CN116512245A - Track optimization method and device for inhibiting residual vibration of flexible joint mechanical arm - Google Patents
Track optimization method and device for inhibiting residual vibration of flexible joint mechanical arm Download PDFInfo
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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
- B25—HAND TOOLS; PORTABLE POWER-DRIVEN TOOLS; MANIPULATORS
- B25J—MANIPULATORS; CHAMBERS PROVIDED WITH MANIPULATION DEVICES
- B25J9/00—Programme-controlled manipulators
- B25J9/16—Programme controls
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- B25J9/161—Hardware, e.g. neural networks, fuzzy logic, interfaces, processor
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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
- B25J9/1628—Programme controls characterised by the control loop
- B25J9/1635—Programme controls characterised by the control loop flexible-arm control
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Abstract
The invention discloses a track optimization method and a track optimization device for inhibiting residual vibration of a flexible joint mechanical arm, wherein the method comprises the following steps: according to the configuration characteristics of the flexible joint mechanical arm and the dynamic parameters thereof, a dynamic model is established, and according to the characteristics of residual vibration, the dynamic model is simplified; according to the characteristics of the S-shaped speed curve, under the consideration of physical constraint conditions, obtaining the constraint relation between the stroke and the running time of the motor; setting an optimization target for inhibiting residual vibration of the flexible joint mechanical arm according to the constraint relation between the stroke and the running time of the motor, and determining a strategy for synchronous optimization of each joint; and calculating the optimal values of 7 time nodes of the S-shaped speed curve of each joint according to the simplified dynamics model and the strategy of synchronous optimization of each joint, thereby obtaining the optimized track of the residual vibration suppression of the flexible joint mechanical arm.
Description
Technical Field
The invention belongs to the technical field of mechanical arm control, and particularly relates to a track optimization method and device for inhibiting residual vibration of a flexible joint mechanical arm.
Background
Residual vibration is an important technical index for controlling the motion of the mechanical arm, particularly in the occasion with higher requirements on efficiency and precision, such as the mechanical arm applied to the semiconductor industry, the use requirement can be met only by having quick and accurate positioning performance, and if the residual vibration is too large and the duration is too long, the operation performance is influenced, and the operation efficiency is also influenced. In order to inhibit excessive residual vibration possibly excited in high-speed motion, an S-shaped speed curve motion planning method is commonly adopted by a servo motion system so as to reduce the impact on a mechanical system as much as possible, thereby reducing the residual vibration. On the basis of a classical S-shaped speed curve planning method, an asymmetric S-shaped speed curve planning method is also provided for further optimizing dynamic characteristics, a dynamic model is combined, dynamic response is used as an optimization target to perform optimization calculation on curve parameters, an optimized S-shaped speed curve under a certain rule can be obtained, and the method can achieve a good effect in single-degree-of-freedom servo motion control.
In the motion control of the mechanical arm with multiple degrees of freedom, a motion planning method of a single degree of freedom servo system is also commonly adopted at present, namely each joint of the mechanical arm is regarded as a decoupling and independent motion system, and a single degree of freedom S-shaped speed curve is adopted to respectively carry out motion planning on each joint. Obviously, there is a dynamic coupling between the joints of the mechanical arm, and the overall optimal effect cannot be obtained by planning each joint individually.
Disclosure of Invention
Aiming at the problems existing in the prior art, the purpose of the embodiment of the application is to provide a track optimization method and a track optimization device for inhibiting residual vibration of a flexible joint mechanical arm so as to achieve the vibration inhibition effect of minimizing the total residual vibration of the mechanical arm.
According to a first aspect of embodiments of the present application, a track optimization method for residual vibration suppression of a flexible joint mechanical arm is provided, including:
according to the configuration characteristics of the flexible joint mechanical arm and the dynamic parameters thereof, a dynamic model is established, and according to the characteristics of residual vibration, the dynamic model is simplified;
according to the characteristics of the S-shaped speed curve, under the consideration of physical constraint conditions, obtaining the constraint relation between the stroke and the running time of the motor;
setting an optimization target for inhibiting residual vibration of the flexible joint mechanical arm according to the constraint relation between the stroke and the running time of the motor, and determining a strategy for synchronous optimization of each joint;
and calculating the optimal values of 7 time nodes of the S-shaped speed curve of each joint according to the simplified dynamics model and the strategy of synchronous optimization of each joint, thereby obtaining the optimized track of the residual vibration suppression of the flexible joint mechanical arm.
Further, the simplified kinetic model is:
（2）
wherein,,is inertia matrix of connecting rod, ">For the centrifugal force and coriolis force terms of the connecting rod, +.>Is the gravity item of the connecting rod, < ->Is a rigidity matrix, wherein->Stiffness values of joints 1 to n, respectively, < >>Is a damping matrix, wherein->Damping values of joints 1 to n, respectively;is a motor position vector, wherein->Motor angles in joints 1 to n, respectively,/->Is a connecting rod position vector, wherein->The link angles in joints 1 to n, respectively.
Further, according to the characteristics of the S-shaped speed curve, under the condition of considering physical constraint, obtaining the constraint relation between the motor travel and the running time comprises the following steps:
dividing the motion process of the asymmetric S-shaped speed curve into 7 sections, wherein the processes of the second section, the fourth section and the sixth section are uniform speed sections, and the rest are non-uniform speed sections;
obtaining the jerk of the non-uniform section according to the constraint condition to be met by the S-shaped curve in the motion planning, wherein the constraint condition to be met by the S-shaped curve in the motion planning is that the acceleration in the uniform section is 0, the speed at the moment of motion termination is 0 and the acceleration at the moment of motion termination is 0;
obtaining the acceleration, the speed and the position of the non-uniform section according to the jerk of the non-uniform section;
and obtaining a constraint relation between the stroke and the running time of the motor according to the acceleration, the speed and the position of the non-uniform section and the physical constraint which is required to be met by the performance constraint of the mechanical arm driving system, wherein the physical constraint which is required to be met by the performance constraint of the mechanical arm driving system is jerk, acceleration and speed are all smaller than the maximum allowable value of the mechanical arm driving system.
Further, the optimization objective of the residual vibration suppression of the flexible joint mechanical arm is that the absolute value of the first peak of the residual vibration of the tail end position of the mechanical arm is minimum.
Further, in the strategy of synchronous optimization of each joint, the constraint condition is that the starting point and the ending point of each joint are the same.
Further, according to the simplified dynamics model and the strategy of synchronous optimization of each joint, an optimized track of residual vibration suppression of the flexible joint mechanical arm is calculated, and the method comprises the following steps:
acquiring given running time and a pose of a termination point corresponding to the tail end of the mechanical arm, obtaining a connecting rod corner corresponding to each joint through inverse kinematics according to the pose of the termination point, and compensating the flexible deformation of the joints caused by gravity to obtain a motor corner, namely a motor stroke, at the termination point corresponding to each joint;
taking 7 time nodes of the S-shaped speed curve of each joint as individuals in a genetic algorithm, combining the running time and the motor travel corresponding to each joint, and obtaining the motor track of each joint according to the strategy of synchronous optimization of each joint so as to obtain a motor position vector;
according to the motor position vector, calculating to obtain a connecting rod position vector by utilizing the simplified dynamic model;
according to the connecting rod position vector and the motor position vector, calculating to obtain the actual pose and the theoretical pose of the tail end of the mechanical arm through a connecting rod forward kinematics calculation equation;
calculating a combined displacement dynamic error according to the actual pose and the theoretical pose of the tail end of the mechanical arm;
and taking the maximum peak amplitude in the preset residual vibration time as the residual vibration size, and carrying out iterative calculation by taking the residual vibration size as an fitness function until the termination condition of a genetic algorithm is met, so as to obtain the optimal values of 7 time nodes of the S-shaped speed curve of each joint.
Further, the actual pose is a pose of the tail end of the mechanical arm obtained by taking the connecting rod position vector into the connecting rod forward kinematics calculation equation, and the theoretical pose is a pose of the tail end of the mechanical arm obtained by taking the motor position vector as the connecting rod position vector into the connecting rod forward kinematics calculation equation.
According to a second aspect of embodiments of the present application, there is provided a trajectory optimization device for residual vibration suppression of a flexible joint mechanical arm, including:
the simplification module is used for establishing a dynamic model according to the configuration characteristics of the flexible joint mechanical arm and the dynamic parameters thereof and simplifying the dynamic model according to the characteristics of residual vibration;
the constraint determining module is used for obtaining the constraint relation between the motor travel and the running time under the condition of considering physical constraint according to the characteristics of the S-shaped speed curve;
the strategy determining module is used for setting an optimization target for inhibiting residual vibration of the flexible joint mechanical arm according to the constraint relation between the stroke of the motor and the running time, and determining a strategy for synchronous optimization of each joint;
and the calculation module is used for calculating the optimal values of 7 time nodes of the S-shaped speed curve of each joint according to the simplified dynamics model and the strategy of synchronous optimization of each joint, so as to obtain an optimized track for inhibiting the residual vibration of the flexible joint mechanical arm.
According to a third aspect of embodiments of the present application, there is provided an electronic device, including:
one or more processors;
a memory for storing one or more programs;
the one or more programs, when executed by the one or more processors, cause the one or more processors to implement the method of the first aspect.
According to a fourth aspect of embodiments of the present application, there is provided a computer readable storage medium having stored thereon computer instructions which, when executed by a processor, implement the steps of the method according to the first aspect.
The technical scheme provided by the embodiment of the application can comprise the following beneficial effects:
as can be seen from the above embodiments, the present application is more suitable for vibration suppression of a multi-degree-of-freedom flexible joint mechanical arm: the method aims at the overall residual vibration suppression effect of the mechanical arm and synchronously optimizes the track curve of each joint, so that the optimal effect of the vibration suppression of the whole arm can be obtained.
It is to be understood that both the foregoing general description and the following detailed description are exemplary and explanatory only and are not restrictive of the application.
Drawings
The accompanying drawings, which are incorporated in and constitute a part of this specification, illustrate embodiments consistent with the application and together with the description, serve to explain the principles of the application.
FIG. 1 is a flowchart illustrating a trajectory optimization method for residual vibration suppression of a flexible joint manipulator according to an exemplary embodiment.
FIG. 2 is a schematic illustration of a flexible joint manipulator dynamics model, according to an example embodiment.
FIG. 3 is a schematic diagram illustrating a vibration response of a robotic arm according to an example embodiment.
FIG. 4 is a schematic diagram illustrating an asymmetric S-shaped velocity profile motion plan, according to an exemplary embodiment.
FIG. 5 is a schematic diagram illustrating a flexible joint manipulator trajectory optimization calculation flow, according to an example embodiment.
FIG. 6 is a block diagram illustrating a trajectory optimization device for residual vibration suppression of a flexible joint manipulator according to an exemplary embodiment.
Fig. 7 is a schematic diagram of an electronic device, according to an example embodiment.
Detailed Description
Reference will now be made in detail to exemplary embodiments, examples of which are illustrated in the accompanying drawings. When the following description refers to the accompanying drawings, the same numbers in different drawings refer to the same or similar elements, unless otherwise indicated. The implementations described in the following exemplary examples are not representative of all implementations consistent with the present application.
The terminology used in the present application is for the purpose of describing particular embodiments only and is not intended to be limiting of the present application. As used in this application and the appended claims, the singular forms "a," "an," and "the" are intended to include the plural forms as well, unless the context clearly indicates otherwise. It should also be understood that the term "and/or" as used herein refers to and encompasses any or all possible combinations of one or more of the associated listed items.
It should be understood that although the terms first, second, third, etc. may be used herein to describe various information, these information should not be limited by these terms. These terms are only used to distinguish one type of information from another. For example, a first message may also be referred to as a second message, and similarly, a second message may also be referred to as a first message, without departing from the scope of the present application. The word "if" as used herein may be interpreted as "at … …" or "at … …" or "responsive to a determination", depending on the context.
FIG. 1 is a flowchart illustrating a trajectory optimization method of residual vibration suppression of a flexible joint manipulator according to an exemplary embodiment, as shown in FIG. 1, the method may include the steps of:
step S11: according to the configuration characteristics of the flexible joint mechanical arm and the dynamic parameters thereof, a dynamic model is established, and according to the characteristics of residual vibration, the dynamic model is simplified;
step S12: according to the characteristics of the S-shaped speed curve, under the consideration of physical constraint conditions, obtaining the constraint relation between the stroke and the running time of the motor;
step S13: setting an optimization target for inhibiting residual vibration of the flexible joint mechanical arm according to the constraint relation between the stroke and the running time of the motor, and determining a strategy for synchronous optimization of each joint;
step S14: and calculating the optimal values of 7 time nodes of the S-shaped speed curve of each joint according to the simplified dynamics model and the strategy of synchronous optimization of each joint, thereby obtaining the optimized track of the residual vibration suppression of the flexible joint mechanical arm.
As can be seen from the above embodiments, the present application is more suitable for vibration suppression of a flexible joint multi-degree of freedom mechanical arm: the method aims at the overall residual vibration suppression effect of the mechanical arm and synchronously optimizes the track curve of each joint, so that the optimal effect of the vibration suppression of the whole arm can be obtained.
In the implementation of the step S11, a dynamic model is established according to the configuration characteristics of the flexible joint mechanical arm and the dynamic parameters thereof, and the dynamic model is simplified according to the characteristics of residual vibration;
specifically, the mechanical arm is a mechanism composed of a link and a joint in series, and is a rigid mechanical arm when both the link and the joint are regarded as rigid members, and is a mechanism in which the link is regarded as rigid members and the joint is regarded as a jointWhen the flexible part is used, the flexible joint mechanical arm is used. The main components in the joint comprise a motor, a speed reducer, a torque sensor and the like, and the speed reducer and the torque sensor are usually arranged between the output end of the motor and a connecting rod and are parts which generate remarkable flexible deformation in the joint. The flexible joint manipulator model is shown in fig. 2, where in the ith flexible joint,、 />the comprehensive rigidity and damping from the output end of the motor to the connecting rod are defined as joint rigidity and joint damping respectively. />、/>The motor rotation angle and the connecting rod rotation angle are respectively. For ease of analysis, here +.>The equivalent motor rotation angle after the reduction ratio has been considered. From the figure, the->And->The flexible deformation of the joints is deviated>. When the joint stiffness is considered to be infinite, the joint is a rigid joint, and the mechanical arm is a rigid mechanical arm.
The flexible joint mechanical arm dynamics equation is shown as follows:
（1）
wherein,,is inertia matrix of connecting rod, ">For the centrifugal force and coriolis force terms of the connecting rod, +.>Is the gravity item of the connecting rod, < ->Is a rigidity matrix, wherein->Stiffness values of joints 1 to n, respectively, < >>Is a damping matrix, wherein->Damping values for joints 1 through n, respectively.Is a motor position vector, wherein->Motor angles in joints 1 to n, respectively, are for ease of analysis, +.>To have considered the equivalent motor rotation angle after the reduction ratio,is a connecting rod position vector, wherein->The link angles in joints 1 to n, respectively.
The mechanical arm has vibration during and after the movement, which are respectively defined as process vibration and residual vibration, as shown in fig. 2. Residual vibration is of small amplitude occurring at the end point of motionReciprocating vibration, the position and posture change is small in the vibration process, and the gravity term is the sameThe variation of (2) is negligible, and can be taken into account in dynamic analysis as a quasi-static quantity>Thus, the kinetic equation of the residual vibration of the flexible joint manipulator can be reduced to:
（2）
in the implementation of the step S12, according to the characteristics of the S-shaped speed curve, under the condition of considering physical constraint, obtaining the constraint relation between the motor travel and the running time;
in particular, this step may comprise the sub-steps of:
step S21: dividing the motion process of the asymmetric S-shaped speed curve into 7 sections, wherein the processes of the second section, the fourth section and the sixth section are uniform speed sections, and the rest are non-uniform speed sections;
specifically, reference [ Bai Ji dun et al, point location operation time optimal motion planning considering damping attenuation ]]The motion process of the asymmetric S-shaped speed curve is divided into 7 sections, and the corresponding time node is set as、/>、/>、/>、、/>、/>As shown in fig. 3.
Step S22: obtaining the jerk of the non-uniform section according to the constraint condition to be met by the S-shaped curve in the motion planning, wherein the constraint condition to be met by the S-shaped curve in the motion planning is that the acceleration in the uniform section is 0, the speed at the moment of motion termination is 0 and the acceleration at the moment of motion termination is 0;
specifically, during 7-segment motion of the asymmetric S-shaped velocity profile, jerk J is expressed as:
（3）
in the aboveThe absolute values of jerk are positive values. Set the time interval asWherein->。
In motion planning, the constraint conditions that the S-shaped curve needs to meet are: 1) Acceleration in the constant speed section is 0; 2) The speed at the moment of motion termination is 0; 3) The acceleration at the moment of motion termination is 0, i.e. needs to satisfy:
（4）
setting the initial value of the position to 0 and the ending time to beI.e. stroke is +.>The method can obtain:
（5）
thus for a given stroke and time interval, jerk can be obtained as:
（6）
in the method, in the process of the invention,，/>，
。
step S23: obtaining the acceleration, the speed and the position of the non-uniform section according to the jerk of the non-uniform section;
specifically, according to the jerk of the non-uniform section, the expressions of acceleration, speed and position can be obtained as follows:
（7）
（8）
（9）
wherein:，/>。
step S24: and obtaining a constraint relation between the stroke and the running time of the motor according to the acceleration, the speed and the position of the non-uniform section and the physical constraint which is required to be met by the performance constraint of the mechanical arm driving system, wherein the physical constraint which is required to be met by the performance constraint of the mechanical arm driving system is jerk, acceleration and speed which are all smaller than the maximum allowable value of the driving system.
Specifically, the physical constraints that the motion process needs to satisfy are:
（10）
wherein,,is the maximum jerk allowed, the absolute value of the acceleration and the velocity. From equation (6), the conversion into a constraint relationship expressed in terms of a known travel and time parameter is known:
（11）
in the specific implementation of the step S13, setting an optimization target for inhibiting residual vibration of the flexible joint mechanical arm according to the constraint relation between the stroke and the running time of the motor, and determining a synchronous optimization strategy of each joint;
specifically, the optimization objective of the residual vibration suppression of the flexible joint mechanical arm is that the absolute value of the first peak of the residual vibration of the tail end position of the mechanical arm is minimum:
the residual vibration is a free damped vibration whose amplitude is gradually reduced, so that the magnitude thereof can be characterized by the maximum amplitude of the residual vibration, as can be seen from FIG. 4, the absolute value of the first peak of the residual vibration can be usedCharacterizing its size.
For the flexible joint mechanical arm, the controllable input quantity is a motor rotation angle, the output vibration phenomenon is represented by a connecting rod rotation angle, and in addition, the pose of the tail end of the mechanical arm can be obtained through calculation of the connecting rod rotation angle by utilizing a forward kinematics calculation formula of the connecting rod of the mechanical arm. The tail end pose of the mechanical arm comprises 3 positions and 3 corners, but the influence on the tail end positioning accuracy is a position change, so that only the vibration quantity of the tail end position is calculated for the problem of residual vibration of the flexible joint mechanical arm.
The track optimization strategy of the flexible joint mechanical arm is as follows, by combining the analysis: under the condition of meeting motion constraint, synchronously optimizing the rotation angle of each joint motor by using an S-shaped speed curve planning methodThe absolute value of the first peak of residual vibration at the tail end position of the mechanical arm is minimum, namely, the optimization target is as follows:
（12）
in the method, in the process of the invention,indicates the joint number>The time parameter serial number of the S-shaped curve representing the motor rotation angle,the j-th time value of the S-shaped curve representing the rotation angle of the ith joint motor. />The first peak amplitude of residual vibration at the end position of the mechanical arm, < >>To optimize the domain. The optimization method simultaneously considers the influence of each joint track on the vibration of the tail end of the mechanical arm, and belongs to multi-joint comprehensive optimization。
In addition to the requirement that each joint satisfies the physical constraint condition of the driving system, the requirement that each joint moves in synchronization is also satisfied, namely, in the optimization strategy of each joint synchronization, the constraint condition is that the starting point and the ending point of each joint are the same, so that the constraint condition of multi-joint synchronization optimization can be expressed as follows:
（13）
wherein i denotes the joint sequence, the parameter subscript i denotes the corresponding parameter of the ith joint, e.gRepresents the maximum acceleration allowed by the ith joint, < ->For the motor stroke of the ith joint, additionally, < >>For the movement planning time, the joints are the same.
In the specific implementation of the step S14, according to the simplified dynamics model and the strategy of synchronous optimization of each joint, calculating the optimal values of 7 time nodes of the S-shaped speed curve of each joint, thereby obtaining an optimized track of the residual vibration suppression of the flexible joint mechanical arm;
and performing multi-axis motion planning based on an S-shaped speed curve, namely performing motion planning on the corners of the motors of all joints according to the synchronization of the S-shaped speed curve, and optimizing each time parameter to minimize residual vibration at the tail end position of the mechanical arm. Based on a dynamic model of the flexible joint mechanical arm, an optimal track is obtained through numerical calculation by utilizing a genetic algorithm, a calculation method and a flow are shown in fig. 5, and the steps can comprise the following substeps:
step S31: acquiring given running time and a pose of a termination point corresponding to the tail end of the mechanical arm, obtaining a connecting rod corner corresponding to each joint through inverse kinematics according to the pose of the termination point, and compensating the flexible deformation of the joints caused by gravity to obtain a motor corner, namely a motor stroke, at the termination point corresponding to each joint;
specifically, the runtime is first determinedAnd the termination point pose corresponds to the tail end of the mechanical arm. The corresponding connecting rod rotation angle at the end point can be obtained by the pose of the tail end of the mechanical arm at the end point through the inverse kinematics of the connecting rod>By compensating for the flexible deformation of the joint due to gravity, the motor rotation angle +.>I.e. motor travel, specifically denoted +.>。
Step S32: taking 7 time nodes of the S-shaped speed curve of each joint as individuals in a genetic algorithm, combining the running time and the motor travel corresponding to each joint, and obtaining the motor track of each joint according to the strategy of synchronous optimization of each joint so as to obtain a motor position vector;
will be in genetic algorithmAs individual, i.e. as parameters to be optimized, a total of 7n parameters to be optimized are assigned to the individual, combined with the known parameters +.>、/>Generating motor tracks of all joints by S-shaped speed curve motion planning>Obtaining a motor position vector +.>。
Step S33: according to the motor position vector, calculating a connecting rod position vector by utilizing the simplified dynamic model;
specifically, by motor position vectorBy->The connecting rod position vector can be calculated>。
Step S34: according to the connecting rod position vector and the motor position vector, calculating the actual pose and the theoretical pose of the tail end of the mechanical arm through the forward kinematics of the mechanical arm;
specifically, the dynamic equation will beCalculated +.>Carrying out calculation by taking a forward kinematics equation to obtain the pose of the tail end of the mechanical arm, defining the pose as the actual pose, and recording the pose as +.>. In addition, the definition will->The pose of the tail end of the mechanical arm calculated by taking the forward kinematics equation is a theoretical pose (the joint is assumed to be free from deformation at the moment), and is recorded as。/>And->Are six-dimensional vectors, and comprise three-axis displacement and three-axis rotation angles under a Cartesian coordinate system, namely，/>。
Step S35: calculating a combined displacement dynamic error according to the actual pose and the theoretical pose of the tail end of the mechanical arm;
specifically, since only the position vibration is concerned, only the combined displacement dynamic error is calculated, and the calculated formula is as a numerical value representing the vibration magnitudeWherein->、/>。
Step S36: taking the maximum peak amplitude in the preset residual vibration time as the residual vibration size, and carrying out iterative calculation by taking the residual vibration size as an fitness function until the termination condition of a genetic algorithm is met, so as to obtain the optimal values of 7 time nodes of the S-shaped speed curve of each joint;
specifically, the simulation time in Simulink is+/>I.e. after the end of the exercise time, +.>Residual vibrational response over time. />The selection basis of (2) is as follows: at->At least 3-4 vibration peaks can be included in the time, so that the maximum peak can be selected to represent the residual vibration magnitude, and the maximum value is selected from a plurality of vibration peaks because errors can exist in numerical calculation, so that the first peak is not necessarily the peak with the maximum amplitude. To->The maximum peak amplitude in time is +.>The residual vibration size was characterized. To->For the fitness function, performing iterative calculation until the fitness function becomes stable and meets the termination condition to obtain +.>Is set to the optimum value of (2).
Corresponding to the embodiment of the track optimization method for inhibiting the residual vibration of the flexible joint mechanical arm, the application also provides an embodiment of the track optimization device for inhibiting the residual vibration of the flexible joint mechanical arm.
FIG. 6 is a block diagram illustrating a trajectory optimization device for residual vibration suppression of a flexible joint manipulator according to an exemplary embodiment. Referring to fig. 6, the apparatus may include:
the simplifying module 21 is used for establishing a dynamic model according to the configuration characteristics of the flexible joint mechanical arm and the dynamic parameters thereof, and simplifying the dynamic model according to the characteristics of residual vibration;
the reasoning module 22 is used for deducing the constraint relation between the motor travel and the running time under the consideration of physical constraint conditions according to the characteristics of the S-shaped speed curve;
the determining module 23 is configured to set an optimization target for inhibiting residual vibration of the flexible joint mechanical arm according to the constraint relationship between the travel and the running time of the motor, and determine a strategy for synchronous optimization of each joint;
and the calculating module 24 is used for calculating the optimal values of 7 time nodes of the S-shaped speed curve of each joint according to the simplified dynamics model and the strategy of synchronous optimization of each joint, so as to obtain an optimized track of residual vibration suppression of the flexible joint mechanical arm.
The specific manner in which the various modules perform the operations in the apparatus of the above embodiments have been described in detail in connection with the embodiments of the method, and will not be described in detail herein.
For the device embodiments, reference is made to the description of the method embodiments for the relevant points, since they essentially correspond to the method embodiments. The apparatus embodiments described above are merely illustrative, wherein the elements illustrated as separate elements may or may not be physically separate, and the elements shown as elements may or may not be physical elements, may be located in one place, or may be distributed over a plurality of network elements. Some or all of the modules may be selected according to actual needs to achieve the purposes of the present application. Those of ordinary skill in the art will understand and implement the present invention without undue burden.
Correspondingly, the application also provides electronic equipment, which comprises: one or more processors; a memory for storing one or more programs; the one or more programs, when executed by the one or more processors, cause the one or more processors to implement the trajectory optimization method of residual vibration suppression of the flexible joint manipulator as described above. As shown in fig. 7, a hardware structure diagram of an arbitrary device with data processing capability, where the trace optimization method for inhibiting residual vibration of a flexible joint mechanical arm provided by the embodiment of the present invention is located, is except for a processor, a memory, a DMA controller, a magnetic disk, and a nonvolatile memory shown in fig. 7, where the arbitrary device with data processing capability in the embodiment is located, generally, according to an actual function of the arbitrary device with data processing capability, other hardware may also be included, which will not be described herein.
Correspondingly, the application further provides a computer readable storage medium, wherein computer instructions are stored on the computer readable storage medium, and the instructions are executed by a processor to realize the track optimization method for inhibiting the residual vibration of the flexible joint mechanical arm. The computer readable storage medium may be an internal storage unit, such as a hard disk or a memory, of any of the data processing enabled devices described in any of the previous embodiments. The computer readable storage medium may also be an external storage device, such as a plug-in hard disk, a Smart Media Card (SMC), an SD Card, a Flash memory Card (Flash Card), or the like, provided on the device. Further, the computer readable storage medium may include both internal storage units and external storage devices of any device having data processing capabilities. The computer readable storage medium is used for storing the computer program and other programs and data required by the arbitrary data processing apparatus, and may also be used for temporarily storing data that has been output or is to be output.
Other embodiments of the present application will be apparent to those skilled in the art from consideration of the specification and practice of the disclosure herein. This application is intended to cover any variations, uses, or adaptations of the application following, in general, the principles of the application and including such departures from the present disclosure as come within known or customary practice within the art to which the application pertains.
It is to be understood that the present application is not limited to the precise arrangements and instrumentalities shown in the drawings, which have been described above, and that various modifications and changes may be effected without departing from the scope thereof.
Claims (10)
1. The track optimization method for inhibiting residual vibration of the flexible joint mechanical arm is characterized by comprising the following steps of:
according to the configuration characteristics of the flexible joint mechanical arm and the dynamic parameters thereof, a dynamic model is established, and according to the characteristics of residual vibration, the dynamic model is simplified;
according to the characteristics of the S-shaped speed curve, under the consideration of physical constraint conditions, obtaining the constraint relation between the stroke and the running time of the motor;
setting an optimization target for inhibiting residual vibration of the flexible joint mechanical arm according to the constraint relation between the stroke and the running time of the motor, and determining a strategy for synchronous optimization of each joint;
and calculating the optimal values of 7 time nodes of the S-shaped speed curve of each joint according to the simplified dynamics model and the strategy of synchronous optimization of each joint, thereby obtaining the optimized track of the residual vibration suppression of the flexible joint mechanical arm.
2. The method of claim 1, wherein the simplified kinetic model is:
（2）
wherein,,is inertia matrix of connecting rod, ">For the centrifugal force and coriolis force terms of the connecting rod, +.>Is the gravity item of the connecting rod, < ->Is a rigidity matrix, wherein->The stiffness values of joints 1 to n respectively,is a damping matrix, wherein->Damping values of joints 1 to n, respectively;is a motor position vector, wherein->Motor angles in joints 1 to n, respectively,/->Is a connecting rod position vector, wherein->The link angles in joints 1 to n, respectively.
3. The method according to claim 1, wherein the obtaining the constraint relation between the motor travel and the running time under the consideration of the physical constraint condition according to the characteristics of the S-shaped speed curve comprises:
dividing the motion process of the asymmetric S-shaped speed curve into 7 sections, wherein the processes of the second section, the fourth section and the sixth section are uniform speed sections, and the rest are non-uniform speed sections;
obtaining the jerk of the non-uniform section according to the constraint condition to be met by the S-shaped curve in the motion planning, wherein the constraint condition to be met by the S-shaped curve in the motion planning is that the acceleration in the uniform section is 0, the speed at the moment of motion termination is 0 and the acceleration at the moment of motion termination is 0;
obtaining the acceleration, the speed and the position of the non-uniform section according to the jerk of the non-uniform section;
and obtaining a constraint relation between the stroke and the running time of the motor according to the acceleration, the speed and the position of the non-uniform section and the physical constraint which is required to be met by the performance constraint of the mechanical arm driving system, wherein the physical constraint which is required to be met by the performance constraint of the mechanical arm driving system is jerk, acceleration and speed are all smaller than the maximum allowable value of the mechanical arm driving system.
4. The method of claim 1, wherein the optimization objective for residual vibration suppression of the flexible articulated arm is that the absolute value of the first peak of residual vibration at the end position of the arm is at a minimum.
5. The method according to claim 1, wherein in the strategy of joint synchronization optimization, the constraint condition is that the starting point and the ending point of each joint are the same.
6. The method of claim 1, wherein calculating an optimized trajectory for residual vibration suppression of the flexible joint manipulator according to the simplified dynamics model and the strategy for joint synchronization optimization comprises:
acquiring given running time and a pose of a termination point corresponding to the tail end of the mechanical arm, obtaining a connecting rod corner corresponding to each joint through inverse kinematics according to the pose of the termination point, and compensating the flexible deformation of the joints caused by gravity to obtain a motor corner, namely a motor stroke, at the termination point corresponding to each joint;
taking 7 time nodes of the S-shaped speed curve of each joint as individuals in a genetic algorithm, combining the running time and the motor travel corresponding to each joint, and obtaining the motor track of each joint according to the strategy of synchronous optimization of each joint so as to obtain a motor position vector;
according to the motor position vector, calculating to obtain a connecting rod position vector by utilizing the simplified dynamic model;
according to the connecting rod position vector and the motor position vector, calculating to obtain the actual pose and the theoretical pose of the tail end of the mechanical arm through a connecting rod forward kinematics calculation equation;
calculating a combined displacement dynamic error according to the actual pose and the theoretical pose of the tail end of the mechanical arm;
and taking the maximum peak amplitude in the preset residual vibration time as the residual vibration size, and carrying out iterative calculation by taking the residual vibration size as an fitness function until the termination condition of a genetic algorithm is met, so as to obtain the optimal values of 7 time nodes of the S-shaped speed curve of each joint.
7. The method of claim 6, wherein the actual pose is a robot end pose obtained by taking the link position vector into the link forward kinematic calculation equation, and the theoretical pose is a robot end pose obtained by taking the motor position vector as a link position vector into the link forward kinematic calculation equation.
8. The utility model provides a track optimizing device of flexible joint arm residual vibration suppression which characterized in that includes:
the simplification module is used for establishing a dynamic model according to the configuration characteristics of the flexible joint mechanical arm and the dynamic parameters thereof and simplifying the dynamic model according to the characteristics of residual vibration;
the constraint determining module is used for obtaining the constraint relation between the motor travel and the running time under the condition of considering physical constraint according to the characteristics of the S-shaped speed curve;
the strategy determining module is used for setting an optimization target for inhibiting residual vibration of the flexible joint mechanical arm according to the constraint relation between the stroke of the motor and the running time, and determining a strategy for synchronous optimization of each joint;
and the calculation module is used for calculating the optimal values of 7 time nodes of the S-shaped speed curve of each joint according to the simplified dynamics model and the strategy of synchronous optimization of each joint, so as to obtain an optimized track for inhibiting the residual vibration of the flexible joint mechanical arm.
9. An electronic device, comprising:
one or more processors;
a memory for storing one or more programs;
the one or more programs, when executed by the one or more processors, cause the one or more processors to implement the method of any of claims 1-7.
10. A computer readable storage medium having stored thereon computer instructions which, when executed by a processor, implement the steps of the method of any of claims 1-7.
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