Robot trajectory optimization method based on dynamic circle center compound motion

Abstract

The invention relates to a robot trajectory optimization method based on dynamic circle center compound motion. The robot trajectory optimization method based on the dynamic circle center compound motion comprises the following steps: initializing trajectory parameters; calculating a dynamic circle center track; the rotation angle of the tail end of the robot is calculated by calculating the posture quaternion of the tail end of the robot, and smooth interpolation is conducted on the rotation angle through a quintic polynomial curve; constructing a local coordinate system of the tail end track of the robot; planning a circumferential swing track, and controlling the circumferential swing track through the trapezoidal speed curve; through real-time pose interpolation calculation, calculating a pose difference parameter and converting a pose quaternion into a pose; and a local position vector is constructed, and pose calculation is completed through the local position vector and the pose. The robot trajectory optimization method based on the dynamic circle center compound motion has the advantages of being good in trajectory generation quality and high in control stability.

Description

Technical Field

[0001] This invention relates to the field of robot trajectory optimization, and in particular to a robot trajectory optimization method based on dynamic circular center composite motion. Background Technology

[0002] Welding robots are widely used in today's manufacturing industry. When faced with complex welding tasks, robots need to employ composite motion welding. Elliptical or circular pendulum trajectories are frequently used in welding, and these trajectories need to be optimized. Welding robot trajectory optimization can significantly improve welding quality and efficiency by ensuring smoothness of motion, continuity of posture, and dynamic feasibility.

[0003] However, in composite motion welding, the robot end effector often suffers from problems such as uneven trajectory, sudden changes in posture, and difficulty in meeting dynamic constraints, resulting in unstable welding quality, motion jitter, or even task failure. Furthermore, when achieving coordinated translational and rotational control, there are problems such as significant translational and rotational coupling effects and limited real-time performance of interpolation algorithms, which affect the quality of trajectory generation and control stability. Summary of the Invention

[0004] Based on this, the purpose of this invention is to provide a robot trajectory optimization method based on dynamic circular center composite motion, which has the advantages of good trajectory generation quality and high control stability.

[0005] A robot trajectory optimization method based on dynamic circular center composite motion specifically includes the following steps:

[0006] S1 initializes the trajectory parameters and verifies their validity; And execute steps S2A to S3A, S2B to S3B; S2A calculates the dynamic circle center trajectory; obtains the dynamic circle center positions at the start and end times, and calculates the distance the dynamic circle center has moved. and total exercise time ; S3A calculates the rotation angle of the robot's end effector by calculating the quaternion of the robot's posture, and then smoothly interpolates the rotation angle using a fifth-order polynomial curve; it outputs the interpolated rotation angle of the robot's end effector. S2B constructs the local coordinate system of the robot's end effector trajectory by building a transformation matrix from the local coordinate system to the world coordinate system; S3B plans the circular oscillation trajectory and controls the circular oscillation trajectory through a trapezoidal velocity curve; it outputs the circular oscillation trajectory controlled by the trapezoidal velocity curve. S4 receives the dynamic center trajectory, robot end effector rotation angle, local coordinate system of robot end effector trajectory constructed in S3B, and circular swing trajectory from step S3A; calculates the attitude difference parameters and converts the attitude quaternion into attitude through real-time pose interpolation; constructs a local position vector and completes the pose calculation through the local position vector and attitude.

[0007] The robot trajectory optimization method based on dynamic circular center composite motion described in this invention decouples the translation and rotation of the robot end-effector trajectory, controls the circular oscillation through trapezoidal velocity, and performs double-layer interpolation by combining attitude quaternions and quintic polynomial curves, thereby improving the smoothness and stability of trajectory generation.

[0008] Furthermore, the robot end-effector trajectory parameters include the oscillation frequency of the robot end-effector. oscillation radius oscillation speed Maximum swing speed acceleration Welding start position vector Weld termination position vector .

[0009] Furthermore, verifying the validity of the trajectory parameters includes verifying whether the input parameters are within a preset range. If the verification is successful, the subsequent steps continue; if the verification fails, an error is reported and the calculation is terminated.

[0010] Furthermore, step S2A specifically includes the following steps: S2A1 via the welding start position vector Weld termination position vector Calculate the unit vector from the starting point to the ending point. ;

[0011] S2A2 via the welding start position vector Weld termination position vector and swing radius Calculate the dynamic center position at the start time. and the dynamic center position at the termination time ;

[0012]

[0013] S2A3 passes through the dynamic center position. and the dynamic center position at the termination time Calculate the distance the dynamic center moves. and total exercise time

[0014]

[0015] .

[0017] Furthermore, step S3A specifically includes the following steps: S3A1 obtains the robot's end effector's initial pose quaternion. and robot end-effector quaternion The robot end-effector pose difference quaternion was calculated. ;

[0018]

[0019]

[0020] in, This is the initial pose matrix of the robot's end effector. The final pose matrix for the robot's end effector; S3A2 uses the quaternion of the robot's end-effector posture difference. Convert to robot end-effector angle representation ,pass Obtain the rotation angle of the robot's end effector ;

[0021]

[0022] S3A3 sets the robot's end-effector position. For time The fifth-degree polynomial and its corresponding speed. and acceleration ;

[0023]

[0024]

[0025] S3A4 determines the coefficients of the fifth-degree polynomial using boundary conditions. to The rotation angle is smoothly interpolated using a fifth-order polynomial curve.

[0026] Furthermore, the boundary conditions include the position, velocity, and acceleration of the robot's end effector at the start and end times; including , , , , , .

[0027] Further, step S2B includes the following steps: S2B1 calculates the unit vector of the welding direction. and the unit vector of the swing direction And given the unit vector in the Z direction of the world coordinate system. ;

[0028]

[0029] S2B2 constructs the rotation matrix of the robot's end effector local coordinate system. Through the rotation matrix of the robot's end effector local coordinate system and welding start position vector This constitutes the transformation matrix from the local coordinate system to the world coordinate system.

[0030]

[0031] .

[0033] Furthermore, step S3B specifically includes the following steps: S3B1 calculates the number of oscillation cycles. Swing angle Maximum angular velocity of oscillation and angular acceleration Plan the circular oscillation trajectory;

[0034]

[0035]

[0036]

[0037] The S3B2 is equipped with a trapezoidal velocity curve, which is used to control the target angle. and angular velocity of oscillation This allows for the control of the circular oscillation trajectory.

[0038] Furthermore, in step S3B2, the trapezoidal velocity curve includes an acceleration segment, a constant speed segment, and a deceleration segment; Let the time period of the acceleration segment be . During the acceleration phase, the target angle and angular velocity of oscillation for:

[0039]

[0040] Let the time interval of the uniform speed segment be . During the uniform velocity segment, the target angle and angular velocity of oscillation for:

[0041]

[0042] in, ; Let the time period of the deceleration segment be . During the uniform velocity segment, the target angle and angular velocity of oscillation for:

[0043]

[0044] in, .

[0045] Furthermore, step S4 specifically includes the following steps: S41 Calculate attitude difference parameters ;

[0046] S42 Calculate attitude quaternions By using spherical linear interpolation, the attitude quaternions are... Transform into posture ;

[0047]

[0048]

[0049] S43 by swing angle and dynamic center position Perform elliptical position interpolation to obtain the coordinates of the robot end effector in the local coordinate system. , , This leads to the construction of local position vectors. ;

[0050]

[0051]

[0052]

[0053]

[0054] S44 transforms the local position vector using coordinate transformation. Mapped to position vector in world coordinate system Through posture and position vector in world coordinate system Complete robot end-effector pose Solution

[0055] .

[0057] To better understand and implement this invention, the following detailed description is provided in conjunction with the accompanying drawings. Attached Figure Description

[0058] Figure 1 This is a schematic diagram of a robot trajectory optimization method based on dynamic circular center composite motion according to an embodiment of the present invention; Figure 2 This is a simulation diagram of the welding trajectory of the robot trajectory optimization method based on dynamic circular center composite motion according to an embodiment of the present invention. Detailed Implementation

[0059] 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.

[0060] In the description of this invention, it should be noted that the terms "first", "second", "third" and "fourth" are used for descriptive purposes only and should not be construed as indicating or implying relative importance.

[0061] Example Please see Figure 1This invention provides a robot trajectory optimization method based on dynamic circular center composite motion. The robot trajectory is a circular oscillating welding trajectory based on a dynamic circular center. The robot end effector oscillates around the dynamic circular center, and the dynamic circular center moves at a constant speed along a straight line.

[0062] The robot trajectory optimization method based on dynamic circular center composite motion of the present invention specifically includes the following steps: S1: Obtain the trajectory parameters of the robot's end effector and verify the validity of the trajectory parameters; and execute steps S2A to S3A and S2B to S3B. S2A: Calculate the dynamic circle center trajectory, obtain the dynamic circle center positions at the start and end times, and calculate the distance the dynamic circle center has moved. and total exercise time ; S3A: Calculates the rotation angle of the robot's end effector, performs smooth interpolation on the rotation angle using a fifth-order polynomial curve, and outputs the interpolated rotation angle of the robot's end effector. S2B: By constructing a transformation matrix from the local coordinate system to the world coordinate system, the local coordinate system of the robot's end effector trajectory is constructed; S3B: Plans the circular oscillation trajectory, controls the circular oscillation trajectory through a trapezoidal velocity curve; outputs the circular oscillation trajectory controlled by the trapezoidal velocity curve. S4: Receive the dynamic center trajectory, robot end effector rotation angle, local coordinate system of robot end effector trajectory constructed in S3B, and circular swing trajectory from step S3A; calculate the attitude difference parameters and convert the attitude quaternion into attitude through real-time pose interpolation; construct the local position vector and complete the pose calculation through the local position vector and attitude.

[0063] Furthermore, in step S1, the robot end-effector trajectory parameters include the oscillation frequency of the robot end-effector. oscillation radius oscillation speed Maximum swing speed acceleration Welding start position vector Weld termination position vector ; Furthermore, verifying the validity of the trajectory parameters includes verifying whether the input parameters are within a preset range. If the verification is successful, the subsequent steps continue; if the verification fails, an error is reported and the calculation is terminated.

[0064] In some embodiments, verifying the validity of input parameters includes verifying the oscillation frequency. oscillation radius oscillation speed Maximum swing speed acceleration The parameters are greater than zero.

[0065] Furthermore, step S2A specifically includes the following steps: S2A1 via welding start position vector Weld termination position vector Calculate the unit vector from the starting point to the ending point. ;

[0066] S2A2 via welding start position vector Weld termination position vector and swing radius Calculate the dynamic center position at the start time. and the dynamic center position at the termination time ;

[0067]

[0068] S2A3 via dynamic center position and the dynamic center position at the termination time Calculate the distance the dynamic center moves. and total exercise time .

[0069]

[0070]

[0071] In some embodiments, step S2A further includes step S2A4 verification. If the verification is successful, continue with the next steps; if the verification fails, report an error and stop the calculation.

[0072] Furthermore, step S3A specifically includes the following steps: S3A1 obtains the robot's end effector's initial pose quaternion. and robot end-effector quaternion The robot end-effector pose difference quaternion was calculated. ;

[0073]

[0074]

[0075] in, This is the initial pose matrix of the robot's end effector. The final pose matrix for the robot's end effector; S3A2 uses the robot's end-effector attitude difference quaternion. Convert to robot end-effector angle representation ,pass Obtain the rotation angle of the robot's end effector ;

[0076]

[0077] S3A3 sets the robot's end-effector position. For time The fifth-degree polynomial and its corresponding speed. and acceleration ;

[0078]

[0079]

[0080] S3A4 determines the coefficients of the quintic polynomial using boundary conditions. to The rotation angle is smoothly interpolated by a fifth-order polynomial curve, and the interpolated rotation angle of the robot end effector is output. Boundary conditions include the position, velocity, and acceleration of the robot's end effector at the start and end times; including , , , , , ; Substitute it , and Solving for the problem, , , ,

[0081]

[0082]

[0083] Further, step S2B includes the following steps: S2B1 calculates the unit vector of the welding direction. and the unit vector of the swing direction And given the unit vector in the Z direction of the world coordinate system. ;

[0084]

[0085] S2B2 constructs the rotation matrix of the robot's end effector local coordinate system. Through the rotation matrix of the robot's end effector local coordinate system and welding start position vector This constitutes the transformation matrix from the local coordinate system to the world coordinate system. .

[0086]

[0087]

[0088] Furthermore, step S3B specifically includes the following steps: S3B1 calculates the number of oscillation cycles. Swing angle Maximum angular velocity of oscillation and angular acceleration Plan the circular oscillation trajectory;

[0089]

[0090]

[0091]

[0092] Among them, the number of oscillation periods The number of cycles and the swing angle of the robot's end effector trajectory oscillation waveform. The total angle of the robot's end effector trajectory around the dynamic center, and the maximum angular velocity of the swing. The maximum angular velocity and angular acceleration of the robot's end effector trajectory around the dynamic center of the circle. This is the angular acceleration of the robot's end effector as it moves around the dynamic center of a circle.

[0093] The S3B2 is equipped with a trapezoidal velocity curve, which is used to control the target angle. and angular velocity of oscillation This allows for the control of the circular oscillation trajectory; the output is a circular oscillation trajectory controlled by a trapezoidal velocity curve. The trapezoidal velocity curve includes an acceleration segment, a constant velocity segment, and a deceleration segment; Let the time period of the acceleration segment be... During the acceleration phase, the target angle and angular velocity of oscillation for:

[0094]

[0095] Let the time interval of the uniform speed segment be . During the uniform velocity segment, the target angle and angular velocity of oscillation for:

[0096]

[0097] in, ; Let the time period of the deceleration segment be... During the uniform velocity segment, the target angle and angular velocity of oscillation for:

[0098]

[0099] in, .

[0100] In some embodiments, step S3B further includes step S3B3: verification If the verification is successful, continue with the next steps; if the verification fails, report an error and stop the calculation.

[0101] In step S3B3, , This is the maximum acceleration; The swing distance of the robot's end effector during the acceleration phase ; Furthermore, the swing distance of the robot's end effector throughout the entire trapezoidal velocity curve. ; and thus obtain ; therefore, ,Will and Substitute them separately Perform verification. If the verification is successful, continue to the next step; if the verification fails, report an error and stop the calculation.

[0102] Furthermore, step S4 specifically includes the following steps: S41 Calculate attitude difference parameters ;

[0103] S42 Calculate attitude quaternions By using spherical linear interpolation, the attitude quaternions are... Transform into posture ;

[0104]

[0105]

[0106] S43 by swing angle and dynamic center position Perform elliptical position interpolation to obtain the coordinates of the robot end effector in the local coordinate system. , , This leads to the construction of local position vectors. ;

[0107]

[0108]

[0109]

[0110]

[0111] in, This represents the initial position of the dynamic center of the circle along the x-axis in the local welding coordinate system at the initial moment (t=0). This represents the initial position of the dynamic center of the circle in the y-axis direction of the local welding coordinate system at the initial moment.

[0112] S44 transforms the local position vector using coordinate transformation. Mapped to position vector in world coordinate system Through posture and position vector in world coordinate system Complete robot end-effector pose Solution.

[0113]

[0114]

[0115] Please see Figure 2 , Figure 2 The image shows a simulation result of the welding trajectory optimized using the robot trajectory optimization method based on dynamic circular center composite motion of the present invention.

[0116] The robot trajectory optimization method based on dynamic circular center composite motion of the present invention simplifies kinematics by decoupling the complex dynamic circular center composite motion into translation and rotation; it controls the circumferential swing angle by planning the trapezoidal velocity curve, and combines a two-layer interpolation strategy of spherical linear interpolation of fifth-order polynomial and attitude quaternion to ensure that the shortest path of smooth motion and attitude rotation under acceleration constraints is obtained.

[0117] The embodiments described above are merely examples of several implementations of the present invention, and while the descriptions are relatively specific and detailed, they should not be construed as limiting the scope of the invention. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of the present invention, and the present invention also intends to include these modifications and variations.

Claims

1. A robot trajectory optimization method based on dynamic center-of-circle compound motion, characterized in that, Specifically, the following steps are included: S1 initializes the trajectory parameters and verifies their validity; And execute steps S2A to S3A, S2B to S3B; S2A calculate dynamic center trajectory; obtain dynamic center position at start time and end time, calculate dynamic center moving distance and total movement time ; S3A calculates the rotation angle of the robot's end effector by calculating the quaternion of the robot's posture, and then smoothly interpolates the rotation angle using a fifth-order polynomial curve; it outputs the interpolated rotation angle of the robot's end effector. S2B constructs the local coordinate system of the robot's end effector trajectory by building a transformation matrix from the local coordinate system to the world coordinate system; S3B plans the circular oscillation trajectory and controls the circular oscillation trajectory through a trapezoidal velocity curve; it outputs the circular oscillation trajectory controlled by the trapezoidal velocity curve. S4 receives the dynamic center trajectory, robot end effector rotation angle, local coordinate system of robot end effector trajectory constructed in S3B, and circular swing trajectory from step S3A; calculates the attitude difference parameters and converts the attitude quaternion into attitude through real-time pose interpolation; constructs a local position vector and completes the pose calculation through the local position vector and attitude.

2. The robot trajectory optimization method based on dynamic circular center composite motion according to claim 1, characterized in that: The robot end trajectory parameters include a robot end swing frequency , a swing radius , a swing speed , a maximum swing speed , an acceleration , a welding start position vector , a welding end position vector .

3. The robot trajectory optimization method based on dynamic center of circle compound motion according to claim 1, characterized in that: The validity of the verification trajectory parameters includes verifying whether the input parameters are within a preset range. If the verification is successful, the subsequent steps continue; if the verification fails, an error is reported and the calculation is stopped.

4. The robot trajectory optimization method based on dynamic circular center composite motion according to claim 2, characterized in that, Step S2A specifically includes the following steps: S2A1 via the welding start position vector Weld termination position vector Calculate the unit vector from the starting point to the ending point. ; S2A2 via the welding start position vector Weld termination position vector and swing radius Calculate the dynamic center position at the start time. and the dynamic center position at the termination time ; S2A3 passes through the dynamic center position. and the dynamic center position at the termination time Calculate the distance the dynamic center moves. and total exercise time 。 5. The robot trajectory optimization method based on dynamic circular center composite motion according to claim 4, characterized in that, Step S3A specifically includes the following steps: S3A1 obtains the robot's end effector's initial pose quaternion. and robot end-effector quaternion The robot end-effector pose difference quaternion was calculated. ; in, This is the initial pose matrix of the robot's end effector. The final pose matrix for the robot's end effector; S3A2 uses the quaternion of the robot's end-effector posture difference. Convert to robot end-effector angle representation ,pass Obtain the rotation angle of the robot's end effector ; S3A3 sets the robot's end-effector position. For time The fifth-degree polynomial and its corresponding speed. and acceleration ; S3A4 determines the coefficients of the fifth-degree polynomial using boundary conditions. to The rotation angle is smoothly interpolated using a fifth-order polynomial curve.

6. The robot trajectory optimization method based on dynamic circular center composite motion according to claim 5, characterized in that: The boundary conditions include the position, velocity, and acceleration of the robot's end effector at the start and end times; including , , , , , .

7. The robot trajectory optimization method based on dynamic circular center composite motion according to claim 5, characterized in that, Step S2B includes the following steps: S2B1 calculates the unit vector of the welding direction. and the unit vector of the swing direction And given the unit vector in the Z direction of the world coordinate system. ; S2B2 constructs the rotation matrix of the robot's end effector local coordinate system. Through the rotation matrix of the robot's end effector local coordinate system and welding start position vector This constitutes the transformation matrix from the local coordinate system to the world coordinate system. 。 8. The robot trajectory optimization method based on dynamic circular center composite motion according to claim 7, characterized in that, Step S3B specifically includes the following steps: S3B1 calculates the number of oscillation cycles. Swing angle Maximum angular velocity of oscillation and angular acceleration Plan the circular oscillation trajectory; The S3B2 is equipped with a trapezoidal velocity curve, which is used to control the target angle. and angular velocity of oscillation This allows for the control of the circular oscillation trajectory.

9. The robot trajectory optimization method based on dynamic circular center composite motion according to claim 8, characterized in that: In step S3B2, the trapezoidal velocity curve includes an acceleration segment, a constant speed segment, and a deceleration segment; Let the time period of the acceleration segment be . During the acceleration phase, the target angle and angular velocity of oscillation for: Let the time interval of the uniform speed segment be . ; During the constant velocity segment, the target angle and angular velocity of oscillation for: in, ; Let the time period of the deceleration segment be . During the uniform velocity segment, the target angle and angular velocity of oscillation for: in, .

10. The robot trajectory optimization method based on dynamic circular center composite motion according to claim 9, characterized in that, Step S4 specifically includes the following steps: S41 Calculate attitude difference parameters ; S42 Calculate attitude quaternions By using spherical linear interpolation, the attitude quaternions are... Transform into posture ; S43 by swing angle and dynamic center position Perform elliptical position interpolation to obtain the coordinates of the robot end effector in the local coordinate system. , , This leads to the construction of local position vectors. ; S44 transforms the local position vector using coordinate transformation. Mapped to position vector in world coordinate system Through posture and position vector in world coordinate system Complete robot end-effector pose Solution 。

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