Robotic arm trajectory planning method based on hybrid polynomial and acceleration smoothing

Abstract

The present invention provides a robot arm trajectory planning method based on a hybrid polynomial and acceleration smoothing, which relates to the field of robot arm control technology and solves the limitations of the robot arm's uneven response and impact caused by sudden acceleration changes during application. The method includes: for two target trajectory points, a quintic polynomial is used to describe the robot arm's motion trajectory; for three target trajectory points including an intermediate point, the velocity and acceleration of the intermediate point are first determined, and then trajectory planning between the two points is used; for four or more target trajectory points, a cubic polynomial interpolation method is used to ensure that the constructed trajectory curve meets the continuity of position, velocity, and acceleration; and acceleration smoothing is achieved by detecting and setting the time between two adjacent curve segments on the trajectory curve. For scenarios with different numbers of trajectory points, the present invention uses the most suitable polynomial for trajectory planning and effectively avoids sudden acceleration changes through acceleration smoothing.

Description

Technical Field

[0001] The present invention relates to the technical field of robotic arm control, and in particular to a robotic arm trajectory planning method based on mixed polynomials and acceleration smoothing. Background Art

[0002] With the rapid development of intelligent manufacturing technology, industrial robotic arms have been widely used in advanced manufacturing fields such as precision assembly, material handling, and welding. In complex working environments, the robotic arm's end effector must complete high-speed and high-precision spatial motion along a predetermined trajectory, which places stringent demands on the trajectory planning capabilities of the motion control system. Trajectory planning, as the intermediate link between path planning and motion control, focuses on generating continuous, smooth trajectories that meet kinematic constraints, directly impacting the robotic arm's motion performance and work quality.

[0003] Existing trajectory planning methods generally use polynomial interpolation algorithms to construct motion trajectories in joint space or Cartesian space. While linear interpolation algorithms are computationally simple, the resulting trajectory exhibits step-like jumps in velocity, causing the actuator to experience transient impact loads. Cubic spline interpolation effectively improves the smoothness of the velocity curve by introducing acceleration continuity constraints and has become the most widely used trajectory generation method in industrial controllers. However, the acceleration derivatives of this method still exhibit discontinuities at path nodes. When the robotic arm is operating at high speed and under heavy load, these sudden changes in high-order motion parameters can induce mechanical vibrations, resulting in end-positioning deviations and severely impacting tasks such as precision assembly that require stringent motion smoothness.

[0004] Theoretical research shows that the root cause of acceleration mutations is that traditional cubic spline curves can only ensure acceleration continuity but cannot achieve a smooth transition of acceleration derivatives. When the robot arm performs high-speed start-stop or path switching actions, this high-order discontinuity will accumulate elastic potential energy in the transmission system, which not only accelerates the mechanical fatigue of key components such as the harmonic reducer, but also causes torque oscillations in the servo motor. Existing improvement schemes often use quintic polynomial interpolation to improve trajectory smoothness, but the resulting complexity of solving the nonlinear equation system increases exponentially, facing the dual challenges of computing resources and response speed in real-time control scenarios.

[0005] In recent years, some research has attempted to optimize acceleration profiles by introducing S-shaped acceleration and deceleration curves, achieving smooth transitions through preset velocity inflection points. While these approaches improve dynamic characteristics, their fixed-pattern acceleration curves struggle to adapt to the geometric characteristics of complex paths, and residual vibrations can still occur when asymmetric trajectories or multiple continuous trajectories are connected. Furthermore, while trajectory optimization schemes based on heuristic algorithms can achieve theoretically optimal solutions, their random search mechanisms result in lengthy computational times, making them difficult to meet the real-time control requirements of highly dynamic scenarios.

[0006] In current industrial applications, trajectory planning algorithms face a trade-off between computational efficiency and motion quality. This tension is particularly acute in high-speed, precision operations. Developing a trajectory planning method that combines high smoothness with low computational complexity, and achieves a continuous transition of all-order motion parameters during robotic arm movement, has become a key technical bottleneck in improving the motion control performance of high-end equipment. Summary of the Invention

[0007] Based on the current status of the background technology, the purpose of the present invention is to solve the limitation problem of non-smooth response of the manipulator, impact, motion accuracy and system stability caused by sudden acceleration in high-speed and precision operation scenarios. Therefore, a manipulator trajectory planning method based on hybrid polynomial and acceleration smoothing is proposed. The present invention integrates quintic polynomial, cubic polynomial and acceleration smoothing technology in the manipulator trajectory planning process. For scenarios with different numbers of trajectory points, the most suitable polynomial is used for trajectory planning. Through acceleration smoothing, sudden acceleration changes are effectively avoided.

[0008] The present invention adopts the following technical solutions to achieve the purpose:

[0009] A robot arm trajectory planning method based on hybrid polynomial and acceleration smoothing, the method comprising the following steps:

[0010] S1. Obtain the number of target trajectory points and corresponding motion parameter requirements in the trajectory planning task, and adopt different trajectory planning schemes based on the number of target trajectory points. The target trajectory point is the three-dimensional space point corresponding to the starting point, middle point, or end point of the preset endpoint of the robot arm on the planned trajectory.

[0011] S2. For trajectory planning between two target trajectory points, a fifth-order polynomial is used to describe the motion trajectory of the robot arm;

[0012] S3. For the trajectory planning between the three target trajectory points including the middle point, first determine the speed and acceleration corresponding to the middle point, then the trajectory planning between the middle point and any other target trajectory point adopts the trajectory planning scheme between the two target trajectory points in step S2;

[0013] S4. For trajectory planning between four or more target trajectory points, a cubic polynomial interpolation method is used to ensure that the trajectory curve formed by multiple target trajectory points meets the continuity of position, velocity, and acceleration; by detecting and setting the time between two adjacent curve segments on the trajectory curve, the acceleration at multiple target trajectory points is smoothed.

[0014] Specifically, in step S2, the form of the fifth-order polynomial used is as follows:

[0015] θ(t)=a+bt+ct2 +dt 3 +et 4 +ft 5

[0016] Where θ(t) represents the change in the position θ of the preset endpoint of the robot arm over time t; a, b, c, d, e, and f are the coefficients of the quintic polynomial to be solved.

[0017] Specifically, the two target trajectory points are used as the starting point and the end point, and after obtaining the corresponding position, velocity, and acceleration of the starting point and the end point, six constraints are formed as follows:

[0018] θ0=θ0(0)=a

[0019]

[0020] θ T =θ0(T)=a+bT+cT 2 +dT 3 +eT 4 +fT 5

[0021]

[0022] Where θ0, v0 and a cc0 Represent the position, velocity and acceleration of the starting point respectively, θ T 、v T and a ccT represent the position, velocity, and acceleration of the endpoint, respectively; T represents the time required to complete the trajectory from the starting point to the end point; by jointly solving the corresponding equations of the above six constraints, the coefficients of the fifth-order polynomial are obtained to realize the trajectory planning between the two target trajectory points.

[0023] Specifically, in step S3, for a trajectory curve that starts from the starting point and reaches the end point after passing through the intermediate point, the intermediate point divides the trajectory curve into two segments, the front and rear segments; the speed v1 corresponding to the intermediate point is solved as follows:

[0024] v ave0 =(S1-S0) / T0

[0025] v ave1 =(S2-S1) / T1

[0026] v1=(v ave0 +v ave1 ) / 2

[0027] Where, v ave0 and v ave1That is, they represent the average speeds corresponding to the two curves; S0, S1 and S2 represent the corresponding positions of the starting point, the middle point and the end point respectively; T0 and T1 represent the time corresponding to the two curves respectively.

[0028] Furthermore, in step S3, for the trajectory curve starting from the starting point and reaching the end point after passing the intermediate point, the intermediate point divides the trajectory curve into two segments, the front and the back curves; if the position change from the starting point to the intermediate point is the same as the position change from the intermediate point to the end point, that is, when the change of the rotation angle of the manipulator at the intermediate point position is a uniform increase or decrease, it can be determined that the speed of the intermediate point is the same as the speed of the manipulator when it is in uniform motion. At this time, the acceleration a of the intermediate point is calculated. cc1 Set it to 0 directly;

[0029] If the position changes from the starting point to the middle point in the opposite way to the position change from the middle point to the end point, it means that the speed of the first and second curve segments increases and decreases. First, calculate the average speed of the two curve segments as follows:

[0030] v ave0 =(S1-S0) / T0

[0031] v ave1 =(S2-S1) / T1

[0032] Where, v ave0 and v ave1 That is, they represent the average speeds of the two curve segments; S0, S1 and S2 represent the corresponding positions of the starting point, the middle point and the end point respectively; T0 and T1 represent the time corresponding to the two curve segments respectively; at this time, let the maximum speed of the first curve segment be 2v ave0 , let the maximum speed of the second curve be 2v ave1 The acceleration a of the middle point is taken as (T0+T1) / 2 after the time from the maximum speed of the first curve segment to the maximum speed of the second curve segment is taken as (T0+T1) / 2. cc1 That is, set it to:

[0033] a cc1 =4(|v ave0 -v ave1 |) / (T0+T1)

[0034] If the speed on the first curve segment remains unchanged and only the speed on the second curve segment increases or decreases, when calculating the average speed v of the second curve segment, ave1 Then, let the maximum speed of the second curve be 2v ave1 , determine the acceleration a corresponding to the second curve cc =4v ave1 / T1; Then, the acceleration a of the midpoint cc1 Set to a cc1=a cc / 2=2v ave1 / T1 or a cc1 =a cc / 4=v ave1 / T1.

[0035] Specifically, in step S4, for a trajectory curve formed by four or more target trajectory points in sequence, the trajectory curve is divided into multiple curve segments by the target trajectory points; the mathematical expression of the cubic polynomial corresponding to the i-th curve segment is as follows:

[0036] θ i (t) = a i +b i t+c i t 2 +d i t 3

[0037] Where θ i (t) represents the position of the i-th curve at time t, a i 、b i 、c i d i is the unknown coefficient of the i-th curve.

[0038] Furthermore, the continuity constraints of position, velocity and acceleration are satisfied between adjacent curve segments; the time required for the i-th curve segment is recorded as T i Finally, the cubic polynomial interpolation method is used, and the constraints that need to be met are as follows:

[0039] Positional continuity, that is, adjacent curve segments have equal positions at their connection points:

[0040] θ i (T i )=θ i+1 (0) = a i +b i T i +c i T i 2 +d i T i 3 =a i+1

[0041] Velocity continuity, that is, the velocities of adjacent curve segments are equal at the connection points:

[0042]

[0043] Acceleration continuity: that is, the accelerations of adjacent curve segments at their connection points are equal:

[0044]

[0045] The acceleration of each target trajectory point is recorded as m i , the position is recorded as S i Then, let m i =2c i , and then according to the continuity constraints of position, velocity and acceleration, the following equation is obtained:

[0046]

[0047] After constructing the corresponding matrix relationship through the above equation, the acceleration vector m is solved to obtain the parameters corresponding to each curve segment.

[0048] Specifically, let the total number of curve segments in the trajectory curve be n, and the total number of target trajectory points be n+1. According to the above equation, the matrix relationship is: Am=6k; where A is the matrix on the left side of the equation, k is the matrix on the right side of the equation, and m represents the acceleration vector. After n curve segments correspond to n equations, the left side of each equation can be combined into matrix A, and the right side can be combined into matrix k, as follows:

[0049]

[0050] The equation corresponding to the matrix relationship Am = 6k above is used to calculate the acceleration vector m through LU decomposition, and then the corresponding acceleration value is determined. Once the acceleration value is determined, the parameters corresponding to each curve segment can be obtained based on the continuity constraints of position, velocity, and acceleration satisfied between adjacent curve segments.

[0051] Preferably, in step S4, for a trajectory curve composed of four or more target trajectory points in sequence, the trajectory curve is divided into multiple segments by the target trajectory points, wherein the time required for the i-th segment curve is recorded as T i ; After the trajectory curve is planned, the time T corresponding to the two adjacent curves is detected i and T i±1 , and at time T i and T i±1 Only when both are smaller than the preset judgment threshold value, it is determined whether to perform the acceleration smoothing operation.

[0052] Specifically, when making a judgment, first detect whether the position change mode corresponding to the first curve segment is the same as the position change mode corresponding to the second curve segment in the two adjacent curve segments, where the position change mode includes the rotation direction and linear movement direction of the robot arm; when the position change modes are the same, no acceleration smoothing operation is performed; when the position change modes are different, the time corresponding to the second curve segment is changed and set to the preset smoothing time value.

[0053] In summary, due to the adoption of this technical solution, the beneficial effects of the present invention are as follows:

[0054] The present invention significantly improves the quality of robotic arm motion while ensuring trajectory continuity by integrating polynomials of different orders with acceleration smoothing technology. For multi-trajectory point planning scenarios, a quintic polynomial is used to construct the trajectory of key sections, achieving high-order smoothing characteristics with continuous acceleration derivatives, fundamentally eliminating the problem of acceleration mutations at path nodes caused by traditional cubic spline interpolation; at the same time, by switching between cubic polynomials, the computational complexity is greatly reduced while ensuring basic smoothness. By dynamically adjusting the polynomial order and time interval parameters, the acceleration curve presents a gradual transition at the trajectory junction, effectively suppressing the elastic vibration of the transmission system and the servo torque fluctuation.

[0055] The acceleration smoothing technology introduced in this invention achieves global optimization of motion parameters while maintaining trajectory generation efficiency by constraining the acceleration change rate of adjacent segments. Compared with the single polynomial interpolation method, this hybrid strategy combines high-order trajectory smoothness with real-time computational feasibility. In particular, when processing multiple continuous trajectories or asymmetric paths, it can avoid residual oscillations caused by fixed-mode acceleration and deceleration curves. In practical applications, this method can significantly reduce the positioning deviation of the end effector of the robot arm, improve the dynamic response stability in high-speed and precision operation scenarios, and extend the service life of key transmission components. BRIEF DESCRIPTION OF THE DRAWINGS

[0056] Figure 1 A schematic diagram briefly describing the overall process of the method of the present invention;

[0057] Figure 2 Schematic diagram of trajectory planning between two target trajectory points in the present invention;

[0058] Figure 3 Schematic diagram of trajectory planning for case 1 of solving the acceleration between three points in the present invention;

[0059] Figure 4 Schematic diagram of trajectory planning for case 2 of solving the acceleration between three points in the present invention;

[0060] Figure 5 Schematic diagram of trajectory planning for case 3 of solving the acceleration between three points in the present invention;

[0061] Figure 6 This is a schematic diagram of the test effect before acceleration smoothing in the present invention;

[0062] Figure 7 Schematic diagram of the test effect after acceleration smoothing in the present invention. DETAILED DESCRIPTION

[0063] To make the objectives, technical solutions, and advantages of the embodiments of the present invention more clear, the technical solutions of the embodiments of the present invention will be clearly and completely described below in conjunction with the accompanying drawings of the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Generally, the components of the embodiments of the present invention described and shown in the drawings herein can be arranged and designed in various different configurations.

[0064] Therefore, the following detailed description of the embodiments of the present invention provided in the accompanying drawings is not intended to limit the scope of the invention as claimed, but rather merely represents selected embodiments of the present invention. All other embodiments derived by persons of ordinary skill in the art based on the embodiments of the present invention without creative effort shall fall within the scope of protection of the present invention.

[0065] Example

[0066] A robot arm trajectory planning method based on hybrid polynomial and acceleration smoothing. The overall process of this method can be found in Figure 1 The method combines quintic polynomials, cubic polynomials, and acceleration smoothing technology. Under different target trajectory points, appropriate polynomials are used for trajectory planning, and acceleration smoothing is used to avoid sudden acceleration changes. The various steps of the method are summarized as follows:

[0067] S1. Obtain the number of target trajectory points and corresponding motion parameter requirements in the trajectory planning task, and adopt different trajectory planning schemes based on the number of target trajectory points. The target trajectory point is the three-dimensional space point corresponding to the starting point, middle point, or end point of the preset endpoint of the robot arm on the planned trajectory.

[0068] S2. For trajectory planning between two target trajectory points, a fifth-order polynomial is used to describe the motion trajectory of the robot arm;

[0069] S3. For the trajectory planning between the three target trajectory points including the middle point, first determine the speed and acceleration corresponding to the middle point, then the trajectory planning between the middle point and any other target trajectory point adopts the trajectory planning scheme between the two target trajectory points in step S2;

[0070] S4. For trajectory planning between four or more target trajectory points, a cubic polynomial interpolation method is used to ensure that the trajectory curve formed by multiple target trajectory points meets the continuity of position, velocity, and acceleration; by detecting and setting the time between two adjacent curve segments on the trajectory curve, the acceleration at multiple target trajectory points is smoothed.

[0071] In step S2, a fifth-order polynomial is used to describe the motion trajectory between the two target trajectory points. The main goal is to optimize the motion between the target trajectory points so that the changes in acceleration and velocity are smoother. The fifth-order polynomial used in this embodiment is as follows:

[0072] θ(t)=a+bt+ct 2 +dt 3 +et 4 +ft 5

[0073] Where θ(t) represents the change in the position θ of the preset endpoint of the robot arm over time t; a, b, c, d, e, and f are the coefficients of the quintic polynomial to be solved.

[0074] Can view at the same time Figure 2 As shown in the figure, the two target trajectory points are respectively used as the starting point and the end point. After obtaining the position, velocity and acceleration corresponding to the starting point and the end point, six constraints are formed as follows:

[0075] θ0=θ0(0)=a

[0076]

[0077] θ T =θ0(T)=a+bT+cT 2 +dT 3 +eT 4 +fT 5

[0078]

[0079] Where θ0, v0 and a cc0 Represent the position, velocity and acceleration of the starting point (in Figure 2 is marked as a0), θ T 、v T and a ccT Represent the position, velocity and acceleration of the end point (in Figure 2 where the corresponding constraints are marked as θ1, v1, and a1, and T represents the time required to complete the trajectory curve from the starting point to the end point. By solving the corresponding equations of the above six constraints, the coefficients of the quintic polynomial are obtained to realize the trajectory planning between the two target trajectory points.

[0080] In step S3, the five-order polynomial is also used to describe the motion trajectory between the three target trajectory points. It is only necessary to first calculate the velocity v1 and acceleration a of the intermediate point. cc1, we can further solve it using the two-point method. For a trajectory curve that starts from the starting point and reaches the end point after passing the middle point, the middle point divides the trajectory curve into two segments, the front and back curves; the speed v1 corresponding to the middle point is solved as follows:

[0081] v ave0 =(S1-S0) / T0

[0082] v ave1 =(S2-S1) / T1

[0083] v1=(v ave0 +v ave1 ) / 2

[0084] Where, v ave0 and v ave1 That is, they represent the average speeds corresponding to the two curves; S0, S1 and S2 represent the corresponding positions of the starting point, the middle point and the end point respectively; T0 and T1 represent the time corresponding to the two curves respectively.

[0085] In this embodiment, the acceleration a of the midpoint cc1 There are several cases; first, see Figure 3 If the position change from the starting point to the middle point is the same as the position change from the middle point to the end point, that is, the change of the robot arm's rotation angle at the middle point is a uniform increase or decrease (the uniform increase or decrease of the robot arm's rotation angle means that the moving speed of its end point trajectory is constant), it can be determined that the speed of the middle point is the same as the speed of the robot arm when it is in uniform motion. At this time, the acceleration a of the middle point is cc1 ( Figure 3 a1) in is directly set to 0. Figure 3 In the figure, the physical quantity with subscript 0 corresponds to the starting point, the physical quantity with subscript 1 corresponds to the middle point, and the physical quantity with subscript 2 corresponds to the end point.

[0086] like Figure 4 As shown, if the position change from the starting point to the middle point is opposite to the position change from the middle point to the end point, it means that the speed of the first and second curve segments increases and decreases. In this case, the average speed of the two curve segments is calculated as follows:

[0087] v ave0 =(S1-S0) / T0

[0088] v ave1 =(S2-S1) / T1

[0089] Where, v ave0 and v ave1That is, they represent the average speeds of the two curve segments; S0, S1 and S2 represent the corresponding positions of the starting point, the middle point and the end point respectively; T0 and T1 represent the time corresponding to the two curve segments respectively; at this time, let the maximum speed of the first curve segment be 2v ave0 , let the maximum speed of the second curve be 2v ave1 The acceleration a of the middle point is taken as (T0+T1) / 2 after the time from the maximum speed of the first curve segment to the maximum speed of the second curve segment is taken as (T0+T1) / 2. cc1 That is, set it to:

[0090] a cc1 =4(|v ave0 -v ave1 |) / (T0+T1)

[0091] Figure 4 In the figure, the physical quantity with subscript 0 corresponds to the starting point, the physical quantity with subscript 1 corresponds to the middle point, and the physical quantity with subscript 2 corresponds to the end point.

[0092] like Figure 5 As shown in the figure, if the speed on the first curve segment remains unchanged and only the speed on the second curve segment increases or decreases, when calculating the average speed v of the second curve segment, ave1 Then, let the maximum speed of the second curve be 2v ave1 , determine the acceleration a corresponding to the second curve cc =4v ave1 / T1; Then, in order to make the acceleration transition smoothly from the first curve to the second curve, the acceleration a can be taken cc 1 / 2 or 1 / 4, that is, the acceleration a at the midpoint cc1 Set to a cc1 =a cc / 2=2v ave1 / T1 or a cc1 =a cc / 4=v ave1 / T1. Figure 5 In the figure, the physical quantity with subscript 0 corresponds to the starting point, the physical quantity with subscript 1 corresponds to the middle point, and the physical quantity with subscript 2 corresponds to the end point.

[0093] In step S4, for a trajectory curve formed by four or more target trajectory points in sequence, the trajectory curve is divided into multiple curve segments by the target trajectory points; the mathematical expression of the cubic polynomial corresponding to the i-th curve segment is as follows:

[0094] θ i (t) = a i +b i t+c i t 2 +d i t 3

[0095] Where θ i (t) represents the position of the i-th curve at time t, a i 、b i 、c i d i is the unknown coefficient of the i-th curve.

[0096] In order to ensure the smoothness of the curve, the continuity constraints of position, velocity and acceleration must be satisfied between adjacent curve segments. The time required for the i-th curve segment is denoted as T i Finally, the cubic polynomial interpolation method is used, and the constraints that need to be met are as follows:

[0097] Positional continuity, that is, adjacent curve segments have equal positions at their connection points:

[0098] θ i (T i )=θ i+1 (0) = a i +b i T i +c i T i 2 +d i T i 3 =a i+1

[0099] Velocity continuity means that the velocities (first-order derivatives) of adjacent curve segments are equal at the connection points:

[0100]

[0101] Acceleration continuity: that is, the acceleration (second-order derivative) of adjacent curve segments at the connection point is equal:

[0102]

[0103] The acceleration of each target trajectory point is recorded as m i , the position is recorded as S i Then, let m i =2c i , and then according to the continuity constraints of position, velocity and acceleration, the following equation is obtained:

[0104]

[0105] After constructing the corresponding matrix relationship through the above equation, the acceleration vector m is solved to obtain the parameters corresponding to each curve segment.

[0106] In this embodiment, the total number of curve segments in the trajectory curve is recorded as n, and the total number of target trajectory points is n+1. According to the above equation, the matrix relationship is: Am=6k; where A is the matrix listed on the left side of the equation, k is the matrix listed on the right side of the equation, and m represents the acceleration vector. After n curve segments correspond to n equations, the left side of each equation can be combined into matrix A, and the right side can be combined into matrix k, as follows:

[0107]

[0108]

[0109] The equation corresponding to the matrix relationship Am = 6k above is used to calculate the acceleration vector m through LU decomposition, and then the corresponding acceleration value is determined. Once the acceleration value is determined, the parameters corresponding to each curve segment can be obtained based on the continuity constraints of position, velocity, and acceleration satisfied between adjacent curve segments.

[0110] In this embodiment, the cubic polynomial interpolation method for four or more target trajectory points is described above. The time for each curve segment is calculated by dividing the position difference by an average speed. When the position difference of a middle curve segment is very small, the corresponding time will also be very small. If the time of two adjacent curve segments is very small, and the position of the first curve segment increases (the robot arm's rotation angle increases) while the position of the second curve segment decreases (the robot arm rotates in the opposite direction and the rotation angle decreases), the speed conversion must be completed in a very short time, which will generate a large acceleration and cause the robot arm to shake violently.

[0111] In order to overcome the above situation, this embodiment preferably adopts the following method:

[0112] The time required for the i-th segment of the curve is recorded as T i After the trajectory curve is planned, the time T corresponding to the two adjacent curves is detected. i and T i±1 , and at time T i and T i±1 Only when both the time of the current curve segment and the adjacent subsequent curve segment are less than 0.3 seconds is a decision made on whether to perform the acceleration smoothing operation. In this embodiment, taking the standard rotational angular velocity of the robotic arm as 30 degrees per second as an example, based on the empirical value of the average speed in practice, the judgment threshold can be set to 0.3 seconds. Only when both the time of the current curve segment and the adjacent subsequent curve segment are less than 0.3 seconds is a decision made on whether to perform the acceleration smoothing operation.

[0113] If the time condition is met, the judgment is first made by detecting whether the position change mode corresponding to the first curve segment is the same as the position change mode corresponding to the second curve segment in the two adjacent curve segments. The position change mode includes the rotation direction and linear movement direction of the robot arm. When the position change modes are the same, there will be no significant change in speed, so the acceleration smoothing operation is not performed. When the position change modes are different, the time corresponding to the second curve segment is changed and set to a preset smoothing time value. In this embodiment, the smoothing time value can be the same as the judgment threshold value, that is, 0.3 seconds.

[0114] The effect of acceleration smoothing operation can be Figure 6 and Figure 7 For comparison, see Figure 6 For the effect of no smoothing, Figure 7 In the two adjacent curves whose time is less than 0.3 seconds, the time of the latter curve is set to 0.3 seconds to achieve smooth acceleration.

Claims

1. A robot arm trajectory planning method based on hybrid polynomial and acceleration smoothing, characterized in that: The steps include: S1. Obtain the number of target trajectory points and corresponding motion parameter requirements in the trajectory planning task, and adopt different trajectory planning schemes based on the number of target trajectory points. The target trajectory point is the three-dimensional space point corresponding to the starting point, middle point, or end point of the preset endpoint of the robot arm on the planned trajectory. S2. For trajectory planning between two target trajectory points, a fifth-order polynomial is used to describe the motion trajectory of the robot arm; S3. For the trajectory planning between the three target trajectory points including the middle point, first determine the speed and acceleration corresponding to the middle point, then the trajectory planning between the middle point and any other target trajectory point adopts the trajectory planning scheme between the two target trajectory points in step S2; S4. For trajectory planning between four or more target trajectory points, a cubic polynomial interpolation method is used to ensure that the trajectory curve formed by the multiple target trajectory points satisfies the continuity of position, velocity, and acceleration; by detecting and setting the time between two adjacent curve segments on the trajectory curve, the acceleration at the multiple target trajectory points is smoothed; In step S3, for the trajectory curve that starts from the starting point and reaches the end point after passing the intermediate point, the intermediate point divides the trajectory curve into two segments, the front and the back curves; if the position change from the starting point to the intermediate point is the same as the position change from the intermediate point to the end point, that is, when the change of the rotation angle of the robot arm at the intermediate point position is a uniform increase or decrease, it can be determined that the speed of the intermediate point is the same as the speed of the robot arm when it is in uniform motion. At this time, the acceleration of the intermediate point is calculated. Set it to 0 directly; If the position changes from the starting point to the middle point in the opposite way to the position change from the middle point to the end point, it means that the speed of the first and second curve segments increases and decreases. First, calculate the average speed of the two curve segments as follows: Where, and That is, they represent the average speeds corresponding to the two curve segments; 、 and Respectively represent the corresponding positions of the starting point, middle point and end point; and Respectively represent the time corresponding to the two curves; At this time, let the maximum speed of the first curve be , let the maximum speed of the second curve be , and the time from the maximum speed of the first curve to the maximum speed of the second curve is taken as After that, the acceleration of the midpoint That is, set it to: If the speed on the first curve segment remains unchanged and only the speed on the second curve segment increases or decreases, when calculating the average speed of the second curve segment, Then, let the maximum speed of the second curve be , determine the acceleration corresponding to the second curve ; Then, the acceleration of the midpoint Set to or .

2. The robot arm trajectory planning method according to claim 1, characterized in that: In step S2, the fifth-order polynomial used is in the following form: Where, Represents the position of the preset end point of the robot arm Over time changes; 、 、 、 、 、 are the coefficients of the quintic polynomial to be solved.

3. The robot arm trajectory planning method according to claim 2, characterized in that: The two target trajectory points are used as the starting point and the end point, and the corresponding positions, velocities, and accelerations are obtained to form six constraints, as shown in the following formula: Where, 、 and Represent the position, velocity and acceleration of the starting point respectively, 、 and Represent the position, velocity and acceleration of the end point respectively, Represents the time required for the trajectory curve from the starting point to the end point; by jointly solving the corresponding equations of the above six constraints, the coefficients of the fifth-order polynomial are obtained to realize the trajectory planning between the two target trajectory points.

4. The robot arm trajectory planning method according to claim 1, wherein: In step S3, for a trajectory curve starting from the starting point and reaching the end point after passing the intermediate point, the intermediate point divides the trajectory curve into two segments, the front and rear segments; the speed corresponding to the intermediate point The solution is as follows: Where, and That is, they represent the average speeds corresponding to the two curve segments; 、 and Respectively represent the corresponding positions of the starting point, middle point and end point; and Respectively represent the time corresponding to the two curves.

5. The robot arm trajectory planning method according to claim 1, wherein: In step S4, for a trajectory curve formed by four or more target trajectory points in sequence, the trajectory curve is divided into multiple curve segments by the target trajectory points; The mathematical representation of the cubic polynomial corresponding to the segment curve is as follows: Where, Representative Segment curve in time The location at the time, 、 、 、 It is Undetermined coefficients of the segment curve.

6. The robot arm trajectory planning method according to claim 5, characterized in that: The continuity constraints of position, velocity and acceleration are satisfied between adjacent curve segments; The time required for a segment curve is recorded as Finally, the cubic polynomial interpolation method is used, and the constraints that need to be met are as follows: Positional continuity, that is, adjacent curve segments have equal positions at their connection points: Velocity continuity, that is, the velocities of adjacent curve segments are equal at the connection points: Acceleration continuity: that is, the accelerations of adjacent curve segments at their connection points are equal: The acceleration of each target trajectory point is recorded as , the position is recorded as After that, order , and then according to the continuity constraints of position, velocity and acceleration, the following equation is obtained: Through the above equations, after constructing the corresponding matrix relationship, solve the acceleration vector , and then the parameters corresponding to each curve are obtained.

7. The robot arm trajectory planning method according to claim 6, characterized in that: The total number of curve segments in the trajectory curve is recorded as , then the total number of target trajectory points is , according to the above equation, we get the matrix relationship: ;in, is the matrix on the left side of the equation, is the matrix on the right side of the equation, represents the acceleration vector; The curve segment corresponds to After the equations are formed, the left sides of the equations can be combined into a matrix , and the right part is combined into the matrix ,as follows: The above matrix relationship The corresponding equation is calculated by LU decomposition to obtain the acceleration vector , and then determine the corresponding acceleration value; once the acceleration value is determined, the parameters corresponding to each curve segment can be obtained based on the continuity constraints of position, velocity and acceleration satisfied between adjacent curve segments.

8. The robot arm trajectory planning method according to claim 1, wherein: In step S4, for a trajectory curve formed by four or more target trajectory points in sequence, the trajectory curve is divided into multiple curve segments by the target trajectory points, wherein the first The time required for the segment curve is recorded as ; After the trajectory curve is planned, the time corresponding to the two adjacent curves is detected. and , and at time and Only when both are smaller than the preset judgment threshold value, it is determined whether to perform the acceleration smoothing operation.

9. The robot arm trajectory planning method according to claim 8, characterized in that: When making a judgment, the first step is to detect whether the position change mode corresponding to the first curve segment is the same as the position change mode corresponding to the second curve segment in the two adjacent curve segments. The position change mode includes the rotation direction and linear movement direction of the robot arm. When the position change mode is the same, the acceleration smoothing operation is not performed. When the position change mode is different, the time corresponding to the second curve segment is changed and set to the preset smoothing time value.

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