CN108544493B - Time optimal trajectory planning method and device for robot operation space - Google Patents

Time optimal trajectory planning method and device for robot operation space Download PDF

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CN108544493B
CN108544493B CN201810321891.9A CN201810321891A CN108544493B CN 108544493 B CN108544493 B CN 108544493B CN 201810321891 A CN201810321891 A CN 201810321891A CN 108544493 B CN108544493 B CN 108544493B
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axis
arc length
acceleration
robot
joint
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CN108544493A (en
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陈盛花
刘勇
林炯辉
祝润泽
黄昕
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Zhongzheng Data Technology Co ltd
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Guangzhou Start To Sail Industrial Robot Co
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    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B25—HAND TOOLS; PORTABLE POWER-DRIVEN TOOLS; MANIPULATORS
    • B25J—MANIPULATORS; CHAMBERS PROVIDED WITH MANIPULATION DEVICES
    • B25J9/00—Programme-controlled manipulators
    • B25J9/16—Programme controls
    • B25J9/1656—Programme controls characterised by programming, planning systems for manipulators
    • B25J9/1664—Programme controls characterised by programming, planning systems for manipulators characterised by motion, path, trajectory planning

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  • Robotics (AREA)
  • Mechanical Engineering (AREA)
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Abstract

本发明公开了一种针对机器人操作空间的时间最优轨迹规划方法和装置。所述方法包括根据操作空间路径和机器人各轴关节位移对时间的各阶导数，计算约束曲线MVC，根据所述操作空间路径和约束曲线MVC，在操作空间内进行路径积分，得到积分路径等步骤。所述装置包括存储器和处理器。本发明将机器人各轴关节位移对时间的各阶导数所受的限制转化为对弧长参数各阶导数的限制，从而将多维度约束条件转化为单一维度约束条件，使得整个轨迹规划过程更为简单高效，各轴关节始终处于约束的饱和状态下，提高机器人的运行效率，在引入各轴关节加速度和加加速度等位移的高阶导数后，所得的轨迹规划结果可以有效减少机器人末端抖动，提高机器人的稳定性。

The invention discloses a time optimal trajectory planning method and device for robot operation space. The method includes the steps of calculating a constraint curve MVC according to the operation space path and each derivative of the joint displacement of each axis of the robot with respect to time, and performing path integration in the operation space according to the operation space path and the constraint curve MVC to obtain an integral path. . The apparatus includes a memory and a processor. The invention converts the restrictions on the derivatives of the joint displacement of each axis of the robot to the restrictions on the derivatives of the arc length parameters, so that the multi-dimensional constraints are converted into single-dimensional constraints, so that the entire trajectory planning process is more efficient. Simple and efficient, the joints of each axis are always in the saturated state of constraints, which improves the operation efficiency of the robot. After introducing the high-order derivatives of the displacements such as the acceleration and jerk of the joints of each axis, the obtained trajectory planning results can effectively reduce the robot end jitter and improve the efficiency of the robot. The stability of the robot.

Description

A kind of time optimal trajectory planning method and apparatus for robot manipulation space
Technical field
The present invention relates to robot automatic control technology field, especially a kind of time for robot manipulation space is most Excellent method for planning track and device.
Background technique
Explanation of nouns
Trajectory planning: needing some task completed according to robot, each pass of robot when to this task of completion The process that section needs mobile displacement, speed, acceleration and these data and the relationship of time to be set.
Time optimal trajectory planning: in the case where various constraint conditions can meet, the shortest track of required time Planning, or most short as optimizing index trajectory planning is optimized using the time used.
Trajectory planning is an indispensable ring during motion planning and robot control, and quality directly affects robot motion Stationarity and production efficiency.The existing trajectory planning for robot manipulation space is mostly with cartesian space constraint condition Based on carry out, do not consider each joint constraint condition.Single method for planning track based on cartesian space constraint can expire The commonly used basic demand of biped robot, but under the application scenarios that stacking and spot welding etc. need robot high-speed cruising, When the Descartes's constraint condition especially set is excessively high, based on cartesian space constraint single method for planning track the shortcomings that just It can be exposed, prevent robot from being competent at the work such as stacking and spot welding well.
Based on cartesian space constraint single method for planning track the shortcomings that and caused consequence mainly have two aspect.The On the one hand, since robot is the system being highly coupled, speed of the robot end under cartesian space is by each The velocity composite in joint, therefore the rate limitation under cartesian space will receive operating space path effects, i.e., it is restricted It is very big, it is constrained with cartesian space carry out trajectory planning merely, joint of robot is easy to be more than restrictive condition, such as occurs Situations such as joint is exceeded the speed limit, so as to cause robot fluctuation of service.On the other hand, the single track based on cartesian space constraint Planing method can only plan the rate limitation of cartesian space, and belong to linear programming, but be influenced by joint Rate limitation condition be curve, based on cartesian space constraint single method for planning track can not be bonded this curve, make It obtains the robot speed of service and is lower than the maximum speed that actually can achieve, reduce production efficiency.
Summary of the invention
In order to solve the above-mentioned technical problem, the first object of the present invention is to provide a kind of for robot manipulation space Time optimal trajectory planning method, second is designed to provide a kind of time optimal trajectory planning for robot manipulation space Device.
First technical solution adopted by the present invention is:
A kind of time optimal trajectory planning method for robot manipulation space, comprising the following steps:
S1. according to each axis joint displacement pair of robot in given operating space related with arc length parameters path, setting The all-order derivative of time calculates constraint curve MVC；
S2. according to the operating space path and constraint curve MVC, path integral is carried out in operating space, it is resulting Path of integration is time optimal trajectory planning result.
Further, the step S2 is specifically included:
S21. the first forward direction integral is carried out since the starting point in the operating space path, the first forward direction integral Track is the first forward direction integral curve, and the first forward direction integral reaches the first forward direction integral curve and constraint curve MVC's Terminate when intersection point；Corresponding arc length parameters are denoted as the first arc length parameters at the end of the first forward direction integral；
S22. arc length parameters begin look for cutting equal to point corresponding to the first arc length parameters from the operating space path It changes a little；
S23. the first reverse integral is carried out since the switching point, the track of first reverse integral is first reversed Integral curve, first reverse integral are tied when reaching the intersection point of the first reverse integral curve and the first forward direction integral curve Then beam carries out the second forward direction integral since the switching point；
S24. repetitive cycling executes step S21-S23, until second forward direction integrates the end in arrival operating space path Until stop；
S25. the second reverse integral is carried out along reverse integral curve since the terminating point in operating space path, described the The track of two reverse integrals is the second reverse integral curve, and second reverse integral reaches the second reverse integral curve and the Terminate when the intersection point of one forward direction integral curve, to obtain path of integration.
Further, the operating space path includes translation curve and posture curve.
Further, movement of the robot in operating space Descartes's speed and Descartes's acceleration are come table It reaches, the all-order derivative of each axis joint displacement versus time includes each axis joint speed and each axis joint acceleration, each axis Joint velocity and each axis joint acceleration respectively correspond the restrictive condition of setting, in the step S1, are calculated by following steps Constraint curve MVC:
S11. according to the geometry of robot, the mapping relations of each axis joint speed and Descartes's speed, each axis are obtained Joint velocity and the mapping relations of Descartes's acceleration and the mapping of each axis joint acceleration and Descartes's acceleration Relationship；
S12. according to the mapping relations of each axis joint speed and Descartes's speed and Descartes's speed and arc length parameters The first restrictive condition of the first derivative for constraining arc length parameters is calculated in the mapping relations of first derivative；
S13. according to the mapping relations and Descartes's acceleration and arc length of each axis joint acceleration and Descartes's acceleration The second restrictive condition of the second dervative for constraining arc length parameters is calculated in the mapping relations of the second dervative of parameter；
S14. according to the mapping relations and Descartes's acceleration of each axis joint acceleration and Descartes's acceleration With the mapping relations of three order derivatives of arc length parameters, the third limitation item of three order derivatives for constraining arc length parameters is calculated Part；
S15. according to the first restrictive condition, the second restrictive condition and third restrictive condition, constraint curve MVC is calculated.
Further, each axis joint speed, each axis joint acceleration and each axis joint acceleration correspond to setting Restrictive condition is
The mapping relations of each axis joint speed and Descartes's speed areIn formula, v is Descartes's speed, and J is Jacobian matrix related with the geometry of robot,For each axis joint speed；
The mapping relations of the first derivative of Descartes's speed and arc length parameters areIn formula, v is Descartes Speed, f (s) are operating space path,For the first derivative of arc length parameters；
First restrictive condition isIn formula, ak(s)=J-1f′ (s)。
Further, the mapping relations of each axis joint acceleration and Descartes's acceleration areIn formula, a For Descartes's acceleration, J is Jacobian matrix related with the geometry of robot,For each axis joint speed,For each axis Joint velocity；
The mapping relations of the second dervative of Descartes's acceleration and arc length parameters areFormula In, a is Descartes's acceleration, and f (s) is operating space path,For the first derivative of arc length parameters,It is the two of arc length parameters Order derivative；
Second restrictive condition isIn formula, bk(s) =J-1[f″(s)-J′ak(s)]；
Further, the mapping relations of each axis joint acceleration and Descartes's acceleration areIn formula, j is Descartes's acceleration, and J is Jacobian matrix related with the geometry of robot,WithRespectively Jacobian matrix to the first derivative and second dervative of time,For each axis joint speed,For each axis joint Acceleration,For each axis joint acceleration；
The mapping relations of Descartes's acceleration and three order derivatives of arc length parameters areIn formula, j is Descartes's acceleration, and f (s) is operating space path,For arc length ginseng Several first derivatives,For the second dervative of arc length parameters,For three order derivatives of arc length parameters；
The third restrictive condition isIn formula, ck(s)=J-1[f″′ (s)-J″ak(s)-2J′bk(s)]。
Further, the first forward direction integral is carried out by following formula and/or the second forward direction integrates:
In formula, siFor current time arc length parameters, si-1For last moment arc length parameters,For the first derivative of s,For s's Second dervative,For three order derivatives of s, TsFor the sampling period.
Further, the first reverse integral and/or the second reverse integral are carried out by following formula:
In formula, siFor current time arc length parameters, si-1For last moment arc length parameters,For the first derivative of s,For s Second dervative,For three order derivatives of s, TsFor the sampling period.
Further, the switching point meets:
In formula, MVC () is constraint curve MVC, and swi is switching point,For the first derivative of arc length parameters s,For arc length The second dervative of parameter s.
Second technical solution adopted by the present invention is:
A kind of time optimal trajectory planning device for robot manipulation space, comprising:
Memory, for storing at least one program；
Processor is grasped for loading at least one described program with executing one kind described in the first technical solution for robot Make the time optimal trajectory planning method in space.
The beneficial effects of the present invention are: by calculating constraint curve MVC, by each of each axis joint displacement versus time of robot Limitation suffered by order derivative is converted into the limitation to arc length parameters all-order derivative, to convert various dimensions constraint condition to single Dimension constraint condition, so that entire trajectory planning process is more simple and efficient.Trajectory planning result can make each axis joint always Under saturation state in constraint, the operational efficiency of robot is improved.Due to considering each axis joint when calculating constraint curve MVC The all-order derivative of displacement versus time, it is resulting after the higher derivative for introducing the displacements such as each axis joint acceleration and acceleration Trajectory planning result can effectively reduce robot end's shake, improve the stability of robot.
Detailed description of the invention
Fig. 1 is the flow chart of method for planning track of the present invention；
Fig. 2 is the targeted operating space path schematic diagram of method for planning track of the present invention；
Fig. 3 is the path of integration figure of the continuous path of the operating space generated according to method for planning track of the present invention.
Specific embodiment
A kind of time optimal trajectory planning method for robot manipulation space of the present invention, as shown in Figure 1, including following Step:
S1. according to each axis joint displacement pair of robot in given operating space related with arc length parameters path, setting The all-order derivative of time calculates constraint curve MVC；
S2. according to the operating space path and constraint curve MVC, path integral is carried out in operating space, it is resulting Path of integration is time optimal trajectory planning result.
Operating space path can mathematically indicate that wherein s is arc length parameters, and operating space path f (s) is with f (s) Given, it is related with the task of robot, while the all-order derivative of each axis joint displacement versus time of robot is also root According to task setting.The all-order derivative of each axis joint displacement versus time of robot includes zero order derivative, first derivative, second order Derivative and three order derivatives etc., zero order derivative are each axis joint displacements itself, and first derivative is each axis joint speed, and second dervative is Each axis joint acceleration, three order derivatives are each axis joint accelerations.
In the present patent application, unless otherwise instructed, is all referred to " derivative " of text or formulae express and the time is led Number.
It is further used as preferred embodiment, the step S2 is specifically included:
S21. the first forward direction integral is carried out since the starting point in the operating space path, the first forward direction integral Track is the first forward direction integral curve, and the first forward direction integral reaches the first forward direction integral curve and constraint curve MVC's Terminate when intersection point；Corresponding arc length parameters are denoted as the first arc length parameters at the end of the first forward direction integral；
S22. arc length parameters begin look for cutting equal to point corresponding to the first arc length parameters from the operating space path It changes a little；
S23. the first reverse integral is carried out since the switching point, the track of first reverse integral is first reversed Integral curve, first reverse integral are tied when reaching the intersection point of the first reverse integral curve and the first forward direction integral curve Then beam carries out the second forward direction integral since the switching point；
S24. repetitive cycling executes step S21-S23, until second forward direction integrates the end in arrival operating space path Until stop；
S25. the second reverse integral is carried out along reverse integral curve since the terminating point in operating space path, described the The track of two reverse integrals is the second reverse integral curve, and second reverse integral reaches the second reverse integral curve and the Terminate when the intersection point of one forward direction integral curve, to obtain path of integration.
In step S21, the starting point in operating space path refers to the point that arc length parameters are zero namely the corresponding point of s=0. It since the starting point in operating space path, is integrated along the first forward direction that the first forward direction integral curve carries out, reaches first Terminate when the intersection point of forward direction integral curve and constraint curve MVC, corresponding arc length parameters at this time are first arc length of particular value Parameter si, i.e. s=si.
The point that step S22 terminates from step S21, that is, the corresponding point of arc length parameters book s=si start to carry out, and search out Switching point can be denoted as swi.
In step S23, the first reverse integral is carried out along the first reverse integral curve since switching point swi, is reached Terminate when the intersection point of the first reverse integral curve and the first forward direction integral curve；Then from the carry out second since switching point swi Forward direction integral.
After executing the step S23, return executes again since step S21, i.e. step S21-S23 constitutes a circulation Body.In different loop bodies, that is, in different circulation rounds, the first forward direction integral curve, the first reverse integral curve and Entity corresponding to the concepts such as switching point can change, that is, the first forward direction integral curve and upper one in epicycle circulation The first forward direction integral curve in wheel circulation may exist difference.More wheel circulations are executed, are reached until second forward direction integrates Until the terminating point in operating space path.
In step S25, the terminating point in operating space path refers to the point of arc length parameters s=sf, and wherein sf is operating space Total arc length in path.
After step S25 is finished, preferably rate smoothing processing can also be carried out for obtained path of integration, So that the effect of path of integration is more excellent.Rate smoothing processing refers to preceding at integral curve and reverse integral intersections of complex curve The rate smoothing processing for meeting each axis joint acceleration restrictive condition is carried out, specifically: it is flat that speed is carried out using dichotomy Sliding processing, until any point intersection on forward direction integral and reverse integral track.
Preferably, above-mentioned each axis joint acceleration restrictive condition are as follows:
In formula, ck (s)=J-1[f″′(s)-J″ak(s)-2J′bk(s)]。
Above-mentioned each axis joint acceleration restrictive condition, can be by each axis joint acceleration and Descartes's acceleration Mapping relationsAnd the mapping relations of Descartes's acceleration and three order derivatives of arc length parametersIt obtains.In the above formulas, j is Descartes's acceleration.
It is further used as preferred embodiment, the operating space path includes translation curve and posture curve.
Translation curve and posture curve use p (s) and q (s) to indicate that then operating space path f (s) can be indicated respectively are as follows:
It is further used as preferred embodiment, the robot movement in operating space Descartes's speed and flute Karr acceleration is expressed, and the all-order derivative of each axis joint displacement versus time includes that each axis joint speed and each axis joint add Speed, each axis joint speed and each axis joint acceleration respectively correspond the restrictive condition of setting, in the step S1, pass through Following steps calculate constraint curve MVC:
S11. according to the geometry of robot, the mapping relations of each axis joint speed and Descartes's speed, each axis are obtained Joint velocity and the mapping relations of Descartes's acceleration and the mapping of each axis joint acceleration and Descartes's acceleration Relationship；
S12. according to the mapping relations of each axis joint speed and Descartes's speed and Descartes's speed and arc length parameters The first restrictive condition of the first derivative for constraining arc length parameters is calculated in the mapping relations of first derivative；
S13. according to the mapping relations and Descartes's acceleration and arc length of each axis joint acceleration and Descartes's acceleration The second restrictive condition of the second dervative for constraining arc length parameters is calculated in the mapping relations of the second dervative of parameter；
S14. according to the mapping relations and Descartes's acceleration of each axis joint acceleration and Descartes's acceleration With the mapping relations of three order derivatives of arc length parameters, the third limitation item of three order derivatives for constraining arc length parameters is calculated Part；
S15. according to the first restrictive condition, the second restrictive condition and third restrictive condition, constraint curve MVC is calculated.
In the prior art, cartesian coordinate system generally is established by origin of components such as the pedestals of robot, robot Descartes's speed, Descartes's acceleration and Descartes's acceleration are moved to express.For each axis joint displacement versus time All-order derivative, generally takes its first derivative, second dervative and three order derivatives, i.e., each axis joint speed, each axis joint acceleration and Each axis joint acceleration.It will be each axis joint speed, each axis joint acceleration and each when task is arranged for robot Axis joint acceleration respectively corresponds the restrictive condition of setting, that is, respectively by each axis joint speed, each axis joint acceleration In a specific range with the limitation of each axis joint acceleration.
By the calculated constraint curve MVC of step S11-S15, reflect in each axis joint speed of setting and each axis pass Under section acceleration constrains jointly, limitation suffered by the first derivative of arc length parameters s.
It is further used as preferred embodiment, each axis joint speed, each axis joint acceleration and each axis joint add The corresponding restrictive condition set of acceleration as
The mapping relations of each axis joint speed and Descartes's speed areIn formula, v is Descartes's speed, For each axis joint speed；
The mapping relations of the first derivative of Descartes's speed and arc length parameters areIn formula, v is Descartes Speed, f (s) are operating space path,For the first derivative of arc length parameters；
First restrictive condition isIn formula, ak(s)=J-1f′ (s)。
Each axis joint speedEach axis joint accelerationWith each axis joint accelerationThe restrictive condition of corresponding setting ForNamely each axis joint speedEach axis joint accelerationAdd with each axis joint AccelerationAll it is limited within the scope of preset maximum value and minimum value, wherein k is the number of specific axis joint, and dof is axis The maximum number in joint.
According to the geometry of robot, the mapping relations of each axis joint speed and Descartes's speed, each axis joint are obtained The mapping relations of speed and Descartes's speed areJ is Jacobian matrix, is determined by the geometry of robot, and flute The mapping relations of the first derivative of karr speed and arc length parameters areBy above-mentioned two mapping relations, that is, it is comprehensive It closes and states two formulas, be available for the first restrictive condition of the first derivative of constraint arc length parameters, that is,In formula, ak(s)=J-1f′(s).First restrictive condition is by arc length parameters First derivative constrains in a certain range.
It is further used as preferred embodiment, the mapping relations of each axis joint acceleration and Descartes's acceleration areIn formula, a is Descartes's acceleration, and J is Jacobian matrix related with the geometry of robot,For each axis Joint velocity,For each axis joint acceleration；
The mapping relations of the second dervative of Descartes's acceleration and arc length parameters areFormula In, a is Descartes's acceleration, and f (s) is operating space path,For the first derivative of arc length parameters,It is the two of arc length parameters Order derivative；
Second restrictive condition isIn formula, bk(s) =J-1[f″(s)-J′ak(s)]。
According to the geometry of robot, the mapping relations of each axis joint acceleration and Descartes's acceleration, each axis are obtained Joint velocity and the mapping relations of Descartes's acceleration areAnd the second order of Descartes's acceleration and arc length parameters The mapping relations of derivative areBy above-mentioned two mapping relations, that is, in summary two formula, it can obtain To the second restrictive condition of the second dervative for constraining arc length parameters, that is,In formula, bk(s)=J-1[f″(s)-J′ak(s)].Second limit Condition processed constrains the second dervative of arc length parameters in a certain range.
It is further used as preferred embodiment, the mapping of each axis joint acceleration and Descartes's acceleration is closed System isIn formula, j is Descartes's acceleration, and J is Jacobi square related with the geometry of robot Battle array,WithRespectively Jacobian matrix to the first derivative and second dervative of time,For each axis joint speed,For each axis pass Acceleration is saved,For each axis joint acceleration；
The mapping relations of Descartes's acceleration and three order derivatives of arc length parameters areIn formula, j is Descartes's acceleration, and f (s) is operating space path,For arc length ginseng Several first derivatives,For the second dervative of arc length parameters,For three order derivatives of arc length parameters；
The third restrictive condition isIn formula, ck(s)=J-1[f″′ (s)-J″ak(s)-2J′bk(s)]。
According to the geometry of robot, the mapping relations of each axis joint acceleration and Descartes's acceleration are obtained, The mapping relations of each axis joint acceleration and Descartes's acceleration areAnd Descartes's acceleration with The mapping relations of three order derivatives of arc length parameters areBy above-mentioned two mapping relations, It is exactly in summary two formula, is available for the third restrictive condition of three order derivatives of constraint arc length parameters, that is,In formula, ck(s)=J-1 [f″′(s)-J″ak(s)-2J′bk(s)].Third restrictive condition constrains three order derivatives of arc length parameters in a certain range.
According to the first restrictive conditionSecond restrictive conditionWith third restrictive conditionExisting mathematics can be used Method calculates constraint curve MVC.In order to ensure the first derivative of calculated arc length parameters s is reasonable, according to the first limitation During condition and the second restrictive condition calculate constraint curve MVC, condition can also be added:In summary three formulas can calculate constraint curve MVC.
It is further used as preferred embodiment, passes through vector product before following formula progress the first forward direction integral and/or second Point:
In formula, siFor current time arc length parameters, si-1For last moment arc length parameters,For the first derivative of s,For s Second dervative,For three order derivatives of s, TsFor the sampling period.
Above-mentioned formula can be used in the first forward direction integral in step S21 and the second forward direction integral in step S23 It carries out.
It is further used as preferred embodiment, the first reverse integral and/or the second reversed product are carried out by following formula Point:
In formula, siFor current time arc length parameters, si-1For last moment arc length parameters,For the first derivative of s,For s's Second dervative,For three order derivatives of s, TsFor the sampling period.
The first reverse integral in step S23 and above-mentioned formula can be used with the second reverse integral in step S25 Come carry out.
It is further used as preferred embodiment, the switching point meets:
In formula, MVC () is constraint curve MVC, and swi is switching point,For the first derivative of arc length parameters s,For arc length The second dervative of parameter s.
In step S22, need to find switching point.According to the method described above, that is found meets condition Point swi be required for switching point.
Fig. 2 and Fig. 3 can intuitively show effect of the invention.Wherein, Fig. 2 is that a targeted operation of the present invention is empty Between path schematic diagram, Fig. 3 is the path of integration figure of the continuous path of the operating space generated according to the method for the present invention, In, curve A is first derivative restrictive curve of each axis joint acceleration to arc length parameters, and curve B is each axis joint speed to arc The first derivative restrictive curve of long parameter, curve C are path of integration.
The present invention also provides a kind of time optimal trajectory planning devices for robot manipulation space, comprising:
Memory, for storing at least one program；
Processor requires any one of 1-9 described a kind of for machine for loading at least one described program with perform claim The time optimal trajectory planning method of device people operating space.
General purpose personal computer can be used to realize in memory and processor, also can be used and is mounted in robot Robot computer.Robot is mounted with the necessary parts such as sensor and executing agency according to the prior art, can obtain institute Necessary data are wanted to be handled for processor, executing agency is able to carry out the processing result of processor.
It is to be illustrated to preferable implementation of the invention, but the implementation is not limited to the invention above Example, those skilled in the art can also make various equivalent variations on the premise of without prejudice to spirit of the invention or replace It changes, these equivalent deformations or replacement are all included in the scope defined by the claims of the present application.

Claims (9)

1.一种针对机器人操作空间的时间最优轨迹规划方法，其特征在于，包括以下步骤：1. a time optimal trajectory planning method for robot operation space, is characterized in that, comprises the following steps: S1.根据给定的与弧长参数有关的操作空间路径、设定的机器人各轴关节位移对时间的各阶导数，计算约束曲线MVC，所述约束曲线MVC为机器人在该路径下允许达到最大速度；S1. Calculate the constraint curve MVC according to the given operation space path related to the arc length parameter and the set derivatives of the joint displacement of each axis of the robot to time, and the constraint curve MVC is the maximum allowed by the robot under this path. speed; S2.根据所述操作空间路径和约束曲线MVC，在操作空间内进行路径积分，所得的积分路径为时间最优的轨迹规划结果；S2. According to the operation space path and the constraint curve MVC, path integration is performed in the operation space, and the obtained integration path is the time-optimized trajectory planning result; 所述步骤S2具体包括：The step S2 specifically includes: S21.从所述操作空间路径的起始点开始进行第一前向积分，所述第一前向积分的轨迹为第一前向积分曲线，所述第一前向积分在到达第一前向积分曲线与约束曲线MVC的交点时结束；所述第一前向积分结束时对应的弧长参数记为第一弧长参数；S21. Perform the first forward integration from the starting point of the operation space path, the trajectory of the first forward integration is the first forward integration curve, and the first forward integration reaches the first forward integration The intersection of the curve and the constraint curve MVC ends; the arc length parameter corresponding to the end of the first forward integration is recorded as the first arc length parameter; S22.从所述操作空间路径中弧长参数等于第一弧长参数所对应的点开始寻找切换点；S22. Starting from the point corresponding to the arc length parameter equal to the first arc length parameter in the operation space path, searching for the switching point; S23.从所述切换点开始进行第一反向积分，所述第一反向积分的轨迹为第一反向积分曲线，所述第一反向积分在到达第一反向积分曲线与第一前向积分曲线的交点时结束，然后从所述切换点开始进行第二前向积分；S23. Carry out the first reverse integration from the switching point, the trajectory of the first reverse integration is the first reverse integration curve, and the first reverse integration reaches the first reverse integration curve and the first reverse integration curve. end at the intersection of the forward integration curves, and then start the second forward integration from the switching point; S24.重复循环执行步骤S21-S23，直到所述第二前向积分到达操作空间路径的终止点为止；S24. Repeat steps S21-S23 in a loop until the second forward integration reaches the termination point of the operation space path; S25.从操作空间路径的终止点开始沿着反向积分曲线进行第二反向积分，所述第二反向积分的轨迹为第二反向积分曲线，所述第二反向积分在到达第二反向积分曲线与第一前向积分曲线的交点时结束，从而得到积分路径。S25. From the end point of the operation space path, perform a second reverse integration along the reverse integration curve, the trajectory of the second reverse integration is the second reverse integration curve, and the second reverse integration reaches the first reverse integration curve. The intersection of the second reverse integration curve and the first forward integration curve ends, thereby obtaining the integration path. 2.根据权利要求1所述的一种针对机器人操作空间的时间最优轨迹规划方法，其特征在于，所述操作空间路径包括平移曲线和姿态曲线。2 . The time optimal trajectory planning method for robot operation space according to claim 1 , wherein the operation space path includes a translation curve and an attitude curve. 3 . 3.根据权利要求2所述的一种针对机器人操作空间的时间最优轨迹规划方法，所述机器人在操作空间中的运动用笛卡尔速度和笛卡尔加速度来表达，所述各轴关节位移对时间的各阶导数包括各轴关节速度和各轴关节加速度，所述各轴关节速度和各轴关节加速度分别对应设定的限制条件，所述步骤S1中，通过以下步骤计算约束曲线MVC：3. a kind of time optimal trajectory planning method for robot operation space according to claim 2, the movement of described robot in operation space is expressed with Cartesian velocity and Cartesian acceleration, and described each axis joint displacement is equal to Each order derivative of time includes the joint velocity of each axis and the joint acceleration of each axis, and the joint velocity of each axis and the joint acceleration of each axis correspond to the set restriction conditions respectively. In the step S1, the constraint curve MVC is calculated by the following steps: S11.根据机器人的几何结构，获得各轴关节速度与笛卡尔速度的映射关系、各轴关节加速度与笛卡尔加速度的映射关系，以及各轴关节加加速度与笛卡尔加加速度的映射关系；S11. According to the geometric structure of the robot, obtain the mapping relationship between the joint speed of each axis and the Cartesian speed, the mapping relationship between the joint acceleration of each axis and the Cartesian acceleration, and the mapping relationship between the joint jerk of each axis and the Cartesian jerk; S12.根据各轴关节速度与笛卡尔速度的映射关系，以及笛卡尔速度与弧长参数的一阶导数的映射关系，计算得到用于约束弧长参数的一阶导数的第一限制条件；S12. According to the mapping relationship between the joint speed of each axis and the Cartesian speed, and the mapping relationship between the Cartesian speed and the first-order derivative of the arc length parameter, calculate the first restriction for constraining the first-order derivative of the arc length parameter; S13.根据各轴关节加速度与笛卡尔加速度的映射关系，以及笛卡尔加速度与弧长参数的二阶导数的映射关系，计算得到用于约束弧长参数的二阶导数的第二限制条件；S13. According to the mapping relationship between the joint acceleration of each axis and the Cartesian acceleration, and the mapping relationship between the Cartesian acceleration and the second-order derivative of the arc-length parameter, calculate and obtain the second restriction condition for constraining the second-order derivative of the arc-length parameter; S14.根据各轴关节加加速度与笛卡尔加加速度的映射关系，以及笛卡尔加加速度与弧长参数的三阶导数的映射关系，计算得到用于约束弧长参数的三阶导数的第三限制条件；S14. According to the mapping relationship between the joint jerk of each axis and the Cartesian jerk, and the mapping relationship between the Cartesian jerk and the third-order derivative of the arc length parameter, calculate and obtain the third limit for constraining the third-order derivative of the arc length parameter condition; S15.根据第一限制条件、第二限制条件和第三限制条件，计算得到约束曲线MVC。S15. Calculate the constraint curve MVC according to the first restriction condition, the second restriction condition and the third restriction condition. 4.根据权利要求3所述的一种针对机器人操作空间的时间最优轨迹规划方法，所述各轴关节速度、各轴关节加速度和各轴关节加加速度对应设定的限制条件为其特征在于：4. A kind of time optimal trajectory planning method for robot operation space according to claim 3, the limit conditions set corresponding to the joint speed of each axis, the joint acceleration of each axis and the jerk of each axis are: It is characterized by: 所述各轴关节速度与笛卡尔速度的映射关系为式中，v为笛卡尔速度，J为与机器人的几何结构有关的雅克比矩阵，为各轴关节速度，为各轴关节加速度，为各轴关节加加速度，为的最小值，为的最大值，为的最小值，为的最大值，为的最小值，为的最大值，k为轴关节的编号，dof为轴关节的最大编号；The mapping relationship between the joint speed of each axis and the Cartesian speed is: where v is the Cartesian velocity, J is the Jacobian matrix related to the geometry of the robot, is the joint speed of each axis, is the joint acceleration of each axis, is the acceleration of each axis joint, for the minimum value of , for the maximum value of , for the minimum value of , for the maximum value of , for the minimum value of , for The maximum value of , k is the number of the axis joint, dof is the maximum number of the axis joint; 所述笛卡尔速度与弧长参数的一阶导数的映射关系为式中，v为笛卡尔速度，f(s)为操作空间路径，为弧长参数的一阶导数；The mapping relationship between the Cartesian velocity and the first derivative of the arc length parameter is: where v is the Cartesian velocity, f(s) is the operating space path, is the first derivative of the arc length parameter; 所述第一限制条件为式中，ak(s)＝J-1f′(s)。The first constraint is In the formula, a k (s)=J -1 f'(s). 5.根据权利要求4所述的一种针对机器人操作空间的时间最优轨迹规划方法，其特征在于：5. a kind of time optimal trajectory planning method for robot operation space according to claim 4, is characterized in that: 所述各轴关节加速度与笛卡尔加速度的映射关系为式中，a为笛卡尔加速度，J为与机器人的几何结构有关的雅克比矩阵，为各轴关节速度，为各轴关节加速度；The mapping relationship between the joint acceleration of each axis and the Cartesian acceleration is: where a is the Cartesian acceleration, J is the Jacobian matrix related to the geometry of the robot, is the joint speed of each axis, is the joint acceleration of each axis; 所述笛卡尔加速度与弧长参数的二阶导数的映射关系为式中，f(s)为操作空间路径；The mapping relationship between the Cartesian acceleration and the second derivative of the arc length parameter is: In the formula, f(s) is the operation space path; 所述第二限制条件为式中，bk(s)＝J-1[f″(s)-J′ak(s)]；The second constraint is In the formula, b k (s)=J -1 [f″(s) -J′ak (s)]; 所述各轴关节加加速度与笛卡尔加加速度的映射关系为式中，j为笛卡尔加加速度，和分别为雅克比矩阵对时间的一阶导数和二阶导数，为各轴关节加加速度；The mapping relationship between the joint jerk of each axis and the Cartesian jerk is: where j is the Cartesian jerk, and are the first and second derivatives of the Jacobian matrix with respect to time, respectively, is the acceleration of each axis joint; 所述笛卡尔加加速度与弧长参数的三阶导数的映射关系为式中，j为笛卡尔加加速度，f(s)为操作空间路径，为弧长参数的一阶导数，为弧长参数的二阶导数，为弧长参数的三阶导数；The mapping relationship between the Cartesian jerk and the third derivative of the arc length parameter is: In the formula, j is the Cartesian acceleration, f(s) is the operation space path, is the first derivative of the arc length parameter, is the second derivative of the arc length parameter, is the third derivative of the arc length parameter; 所述第三限制条件为式中，ck(s)＝J-1[f″′(s)-J″ak(s)-2J′bk(s)]。The third constraint is In the formula, c k (s)=J −1 [f″′(s)-J″ ak (s)-2J′b k (s)]. 6.根据权利要求1-5任一项所述的一种针对机器人操作空间的时间最优轨迹规划方法，其特征在于，通过以下公式进行第一前向积分和/或第二前向积分：6. a kind of time optimal trajectory planning method for robot operation space according to any one of claim 1-5, it is characterized in that, carry out the first forward integration and/or the second forward integration by the following formula: 式中，si为当前时刻弧长参数，si-1为上一时刻弧长参数，为s的一阶导数，为s的二阶导数，为s的三阶导数，Ts为采样周期。In the formula, s i is the arc length parameter at the current moment, s i-1 is the arc length parameter at the previous moment, is the first derivative of s, is the second derivative of s, is the third derivative of s, and T s is the sampling period. 7.根据权利要求6所述的一种针对机器人操作空间的时间最优轨迹规划方法，其特征在于，通过以下公式进行第一反向积分和/或第二反向积分：7. A kind of time optimal trajectory planning method for robot operation space according to claim 6, is characterized in that, carry out the first inverse integration and/or the second inverse integration by following formula: 式中，si为当前时刻弧长参数，si-1为上一时刻弧长参数，为s的一阶导数，为s的二阶导数，为s的三阶导数，Ts为采样周期。In the formula, s i is the arc length parameter at the current moment, s i-1 is the arc length parameter at the previous moment, is the first derivative of s, is the second derivative of s, is the third derivative of s, and T s is the sampling period. 8.根据权利要求1-5任一项所述的一种针对机器人操作空间的时间最优轨迹规划方法，其特征在于，所述切换点满足：8. The time-optimal trajectory planning method for a robot operating space according to any one of claims 1-5, wherein the switching point satisfies: 式中，MVC(·)为约束曲线MVC，swi为切换点，为弧长参数s的一阶导数，为弧长参数s的二阶导数。In the formula, MVC( ) is the constraint curve MVC, swi is the switching point, is the first derivative of the arc length parameter s, is the second derivative of the arc length parameter s. 9.一种针对机器人操作空间的时间最优轨迹规划装置，其特征在于，包括：9. A time optimal trajectory planning device for robot operation space, characterized in that, comprising: 存储器，用于存储至少一个程序；a memory for storing at least one program; 处理器，用于加载所述至少一个程序以执行权利要求1-8任一项所述一种针对机器人操作空间的时间最优轨迹规划方法。The processor is configured to load the at least one program to execute the time-optimal trajectory planning method for the robot operation space according to any one of claims 1-8.
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