CN116352725B - Three-time three-section type mechanical arm track planning method, system, equipment and medium - Google Patents
Three-time three-section type mechanical arm track planning method, system, equipment and medium Download PDFInfo
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- CN116352725B CN116352725B CN202310579238.3A CN202310579238A CN116352725B CN 116352725 B CN116352725 B CN 116352725B CN 202310579238 A CN202310579238 A CN 202310579238A CN 116352725 B CN116352725 B CN 116352725B
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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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- B—PERFORMING OPERATIONS; TRANSPORTING
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- B25J9/00—Programme-controlled manipulators
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Abstract
The application discloses a three-time three-section type mechanical arm track planning method, a system, equipment and a medium, which relate to the technical field of mechanical arm track planning and comprise the following steps: according to given initial position, initial posture, final position, final posture, maximum speed and maximum acceleration, respectively determining position movement time and posture movement time from initial to final according to acceleration, uniform speed and deceleration stages; judging the position movement time and the gesture movement time, taking the longer time of the two as the given time, keeping the path track parameter unchanged for the movement with the longer time, re-planning the movement with the shorter time according to the given time, and obtaining the planned path of the mechanical arm according to the finally determined actual track parameters under the position movement and the gesture movement. The impact is minimum in the movement process, the time is guaranteed to be optimal, meanwhile, the position change and the posture change are considered, and the acceleration is guaranteed not to be suddenly changed in the operation process.
Description
Technical Field
The application relates to the technical field of mechanical arm track planning, in particular to a three-time three-section mechanical arm track planning method, system, equipment and medium.
Background
When the track planning is carried out on the mechanical arm, a secondary T-shaped track algorithm and a secondary S-shaped curve track algorithm are mostly adopted. The T-type trajectory algorithm can realize optimal running time of the mechanical arm, but there is abrupt change of acceleration in the running process, so that the joint has impact, because if the acceleration is not zero when the maximum speed is reached, the acceleration is required to be instantaneously reduced to zero, the abrupt change of acceleration can exist, the abrupt change of jerk can also cause the impact of the joint, and the T-type trajectory has the problem. The S-shaped curve track algorithm can ensure stable change of acceleration speed in operation, and effectively avoid impact, but the track running time of the mode is obviously prolonged, and the time cannot be optimized.
Disclosure of Invention
In order to solve the problems, the application provides a three-time three-section type mechanical arm track planning method, a system, equipment and a medium, which can ensure that the time is optimal while the impact is minimum in the motion process, and simultaneously ensure that the acceleration is not suddenly changed in the operation process by considering the position change and the posture change.
In order to achieve the above purpose, the present application adopts the following technical scheme:
in a first aspect, the present application provides a method for planning a trajectory of a three-time three-segment mechanical arm, including:
according to a given starting position, a starting gesture, a termination position, a termination gesture, a maximum speed and a maximum acceleration, respectively determining the position movement time and the gesture movement time from a starting point to a terminal point according to the stages of acceleration, uniform speed and deceleration; wherein, the liquid crystal display device comprises a liquid crystal display device,
determining the maximum jerk according to the given maximum speed and the maximum acceleration, and inverting the maximum speed, the maximum acceleration and the maximum jerk to obtain respective corresponding minimum values, thereby determining the movement time and the total movement time of each stage;
judging whether the uniform speed time is greater than zero, if so, keeping the motion time and the total motion time of each stage unchanged, taking a given track parameter as a path track parameter, and if not, determining the motion time, the total motion time and the path track parameter of each stage in a mode of continuous acceleration or minimum motion time;
judging the position movement time and the gesture movement time, taking the longer time of the two as the given time, keeping the path track parameter unchanged for the movement with the longer time, re-planning the movement with the shorter time according to the given time, and obtaining the planned path of the mechanical arm according to the finally determined actual track parameters under the position movement and the gesture movement.
Alternatively, in determining the position movement time or the posture movement time:
obtaining maximum jerk according to a given maximum acceleration and maximum speed;
determining acceleration time according to the ratio of the maximum acceleration to the maximum jerk;
determining a deceleration time according to the ratio of the minimum acceleration to the minimum jerk;
according to maximum speedv max Acceleration timeTime of deceleration->Determining a constant speed time by a position or posture change parameter>The method comprises the steps of carrying out a first treatment on the surface of the I.e. < ->；
Wherein N is the total length of the path or the total angle of the gesture change.
In an alternative embodiment, in determining the position movement time or the gesture movement time, the acceleration is continuously as follows:
determining the maximum acceleration of the path in the path track parameters according to the symmetry and the maximum jerk of the path;
determining acceleration time and deceleration time according to the ratio of the maximum acceleration to the maximum jerk of the path, wherein the acceleration time and the deceleration time are equal, and the uniform speed time is zero;
according to maximum jerkAnd acceleration time->Determining a path maximum speed in path trajectory parametersI.e. +.>。
In an alternative embodiment, in determining the position movement time or the gesture movement time, the minimum movement time is as follows:
the acceleration time and the deceleration time are obtained by solving an equation, the acceleration time is equal to the deceleration time, the uniform speed time is zero, and the equation is:wherein N is the total length of the path or the total angle of the gesture change;
will give a maximum accelerationPath maximum acceleration as path trajectory parameter>Obtaining the maximum speed of the path in the path track parameters according to the maximum acceleration, the acceleration time and the maximum jerk of the path>I.e.。
As an alternative embodiment, the process of rescheduling a shorter motion at a given time includes:
according to a given time T, a given maximum speedDetermining acceleration time and uniform speed time according to the position or posture change parameters;
wherein the acceleration timeThe method comprises the following steps: />；
Constant speed timeThe method comprises the following steps: />；
Wherein N is the total length of the path or the total angle of the gesture change;
subtracting the acceleration time and the uniform speed time from the given time to obtain the deceleration time;
determining an actual maximum jerk according to the given maximum speed and the acceleration time, obtaining the actual maximum acceleration in the actual track parameter according to the product of the actual maximum jerk and the acceleration time, and taking the given maximum speed as the actual maximum speed;
judging whether the uniform speed time is greater than zero, if so, the motion time and the actual track parameters of each stage are unchanged, and if not, the motion time and the actual track parameters of each stage are determined in an acceleration continuous mode.
As an alternative embodiment, in the process of rescheduling the motion with shorter time according to the given time, the acceleration is continuously as follows:
setting the uniform speed time to be zero, wherein the acceleration time and the deceleration time are half of the given time;
determining the actual maximum jerk, i.e. based on a given time and position or attitude change parameterWherein N is the total length of the path or the total angle of the gesture change;
obtaining the actual maximum acceleration according to the product of the actual maximum jerk and the acceleration time;
the actual maximum speed is obtained from half the product of the actual maximum acceleration and the acceleration time.
As an alternative implementation manner, the path length and the attitude change angle of each moment in each stage are respectively obtained according to the actual track parameters;
obtaining a linear interpolation parameter according to the ratio of the length of each section of path to the total length of the path;
if the gesture changes, obtaining a gesture interpolation parameter according to the gesture change angle and the ratio of the quaternion included angles obtained by the initial gesture and the ending gesture; if the gesture does not change, the gesture interpolation parameter is zero;
and respectively performing position interpolation and posture interpolation according to the linear interpolation parameters and the posture interpolation parameters to obtain a planning path of the mechanical arm.
As an alternative embodiment, the location interpolation is: determining the change amount of the xyz direction according to the starting position and the ending position; and multiplying the variation of each direction by the linear interpolation parameter and adding the coordinate value of the corresponding direction to obtain the coordinate value of the direction after position interpolation.
As an alternative embodiment, the pose interpolation is: and carrying out interpolation operation on the gesture by adopting a quaternion sphere, and taking the opposite number from the cosine of the quaternion included angle if the quaternion included angle is smaller than zero.
In a second aspect, the present application provides a three-time three-segment robotic arm trajectory planning system, comprising:
a time determination module configured to determine a position movement time and an attitude movement time from start to end according to the given start position, start attitude, end position, end attitude, maximum speed, and maximum acceleration, respectively, at the stages of acceleration, uniform speed, and deceleration; wherein, the liquid crystal display device comprises a liquid crystal display device,
determining the maximum jerk according to the given maximum speed and the maximum acceleration, and inverting the maximum speed, the maximum acceleration and the maximum jerk to obtain respective corresponding minimum values, thereby determining the movement time and the total movement time of each stage;
judging whether the uniform speed time is greater than zero, if so, keeping the motion time and the total motion time of each stage unchanged, taking a given track parameter as a path track parameter, and if not, determining the motion time, the total motion time and the path track parameter of each stage in a mode of continuous acceleration or minimum motion time;
the track parameter determining module is configured to judge the size of the position movement time and the gesture movement time, the longer time in the two is taken as the given time, the track parameter of the path is kept unchanged for the movement with the longer time, the movement with the shorter time is re-planned according to the given time, and the planned path of the mechanical arm is obtained according to the finally determined actual track parameters of the position movement and the gesture movement.
In a third aspect, the application provides an electronic device comprising a memory and a processor and computer instructions stored on the memory and running on the processor, which when executed by the processor, perform the method of the first aspect.
In a fourth aspect, the present application provides a computer readable storage medium storing computer instructions which, when executed by a processor, perform the method of the first aspect.
Compared with the prior art, the application has the beneficial effects that:
the application provides a three-time three-section type mechanical arm track planning method, a system, equipment and a medium, acceleration is carried out at maximum until the acceleration is zero, the maximum speed is reached, then the motion is carried out at constant speed at the maximum speed, the maximum jerk at the moment is determined, the continuity of the acceleration and jerk is ensured, because jerk is a parameter for measuring impact, jerk mutation can cause impact of joints, and also because the sudden change of the acceleration exists when the acceleration is not zero when the maximum speed is reached, the sudden change of the acceleration exists when the acceleration is required to be instantaneously reduced to zero.
The application provides a three-time three-section type mechanical arm track planning method, a system, equipment and a medium, and simultaneously considers position change and attitude change to realize track planning with optimal time.
The application provides a three-time three-section type mechanical arm track planning method, a system, equipment and a medium, which avoid abrupt acceleration changes in the running process, consider time optimization, set positions and postures of a starting point and a finishing point, limit maximum speed and acceleration, automatically give a track meeting requirements and reduce impact in a limited way.
Additional aspects of the application will be set forth in part in the description which follows and, in part, will be obvious from the description, or may be learned by practice of the application.
Drawings
The accompanying drawings, which are included to provide a further understanding of the application and are incorporated in and constitute a part of this specification, illustrate embodiments of the application and together with the description serve to explain the application.
Fig. 1 is a flowchart of a three-time three-segment type mechanical arm track planning method provided in embodiment 1 of the present application;
FIG. 2 is a flow chart of determining movement time according to embodiment 1 of the present application;
fig. 3 is a plan flowchart of a given time provided in embodiment 1 of the present application.
Detailed Description
The application is further described below with reference to the drawings and examples.
It should be noted that the following detailed description is exemplary and is intended to provide further explanation of the application. Unless defined otherwise, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this application belongs.
It is noted that the terminology used herein is for the purpose of describing particular embodiments only and is not intended to be limiting of exemplary embodiments according to the present application. As used herein, unless the context clearly indicates otherwise, the singular forms also are intended to include the plural forms, and furthermore, it is to be understood that the terms "comprises" and "comprising" and any variations thereof are intended to cover non-exclusive inclusions, such as, for example, processes, methods, systems, products or devices that comprise a series of steps or units, are not necessarily limited to those steps or units that are expressly listed, but may include other steps or units that are not expressly listed or inherent to such processes, methods, products or devices.
Embodiments of the application and features of the embodiments may be combined with each other without conflict.
Example 1
The embodiment provides a three-time three-section type mechanical arm track planning method, which is used for the following steps of:
according to given initial position, initial posture, final position, final posture, maximum speed and maximum acceleration, respectively determining position movement time and posture movement time from initial to final according to acceleration, uniform speed and deceleration stages; wherein, the liquid crystal display device comprises a liquid crystal display device,
determining the maximum jerk according to the given maximum speed and the maximum acceleration, and inverting the maximum speed, the maximum acceleration and the maximum jerk to obtain respective corresponding minimum values, thereby determining the movement time and the total movement time of each stage;
judging whether the uniform speed time is greater than zero, if so, keeping the motion time and the total motion time of each stage unchanged, taking a given track parameter as a path track parameter, and if not, determining the motion time, the total motion time and the path track parameter of each stage in a mode of continuous acceleration or minimum motion time;
judging the position movement time and the gesture movement time, taking the longer time of the two as the given time, keeping the path track parameter unchanged for the movement with the longer time, re-planning the movement with the shorter time according to the given time, and obtaining the planned path of the mechanical arm according to the finally determined actual track parameters under the position movement and the gesture movement.
The method of this embodiment is described in detail below with reference to fig. 1.
In the present embodiment, a given starting position S is first obtained 0 Termination position D 0 Initial attitudeQ s Terminating gestureQ d Maximum speed of position movementv max Maximum acceleration of position movementa max 、Maximum speed of gesture movementvq max Maximum acceleration of gesture movementdvq max Interpolation periodtS is used as the starting point 0 Expressed as s for end point 1 And (3) representing.
Determining the total length of the path on the straight line distance according to the starting position and the ending position:
；
where S () is the value of the start position vector in three-dimensional space, and D () is the value of the end position vector in three-dimensional space; if s= [1,2,3], d= [ -3, -2, -1], then S (1) = 1, S [2] = 2, S (3) = 3, D (1) = -3, D (2) = -2, D (3) = -1.
For the acquired initial gestureQ s Terminating gesturesQ d Initializing; the method specifically comprises the following steps:
(1) Given the initial attitude of the mechanical armQ s Terminating gesturesQ d The ZYX euler angle of (c) is converted into a quaternion and unitized:
q 1 =Q s ；q 2 =Q d ；
wherein, the liquid crystal display device comprises a liquid crystal display device,q 1 is the quaternion of the unitized starting pose,q 2 a quaternion of the unitized ending gesture.
(2) Obtaining a quaternion included angle cosine according to the quaternion inner product, obtaining a quaternion included angle sine according to the quaternion included angle cosine, and obtaining a quaternion included angle omega according to the quaternion included angle cosine and the quaternion included angle sine, namely from q 1 Change to q 2 The total angle of the gesture change needing to rotate is omega, and the method specifically comprises the following steps:
cos(Ω)=q 1.w *q 2.w +q 1.i *q 2.i +q 1.j *q 2.j +q 1.k *q 2.k ；
；
；
wherein, the liquid crystal display device comprises a liquid crystal display device,atanis an arctangent function; w, i, j, k are all representation parameters of quaternions.
In the embodiment, the whole path is divided into an acceleration stage, a uniform velocity stage and a deceleration stage, and the position movement time and the gesture movement time from the beginning to the end are respectively determined; the following gives a specific procedure for calculating the position movement time, as shown in fig. 2, including:
(1) Accelerating by using the maximum position movement acceleration until the position movement acceleration is 0, achieving the maximum position movement speed, then uniformly moving at the maximum position movement speed, and ensuring the continuity of the position movement acceleration, wherein the continuity refers to no abrupt change in the movement process, and if the acceleration is not 0 when the maximum position movement acceleration is achieved, the abrupt change exists when the acceleration is required to be instantaneously reduced to 0; at this time, calculating the maximum jerk of the position movement:
；
wherein, the liquid crystal display device comprises a liquid crystal display device,the maximum jerk of the position movement is represented as a rate of change of the position movement acceleration, which is a constant value to ensure that the position movement acceleration is 0 when the maximum speed of the position movement is reached.
(2) The maximum speed of the position movement, the maximum acceleration of the position movement and the maximum jerk of the position movement are inverted to obtain the minimum speed of the position movementMinimum acceleration of position movement>And minimum jerk of position movement +.>：
。
(3) Determining position motion acceleration time based on position motion maximum acceleration and position motion maximum jerk：
；
Determining a position motion deceleration time based on the position motion minimum acceleration and the position motion minimum jerk：
；
Determining a uniform velocity time of the position motion according to the maximum velocity of the position motion, the acceleration time of the position motion, the deceleration time of the position motion, the starting position and the ending position：
；
If here the gesture motion uniform time is calculatedIf so, the method comprises the following steps:
。
(4) Judging whether the uniform time is greater than zero;
(4-1) ifIndicating that a constant speed section exists, the maximum speed can be reached, planning can be carried out according to the maximum acceleration of the position movement and the maximum jerk of the position movement, the acceleration time of the position movement, the constant speed time of the position movement and the deceleration time of the position movement calculated in the step (3) are unchanged, and the total time of the position movement is->；
And taking the given track parameter as the track parameter of the path, namelyThe maximum speed reached in the whole routeEqual to the speed of the constant speed section, i.e. the maximum speed of the movement of a given position +.>Maximum acceleration achieved in the whole pathEqual to the maximum acceleration of the movement of a given position +.>Maximum deceleration achieved in the entire route +.>The inverse value of the maximum acceleration of the given position movement is equal to the other parameters.
(4-2) ifThe method includes the steps that if a path is short and a constant speed section does not exist, the motion time, the total motion time and path track parameters of each stage are redetermined in a mode of continuous acceleration or minimum motion time;
(4-2-1) in a continuous acceleration manner:
(1) calculating the maximum acceleration of the position motion path in the path track parameters according to the path symmetry, which is the maximum acceleration which can be achieved in the whole path in principle, and adopting different symbols for distinguishing from other stages; the maximum acceleration of the position motion path is:
；
(2) the position movement acceleration time, the position movement deceleration time and the position movement uniform speed time are respectively as follows:
；
(3) the maximum speed of the position motion path in the path track parameters is as follows:
。
(4-2-1) ensuring time optimization in a mode of minimum movement time:
(1) solving the following equation to obtain the position movement acceleration time, the position movement deceleration time and the position movement uniform time:
(2) maximum acceleration of position motion path in path trajectory parametersEqual to the given maximum acceleration of the position movement, the minimum acceleration of the position movement path in the path track parameter +.>Inverse value of maximum acceleration equal to given position movement:
；
(3) the maximum speed of the position motion path in the path track parameters is as follows:
。
through the process, the acceleration time, the deceleration time, the uniform speed time, the total movement time and the path track parameters of the position movement can be obtained, wherein the path track parameters comprise the maximum speed of the position movement path, the maximum acceleration of the position movement path, the starting position, the ending position and the like.
Similarly, the acceleration time, the deceleration time, the uniform speed time and the total movement time of the gesture movementAnd the calculation of path track parameters is consistent with the position movement, and the difference is that the maximum speed of the gesture movement and the maximum acceleration adopt the maximum speed of the gesture movementvq max And maximum acceleration of gesture motiondvq max Other processes are consistent and will not be described in detail herein.
In the embodiment, the position movement time and the gesture movement time are judged, the longer time in the two is taken as the given time, the path track parameter is kept unchanged for the longer time, and the shorter time movement is re-planned according to the given time; taking the example that the gesture movement time is longer than the position movement time, the gesture movement time is adopted as the total movement time, the gesture movement time is used as the given time of the position movement, and the three-time three-section track planning of the given time is carried out.
As shown in fig. 3, the method specifically includes:
(1) the given maximum speed, maximum acceleration and maximum jerk of the position movement are inverted to obtain minimum speed, minimum acceleration and minimum jerk of the position movement:
；
(2) calculating acceleration time, deceleration time and uniform speed time of each stage according to the given time:
；
where T is the longer of the two, here the position movement time.
(3) Determining an actual maximum jerk and an actual minimum jerk according to a given maximum speed and acceleration time, and redefining an actual maximum jerk and an actual minimum jerk of the position movement according to the maximum jerk and the acceleration time, wherein the actual maximum jerk and the actual minimum jerk are also in principle the maximum acceleration which can be achieved in the whole route, and different signs are adopted for distinguishing the maximum jerk and the acceleration time from other phases; the method comprises the following steps:
；
(4) judging whether the uniform time is greater than zero;
if it isThe final determined actual maximum speed of the position movement is the given maximum speed of the position movement, and the total time is respectively:
；
if it isAnd (3) indicating that the maximum speed cannot be reached, and re-planning by adopting an acceleration continuous mode, wherein the finally determined track parameters are as follows:
acceleration time, deceleration time and uniform velocity time are respectively:；
the actual maximum jerk and the actual minimum jerk are:；
the actual maximum acceleration and the actual minimum acceleration are:；
the actual maximum speed is:。
similarly, if the position movement time is greater than the gesture movement time, planning the gesture movement by adopting a given time, and the calculation process is consistent, which is not described herein.
In this embodiment, the process of obtaining the planned path of the mechanical arm according to the finally determined trajectory parameters under the position motion and the gesture motion includes:
(1) According to a given interpolation periodtAnd (3) carrying out upward rounding on the planning steps:；
(2) Obtaining the path length of each moment in each motion stage according to the acceleration time, the deceleration time, the actual maximum speed and the actual maximum acceleration in the finally determined actual track parameters:
t>0 and t<T a When (1):；
t>T a and t is<T a +T v When (1):；
t>T a +T v and t is<And T is as follows:
；
(3) Normalizing the path length of each section to obtain a linear interpolation parameter:；
(4) Obtaining the gesture change angle of each stage of motion according to the acceleration and deceleration time, speed and acceleration of gesture changeThe calculation process and the step (2) are the same principle and are not repeated;
if the gesture changes, the gesture change angle is not zero, and the obtained gesture change angle of each time interval under unit length, namely the gesture interpolation parameter is:
；
if the posture is not changed。
(5) Performing position interpolation operation on the position motion by adopting linear interpolation parameters;
(5-1) calculating the variation in the x, y and z directions:；
the (5-2) position interpolation is:；
(6) Performing gesture interpolation operation on gesture movement by adopting a quaternion sphere; if the quaternion included angle is smaller than zero, taking the opposite number to the cosine of the quaternion included angle;
(6-1) if the cosine of the quaternion included angle is greater than the set threshold (e.g., 0.9995), linear interpolation is adopted:；
(6-2) otherwise, using quaternion spherical interpolation:；
(6-3) interpolating quaternions:。
so far, the position and the gesture corresponding to each moment point are obtained, and the planning is finished.
Example 2
The embodiment provides a three-time three-section type mechanical arm track planning system, which comprises:
a time determination module configured to determine a position movement time and an attitude movement time from start to end according to the given start position, start attitude, end position, end attitude, maximum speed, and maximum acceleration, respectively, at the stages of acceleration, uniform speed, and deceleration; wherein, the liquid crystal display device comprises a liquid crystal display device,
determining the maximum jerk according to the given maximum speed and the maximum acceleration, and inverting the maximum speed, the maximum acceleration and the maximum jerk to obtain respective corresponding minimum values, thereby determining the movement time and the total movement time of each stage;
judging whether the uniform speed time is greater than zero, if so, keeping the motion time and the total motion time of each stage unchanged, taking a given track parameter as a path track parameter, and if not, determining the motion time, the total motion time and the path track parameter of each stage in a mode of continuous acceleration or minimum motion time;
the track parameter determining module is configured to judge the size of the position movement time and the gesture movement time, the longer time in the two is taken as the given time, the track parameter of the path is kept unchanged for the movement with the longer time, the movement with the shorter time is re-planned according to the given time, and the planned path of the mechanical arm is obtained according to the finally determined actual track parameters of the position movement and the gesture movement.
It should be noted that the above modules correspond to the steps described in embodiment 1, and the above modules are the same as examples and application scenarios implemented by the corresponding steps, but are not limited to those disclosed in embodiment 1. It should be noted that the modules described above may be implemented as part of a system in a computer system, such as a set of computer-executable instructions.
In further embodiments, there is also provided:
an electronic device comprising a memory and a processor and computer instructions stored on the memory and running on the processor, which when executed by the processor, perform the method described in embodiment 1. For brevity, the description is omitted here.
It should be understood that in this embodiment, the processor may be a central processing unit CPU, and the processor may also be other general purpose processors, digital signal processors DSP, application specific integrated circuits ASIC, off-the-shelf programmable gate array FPGA or other programmable logic device, discrete gate or transistor logic devices, discrete hardware components, or the like. A general purpose processor may be a microprocessor or the processor may be any conventional processor or the like.
The memory may include read only memory and random access memory and provide instructions and data to the processor, and a portion of the memory may also include non-volatile random access memory. For example, the memory may also store information of the device type.
A computer readable storage medium storing computer instructions which, when executed by a processor, perform the method described in embodiment 1.
The method in embodiment 1 may be directly embodied as a hardware processor executing or executed with a combination of hardware and software modules in the processor. The software modules may be located in a random access memory, flash memory, read only memory, programmable read only memory, or electrically erasable programmable memory, registers, etc. as well known in the art. The storage medium is located in a memory, and the processor reads the information in the memory and, in combination with its hardware, performs the steps of the above method. To avoid repetition, a detailed description is not provided herein.
Those of ordinary skill in the art will appreciate that the elements of the various examples described in connection with the present embodiments, i.e., the algorithm steps, can be implemented as electronic hardware or combinations of computer software and electronic hardware. Whether such functionality is implemented as hardware or software depends upon the particular application and design constraints imposed on the solution. Skilled artisans may implement the described functionality in varying ways for each particular application, but such implementation decisions should not be interpreted as causing a departure from the scope of the present application.
While the foregoing description of the embodiments of the present application has been presented in conjunction with the drawings, it should be understood that it is not intended to limit the scope of the application, but rather, it is intended to cover all modifications or variations within the scope of the application as defined by the claims of the present application.
Claims (8)
1. The three-time three-section type mechanical arm track planning method is characterized by comprising the following steps of:
according to a given starting position, a starting gesture, a termination position, a termination gesture, a maximum speed and a maximum acceleration, respectively determining the position movement time and the gesture movement time from a starting point to a terminal point according to the stages of acceleration, uniform speed and deceleration; wherein, the liquid crystal display device comprises a liquid crystal display device,
determining the maximum jerk according to the given maximum speed and the maximum acceleration, and inverting the maximum speed, the maximum acceleration and the maximum jerk to obtain respective corresponding minimum values, thereby determining the movement time and the total movement time of each stage;
judging whether the uniform speed time is greater than zero, if so, keeping the motion time and the total motion time of each stage unchanged, taking a given track parameter as a path track parameter, and if not, determining the motion time, the total motion time and the path track parameter of each stage in a mode of continuous acceleration or minimum motion time;
judging the position movement time and the gesture movement time, taking the longer time of the two as the given time, keeping the path track parameter unchanged for the longer time movement, re-planning the shorter time movement according to the given time, and obtaining the planned path of the mechanical arm according to the finally determined actual track parameters under the position movement and the gesture movement;
in determining the position movement time or the posture movement time:
obtaining maximum jerk according to a given maximum acceleration and maximum speed;
determining acceleration time according to the ratio of the maximum acceleration to the maximum jerk;
determining a deceleration time according to the ratio of the minimum acceleration to the minimum jerk;
according to maximum speedv max Acceleration timeTime of deceleration->Determining uniform velocity time by position or posture change parametersThe method comprises the steps of carrying out a first treatment on the surface of the I.e. < ->；
In the process of determining the position movement time or the gesture movement time, the acceleration continuous mode is as follows:
determining the maximum acceleration of the path in the path track parameters according to the symmetry and the maximum jerk of the path;
determining acceleration time and deceleration time according to the ratio of the maximum acceleration to the maximum jerk of the path, wherein the acceleration time and the deceleration time are equal, and the uniform speed time is zero;
according to maximum jerkAnd acceleration time->Determining a maximum speed of the path in the path trajectory parameters +.>I.e.；
In the process of determining the position movement time or the gesture movement time, the mode of the minimum movement time is as follows:
the acceleration time and the deceleration time are obtained by solving an equation, the acceleration time is equal to the deceleration time, the uniform speed time is zero, and the equation is:wherein N is the total length of the path or the total angle of the gesture change;
will give a maximum accelerationPath maximum acceleration as path trajectory parameter>Obtaining the maximum speed of the path in the path track parameters according to the maximum acceleration, the acceleration time and the maximum jerk of the path>I.e.。
2. The method for three-time three-segment robotic arm trajectory planning of claim 1, wherein the re-planning of shorter motions at a given time comprises:
according to a given time T, a given maximum speedDetermining acceleration time and uniform speed time according to the position or posture change parameters;
wherein the acceleration timeThe method comprises the following steps: />；
Constant speed timeThe method comprises the following steps: />；
Subtracting the acceleration time and the uniform speed time from the given time to obtain the deceleration time;
determining an actual maximum jerk according to the given maximum speed and the acceleration time, obtaining the actual maximum acceleration in the actual track parameter according to the product of the actual maximum jerk and the acceleration time, and taking the given maximum speed as the actual maximum speed;
judging whether the uniform speed time is greater than zero, if so, the motion time and the actual track parameters of each stage are unchanged, and if not, the motion time and the actual track parameters of each stage are determined in an acceleration continuous mode.
3. The method for planning a trajectory of a three-time three-segment type mechanical arm according to claim 2, wherein in the process of re-planning a motion with a shorter time according to a given time, the acceleration is continuously as follows:
setting the uniform speed time to be zero, wherein the acceleration time and the deceleration time are half of the given time;
determining the actual maximum jerk, i.e. based on a given time and position or attitude change parameter，
Obtaining the actual maximum acceleration according to the product of the actual maximum jerk and the acceleration time;
the actual maximum speed is obtained from half the product of the actual maximum acceleration and the acceleration time.
4. The method for planning the trajectory of the three-time three-segment type mechanical arm according to claim 1, wherein,
respectively obtaining the path length and the attitude change angle of each moment in each stage according to the actual track parameters;
obtaining a linear interpolation parameter according to the ratio of the length of each section of path to the total length of the path;
if the gesture changes, obtaining a gesture interpolation parameter according to the gesture change angle and the ratio of the quaternion included angles obtained by the initial gesture and the ending gesture; if the gesture does not change, the gesture interpolation parameter is zero;
and respectively performing position interpolation and posture interpolation according to the linear interpolation parameters and the posture interpolation parameters to obtain a planning path of the mechanical arm.
5. The method for three-time three-segment robot arm trajectory planning according to claim 4, wherein,
the position interpolation is as follows: determining the change amount of the xyz direction according to the starting position and the ending position; multiplying the variation of each direction by the linear interpolation parameter and adding the coordinate value of the corresponding direction to obtain the coordinate value after the position interpolation of the direction;
the gesture interpolation is as follows: and carrying out interpolation operation on the gesture by adopting a quaternion sphere, and taking the opposite number from the cosine of the quaternion included angle if the quaternion included angle is smaller than zero.
6. Three syllogic arm track planning system, its characterized in that includes:
a time determination module configured to determine a position movement time and an attitude movement time from start to end according to the given start position, start attitude, end position, end attitude, maximum speed, and maximum acceleration, respectively, at the stages of acceleration, uniform speed, and deceleration; wherein, the liquid crystal display device comprises a liquid crystal display device,
determining the maximum jerk according to the given maximum speed and the maximum acceleration, and inverting the maximum speed, the maximum acceleration and the maximum jerk to obtain respective corresponding minimum values, thereby determining the movement time and the total movement time of each stage;
judging whether the uniform speed time is greater than zero, if so, keeping the motion time and the total motion time of each stage unchanged, taking a given track parameter as a path track parameter, and if not, determining the motion time, the total motion time and the path track parameter of each stage in a mode of continuous acceleration or minimum motion time;
the track parameter determining module is configured to judge the sizes of the position movement time and the gesture movement time, the longer time in the two is taken as the given time, the track parameter of the path is kept unchanged for the longer time, the movement with the shorter time is re-planned according to the given time, and the planned path of the mechanical arm is obtained according to the finally determined actual track parameters of the position movement and the gesture movement;
in determining the position movement time or the posture movement time:
obtaining maximum jerk according to a given maximum acceleration and maximum speed;
determining acceleration time according to the ratio of the maximum acceleration to the maximum jerk;
determining a deceleration time according to the ratio of the minimum acceleration to the minimum jerk;
according to maximum speedv max Acceleration timeTime of deceleration->Determining uniform velocity time by position or posture change parametersThe method comprises the steps of carrying out a first treatment on the surface of the I.e. < ->；
In the process of determining the position movement time or the gesture movement time, the acceleration continuous mode is as follows:
determining the maximum acceleration of the path in the path track parameters according to the symmetry and the maximum jerk of the path;
determining acceleration time and deceleration time according to the ratio of the maximum acceleration to the maximum jerk of the path, wherein the acceleration time and the deceleration time are equal, and the uniform speed time is zero;
according to maximum jerkAnd acceleration time->Determining a maximum speed of the path in the path trajectory parameters +.>I.e.；
In the process of determining the position movement time or the gesture movement time, the mode of the minimum movement time is as follows:
the acceleration time and the deceleration time are obtained by solving an equation, the acceleration time is equal to the deceleration time, the uniform speed time is zero, and the equation is:wherein N is the total length of the path or the total angle of the gesture change;
will give a maximum accelerationPath maximum acceleration as path trajectory parameter>Obtaining the maximum speed of the path in the path track parameters according to the maximum acceleration, the acceleration time and the maximum jerk of the path>I.e.。
7. An electronic device comprising a memory and a processor and computer instructions stored on the memory and running on the processor, which when executed by the processor, perform the method of any one of claims 1-5.
8. A computer readable storage medium storing computer instructions which, when executed by a processor, perform the method of any of claims 1-5.
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