corresponding joint positions and torque data of joint 3 under no-load and loaded conditions, and then identify the MX of the gravity parameter of the load using the least squares method. L and MY L Components. Further, with joints 1 and 2 fixed at zero position, multiple reciprocating S-curve excitation trajectories with different maximum accelerations are applied to joint 3. The corresponding joint positions and torque data of joint 3 under no-load and loaded conditions are obtained. Then, a linear relationship graph of the load inertial torque corresponding to different maximum accelerations is fitted. The ZZ value of the load inertial parameters is identified based on the slope of this linear relationship graph. L Quantity.

[0060] Step 2: Fix joints 1 and 3 at the zero position, apply a reciprocating S-curve excitation trajectory to joint 2, obtain the corresponding joint positions and torque data of joint 2 under no-load and loaded conditions, and then identify the gravity parameter M of the load using the least squares method. L and MZ L The value after linear combination. Further, with joints 1 and 3 fixed at zero, multiple reciprocating S-curve excitation trajectories with different maximum accelerations are applied to joint 2. The corresponding joint positions and torque data of joint 2 under no-load and loaded conditions are obtained. Then, a linear relationship graph of the load inertial torque corresponding to different maximum accelerations is fitted. The XX value of the load inertial parameter is identified based on the slope of this linear relationship graph. L Next, simply fix joint 3 at 90 degrees and repeat the above inertial parameter identification steps to obtain the YY inertial parameters of the load. L Quantity.

[0061] The third step involves fixing joints 2 and 3 at their zero positions, applying a reciprocating S-curve excitation trajectory to joint 1, and obtaining the corresponding joint positions and torque data for joint 1 under no-load and loaded conditions. Then, the gravity parameter M of the load is identified using the least squares method. L and MZ L The value after linear combination. Based on M from steps two and three. L and MZ L Two linear combinations of can be used to solve for M. L and MZ L.

[0062] The load dynamics parameters include the load's gravity parameters and the diagonal terms of the inertia tensor parameters.

[0063] Because the magnitude of the off-diagonal terms of the inertia tensor is usually small and negligible, they are only necessary to consider for loads with large mass and severe eccentricity. Existing methods can be used to identify the off-diagonal terms of the inertia tensor parameters. For example, by minimizing the excitation trajectory with the condition number, the off-diagonal terms of the load's inertia tensor parameters can be identified using least squares.

[0064] The method proposed in this invention will be specifically explained below using a six-axis robotic arm as an example:

[0065] Similar to the dynamic parameters of the robotic arm itself, the dynamic parameters of the load are also determined by the gravitational parameter β. lg =[M L ,MX L ,MY L MZ L ] T and inertial parameter β lm =[XX L ,XY L XZ L YY L YZ L ZZ L ] T Composition, in which M L For load quality, MX L ,MY L MZ L XX represents the product of the three coordinate values ​​of the load mass and the load centroid, respectively. L YY L ZZ L These are the three diagonal terms of the inertia tensor, XY L XZ L YZ L Let T represent the three typically negligible off-diagonal terms of the inertia tensor, and let T denote the transpose operation. When the robotic arm moves along the same trajectory twice, once with a load and once without a load, the joint torque difference Δτ can be linearly parameterized as:

[0066]

[0067] Where, q, These are joint position, velocity, and acceleration, respectively. Let Δτ be the regression matrix with respect to the inertia parameter. Let Δτ be the regression matrix with respect to the gravity parameter, and δ be the regression matrix. f This indicates how frictional force changes with different loads.

[0068] Therefore, the problem of identifying the dynamic parameters of the end-effector load can be described as follows: design the excitation trajectory of the robot arm motion, let the robot arm move along the excitation trajectory twice, once with a load and once without a load, and use the recorded joint torque input difference and motion output to accurately estimate the dynamic parameters of the end-effector load.

[0069] Unlike identifying the dynamic parameters of the robotic arm itself, identifying the load dynamic parameters requires the robotic arm to move along the same trajectory twice, with and without load. The corresponding joint torque difference Δτ i This represents the impact of the end-effector load on the overall dynamics. For a 6-axis robotic arm, joints 3, 5, and 6 are selected for motion; identification can be completed using only the data from axes 3, 5, and 6. The aforementioned decoupling identification process operates only one joint at a time, while the specific method for fixing the other joints is applied to the 6-axis robotic arm as follows: To simplify Δτ6, MY is decoupled... L ,MY L ZZ L When the 6th axis executes the reciprocating S-curve excitation trajectory, all other axes are fixed at zero position, corresponding to one set of motion; to simplify Δτ5, M is decoupled. L MZ L ,XX L YY L When the 5th axis executes a reciprocating S-curve excitation trajectory, the 6th axis can be fixed at 0 degrees and 90 degrees respectively, and all other axes can be fixed at zero. Therefore, this corresponds to two sets of motions. To simplify Δτ3, M is decoupled. L MZ L When the reciprocating S-curve excitation trajectory is executed on the third axis, all other axes are fixed at zero, thus corresponding to one set of motion. From the above simplification process, the symbolic equation of formula (5) can be written as:

[0070]

[0071] Δτ3=g(L4s3+L5c3+L6c3)M L +gs3MX L +gc3MZ L +δ f3

[0072] Where g is the acceleration due to gravity, and L4, L5, L6 are the corresponding link lengths, usually defined in the DH parameter table. s3, c3, s5, c5, s6, c6 are abbreviations for sin(q3), cos(q3), sin(q5), cos(q5), sin(q6), and cos(q6), respectively. 66δ is an abbreviation for sin(q6), where Δτ3, Δτ5, and Δτ6 represent the torque differences between joints 3, 5, and 6 under load and unloaded conditions, respectively. f6 ,δ f5 ,δ f3 This indicates the change in frictional torque caused by different load conditions at the end.

[0073] The trajectory used to identify the load gravity parameters is a reciprocating S-shaped curve excitation trajectory for joints 3, 5, and 6, running from the negative limit to the positive limit, while keeping all other joints stationary at zero position. During the operation, the position and torque information of each joint are recorded.

[0074] Under the same operating conditions (temperature, lubrication, or end load), the joint friction torque changes of segments CV1 and CV2 should be the same, so we have formula (7):

[0075]

[0076] in, The frictional torque variation of the i-th joint in segment CV1 is caused by different load conditions at the end. The frictional torque change of the i-th joint caused by different load conditions at the end of segment CV2.

[0077] Substituting equations (7) and (5) into equation (6), and noting that the joint acceleration is zero, by eliminating the change in joint friction torque, we can obtain the result in equation (6).

[0078]

[0079] In the formula, The effect of the load on the i-th joint torque of segment CV1. and These represent the joint torques of joint i in segments CV1 and CV2, respectively, when the robotic arm follows the excitation trajectory with an end-effector load. and This represents the joint torque of joint i in segments CV1 and CV2 when the robotic arm is running the excitation trajectory without an end-effector load.

[0080] The load gravity parameter identification method proposed in formula (8) is used to analyze the change of friction torque δ under different loads or temperatures. fi It exhibits robustness because the reciprocating S-shaped excitation trajectory is symmetrical, allowing the CV1 and CV2 segments of each experiment to offset δ. fi The change is shown in Equation (8). In contrast, the coupled parameter identification method that directly uses regression Equation (6) to identify all load dynamic parameters at once cannot eliminate δ. fiThis will lead to a decrease in the accuracy of load parameter identification.

[0081] As shown in formula (6), data from segments CV1 and CV2 of joint 6 are sufficient to identify MXL and MYL. However, identifying ML and MZL requires data from joints 3 and 5, because the regressions ML and MZL are linearly correlated, meaning that each identification only yields the sum of these two parameters. Intuitively, ML and MZL cannot be identified using data from a single joint, as the impact of a load with a longer center-of-gravity distance and lighter mass on a single joint is the same as that of a load with a shorter center-of-gravity distance and heavier mass. Therefore, to identify ML and MZL, data from both joints must be combined. Furthermore, data from joint 5 is more reliable than data from joint 3 because it exhibits less wave dynamics and flexibility disturbances.

[0082] In mathematical implementation, the linear regression formula (6) can be obtained by setting all link dynamic parameters in the inverse dynamics to zero. Combining formulas (6) and (8), the four load gravity parameters ML, MXL, MYL, and MZL can be estimated using the least squares method using the data from segments CV1 and CV2. The results of the load gravity parameter identification are as follows: Figure 3 , Figure 4 and Figure 5 As shown.

[0083] To identify the load inertia parameters, according to regression formula (6), the excitation trajectory only involves the motion of joints 5 and 6. To identify ZZL, the excitation trajectory is a series of reciprocating S-curve excitation trajectories with different accelerations applied to joint 6. To identify XXL and YYL, joint 6 is fixed at zero position and 90° respectively, and then a series of reciprocating S-curve excitation trajectories with different accelerations are applied to joint 5.

[0084] Identifying the load inertia parameters requires data from segments CA and CD, specifically the CA1 / CD2 and CA2 / CD1 motion segments, to extract the inertial torque Δτ. mi Using acceleration and inertial torque Δτ6-gs6MX L +gc6MY L Performing linear regression yields a regression line, the slope of which is ZZL. Similarly, XXL corresponds to the acceleration when q6 = 90°. With inertial torque The slope of the normal line, YYL, corresponds to the acceleration when q6 = 0. With inertial torque The slope of the regression line and the results of load inertia parameter identification are as follows: Figure 6 As shown.

[0085] Because the order of magnitude of the off-diagonal terms of the inertia tensor is usually small and negligible, this step is only considered when the load mass is large and the eccentricity is severe. In the robotic arm used to verify the example of this invention, this off-diagonal term was ignored due to the small load capacity (only 3 kg). Otherwise, existing methods can be used to identify the off-diagonal terms of the inertia tensor parameters. For example, the off-diagonal terms of the load's inertia tensor parameters can be identified using least squares by minimizing the excitation trajectory with the condition number. Specifically:

[0086] The design employs an excitation trajectory with only off-diagonal parameters. The trajectory is composed of a superposition of five Fourier harmonics, with the unknown harmonic amplitudes serving as the optimization term. The optimization objective is to minimize the condition number of the excitation trajectory with respect to the off-diagonal parameters. Equality constraints are applied to the initial position, initial velocity, and initial acceleration of the trajectory, while inequality constraints are applied to the upper and lower bounds of position, velocity, and acceleration. After running the excitation trajectory, joint position and torque information are collected. Gravity parameters and diagonal inertial parameters are set as known terms (as identified previously), and the off-diagonal inertial parameters are obtained through least squares calculation.

[0087] For the identification of end-load dynamic parameters, this invention compares the following two methods:

[0088] Method 1: The decoupling dynamic parameter identification method proposed in this invention.

[0089] Method 2: Coupled Dynamics Parameter Identification Method. The method for designing the excitation trajectory is to minimize the conditional value of the information matrix obtained from the regression of the load dynamics parameters. The optimized excitation trajectory of each joint is as follows: Figure 7 As shown, only joints 3, 5, and 6 are in motion; these three axes operate simultaneously during the experiment, while joints 1, 2, and 4 are stationary. The conditional value of the trajectory information matrix is ​​19.48. Then, all load dynamic parameters are identified at once using the least squares method through regression equation (6).

[0090] The load dynamic parameter identification method was validated by identifying the dynamic parameters of three different loads (two symmetrical loads and one asymmetrical load) and comparing them with the true values ​​of the dynamic parameters of the solid model built in SolidWorks modeling software. Figure 4 As shown in Table 1, the identified load dynamic parameters are as follows.

[0091] Table 1. Results of Load Dynamics Parameter Identification

[0092]

[0093]

[0094] Both the fully decoupled identification method and the coupled identification method identify load dynamic parameters that are very close to the true values, but the fully decoupled identification method has higher accuracy, especially for load inertia parameters, thus verifying the superiority of the proposed fully decoupled load dynamic parameter identification method.

[0095] Finally, the feasibility and advantages of the method of the present invention were verified through the embodiments.

Claims

1. A fully decoupled identification method for load dynamic parameters of a serially connected robotic arm, characterized in that, Includes the following steps: Step 1: Construct a load dynamics model for the tandem robotic arms; Step 2: Determine the three motion joints of the connected robotic arm, conduct excitation trajectory experiments for the three motion joints respectively, and obtain the joint positions and torque data for the three motion joints. Step 3: Combining the load dynamics model of the tandem robotic arm, the load dynamics parameters of the tandem robotic arm are fully decoupled and identified using the joint positions and torque data of the three motion joints, and the identified load dynamics parameters are obtained.

2. The fully decoupled identification method for load dynamic parameters of a serially connected robotic arm according to claim 1, characterized in that, In the second step, the three motion joints of the connected robotic arm are determined, specifically including: The joint connected to the load is designated as one of the motion joints and recorded as the end joint. Among the joints other than the end joint in the tandem robotic arm, two joints are selected. When the unselected joints are all stationary at zero position, the rotation axes of the two selected joints are parallel. The two selected joints are then designated as the other two motion joints, thus obtaining the three motion joints of the tandem robotic arm.

3. The fully decoupled identification method for load dynamic parameters of a serially connected robotic arm according to claim 1, characterized in that, In the second step of the excitation trajectory experiment, the excitation trajectory is a symmetrical reciprocating S-shaped curve. The reciprocating S-shaped curve consists of two trajectories with opposite directions but symmetrical motion. The positive trajectory includes 7 velocity stages, namely, acceleration stage, uniform acceleration stage, deceleration stage, uniform speed stage, deceleration stage, deceleration-uniform speed stage, and deceleration-acceleration stage.

4. The fully decoupled identification method for load dynamic parameters of a serially connected robotic arm according to claim 1, characterized in that, In the second step, the excitation trajectory experiment includes the following experiments: One joint is designated as the target joint. All other joints in the connected robotic arm are kept at zero position. Excitation trajectory experiments are conducted under both no-load and loaded conditions to obtain the corresponding joint position and torque data of the target joint under no-load and loaded conditions. The other two joints are then designated as target joints and excitation trajectory experiments are conducted to obtain the corresponding joint position and torque data of the other two joints under no-load and loaded conditions. The joint closest to the distal joint among the other two joints is used as the reference joint. All joints in the tandem robotic arm except for the end joint and the reference joint are kept at zero position. The end joint is fixed at zero position. The acceleration of the uniform acceleration segment and the deceleration segment in the excitation trajectory are changed. A series of excitation trajectory experiments with different accelerations are applied to the reference joint to obtain the first joint position and torque data of the reference joint under different accelerations. In addition, all joints in the tandem robotic arm except for the end joint and the reference joint are kept at zero position, the end joint is fixed at 90°, the acceleration of the uniform acceleration segment and the deceleration segment in the excitation trajectory are changed, and a series of excitation trajectory experiments with different accelerations are applied to the reference joint to obtain the second joint position and torque data of the reference joint under different accelerations. In the tandem robotic arm, all joints except the end effector are kept at zero position. The acceleration of the uniform acceleration segment and the deceleration segment in the excitation trajectory are changed, and a series of excitation trajectory experiments with different accelerations are applied to the end effector to obtain the joint position and torque data of the end effector under different accelerations; thus, the joint position and torque data corresponding to the three motion joints are obtained.

5. The fully decoupled identification method for load dynamic parameters of a serially connected robotic arm according to claim 1, characterized in that, The third step is specifically as follows: For each motion joint, the torque data under no-load and loaded conditions at the uniform speed segment of the excitation trajectory are subtracted to obtain the torque difference data of the uniform speed segment of that motion joint; after traversing and processing the torque data of the three motion joints, the torque difference data of the uniform speed segment of the three motion joints is obtained; combined with the load dynamics model of the serial robotic arm, the gravity parameters of the load are identified using the torque difference data of the uniform speed segment of the three motion joints. By using the joint position and torque data of the end joint under different accelerations, the first joint position and torque data of the reference joint under different accelerations, and the second joint position and torque data of the reference joint under different accelerations, the diagonal terms of the inertia tensor parameters are identified, thereby obtaining the identified load dynamic parameters.

6. The fully decoupled identification method for load dynamic parameters of a serial robotic arm according to claim 1, characterized in that, The load dynamic parameters include the load's gravity parameters and the diagonal term of the inertia tensor parameters.

7. A computer device comprising a memory and a processor, wherein the memory stores a computer program, characterized in that, When the processor executes the computer program, it implements the steps of the method according to any one of claims 1 to 6.

8. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by a processor, it implements the steps of the method according to any one of claims 1 to 6.

9. A computer program product comprising a computer program / instructions, characterized in that, When the computer program / instructions are executed by the processor, they implement the steps of the method described in any one of claims 1 to 6.

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