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 PDFInfo
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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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- 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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Abstract
The invention discloses a time optimal trajectory planning method and device for a robot operation space. The method comprises the steps of calculating a constraint curve MVC according to an operation space path and each order derivative of displacement of each axis joint of the robot to time, and performing path integration in an 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 limitation of each derivative of each axial joint displacement of the robot on time into the limitation of each derivative of arc length parameters, thereby converting multidimensional constraint conditions into single-dimensional constraint conditions, enabling the whole track planning process to be simpler and more efficient, enabling each axial joint to be always in a constrained saturated state, improving the running efficiency of the robot, and after introducing the high-order derivatives of each axial joint displacement such as acceleration, jerk and the like, the obtained track planning result can effectively reduce the terminal jitter of the robot and improve the stability of the robot.
Description
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. a kind of time optimal trajectory planning method for robot manipulation space, which comprises the following steps:
S1. according to given operating space related with arc length parameters path, each axis joint displacement versus time of robot of setting
All-order derivative, calculate constraint curve MVC, the constraint curve MVC be robot allow to reach maximum speed under the path；
S2. according to the operating space path and constraint curve MVC, path integral, resulting integral are carried out in operating space
Path is time optimal trajectory planning result；
The step S2 is specifically included:
S21. the first forward direction integral, the track of the first forward direction integral are carried out since the starting point in the operating space path
For the first forward direction integral curve, the first forward direction integral is in the intersection point for reaching the first forward direction integral curve and constraint curve MVC
When terminate；Corresponding arc length parameters are denoted as the first arc length parameters at the end of the first forward direction integral；
S22. from the operating space path arc length parameters be equal to the first arc length parameters corresponding to point begin look for switching point；
S23. the first reverse integral is carried out since the switching point, the track of first reverse integral is the first reverse integral
Curve, first reverse integral terminate when reaching the intersection point of the first reverse integral curve and the first forward direction integral curve, so
The second forward direction integral is carried out since the switching point afterwards；
S24. repetitive cycling executes step S21-S23, until second forward direction integrates the terminating point in arrival operating space path
Until；
S25. the second reverse integral is carried out along reverse integral curve since the terminating point in operating space path, described second is anti-
It is the second reverse integral curve to the track of integral, second reverse integral is before reaching the second reverse integral curve and first
To integral curve intersection point when terminate, to obtain path of integration.
2. a kind of time optimal trajectory planning method for robot manipulation space according to claim 1, feature
It is, the operating space path includes translation curve and posture curve.
3. a kind of time optimal trajectory planning method for robot manipulation space according to claim 2, the machine
Movement of the device people in operating space is expressed with Descartes's speed and Descartes's acceleration, each axis joint displacement versus time
All-order derivative include each axis joint speed and each axis joint acceleration, each axis joint speed and each axis joint acceleration point
The restrictive condition that Dui Ying do not set in the step S1, passes through following steps and calculates constraint curve MVC:
S11. according to the geometry of robot, mapping relations, each axis joint of each axis joint speed and Descartes's speed are obtained
The mapping relations and each axis joint acceleration of acceleration and Descartes's acceleration and the mapping of Descartes's acceleration are closed
System；
S12. according to each axis joint speed and the mapping relations of Descartes's speed and the single order of 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 derivative；
S13. according to the mapping relations and Descartes's acceleration and arc length parameters of each axis joint acceleration and Descartes's acceleration
Second dervative mapping relations, the second restrictive condition of the second dervative for constraining arc length parameters is calculated；
S14. according to the mapping relations and Descartes's acceleration and arc of each axis joint acceleration and Descartes's acceleration
The third restrictive condition of three order derivatives for constraining arc length parameters is calculated in the mapping relations of three order derivatives of long parameter；
S15. according to the first restrictive condition, the second restrictive condition and third restrictive condition, constraint curve MVC is calculated.
4. a kind of time optimal trajectory planning method for robot manipulation space according to claim 3, described each
Axis joint speed, the corresponding restrictive condition set of each axis joint acceleration and each axis joint acceleration asIt is characterized by:
The mapping relations of each axis joint speed and Descartes's speed areIn formula, v is Descartes's speed, and J is and machine
The related Jacobian matrix of the geometry of device people,For each axis joint speed,For each axis joint acceleration,For each axis joint
Acceleration,ForMinimum value,ForMaximum value,ForMinimum value,ForMaximum value,ForMinimum value,ForMaximum value, k is the number of axis joint, and dof is the maximum number of axis joint；
The mapping relations of the first derivative of Descartes's speed and arc length parameters areIn formula, v is Descartes's speed
Degree, f (s) are operating space path,For the first derivative of arc length parameters；
First restrictive condition isIn formula, ak(s)=J-1f′(s)。
5. a kind of time optimal trajectory planning method for robot manipulation space according to claim 4, feature
It is:
The mapping relations of each axis joint acceleration and Descartes's acceleration areIn formula, a is Descartes's acceleration
Degree, J are Jacobian matrix related with the geometry of robot,For each axis joint speed,For each axis joint acceleration；
The mapping relations of the second dervative of Descartes's acceleration and arc length parameters areIn formula, f (s)
For operating space path；
Second restrictive condition isIn formula, bk(s)=J-1
[f″(s)-J′ak(s)]；
The mapping relations of each axis joint acceleration and Descartes's acceleration areIn formula, j is flute
Karr acceleration,WithRespectively Jacobian matrix to the first derivative and second dervative of time,Add for each axis joint
Speed；
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)]。
6. a kind of time optimal trajectory planning side for robot manipulation space according to claim 1-5
Method, which is characterized in that 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 the second order of s
Derivative,For three order derivatives of s, TsFor the sampling period.
7. a kind of time optimal trajectory planning method for robot manipulation space according to claim 6, feature
It is, the first reverse integral and/or the second reverse integral is 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 the second order of s
Derivative,For three order derivatives of s, TsFor the sampling period.
8. a kind of time optimal trajectory planning side for robot manipulation space according to claim 1-5
Method, which is characterized in that 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 parameters s
Second dervative.
9. a kind of time optimal trajectory planning device for robot manipulation space characterized by comprising
Memory, for storing at least one program；
Processor requires any one of 1-8 described a kind of for robot for loading at least one described program with perform claim
The time optimal trajectory planning method of operating space.
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