CN116069044B - Multi-robot cooperative transportation capacity hybrid control method - Google Patents
Multi-robot cooperative transportation capacity hybrid control method Download PDFInfo
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Abstract
The invention discloses a multi-robot cooperative transportation capacity hybrid control method, which comprises the steps of firstly, establishing a cooperative transportation dynamics model of a plurality of robots; setting a robot position error, introducing an error conversion function to perform error conversion, processing the position error after the robot conversion, and combining a collaborative handling dynamics model to obtain an error transfer dynamics model; rewriting an error transfer dynamics model, setting a sliding mode function and a disturbance estimation error, designing a specified performance controller according to the rewritten error transfer dynamics model, the sliding mode function and the disturbance estimation error, and calculating the input torque of the robot; then presetting an impedance model, a spring model and environmental stiffness estimation, and calculating to obtain the contact force estimation and the position of the robot end effector; and finally, constructing a mathematical simulation model, and verifying the effectiveness of the multi-robot cooperative transportation control method. The method can ensure the precision and the safety of a plurality of robots in the cooperative transportation process.
Description
Technical Field
The invention relates to the technical field of multi-robot cooperative transportation control, in particular to a multi-robot cooperative transportation capacity and position hybrid control method.
Background
In recent years, intelligent manufacturing technologies typified by robots are becoming a new trend for high-quality manufacturing of large and complex parts of major equipment. Compared with a numerical control machine tool, the robot or roboticized equipment has the advantages of flexible movement, large working space, strong parallel coordination operation capability and the like, is easy to integrate multiple types of sensors, can adapt to complex processing environments, and a multi-robot manufacturing system consisting of single roboticized equipment with a certain scale can further increase the working space and the dexterity of robot operation, so that the design of the multi-robot high-precision and high-safety autonomous control method has important significance for intelligent manufacturing.
The multi-mobile robot realizes unmanned mode from remote control driving to autonomous control of an onboard computer. Mobile robots are mature mobile platforms, and different components can be carried on the mobile platforms to be applied to different fields. For example, the fields of state detection, target tracking and the like have the potential of mobile robot application. Among these applications, the mobile platform needs to be equipped with a mechanical arm, and the two are combined to form a mobile robot, so that the high-end equipment can bring great convenience to industry. As researchers go deep into this field, the application of mobile robot-mounted mechanical arms in practice has been realized by students. For example, the tasks of grabbing and assembling are flexibly completed, the contact force measurement work is completed instead of a force sensor, and the bionic work is completed by means of a parallel mechanical arm.
As an essential link in the intelligent manufacturing industry, cooperative conveyance of multiple robots is an essential link, and although some students have studied it to some extent, some technical difficulties still exist to overcome. In the motion process of robots, the problem of mutual interference among robots under the external disturbance action environment is certainly one of the current research hotspots; secondly, the object and the robot itself are damaged to some extent by the pressing or the like of the robot arm against the object under the position control alone.
Disclosure of Invention
The invention aims to solve the technical problem that the invention provides a multi-robot cooperative transportation capacity hybrid control method in consideration of the precision requirement and the safety of a plurality of robots in the cooperative transportation process.
A multi-robot cooperative transport capacity hybrid control method comprises the following steps:
s1, establishing a carrying dynamics model of a robot, and establishing a cooperative carrying dynamics model of a robot system formed by a plurality of robots according to the carrying dynamics model of the robot;
s2, setting a robot position error, and introducing an error conversion function to convert the robot position error to obtain a robot converted position error, and obtaining an error transfer dynamics model according to the robot converted position error and the collaborative transport dynamics model;
s3, rewriting an error transfer dynamics model to obtain a rewritten error transfer dynamics model, setting a sliding mode function and a disturbance estimation error, designing a specified performance controller according to the rewritten error transfer dynamics model, the sliding mode function and the disturbance estimation error, and calculating an input torque of the robot system according to the specified performance controller;
s4, presetting an impedance model, a spring model and environmental stiffness estimation, designing an impedance control method according to the impedance model, the spring model and the environmental stiffness estimation, and calculating the contact force estimation and the position of the end effector of the robot system;
s5, constructing a mathematical simulation model according to the cooperative transportation dynamics model, the error transfer dynamics model and the specified performance controller, inputting the calculated input moment of the robot system, the contact force estimation and the position of the end effector of the robot system into the simulation model, and verifying the effectiveness of the cooperative transportation control method of the robot system.
Preferably, the collaborative handling dynamics model in S1 is specifically:
wherein, the liquid crystal display device comprises a liquid crystal display device,
in the method, in the process of the invention,
for symmetrical positive determination of the inertial matrix of the robotic system, < >>
For the centrifugal term and the kroot term matrix of the robot system, < >>
For the total friction force generated by the robotic system during modeling>
For the velocity jacobian from the joint vector of the robot system to the working space +.>
Gravitational acceleration matrix>
Is a joint vector of the robotic system, +.>
And->
Joint vectors of the robot system, respectively +.>
First and second derivatives of +.>
For the degree of freedom of the robotic system,
，/>
is->
Degree of freedom of the personal robot, < >>
For the actual contact force of the end effector of the robotic system,/->
Is the input torque of the robot system.
Preferably, S2 specifically includes:
s21, setting specified performance and performance function of the robot, and determining position error of the robot according to the specified performance and performance function;
s22, setting an error conversion function, and converting the position error of the robot by using the error conversion function to obtain the position error after the robot is converted;
s23, building a position error after the conversion of the robot system according to the position error after the conversion of the robot, processing the position error after the conversion of the robot system, and combining the collaborative handling dynamics model to obtain an error transfer dynamics model.
Preferably, the error transfer dynamics model in S23 has the specific formula:
wherein, the liquid crystal display device comprises a liquid crystal display device,
in the method, in the process of the invention,
position error after conversion for robot system +.>
Second derivative of>
For symmetrical positive determination of the inertial matrix of the robotic system, < >>
For the centrifugal term and the kroot term matrix of the robot system, < >>
For the velocity jacobian from the joint vector of the robot system to the working space +.>
Gravitational acceleration matrix>
And->
Upper and lower bounds representing specified performance of the ith robotic system,/->
Representing the performance function of the i-th robot, < ->
For the input torque of the robot system, +.>
Position error for robot system +.>
First derivative of>
For the position error of the ith robot, < +.>
Joint vector for robot system +.>
First derivative of>
For the joint vector of the ith robot, < +.>
For the desired position of the robot system +.>
Second derivative of>
For the desired position of the ith robot, < +.>
For the actual contact force of the end effector of the robotic system,/->
、/>
、/>
、/>
Is an intermediate variable of the error transfer dynamics model.
Preferably, S3 specifically includes:
s31, rewriting the error transfer dynamics model to obtain a rewritten error transfer dynamics model, wherein the rewritten error transfer dynamics model comprises a specified performance controller;
s32, setting a sliding mode function according to the position error after the conversion of the robot system in the step S23;
s33, setting a disturbance estimation error, and setting a first Lyapunov function according to the sliding mode function and the disturbance estimation error;
s34, judging the stability of the error transfer dynamics model according to the first Lyapunov function, and designing a corresponding specified performance controller when the error transfer dynamics model is stable.
Preferably, the specified performance controller in S34 may be specifically formulated as:
in the method, in the process of the invention,
for the input torque of the robot system, +.>
For symmetrical positive determination of the inertial matrix of the robotic system, < >>
For the sliding mode function, +.>
To prescribe performance controller gain, +.>
For disturbance estimation, i.e. the actual disturbance +.>
Estimate of (2)，/>
First derivative of position error after conversion for robotic system,/->
For the diagonal gain matrix>
Position error for robot system +.>
First derivative of>
Position error after conversion for robot system +.>
First derivative of>
、/>
Is an intermediate variable of the error transfer dynamics model.
Preferably, S4 specifically includes:
s41, presetting an impedance model and a spring model, and deducing a contact force error of the end effector according to the impedance model and the spring model;
s42, obtaining a force tracking error transfer dynamics model according to the contact force error and the impedance model of the end effector;
s43, designing environmental rigidity estimation, namely designing second and third Lyapunov functions according to the force tracking error transfer dynamics model and the environmental rigidity estimation, and deriving first derivatives of the environmental rigidity estimation through the second and third Lyapunov functions;
s44, obtaining a contact force estimation of the end effector of the robot system according to the first derivative of the environmental stiffness estimation and the spring model;
s45, obtaining the position of the end effector of the robot system according to the contact force error and the impedance model of the end effector.
Preferably, the force tracking error transfer dynamics model in S42 is specifically:
in the method, in the process of the invention,
、/>
、/>
inertia, damping and stiffness of the impedance model of the i-th robot, respectively,/i>
For the i-th robot environmental stiffness +.>
Estimated value of ∈10->
Error of contact force for the ith robot end effector, +.>
And->
Contact force errors of the i-th robotic end effector, respectively +.>
First and second derivatives of +.>
。
Preferably, the contact force estimation of the end effector of the robotic system in S44 is given by:
in the method, in the process of the invention,
estimating for the contact force of the ith robot end effector,/for the contact force of the ith robot end effector>
For the i-th robot environmental stiffness +.>
Estimate of->
For the position of the i-th robotic end effector,/->
Is the position of the target object.
Preferably, the position of the end effector of the robotic system in S45 is given by:
in the method, in the process of the invention,
position of i-th robot end effector output for impedance model, +.>
First derivative of the i-th robot end effector position output for the impedance model, +.>
The i-th robot end effector position input for impedance model, < >>
，/>
、/>
Inertia, damping and stiffness of the ith impedance model, respectively,/->
And->
First and second derivatives of the ith robot end effector position, respectively, input for the impedance model,/->
For the position error of the ith robot end effector,/->
For the i-th robot environmental stiffness +.>
Is a function of the estimate of (2).
According to the multi-robot cooperative transportation capacity hybrid control method, the strict error control among a plurality of robots is realized by designing the specified performance controller, and the precision in the cooperative transportation process is ensured; the contact force estimation method and the impedance control of the robot end effector are designed by adopting the self-adaptive impedance force control method, so that the safety of the robot in the carrying process is ensured.
Drawings
FIG. 1 is a flow chart of a multi-robot cooperative transportation capacity bit hybrid control method according to an embodiment of the invention;
FIG. 2 is a top view of a multi-robot co-handling in accordance with one embodiment of the present invention;
FIG. 3 is a schematic diagram of a multi-robot co-handling scenario in accordance with an embodiment of the present invention;
FIG. 4 is a schematic diagram of a multi-robot cooperative transportation capacity hybrid control method according to an embodiment of the invention;
FIG. 5 is an illustration of the control error of the x-axis component of the robot 1 during the co-handling of three robots in accordance with one embodiment of the present invention;
FIG. 6 is an illustration of the control error of the x-axis component of the robot 2 during the co-handling of three robots in accordance with one embodiment of the present invention;
FIG. 7 is an illustration of the control error of the x-axis component of the robot 3 during the co-handling of three robots in accordance with one embodiment of the present invention;
FIG. 8 is an effect diagram of a three robot co-handling process in accordance with one embodiment of the present invention;
fig. 9 is a force tracking effect diagram of the three robots in cooperation with the transfer process robot 1 in an embodiment of the present invention;
FIG. 10 is a diagram showing the force tracking effect of three robots in cooperation with the handling process robot 2 according to an embodiment of the present invention;
fig. 11 is a force tracking effect diagram of the three robots in cooperation with the transfer process robot 3 in an embodiment of the present invention.
Detailed Description
In order to make the technical scheme of the present invention better understood by those skilled in the art, the present invention will be further described in detail with reference to the accompanying drawings.
A multi-robot cooperative transport capacity hybrid control method specifically comprises the following steps:
s1, establishing a carrying dynamics model of a robot, and establishing a cooperative carrying dynamics model of a robot system formed by a plurality of robots according to the carrying dynamics model of the robot;
s2, setting a robot position error, and introducing an error conversion function to convert the robot position error to obtain a robot converted position error, and obtaining an error transfer dynamics model according to the robot converted position error and the collaborative transport dynamics model;
s3, rewriting an error transfer dynamics model to obtain a rewritten error transfer dynamics model, setting a sliding mode function and a disturbance estimation error, designing a specified performance controller according to the rewritten error transfer dynamics model, the sliding mode function and the disturbance estimation error, and calculating an input torque of the robot system according to the specified performance controller;
s4, presetting an impedance model, a spring model and environmental stiffness estimation, designing an impedance control method according to the impedance model, the spring model and the environmental stiffness estimation, and calculating the contact force estimation and the position of the end effector of the robot system;
s5, constructing a mathematical simulation model according to the cooperative transportation dynamics model, the error transfer dynamics model and the specified performance controller, inputting the calculated input moment of the robot system, the contact force estimation and the position of the end effector of the robot system into the simulation model, and verifying the effectiveness of the cooperative transportation control method of the robot system.
Specifically, referring to fig. 1, 2, 3 and 4, fig. 1 is a flowchart of a method for controlling the cooperative conveyance capacity of multiple robots according to an embodiment of the present invention; FIG. 2 is a top view of a multi-robot co-handling in accordance with one embodiment of the present invention; FIG. 3 is a schematic diagram of a multi-robot co-handling scenario in accordance with an embodiment of the present invention; FIG. 4 is a schematic diagram of a multi-robot cooperative transportation capability hybrid control method according to an embodiment of the invention.
A multi-robot cooperative transportation capacity hybrid control method comprises the steps of firstly, establishing a transportation dynamics model of a single robot, and establishing a cooperative transportation dynamics model of a robot system formed by a plurality of robots on the basis of the transportation dynamics model; then setting a robot position error, introducing an error conversion function to convert the robot position error, and establishing an error transfer dynamics model according to the robot converted position error and a collaborative handling dynamics model design error transfer method; then, rewriting the error transfer dynamics model, setting a sliding mode function and a disturbance estimation error, designing a specified performance controller according to the rewritten error transfer dynamics model, the sliding mode function and the disturbance estimation error, and calculating to obtain an input torque; then presetting an impedance model, a spring model and an environmental stiffness estimation, and designing an impedance control method according to the impedance model, the spring model and the environmental stiffness estimation to calculate an impedance position output, wherein the impedance position output comprises a contact force estimation and a position of an end effector of the robot system; and finally, constructing a mathematical simulation model according to the cooperative transportation dynamics model, the error transfer dynamics model, the specified performance controller and the impedance controller, and verifying the effectiveness of the cooperative transportation method of the multiple robots.
In one embodiment, the collaborative handling dynamics model in S1 is specifically:
wherein, the liquid crystal display device comprises a liquid crystal display device,
in the method, in the process of the invention,
for symmetrical positive determination of the inertial matrix of the robotic system, < >>
For the centrifugal term and the kroot term matrix of the robot system, < >>
For the total friction force generated by the robotic system during modeling>
For the velocity jacobian from the joint vector of the robot system to the working space +.>
Gravitational acceleration matrix>
Is a joint vector of the robotic system, +.>
And->
Joint vectors of the robot system, respectively +.>
First and second derivatives of +.>
For the degree of freedom of the robotic system,
，/>
is->
Degree of freedom of the personal robot, < >>
For the actual contact force of the end effector of the robotic system,/->
Is the input torque of the robot system.
Specifically, the establishment of the cooperative conveyance dynamics model of the robot system includes the steps of:
1) Establishing a dynamics model of a single robot:
wherein, the liquid crystal display device comprises a liquid crystal display device,
in the method, in the process of the invention,
for the symmetric positive inertia matrix of the ith robot,/->
For the centrifugal term and the cliori term matrix of the ith robot, +.>
Friction force generated for the ith robot modeling procedure,/->
Gravity acceleration matrix of the i-th robot, < ->
For the gravity acceleration vector of the i-th robot,>
is the joint vector (comprising a mobile end and a mechanical arm) of the ith robot,/of the ith robot>
And->
Joint vector of i-th robot, respectively +.>
First and second derivatives of +.>
Input moment for the ith robot, < +.>
Force applied to the end effector of the ith robot, +.>
For the joint vector from the ith robot +.>
To the workspace->
The velocity jacobian matrix of (2) can be obtained by a force transfer process, specifically as follows:
The working space of the robot system is:
。
2) Establishing a cooperative conveyance dynamics model of a robot system consisting of a plurality of robots:
wherein, the liquid crystal display device comprises a liquid crystal display device,
in the method, in the process of the invention,
for symmetrical positive determination of the inertial matrix of the robotic system, < >>
For the centrifugal term and the kroot term matrix of the robot system, < >>
For the total friction force generated by the robotic system during modeling>
Is a joint vector of the robotic system, +.>
For the velocity jacobian from the joint vector of the robot system to the working space +.>
For the total degree of freedom of the robotic system, +.>
Is->
Degree of freedom of the personal robot, < >>
Representing the real number domain.
In one embodiment, S2 specifically includes:
s21, setting specified performance and performance function of the robot, and determining position error of the robot according to the specified performance and performance function;
s22, setting an error conversion function, and converting the position error of the robot by using the error conversion function to obtain the position error after the robot is converted;
s23, building a position error after the conversion of the robot system according to the position error after the conversion of the robot, processing the position error after the conversion of the robot system, and combining the collaborative handling dynamics model to obtain an error transfer dynamics model.
In one embodiment, the error transfer dynamics model in S23 is specifically formulated as:
wherein, the liquid crystal display device comprises a liquid crystal display device,
in the method, in the process of the invention,
position error after conversion for robot system +.>
Second derivative of>
For symmetrical positive determination of the inertial matrix of the robotic system, < >>
For the centrifugal term and the kroot term matrix of the robot system, < >>
For the velocity jacobian from the joint vector of the robot system to the working space +.>
Gravitational acceleration matrix>
And->
Upper and lower bounds representing specified performance of the ith robotic system,/->
Representing the performance function of the i-th robot, < ->
For the input torque of the robot system, +.>
Position error for robot system +.>
First derivative of>
For the position error of the ith robot, < +.>
Joint vector for robot system +.>
First derivative of>
For the joint vector of the ith robot, < +.>
For the desired position of the robot system +.>
Second derivative of>
For the desired position of the ith robot, < +.>
For the actual contact force of the end effector of the robotic system,/->
、/>
、/>
、/>
Is an intermediate variable of the error transfer dynamics model.
Specifically, since the desired position of each robot is bounded, the position error of the robot can be defined based on this:
in the method, in the process of the invention,
for the position error of the ith robot, < +.>
For the joint vector of the ith robot, < +.>
Is the expected position of the ith robot.
Defining upper and lower bounds and performance functions of the specified performance of the robot, and setting a position error range of the robot according to the upper and lower bounds and the performance functions of the specified performance:
wherein, the liquid crystal display device comprises a liquid crystal display device,
in the method, in the process of the invention,
and->
Upper and lower bounds of performance are specified for the ith robot, respectively, ">
For the performance function of the ith robot, < +.>
、/>
、/>
All are normal numbers and are added with->
And->
Respectively represent performance functions->
At->
And->
Value of time, and
，/>
the approximation speed of the performance function of the i-th robot is represented.
In order to achieve prescribed performance control for a plurality of robots, an error transfer dynamics model needs to be designed, and the design process is as follows:
1) Firstly, introducing an error conversion function to perform error conversion on the position error of each robot to obtain the position error after the robot conversion:
setting an error transfer function
，/>
The error transfer function satisfies
。
And obtaining a position error after the conversion of the robot through error conversion:
wherein, the liquid crystal display device comprises a liquid crystal display device,
in the method, in the process of the invention,
position error after conversion for the ith robot, +.>
And->
Upper and lower bounds of performance are specified for the ith robot, respectively, ">
For the position error of the ith robot, < +.>
For the performance function of the ith robot, < +.>
Is an intermediate variable.
On this basis, the position error after the conversion of the robot system can be expressed as:
2) And (3) solving a first derivative of the position error after the conversion of the robot system:
wherein, the liquid crystal display device comprises a liquid crystal display device,
in the method, in the process of the invention,
、/>
is an intermediate variable.
3) Solving a second derivative of the position error after the conversion of the robot system, and combining the collaborative handling dynamics model to obtain an error transfer dynamics model:
and (3) obtaining a second derivative of the position error after the conversion of the robot system:
substituting the collaborative handling dynamics model formula (2) into the formula (8) above can obtain an error transfer dynamics model, and the specific formula is as follows:
wherein, the liquid crystal display device comprises a liquid crystal display device,
in the method, in the process of the invention,
second derivative of position error after conversion for robot system,/->
For symmetrical positive determination of the inertial matrix of the robotic system, < >>
Gravitational acceleration matrix>
For the input torque of the robot system, +.>
Is the second derivative of the desired position of the robotic system,/->
Is an intermediate variable.
In one embodiment, S3 specifically includes:
s31, rewriting the error transfer dynamics model to obtain a rewritten error transfer dynamics model, wherein the rewritten error transfer dynamics model comprises a specified performance controller;
s32, setting a sliding mode function according to the position error after the conversion of the robot system in the step S23;
s33, setting a disturbance estimation error, and setting a first Lyapunov function according to the sliding mode function and the disturbance estimation error;
s34, judging the stability of the error transfer dynamics model according to the first Lyapunov function, and designing a corresponding specified performance controller when the error transfer dynamics model is stable.
In one embodiment, the specified performance controller in S34 may be specifically formulated as:
in the method, in the process of the invention,
for the input torque of the robot system, +.>
For symmetrical positive determination of the inertial matrix of the robotic system, < >>
For the sliding mode function, +.>
To prescribe performance controller gain, +.>
For disturbance estimation, i.e. the actual disturbance +.>
Estimated value of ∈10->
First derivative of position error after conversion for robotic system,/->
For the diagonal gain matrix>
Position error for robot system +.>
First derivative of>
Position error after conversion for robot system +.>
First derivative of>
、/>
Is an intermediate variable of the error transfer dynamics model.
Specifically, the performance controller is designed and regulated according to an error transfer dynamics model, and the process is as follows:
1) Rewriting the error transfer dynamics model formula to obtain a rewritten error transfer dynamics model
Wherein, the liquid crystal display device comprises a liquid crystal display device,
（11）
in the method, in the process of the invention,
for control input, an intermediate variable is used for ++through equation (11)>
Is a solution to (a). />
Is the actual disturbance, i.e. the sum of the forces experienced by the robotic end effector during handling and the internal and external disturbance forces.
2) Setting a sliding mode function according to the position error after the conversion of the robot system and the first derivative thereof
In the method, in the process of the invention,
for the sliding mode function, +.>
For the diagonal gain matrix>
Position error after conversion for robot system, +.>
Is the first derivative of the position error after the robotic system conversion.
3) Solving a first derivative of the sliding mode function, and combining the rewritten error transfer dynamics model (10) to obtain the first derivative of the sliding mode function:
in the method, in the process of the invention,
is the first derivative of the sliding mode function.
4) According to external disturbance
Disturbance estimation->
Calculating disturbance estimation error->
：
In order to verify the stability of the error transfer dynamics model, the rewritten error transfer dynamics model and the error disturbance estimation error model, a Lyapunov function is introduced and related parameters are solved, and the specific process is as follows:
1) On the basis of the rewritten error transfer dynamics model (10), the sliding mode function is taken into account
Error of disturbance estimation>
Setting a first Lyapunov function:
in the method, in the process of the invention,
for the first Lyapunov function, < ->
Error is estimated for disturbance +.>
Is a sliding mode function.
Solving a first derivative of the first lyapunov function in the formula (16), and substituting the formula (14) into the formula (16) can obtain:
in the method, in the process of the invention,
is the first derivative of the first Lyapunov function,/and>
for actual disturbance +.>
Error is estimated for disturbance +.>
For control input, is an intermediate variable, < +.>
For the first derivative of the disturbance estimation error, +.>
Is a sliding mode function.
2) The performance controller is specified according to the first derivative design of the first lyapunov function:
when the first derivative of the first Lyapunov function is not greater than 0, i.e
In this case, the previously obtained error transfer dynamics model, the rewritten error transfer dynamics model, and the disturbance estimation error are described as being stable. Thus, by calculation, the value of +.>
When the corresponding prescribed performance controller needs to be designed as:
thus, can be performed by the formula (18)
On the basis of which the input torque of the robot system is calculated by means of the formula (11)>
Wherein->
The specific formula can be obtained by using an interference observer as follows:
in the method, in the process of the invention,
for the sliding mode function, +.>
To prescribe performance controller gain, +.>
For disturbance estimation, i.e. the actual disturbance +.>
Estimated value of ∈10->
Is a positive gain matrix.
3) Evaluating disturbance according to equation (19)
Is the first derivative of (a):
in the method, in the process of the invention,
is the first derivative of the disturbance estimate.
4) Estimating an error by perturbation according to equation (15) and equation (20)
And the first derivative of the disturbance estimate +.>
The first derivative of the disturbance estimation error is calculated, and the specific formula is as follows:
in the method, in the process of the invention,
error is estimated for disturbance +.>
For the first derivative of the disturbance estimation error, +.>
Is a positive gain matrix.
5) Substituting the formulas (18) and (21) into the formula (17), and calculating to obtain the first derivative of the first Lyapunov function:
as can be seen from the analysis formula (22), in order to make
Should be +.>
. It is assumed that the rate of change of external disturbance is +.>
It can still be considered as unknown bounded, i.e.>
. From the inequality it can be derived:
substituting the above equation (23) into equation (22) can yield:
wherein, the liquid crystal display device comprises a liquid crystal display device,
in the method, in the process of the invention,
to prescribe performance controller gain, +.>
Is a positive gain matrix>
Is a unit vector.
From the above, it can be derived that: when the first derivative of the Lyapunov function
Less than zero, thenMeaning that the robot system is position error after conversion +.>
Trend toward 0 and asymptotically stabilize.
From the following components
And equation (18) computes a specified performance controller, which can be expressed as:
in the method, in the process of the invention,
is the input torque of the robot system.
In one embodiment, S4 specifically includes:
s41, presetting an impedance model and a spring model, and deducing a contact force error of the end effector according to the impedance model and the spring model;
s42, obtaining a force tracking error transfer dynamics model according to the contact force error and the impedance model of the end effector;
s43, designing environmental rigidity estimation, namely designing second and third Lyapunov functions according to the force tracking error transfer dynamics model and the environmental rigidity estimation, and deriving first derivatives of the environmental rigidity estimation through the second and third Lyapunov functions;
s44, obtaining a contact force estimation of the end effector of the robot system according to the first derivative of the environmental stiffness estimation and the spring model;
s45, obtaining the position of the end effector of the robot system according to the contact force error and the impedance model of the end effector.
In one embodiment, the force tracking error transfer dynamics model in S42 is specifically:
in the method, in the process of the invention,
、/>
、/>
inertia, damping and stiffness of the impedance model of the i-th robot, respectively,/i>
For the i-th robot environmental stiffness +.>
Estimated value of ∈10->
Error of contact force for the ith robot end effector, +.>
And->
Contact force errors of the i-th robotic end effector, respectively +.>
First and second derivatives of +.>
。
In one embodiment, the contact force estimation of the robotic system end effector in S44 is given by:
in the method, in the process of the invention,
estimating for the contact force of the ith robot end effector,/for the contact force of the ith robot end effector>
For the i-th robot environmental stiffness +.>
Estimate of->
For the position of the i-th robotic end effector,/->
Is the position of the target object.
In one embodiment, the position of the end effector of the robotic system in S45 is specifically expressed as:
in the method, in the process of the invention,
position of i-th robot end effector output for impedance model, +.>
First derivative of the i-th robot end effector position output for the impedance model, +.>
The i-th robot end effector position input for impedance model, < >>
，/>
、/>
Inertia, damping and stiffness of the ith impedance model, respectively,/->
And->
First and second derivatives of the ith robot end effector position, respectively, input for the impedance model,/->
For the position error of the ith robot end effector,/->
For the i-th robot environmental stiffness +.>
Is a function of the estimate of (2).
Specifically, considering the handling safety of the end effector of the robot system, designing an impedance control method, and calculating to obtain the contact force estimation of the end effector of the robot system and the position of the end effector of the robot system, wherein the process is as follows:
1) Defining generalized target impedance models
In the method, in the process of the invention,
end effector position output for the ith robot impedance model, i.e. impedance reference position output, +.>
End effector position input for the ith robot impedance model, +.>
，/>
、/>
Inertia, damping and stiffness of the ith impedance model, respectively,/->
Is the contact force error of the ith robotic end effector.
2) Defining a contact force error of the end effector:
in the method, in the process of the invention,
error of contact force for the ith robot end effector, +.>
Reference contact force (simply referred to as reference force) for the i-th robot end effector,>
the actual contact force (simply referred to as the actual force) of the i-th robotic end effector. In practical application, the actual force of the end effector +.>
Can be obtained from a spring model, which can be expressed as:
in the method, in the process of the invention,
for the position of the i-th robotic end effector,/->
For the position of the target object->
Environmental stiffness of the i-th robot, +.>
。/>
3) The position of the robot end effector is calculated from equations (27) and (28):
assuming that the position of the robot end effector reaches the position of the end effector output by the impedance model, i.e
From equations (28) and (29) it can be derived:
in the method, in the process of the invention,
error of contact force for the ith robot end effector, +.>
For the stiffness of the i-th impedance model,
reference force for the ith robot end effector,/->
The i-th robot end effector position input for impedance model, < >>
Is the ith robot environmental stiffness.
From the above equation (30), once the robot system reaches a steady state, the contact force error of the i-th robot end effector is calculated to be the steady state
Equal to 0 (i.e.)>
) The following conditions must be satisfied:
is provided with
For the i-th robot environmental stiffness +.>
Is estimated by the environmental stiffness>
Instead of the environmental stiffness in equations (29) and (31), respectively:
definition of the definition
For the position error of the ith robot end effector,/->
Subtracting the above formulas (32) and (33) yields the relationship between the contact force error of the end effector and the position error of the end effector:
in the method, in the process of the invention,
error of contact force for the ith robot end effector, +.>
For the position error of the ith robot end effector,/->
Is the estimated value of the environmental rigidity of the ith robot.
Substituting equation (34) into the impedance model in equation (26) to obtain a force tracking error transfer dynamics model:
defining an environmental stiffness estimation error:
in the method, in the process of the invention,
an error is estimated for the ith robot environmental stiffness.
Based on the force tracking error transfer dynamics model in equation (35), consider the contact force error of the ith robotic end effector
Error of estimation of stiffness to environment>
Setting a second Lyapunov function:
in the method, in the process of the invention,
for the second Lyapunov function, < ->
For mathematical notation, we mean summing the elements on the diagonal inside the matrix.
Solving the first derivative of the second lyapunov function:
setting a third Lyapunov function:
in the method, in the process of the invention,
is a third lyapunov function.
Solving the first derivative of the third lyapunov function:
first derivative of second Lyapunov function
And the first derivative of the third Lyapunov function +.>
The summation can be given by:
from the analysis of equation (41), it can be seen that in order to make the contact force error of the end effector
Convergence should be such that
The first derivative of the design environmental stiffness estimate is therefore as follows:
substituting equation (42) into equation (41) can yield:
in summary, the contact force error of the ith robotic end effector tends to infinity over time
The contact force estimate for the robotic end effector can be derived from the first derivative of the environmental stiffness estimate designed in equation (42) and the spring model in equation (28):
according to the impedance model in equation (26) and the contact force error of the end effector in equation (34)
The position of the end effector of the robot can be calculated by the following specific formula: />
In the method, in the process of the invention,
the position of the i-th robot end effector output for the impedance model, i.e. the impedance reference position output, +.>
First derivative of the i-th robot end effector position output for the impedance model, +.>
The i-th robot end effector position input for impedance model, < >>
，/>
、/>
The inertia, damping and stiffness of the ith impedance model,
and->
First and second derivatives of the ith robot end effector position, respectively, input for the impedance model,/->
For the position error of the ith robot end effector,/->
For the i-th robot environmental stiffness +.>
Is a function of the estimate of (2).
And finally, constructing a mathematical simulation model according to the cooperative transportation dynamics model, the error transfer dynamics model and the specified performance controller, inputting the calculated input moment of the robot system, the contact force estimation and the position of the robot end effector into the simulation model, and verifying the effectiveness of the cooperative transportation control method of the robot system. The method mainly comprises the following steps:
in the free motion process of the robot, calculating the position error of the robot by the reference position and the actual position of the robot
Converting the position error of the robot through an error conversion function to obtain a position error after the conversion of the robot system, obtaining an error transfer dynamics model according to the position error after the conversion of the robot system and the collaborative transport dynamics model, and settingThe performance controller is defined and the input moment required by the movement of the robot system is calculated>
After which the input moment is->
Inputting the position calculation formula of the robot end effector to a cooperative conveyance dynamics model to cooperatively convey the plurality of robots, and in the cooperative conveyance process, calculating the position of the robot end effector from the position calculation formula of the robot end effector, and inputting the position calculation formula to a robot system to calculate a position error->
Thereby realizing robot position control.
Specifically, the simulation curves verify position tracking performance and force estimation performance. Referring to fig. 5 to 11, fig. 5, 6 and 7 are respectively x-axis component control errors of the robots 1, 2 and 3 in the process of co-carrying three robots according to an embodiment of the present invention; FIG. 8 is an effect diagram of a three robot co-handling process in accordance with one embodiment of the present invention; fig. 9, 10 and 11 are diagrams showing force tracking effects of the three robots 1, 2 and 3, respectively, in the cooperative conveyance process according to an embodiment of the present invention.
As can be seen from fig. 5 to fig. 7, the robot moving platform is strictly limited within the error safety range in the process of carrying, so that the precision and safety of the carrying process are ensured; FIG. 8 is an effect diagram of a cooperative carrying process of three robots, and as can be seen from FIG. 8, the robots can complete track tracking with smaller errors; in fig. 9 to 11, the mechanical arm can perform tracking control of a desired force, and safety in handling is ensured.
The multi-robot cooperative transportation capacity position hybrid control method has the following advantages:
1. the strict error control of a plurality of robots is realized by designing a specified performance controller, so that the precision in the carrying process is ensured;
2. the contact force estimation and the impedance control of the end effector of the robot are designed by adopting the self-adaptive impedance force control method, so that the safety performance of the robot in the carrying process is ensured.
The multi-robot cooperative transportation capacity hybrid control method provided by the invention is described in detail above. The principles and embodiments of the present invention have been described herein with reference to specific examples, the description of which is intended only to facilitate an understanding of the core concepts of the invention. It should be noted that it will be apparent to those skilled in the art that various modifications and adaptations of the invention can be made without departing from the principles of the invention and these modifications and adaptations are intended to be within the scope of the invention as defined in the following claims.
Claims (8)
1. A multi-robot cooperative transport capacity hybrid control method, the method comprising:
s1, establishing a carrying dynamics model of a robot, and establishing a cooperative carrying dynamics model of a robot system formed by a plurality of robots according to the carrying dynamics model of the robot;
s2, setting a robot position error, and converting the robot position error by introducing an error conversion function to obtain a robot converted position error, and obtaining an error transfer dynamics model according to the robot converted position error and the collaborative handling dynamics model;
s3, rewriting the error transfer dynamics model to obtain a rewritten error transfer dynamics model, setting a sliding mode function and a disturbance estimation error, designing a specified performance controller according to the rewritten error transfer dynamics model, the sliding mode function and the disturbance estimation error, and calculating the input torque of the robot system according to the specified performance controller;
s4, presetting an impedance model, a spring model and environmental stiffness estimation, designing an impedance control method according to the impedance model, the spring model and the environmental stiffness estimation, and calculating the contact force estimation and the position of the end effector of the robot system;
s5, constructing a mathematical simulation model according to the cooperative transportation dynamics model, the error transfer dynamics model and the specified performance controller, inputting the calculated input moment of the robot system, the contact force estimation and the position of the end effector of the robot system into the simulation model, and verifying the effectiveness of the cooperative transportation control method of the robot system;
the step S3 specifically comprises the following steps:
s31, rewriting the error transfer dynamics model to obtain a rewritten error transfer dynamics model, wherein the rewritten error transfer dynamics model comprises a specified performance controller;
s32, setting a sliding mode function according to the position error after the conversion of the robot system in the step S23;
s33, setting a disturbance estimation error, and setting a first Lyapunov function according to the sliding mode function and the disturbance estimation error;
s34, judging the stability of the error transfer dynamics model according to the first Lyapunov function, and designing a corresponding specified performance controller when the error transfer dynamics model is stable;
the specific performance controller in S34 may be specifically expressed as:
2. The multi-robot cooperative transportation capacity bit mixture control method according to claim 1, wherein the cooperative transportation dynamics model in S1 is specifically:
3. The multi-robot cooperative transportation capacity bit mixture control method according to claim 2, wherein S2 specifically comprises:
s21, setting specified performance and performance function of the robot, and determining position error of the robot according to the specified performance and performance function;
s22, setting an error conversion function, and converting the position error of the robot by using the error conversion function to obtain the position error after the robot is converted;
s23, building a robot system post-conversion position error according to the robot post-conversion position error, processing the robot system post-conversion position error, and combining the collaborative handling dynamics model to obtain an error transfer dynamics model.
4. The multi-robot cooperative transportation capacity bit mixture control method of claim 3, wherein the error transfer dynamics model in S23 has a specific formula:
5. The multi-robot cooperative transportation capacity bit mixture control method according to claim 1, wherein S4 specifically comprises:
s41, presetting an impedance model and a spring model, and deducing a contact force error of the end effector according to the impedance model and the spring model;
s42, obtaining a force tracking error transfer dynamics model according to the contact force error of the end effector and the impedance model;
s43, designing an environmental stiffness estimation, designing second and third Lyapunov functions according to the force tracking error transfer dynamics model and the environmental stiffness estimation, and deriving a first derivative of the environmental stiffness estimation through the second and third Lyapunov functions;
s44, obtaining a contact force estimation of the end effector of the robot system according to the first derivative of the environmental stiffness estimation and the spring model;
s45, obtaining the position of the end effector of the robot system according to the contact force error of the end effector and the impedance model.
6. The multi-robot cooperative transportation capacity bit mixture control method according to claim 5, wherein the force tracking error transfer dynamics model in S42 is specifically:
7. The method for controlling the hybrid of the cooperative conveyance capacities of multiple robots as claimed in claim 6, wherein the contact force estimation of the end effector of the robot system in S44 is as follows:
8. The method for controlling the hybrid of the cooperative transportation capacity of multiple robots according to claim 7, wherein the position of the end effector of the robot system in S45 is as follows:
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