Novel asymmetric trajectory planning method and system based on cosine optimization

Abstract

The invention discloses a novel asymmetric trajectory planning method and system based on cosine optimization, and belongs to the technical field of trajectory planning. Comprising the steps that a cosine asymmetric trajectory planning model is constructed, and the cosine asymmetric trajectory planning model divides the motion process into three stages of acceleration, constant speed and deceleration; a target stroke # imgabs0 # is obtained based on the target stroke, the track level to which the target stroke # imgabs1 # belongs is determined, and the tracks at least comprise a long-distance track, a middle-distance track and a short-distance track; and selecting corresponding model parameters according to the trajectory level to which the target travel # imgabS2 # belongs, and performing trajectory planning by the cosine asymmetric trajectory planning model based on the selected corresponding model parameters. According to the method, severe fluctuation in a traditional sine asymmetric trajectory model is avoided, so that flexible impact and vibration are reduced, and the stability and control precision of the system are improved. The novel model can keep higher smoothness in the whole movement process, so that the movement track is more natural and smoother.

Description

Technical Field

[0001] The present invention belongs to the technical field of trajectory planning, and in particular, relates to a novel asymmetric trajectory planning method and system based on cosine optimization. Background Art

[0002] Motion planning is an integral part of systems such as robots, automation equipment, and CNC machine tools. Its goal is to generate smooth, effective, and safe motion trajectories to ensure that the system can move from the starting position to the target position within a predetermined time while satisfying speed, acceleration, and other dynamic constraints. The following is the technical background of several common motion planning methods:

[0003] The S-curve motion planning method generates smooth velocity and position curves through gradually changing acceleration, thus avoiding the sudden changes in the traditional trapezoidal velocity curve. The S-curve consists of an acceleration section, a constant speed section, and a deceleration section. The velocity curves of the acceleration section and the deceleration section are S-shaped, and their acceleration gradually changes at the beginning and end, thus forming a smooth transition. Although S-curve motion planning can generate smooth velocity and acceleration curves and reduce the impact and vibration of the mechanical system, its implementation process is relatively complex and requires a large amount of calculation. In addition, the optimization and adjustment of S-curve planning requires precise parameter selection and debugging, which increases the complexity of system design and maintenance.

[0004] Trapezoidal velocity curve is one of the simplest and most commonly used methods in motion planning. Its velocity curve consists of three parts: acceleration section, constant speed section and deceleration section. The velocity changes in the acceleration section and deceleration section are linear, while the constant speed section keeps the speed constant. The advantage of the trapezoidal velocity curve method is that it is simple to calculate, easy to implement, and can quickly generate motion trajectories. However, the main defect of the trapezoidal velocity curve is that its acceleration has a sudden change between the acceleration section and the deceleration section. This sudden change can cause shock and vibration of the mechanical system, which may lead to mechanical wear and system instability, especially under high speed and high load conditions. Due to the sudden change in acceleration, the system has poor smoothness in the transition section and is not suitable for applications that require high motion smoothness and accuracy. In addition, in some complex path planning, the trapezoidal velocity curve is difficult to provide sufficient flexibility and cannot adapt to dynamic environments and diverse motion requirements.

[0005] Polynomial trajectory motion planning uses high-order polynomials to generate motion trajectories, and quintic polynomials or higher-order polynomials are common. By designing the coefficients of the polynomial, the initial and terminal positions, velocity, acceleration, and higher-order derivatives of the motion can be precisely controlled, thereby generating a very smooth motion trajectory. However, its main drawback is its high computational complexity. Solving the coefficients of the polynomial requires a lot of calculations, especially for high-order polynomials, which may not be met in systems with high real-time requirements. In addition, the polynomial trajectory is very sensitive to initial and boundary conditions, and any slight change may cause a large deviation in the trajectory. The design and adjustment of polynomial trajectories require a high level of mathematical background and experience, and it is difficult for non-professional users to use and maintain them. In dynamic and highly uncertain environments, polynomial trajectories have poor adaptability and are difficult to cope with real-time changes.

[0006] In the traditional sinusoidal asymmetric trajectory planning algorithm, the non-smoothness of the Jerk curve and the flexible impact are the main problems. Jerk is the rate of change of acceleration, which affects the dynamic performance and stability of the system. In the sinusoidal asymmetric trajectory, the sudden change or non-smoothness of the Jerk curve will cause severe vibration and impact in the system, especially under high speed or heavy load conditions. This flexible impact will damage the mechanical components and reduce the life and reliability of the system. Summary of the invention

[0007] In view of the problems in the related art, the present invention proposes a novel asymmetric trajectory planning method and system based on cosine optimization to overcome the above-mentioned technical problems existing in the existing related art. BRIEF DESCRIPTION OF THE DRAWINGS

[0008] Figure 1 This is the cosine asymmetric trajectory planning model diagram disclosed in Example 1.

[0009] Figure 2 This is a model diagram of the mid-distance trajectory planning of Example 1.

[0010] Figure 3 This is a model diagram of short-distance trajectory planning in Example 1.

[0011] Figure 4 It is a power spectrum analysis comparison diagram of Example 1.

[0012] Figure 5 This is a vibration simulation model diagram of Example 1. DETAILED DESCRIPTION

[0013] In the traditional sinusoidal asymmetric trajectory planning algorithm, the non-smoothness of the Jerk curve and the flexible impact are the main problems. Jerk is the rate of change of acceleration, which affects the dynamic performance and stability of the system. In the sinusoidal asymmetric trajectory, the sudden change or non-smoothness of the Jerk curve will cause severe vibration and impact in the system, especially under high speed or heavy load conditions. This flexible impact will damage the mechanical components and reduce the life and reliability of the system.

[0014] Example 1

[0015] like Figure 1 As shown, a novel asymmetric trajectory planning method based on cosine optimization includes the following steps:

[0016] Constructing a cosine asymmetric trajectory planning model, wherein the cosine asymmetric trajectory planning model divides the motion process into three stages: acceleration, uniform speed and deceleration, and uses a cosine function to describe the acceleration changes in the acceleration and deceleration stages; the motion parameters of the cosine asymmetric trajectory planning model include at least three groups: long-distance trajectory motion parameters, medium-distance trajectory motion parameters and short-distance trajectory motion parameters;

[0017] Obtaining the target travel distance S based on the target travel distance t , and determine the target travel S t The track level, the track level includes at least: long-distance track, medium-distance track and short-distance track;

[0018] According to the target travel S t The corresponding model parameters are selected at the trajectory level, and the cosine asymmetric trajectory planning model performs trajectory planning based on the selected corresponding model parameters.

[0019] In a further embodiment, the construction process of the cosine asymmetric trajectory planning model is as follows:

[0020] The cosine programming acceleration equation J is used, which is expressed as follows:

[0021]

[0022] Integrating the jerk equation J yields the acceleration equation A:

[0023]

[0024] Integrating the acceleration equation A yields the velocity equation V:

[0025]

[0026] Where k is the period parameter of the trigonometric function, p is the scaling factor of k, i is the motion phase, i = 1, 2, ..., 9; t iis the time node corresponding to each movement stage i, Δt i =tt i ; α i t = t i The instantaneous acceleration at time v i is the speed corresponding to each motion stage i; V max , A max and J max are the maximum speed, maximum acceleration and maximum jerk of the corresponding trajectory length, respectively. The corresponding trajectory length can be a long-distance trajectory, a medium-distance trajectory and a short-distance trajectory.

[0027] The above gives the improved cosine asymmetric trajectory planning model, but the motion parameters are not completely given. This is because the motion parameters of the trajectory model are not only related to J max , A max and V max and other system parameters, and is also affected by the target stroke S t According to the distance of the target journey, the trajectory model can be divided into three cases: long distance, medium distance and short distance.

[0028] Therefore, the travel distance S of this embodiment is determined t The process of determining the trajectory level is as follows:

[0029] Preset the critical maximum distance value S1 and the critical minimum distance value S2. t > S1, the current target trip is classified as a long-distance trajectory; if S2 < S t ≤S1, the current target trip is classified as a medium-distance trajectory; if S t ≤S2, the current target trip is classified as a short-distance trajectory.

[0030] Based on the determination of the above trajectory level, you can refer to Figure 1 When the trajectory level is a long-distance trajectory, the entire motion process includes: acceleration segments T1, T2 and T3 divided according to a predetermined duration, deceleration segments T4, T5 and T6 divided according to a predetermined duration, a uniform speed segment T7 divided according to a predetermined duration, and deceleration segments T8 and T9 divided according to a predetermined duration;

[0031] The process of determining the long-distance trajectory motion parameters is as follows:

[0032]

[0033] The duration of T2 and k are calculated according to the above formula, and T1, T3, T4, T6, T7, T8 and T9 are calculated using the following formula:

[0034]

[0035] In the formula, S t is the travel distance, and S1 is the preset critical maximum value of the distance. In other words, this stage does not include T5.

[0036] Combination Figure 2 , when the trajectory level is a medium-distance trajectory, the entire motion process includes: acceleration segments T1, T2 and T4 divided according to a predetermined duration, deceleration segments T4, T5 and T6 divided according to a predetermined duration, and deceleration segments T8 and T9 divided according to a predetermined duration;

[0037] The process of determining the mid-range trajectory motion parameters is as follows:

[0038]

[0039] According to the above formula, the duration of T2 and p can be calculated. Considering that the current trajectory is a medium-distance trajectory, the durations of T1, T3, T5, T6, T7, and T8 can be calculated using the following formula:

[0040]

[0041] In the formula, A max 、V max They are the maximum acceleration and maximum speed of the mid-distance trajectory. In other words, this stage does not include T9.

[0042] Another example Figure 3 ,When the trajectory level is a short-distance trajectory, the entire motion process includes: acceleration segment T1, deceleration segment T2, and deceleration segments T3 and T4;

[0043] The process of determining the long-distance trajectory motion parameters is as follows:

[0044]

[0045] Furthermore, T1, T2, T3, and T4 are expressed in the following form:

[0046]

[0047] In a further embodiment, the cosine asymmetric trajectory planning model is subject to the following constraints:

[0048]

[0049] In the formula, t s is the starting time, t f is the end time, t is the current time, V is the current speed, A is the acceleration equation, J is the jerk equation, V max , A max and Jmax are the maximum velocity, maximum acceleration and maximum jerk of the trajectory of corresponding length, and P is the displacement.

[0050] Based on the above modeling process, in order to compare the motion characteristics of the new cosine asymmetric trajectory planning and the traditional sine asymmetric trajectory planning, power spectrum analysis and vibration simulation analysis were performed respectively.

[0051] Frequency domain analysis can verify the smoothness of motion control signals. Figure 4 This is a power spectrum analysis comparison between the new cosine asymmetric trajectory planning and the traditional sine asymmetric trajectory planning. Figure 4 It can be seen that the power spectrum of the cosine asymmetric trajectory planning algorithm disclosed in this embodiment has a smaller fluctuation range than the power spectrum of the traditional sine asymmetric trajectory planning algorithm and has better stability. Power spectrum analysis is used to evaluate the frequency characteristics of the new cosine asymmetric trajectory planning model in practical applications. By performing spectral analysis on the motion trajectory, the frequency components in the motion process can be identified and whether there is undesirable high-frequency noise or vibration. Power spectrum analysis can help verify whether the cosine asymmetric trajectory model effectively reduces the high-frequency components in the Jerk curve, thereby reducing the vibration and impact of the system. By comparing the power spectra of the traditional sine asymmetric trajectory and the new cosine asymmetric trajectory, you can intuitively understand the effect of the new model in reducing vibration and improving motion smoothness.

[0052] Establish as Figure 5 In the vibration simulation model shown in the figure, c is the damping coefficient, q is the elastic coefficient, m1 is the mass of the flexibly connected object, x is the displacement of m1, f is the force acting on m1, m2 is the mass of the motor-driven object, a is the acceleration of the motor-driven object, and k is the periodic parameter of the trigonometric function.

[0053] Analysis of m1 yields:

[0054] Analysis of m2 yields: f = m2a;

[0055] Then we can get the following formula: In the formula, ω n is the natural oscillation frequency and ζ is the damping ratio.

[0056] By simulating the model, we can simulate the vibration of the system during actual motion and analyze its impact on the overall motion accuracy. Vibration error simulation can help identify possible sources of error during motion and verify whether the new model can effectively reduce these errors and provide smoother motion control. By comparing with traditional trajectory planning methods, we can quantify the improvement of the new model in reducing vibration errors, thereby further optimizing the trajectory planning strategy.

[0057] Example 2

[0058] In order to implement the novel asymmetric trajectory planning method based on cosine optimization described in Example 1, this embodiment discloses a novel asymmetric trajectory planning system based on cosine optimization, including:

[0059] The first module is configured to construct a cosine asymmetric trajectory planning model, wherein the cosine asymmetric trajectory planning model divides the motion process into three stages: acceleration, uniform speed, and deceleration, and uses a cosine function to describe the acceleration changes in the acceleration and deceleration stages; the motion parameters of the cosine asymmetric trajectory planning model include at least three groups: long-distance trajectory motion parameters, medium-distance trajectory motion parameters, and short-distance trajectory motion parameters;

[0060] The second module is configured to obtain a target travel distance S based on the target travel distance t , and determine the target travel S t The track level, the track level includes at least: long-distance track, medium-distance track and short-distance track;

[0061] The third module is configured to calculate the target travel distance S t The corresponding model parameters are selected at the trajectory level, and the cosine asymmetric trajectory planning model performs trajectory planning based on the selected corresponding model parameters.

Claims

1. A novel asymmetric trajectory planning method based on cosine optimization, characterized in that: The following steps are involved: Constructing a cosine asymmetric trajectory planning model, wherein the cosine asymmetric trajectory planning model divides the motion process into three stages: acceleration, uniform speed and deceleration, and uses a cosine function to describe the acceleration changes in the acceleration and deceleration stages; the motion parameters of the cosine asymmetric trajectory planning model include at least three groups: long-distance trajectory motion parameters, medium-distance trajectory motion parameters and short-distance trajectory motion parameters; Get the target trip based on the target trip , and determine the target itinerary The track level, the track level includes at least: long-distance track, medium-distance track and short-distance track; According to the target itinerary The corresponding model parameters are selected for the trajectory level, and the cosine asymmetric trajectory planning model performs trajectory planning based on the selected corresponding model parameters.

2. A novel asymmetric trajectory planning method based on cosine optimization according to claim 1, characterized in that: The construction process of the cosine asymmetric trajectory planning model is as follows: The cosine programming acceleration equation J is used, which is expressed as follows: ； Integrating the jerk equation J yields the acceleration equation A: ； Integrating the acceleration equation A yields the velocity equation V: ； Where k is the period parameter of the trigonometric function, p is the scaling factor of k, i For the movement stage, ; For each exercise stage i The corresponding time node, ; for The instantaneous acceleration of the moment, For each exercise stage i The corresponding speed; , and are the maximum velocity, maximum acceleration and maximum jerk corresponding to the trajectory length respectively.

3. The novel asymmetric trajectory planning method based on cosine optimization according to claim 1 is characterized in that: Determine the trip distance The process of determining the trajectory level is as follows: Pre-set distance critical maximum value and distance critical minimum ,like , then the current target trip is classified as a long-distance trajectory; if , then the current target trip is classified as a medium-distance trajectory; if , the current target trip is classified as a short-distance trajectory.

4. The novel asymmetric trajectory planning method based on cosine optimization according to claim 1 is characterized in that: When the trajectory level is a long-distance trajectory, the entire motion process includes: acceleration segments divided according to the predetermined duration and , deceleration and acceleration segments divided according to the predetermined duration and , divided into uniform speed segments according to the predetermined duration , and deceleration segments divided according to predetermined durations and ; The process of determining the long-distance trajectory motion parameters is as follows: ； According to the above formula, we can calculate The duration and k , and calculated using the following formula , , , , and Duration: ； In the formula, is the travel distance, is the preset critical maximum distance.

5. The novel asymmetric trajectory planning method based on cosine optimization according to claim 1 is characterized in that: When the trajectory level is a medium-distance trajectory, the entire motion process includes: acceleration segments divided according to the predetermined duration and , deceleration and acceleration segments divided according to the predetermined duration and , and deceleration segments divided according to predetermined durations and ; The process of determining the mid-range trajectory motion parameters is as follows: ； According to the above formula, we can calculate The duration and p , considering the current mid-range trajectory, and using the following formula to calculate , , , ,and Duration: ； In the formula, , are the maximum acceleration and maximum speed of the mid-distance trajectory respectively.

6. A novel asymmetric trajectory planning method based on cosine optimization according to claim 1, characterized in that: When the trajectory level is a short-distance trajectory, the entire motion process includes: acceleration segment , deceleration and acceleration stage and reduction section ; The process of determining the long-distance trajectory motion parameters is as follows: ； Furthermore, , , It is expressed in the following form: 。 7. The novel asymmetric trajectory planning method based on cosine optimization according to claim 1 is characterized in that: The cosine asymmetric trajectory planning model is subject to the following constraints: ； In the formula, For the start time, is the end time, t is the current time, V is the current speed, A is the acceleration equation, J is the jerk equation, , and are the maximum velocity, maximum acceleration and maximum jerk of the corresponding trajectory respectively, and P is the displacement.

8. A novel asymmetric trajectory planning system based on cosine optimization, used to implement the novel asymmetric trajectory planning method based on cosine optimization as claimed in any one of claims 1 to 7, characterized in that: include: The first module is configured to construct a cosine asymmetric trajectory planning model, wherein the cosine asymmetric trajectory planning model divides the motion process into three stages: acceleration, uniform speed, and deceleration, and uses a cosine function to describe the acceleration changes in the acceleration and deceleration stages; the motion parameters of the cosine asymmetric trajectory planning model include at least three groups: long-distance trajectory motion parameters, medium-distance trajectory motion parameters, and short-distance trajectory motion parameters; The second module is configured to obtain a target trip based on the target trip , and determine the target itinerary The track level, the track level includes at least: long-distance track, medium-distance track and short-distance track; The third module is set up according to the target travel The corresponding model parameters are selected at the trajectory level, and the cosine asymmetric trajectory planning model performs trajectory planning based on the selected corresponding model parameters.

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