阅读说明：本技术 兼具运动效率与柔性的轨迹规划加减速控制方法及系统 (Track planning acceleration and deceleration control method and system with both motion efficiency and flexibility ) 是由 刘红俐 金雨昇 朱其新 于 2021-08-16 设计创作，主要内容包括：本发明涉及一种兼具运动效率与柔性的轨迹规划加减速控制方法及系统,方法包括利用余弦算法和多项式算法构建加减速曲线模型；根据加减速曲线模型规划运动轨迹,在保持运动平滑程度的同时兼具运动效率。本发明利用余弦算法和多项式算法构建加减速曲线模型,一方面减少了加减速过程中运动系统受到的柔性冲击,增强了运动控制的平滑度,另一方面使加加速度的运动曲线能够在到达最大加加速度后得到保持,显著提高运动效率,解决了现有技术中在保持运动平滑程度的同时无法兼具运动效率的问题。(The invention relates to a track planning acceleration and deceleration control method and system with both motion efficiency and flexibility, wherein the method comprises the steps of constructing an acceleration and deceleration curve model by utilizing a cosine algorithm and a polynomial algorithm; and planning a motion track according to the acceleration and deceleration curve model, and keeping the motion smoothness and motion efficiency. According to the acceleration and deceleration curve model, the cosine algorithm and the polynomial algorithm are used for constructing the acceleration and deceleration curve model, so that on one hand, flexible impact on a motion system in the acceleration and deceleration process is reduced, smoothness of motion control is enhanced, on the other hand, the motion curve of the acceleration can be maintained after the maximum acceleration is reached, the motion efficiency is remarkably improved, and the problem that the motion efficiency cannot be achieved while the motion smoothness is maintained in the prior art is solved.)

1. A trajectory planning acceleration and deceleration control method with both motion efficiency and flexibility is characterized by comprising the following steps:

constructing an acceleration and deceleration curve model by utilizing a cosine algorithm and a polynomial algorithm;

and planning a motion track according to the acceleration and deceleration curve model, and keeping the motion smoothness and motion efficiency.

2. The trajectory planning acceleration and deceleration control method with both motion efficiency and flexibility as claimed in claim 1, characterized in that: the acceleration and deceleration curve model comprises an acceleration algorithm, and the acceleration algorithm is as follows:

in the formula, t₁-t₁₅Is a fifteen-stage time of the acceleration and deceleration process, j_maxFor maximum allowable jerk value, k is a trigonometric function period parameter, Δ t_i＝t-t_i。

3. The trajectory planning acceleration and deceleration control method with both exercise efficiency and flexibility as claimed in claim 2The method is characterized in that: the acceleration and deceleration process of the acceleration and deceleration curve model comprises fifteen sections which are respectively an acceleration section t₁Uniformly-adding acceleration section t₂A decreasing and increasing acceleration section t₃Uniform acceleration section t₄Decreasing acceleration section t₅Acceleration section t of uniform decreasing₆Acceleration section t of addition and subtraction₇And a constant speed section t₈Decreasing and decelerating section t₉Speed reduction section t₁₀Plus-minus deceleration section t₁₁Uniform speed reduction section t₁₂Acceleration and deceleration section t₁₃Uniform acceleration and deceleration section t₁₄And deceleration section t₁₅。

4. The trajectory planning acceleration and deceleration control method with both exercise efficiency and flexibility as claimed in claim 3, characterized in that: t is t₁＝t₃＝t₅＝t₇＝t₉＝t₁₁＝t₁₃＝t₁₅。

5. The trajectory planning acceleration and deceleration control method with both exercise efficiency and flexibility as claimed in claim 3, characterized in that: t is t₂＝t₆＝t₁₀＝t₁₄。

6. The trajectory planning acceleration and deceleration control method with both exercise efficiency and flexibility as claimed in claim 3, characterized in that: t is t₄＝t₁₂。

7. The trajectory planning acceleration and deceleration control method with both motion efficiency and flexibility as claimed in claim 2, characterized in that: the acceleration and deceleration curve model comprises an acceleration algorithm, and the acceleration algorithm is as follows:

in the formula, t₁-t₁₅Is a fifteen-stage time of the acceleration and deceleration process, j_maxK is the period of the trigonometric function for the maximum allowable jerk valueParameter, Δ t_i＝t-t_i，a_maxIs the maximum acceleration value allowed.

8. The trajectory planning acceleration and deceleration control method with both exercise efficiency and flexibility as claimed in claim 7, characterized in that: the acceleration and deceleration curve model comprises a speed algorithm, and the speed algorithm is as follows:

in the formula, t₁-t₁₅Is a fifteen-stage time of the acceleration and deceleration process, j_maxFor maximum allowable jerk value, k is a trigonometric function period parameter, Δ t_i＝t-t_i，a_maxTo the maximum acceleration value allowed, v_maxAs maximum speed value, a_iIs at t_iInstantaneous acceleration value of time, v_iIs at t_iInstantaneous speed value of the moment.

9. The trajectory planning acceleration and deceleration control method with both exercise efficiency and flexibility as claimed in claim 8, characterized in that: the acceleration and deceleration curve model comprises a displacement algorithm, and the displacement algorithm is as follows:

in the formula, t₁-t₁₅Is a fifteen-stage time of the acceleration and deceleration process, j_maxFor maximum allowable jerk value, k is a trigonometric function period parameter, Δ t_i＝t-t_i，a_maxTo the maximum acceleration value allowed, v_maxAs maximum speed value, a_iIs at t_iInstantaneous acceleration value of time, v_iIs at t_iInstantaneous value of the time of day, p_iIs at t_iThe instantaneous cumulative displacement of the moment.

10. A track planning acceleration and deceleration control system with both movement efficiency and flexibility is characterized by comprising:

the model building module is used for building an acceleration and deceleration curve model by utilizing a cosine algorithm and a polynomial algorithm;

and the motion trail planning module is used for planning a motion trail according to the acceleration and deceleration curve model, and the motion efficiency is realized while the motion smoothness is kept.

Technical Field

The invention relates to the technical field of servo system motion control, in particular to a track planning acceleration and deceleration control method and system with both motion efficiency and flexibility.

Background

In the automatic control, the acceleration and deceleration control technology is an important means and reliable guarantee that the system can keep high efficiency and stability and reduce errors in the motion. The core of the acceleration and deceleration algorithm is the optimal fusion of pursuit efficiency and flexibility, and on the premise of ensuring the motion precision of the system, the acceleration and deceleration algorithm aims to improve the motion efficiency and simultaneously reduces the problems of impact, step loss, overtravel, oscillation and the like generated in the motion process as much as possible.

In the traditional acceleration and deceleration algorithms, the acceleration value of a linear acceleration and deceleration algorithm and an exponential acceleration and deceleration algorithm is not zero when the system motion is started and stopped, sudden change exists, and the impact generated under the condition of high speed and heavy load is particularly obvious. The S-curve acceleration and deceleration algorithm is a seven-segment acceleration and deceleration algorithm, and can reduce flexible impact generated by speed change under high movement efficiency. The introduction of trigonometric function algorithm further reduces the soft shock generated by the speed variation, but the motion efficiency is reduced.

The trajectory planning algorithm of the trigonometric function type undergoes a series of improvement development of sine acceleration, sine jerk and cosine-like jerk, the smoothness degree of the system motion is greatly improved, but at the same time, the motion efficiency of the whole motion process is reduced and ignored, as shown in fig. 1. Therefore, how to improve the motion efficiency while keeping the motion smoothness is a problem to be solved.

Disclosure of Invention

The invention aims to solve the technical problem that the prior art can not have the movement efficiency while keeping the movement smoothness.

In order to solve the above technical problems, the present invention provides a trajectory planning acceleration and deceleration control method with both motion efficiency and flexibility, comprising:

constructing an acceleration and deceleration curve model by utilizing a cosine algorithm and a polynomial algorithm;

and planning a motion track according to the acceleration and deceleration curve model, and keeping the motion smoothness and motion efficiency.

In one embodiment of the present invention, the acceleration and deceleration curve model includes a jerk algorithm as follows:

in the formula, t₁-t₁₅Is a fifteen-stage time of the acceleration and deceleration process, j_maxK is a trigonometric function for the maximum allowable jerk valuePeriod parameter, Δ t_i＝t-t_i。

In one embodiment of the present invention, the acceleration and deceleration process of the acceleration and deceleration curve model includes fifteen segments, which are acceleration and deceleration segments t respectively₁Uniformly-adding acceleration section t₂A decreasing and increasing acceleration section t₃Uniform acceleration section t₄Decreasing acceleration section t₅Acceleration section t of uniform decreasing₆Acceleration section t of addition and subtraction₇And a constant speed section t₈Decreasing and decelerating section t₉Speed reduction section t₁₀Plus-minus deceleration section t₁₁Uniform speed reduction section t₁₂Acceleration and deceleration section t₁₃Uniform acceleration and deceleration section t₁₄And deceleration section t₁₅。

In one embodiment of the invention, t₁＝t₃＝t₅＝t₇＝t₉＝t₁₁＝t₁₃＝t₁₅。

In one embodiment of the invention, t₂＝t₆＝t₁₀＝t₁₄。

In one embodiment of the invention, t₄＝t₁₂。

In one embodiment of the present invention, the acceleration-deceleration curve model comprises an acceleration algorithm, which is as follows:

in the formula, t₁-t₁₅Is a fifteen-stage time of the acceleration and deceleration process, j_maxFor maximum allowable jerk value, k is a trigonometric function period parameter, Δ t_i＝t-t_i，a_maxIs the maximum acceleration value allowed.

In one embodiment of the present invention, the acceleration and deceleration curve model comprises a velocity algorithm as follows:

in the formula, t₁-t₁₅Is a fifteen-stage time of the acceleration and deceleration process, j_maxFor maximum allowable jerk value, k is a trigonometric function period parameter, Δ t_i＝t-t_i，a_maxTo the maximum acceleration value allowed, v_maxAs maximum speed value, a_iIs at t_iInstantaneous acceleration value of time, v_iIs at t_iInstantaneous speed value of the moment.

In one embodiment of the present invention, the acceleration and deceleration curve model comprises a displacement algorithm, which is as follows:

in the formula, t₁-t₁₅Is a fifteen-stage time of the acceleration and deceleration process, j_maxFor maximum allowable jerk value, k is a trigonometric function period parameter, Δ t_i＝t-t_i，a_maxTo the maximum acceleration value allowed, v_maxAs maximum speed value, a_iIs at t_iInstantaneous acceleration value of time, v_iIs at t_iInstantaneous value of the time of day, p_iIs at t_iThe instantaneous cumulative displacement of the moment.

In addition, the invention also provides a track planning acceleration and deceleration control system with both motion efficiency and flexibility, which comprises:

the model building module is used for building an acceleration and deceleration curve model by utilizing a cosine algorithm and a polynomial algorithm;

and the motion trail planning module is used for planning a motion trail according to the acceleration and deceleration curve model, and the motion efficiency is realized while the motion smoothness is kept.

The invention has the beneficial effects that: according to the acceleration and deceleration curve model, the cosine algorithm and the polynomial algorithm are used for constructing the acceleration and deceleration curve model, so that on one hand, flexible impact on a motion system in the acceleration and deceleration process is reduced, smoothness of motion control is enhanced, on the other hand, the motion curve of the acceleration can be maintained after the maximum acceleration is reached, the motion efficiency is remarkably improved, and the problem that the motion efficiency cannot be achieved while the motion smoothness is maintained in the prior art is solved.

Drawings

In order that the present disclosure may be more readily and clearly understood, reference will now be made in detail to the present disclosure, examples of which are illustrated in the accompanying drawings.

FIG. 1 is a simulated contrast plot of a conventional sinusoidal jerk algorithm and a sinusoidal jerk algorithm.

Fig. 2 is a schematic flow chart of a trajectory planning acceleration and deceleration control method with both motion efficiency and flexibility according to the present invention.

FIG. 3 is a graph of the trajectory planning motion of the acceleration-deceleration curve model of the present invention.

FIG. 4 is a diagram of simulation results of the acceleration/deceleration curve model of the present invention.

Fig. 5 is a diagram of simulation results of a general cosine-like algorithm.

FIG. 6 is a mechanical model diagram of a vibration test.

FIG. 7 is a diagram of a vibration simulation Simulink model.

FIG. 8 is a graph of vibration test input acceleration signals.

FIG. 9 shows the vibration simulation results of the acceleration/deceleration curve model of the present invention

Fig. 10 is a vibration simulation result of a general cosine-like algorithm.

Detailed Description

The present invention is further described below in conjunction with the following figures and specific examples so that those skilled in the art may better understand the present invention and practice it, but the examples are not intended to limit the present invention.

Example one

The following introduces a trajectory planning acceleration and deceleration control method with both motion efficiency and flexibility provided by an embodiment of the present invention.

Referring to fig. 2, a method for controlling acceleration and deceleration in a trajectory plan with both motion efficiency and flexibility according to an embodiment of the present invention includes the following steps:

s100: and (4) constructing an acceleration and deceleration curve model by utilizing a cosine algorithm and a polynomial algorithm.

S200: and planning a motion track according to the acceleration and deceleration curve model, and keeping the motion smoothness and motion efficiency.

In S100, the acceleration and deceleration process of the acceleration and deceleration curve model includes fifteen segments, which are respectively an acceleration segment t₁Uniformly-adding acceleration section t₂A decreasing and increasing acceleration section t₃Uniform acceleration section t₄Decreasing acceleration section t₅Acceleration section t of uniform decreasing₆Acceleration section t of addition and subtraction₇And a constant speed section t₈Decreasing and decelerating section t₉Speed reduction section t₁₀Plus-minus deceleration section t₁₁Uniform speed reduction section t₁₂Acceleration and deceleration section t₁₃Uniform acceleration and deceleration section t₁₄And deceleration section t₁₅From the symmetry of acceleration and deceleration, it can be seen that: t is t₁＝t₃＝t₅＝t₇＝t₉＝t₁₁＝t₁₃＝t₁₅，t₂＝t₆＝t₁₀＝t₁₄，t₄＝t₁₂。

The acceleration and deceleration curve model comprises an acceleration algorithm, and the expression of the acceleration algorithm is as follows:

in the formula, t₁-t₁₅Is a fifteen-stage time of the acceleration and deceleration process, j_maxFor maximum allowable jerk value, k is a trigonometric function period parameter, Δ t_i＝t-t_i。

The expressions of the acceleration algorithm, the speed algorithm and the displacement algorithm can be derived according to the expressions of the jerk algorithm as follows:

in the formula, t₁-t₁₅Is a fifteen-stage time of the acceleration and deceleration process, j_maxFor maximum allowable jerk value, k is a trigonometric function period parameter, Δ t_i＝t-t_i，a_maxTo the maximum acceleration value allowed, v_maxAs maximum speed value, a_iIs at t_iInstantaneous acceleration value of time, v_iIs at t_iInstantaneous value of the time of day, p_iIs at t_iThe instantaneous cumulative displacement of the moment.

In conclusion, the acceleration and deceleration curve model is constructed by utilizing the cosine algorithm and the polynomial algorithm, so that the flexible impact on a motion system in the acceleration and deceleration process is reduced, the smoothness of motion control is enhanced, the motion curve of the acceleration can be maintained after the maximum acceleration is reached, the motion efficiency is obviously improved, and the problem that the motion efficiency cannot be achieved while the motion smoothness is maintained in the prior art is solved.

FIG. 3 is a diagram of a trajectory planning motion curve of the acceleration/deceleration curve model of the present invention, wherein a horizontal segment is constructed by using a polynomial when the jerk of the system reaches the maximum value, so that the maximum jerk is maintained, thereby improving the motion efficiency of the system. Meanwhile, the derivative of the cosine at the maximum value is the same as that of the horizontal segment, so that the smoothness of the motion track is not influenced.

In order to verify the effectiveness and the movement efficiency of the acceleration and deceleration curve model, the trajectory plan of the acceleration and deceleration curve model is compared with the trajectory plan of a common cosine-like acceleration and deceleration algorithm under the same parameter requirement through MATLAB simulation.

(1) k value determination

The constraints on the motion curves are as follows:maximum jerk j_maxMaximum acceleration a of 8mm/s3_max＝16mm/s²Maximum velocity v_max80mm/S, 2000mm total stroke S, 1. Fig. 4 and 5 are simulation result diagrams of the acceleration and deceleration curve model and the general cosine-like algorithm, respectively. It can be seen from the comparison of the two graphs that the maximum acceleration of the common cosine-like algorithm is limited under the condition that the k value is determined, so that the accelerated motion stage is long, and the overall motion efficiency is low. The acceleration and deceleration curve model can achieve the maximum acceleration specified by the system through the maintenance of the maximum acceleration, the motion efficiency is improved, and meanwhile, the error caused by the transmission of the acceleration and deceleration signals can be effectively reduced in a longer uniform motion stage.

(2) k is uncertain

When the value of k is uncertain, a physical model shown in fig. 6 is established, and residual vibration generated by the acceleration and deceleration curve model and the common cosine-like algorithm is simulated by using a Simulink simulation model (a visual simulation tool in MATLAB) shown in fig. 7.

FIG. 6 is a simplified single axis motion platform, wherein m₁Is a flexibly connected mass m₂The mass is equal weight block dragged by the motor, q is spring coefficient, and c is damping coefficient. This system ignores frictional effects. When m is₂When dragged by the motor at an acceleration a, m₁The applied force is as follows:

f＝m₂a

to m₁The analysis can yield:

in the formula, x is m₁The displacement after being stressed can also be expressed as follows:

in the formula, ω_nIs the natural oscillation frequency, zeta is the damping ratio. In simulation experiment, take m₂/m₁＝0.1，ω_n150.8rad/s, ζ 3%. Fig. 8 is an acceleration signal input in a simulation experiment, and fig. 9 and 10 are vibration simulation results of an acceleration/deceleration curve model and a general cosine-like algorithm according to the present invention, respectively. Vibration analysis is performed on the acceleration section in fig. 9 and 10, and the maximum vibration amplitude of the ordinary cosine-like algorithm in the acceleration stage is measured to be 84nm, and the maximum vibration amplitude of the acceleration stage of the acceleration and deceleration curve model of the invention is measured to be 17 nm.

Under the condition of different values of k, the performance of the acceleration and deceleration curve model provided by the invention is superior to that of a common cosine-like algorithm, namely the acceleration and deceleration curve model with both motion efficiency and flexibility has better motion control performance.

Example two

In the following, a trajectory planning acceleration and deceleration control system with both motion efficiency and flexibility provided by the second embodiment of the present invention is introduced, and a trajectory planning acceleration and deceleration control system with both motion efficiency and flexibility described below and a trajectory planning acceleration and deceleration control method with both motion efficiency and flexibility described above may be referred to correspondingly.

The second embodiment of the present invention provides a trajectory planning acceleration and deceleration control system with both motion efficiency and flexibility, including:

the model building module is used for building an acceleration and deceleration curve model by utilizing a cosine algorithm and a polynomial algorithm;

and the motion trail planning module is used for planning a motion trail according to the acceleration and deceleration curve model, and the motion efficiency is achieved while the motion smoothness is kept.

The trajectory planning acceleration and deceleration control system with both motion efficiency and flexibility of the embodiment is used to implement the trajectory planning acceleration and deceleration control method with both motion efficiency and flexibility, so that the specific implementation of the system can be seen in the foregoing embodiment of the trajectory planning acceleration and deceleration control method with both motion efficiency and flexibility, and therefore, the specific implementation thereof can refer to the description of the corresponding partial embodiments, and will not be further described herein.

In addition, since the trajectory planning acceleration and deceleration control system with both motion efficiency and flexibility of this embodiment is used to implement the trajectory planning acceleration and deceleration control method with both motion efficiency and flexibility, the function corresponds to that of the above method, and is not described herein again.

As will be appreciated by one skilled in the art, embodiments of the present application may be provided as a method, system, or computer program product. Accordingly, the present application may take the form of an entirely hardware embodiment, an entirely software embodiment or an embodiment combining software and hardware aspects. Furthermore, the present application may take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, and the like) having computer-usable program code embodied therein.

The present application is described with reference to flowchart illustrations and/or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the application. It will be understood that each flow and/or block of the flow diagrams and/or block diagrams, and combinations of flows and/or blocks in the flow diagrams and/or block diagrams, can be implemented by computer program instructions. These computer program instructions may be provided to a processor of a general purpose computer, special purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, create means for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.

These computer program instructions may also be stored in a computer-readable memory that can direct a computer or other programmable data processing apparatus to function in a particular manner, such that the instructions stored in the computer-readable memory produce an article of manufacture including instruction means which implement the function specified in the flowchart flow or flows and/or block diagram block or blocks.

These computer program instructions may also be loaded onto a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer implemented process such that the instructions which execute on the computer or other programmable apparatus provide steps for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.

It should be understood that the above examples are only for clarity of illustration and are not intended to limit the embodiments. Other variations and modifications will be apparent to persons skilled in the art in light of the above description. And are neither required nor exhaustive of all embodiments. And obvious variations or modifications of the invention may be made without departing from the spirit or scope of the invention.