CN116810803B - Robust control method for joint module of cooperative robot - Google Patents
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Abstract
The invention relates to the field of robot joint module control, in particular to a robust control method for a cooperative robot joint module, which comprises the following steps: establishing a general dynamics model A of a constrained joint module system according to uncertain factors in a mechanical system, determining a dynamics model B of the joint module system optimized for friction force in a harmonic reducer in a magnetic field directional control mode, obtaining ideal nominal constraint force by combining the dynamics model A with the dynamics model B, determining robust control force according to the uncertain factors, and obtaining control force of a joint module of a cooperative robot according to the ideal nominal constraint force and the robust control force. According to the invention, by determining the external interference and uncertain factors of system parameters, the accurate control of the joint module system is realized, the anti-interference capability of the joint module of the cooperative robot is obviously improved, and the response speed and stability of the joint module of the cooperative robot can be improved.
Description
Technical Field
The invention relates to the field of robot joint module control, in particular to a robust control method for a joint module of a cooperative robot.
Background
With the increasing application of robots in social production and life, how robots cooperate with people becomes a popular research direction. In order to achieve the aim, the cooperative robot has the advantages of combining the efficiency of the robot and the wisdom of human beings, having the advantages of flexibility, safety, convenience and the like, and can remarkably promote the development of manufacturing industry. The joint module is an indispensable power source of the cooperative robot, and is widely applied to the cooperative robot due to the advantages of compact structure, quick response to electric signals, high transmission efficiency, stable operation and the like.
The cooperative robot may encounter uncertain factors such as load torque disturbance, electromagnetic disturbance, friction of a harmonic reducer and the like during actual application, and the control precision of the joint module is easily affected due to high complexity of the joint module system.
Disclosure of Invention
Aiming at the defects existing in the prior art, the invention provides the following technical scheme:
a robust control method of a joint module of a cooperative robot comprises the following steps:
s1, establishing a general dynamic model A of the constrained joint module system according to uncertain factors in the mechanical system.
S2, determining a dynamic model B of the joint module system which is optimized for friction force in the harmonic reducer in a magnetic field orientation control mode.
S3, dividing the control force into an ideal nominal constraint force and a robust control force according to the active constraint of the target task and the uncertain factors in the joint module system.
S4, combining the dynamic model A with the dynamic model B to obtain ideal nominal constraint force, and determining robust control force according to uncertain factors.
S5, obtaining the control force of the joint module of the cooperative robot according to the ideal nominal constraint force and the robust control force.
As an improvement of the above solution, the step S1 considers a general dynamic model a of uncertainty factors, including the following formula:
wherein t represents the time in the collaborative robot system,represents the angle of a joint in a collaborative robotic system, < >>Represents angular velocity in a collaborative robotic system, < >>Represents angular acceleration in a collaborative robotic system, < >>R n Represents an n-dimensional space, delta (t) represents an uncertain parameter in a mechanical system, and tau represents a joint moduleThe control inputs of the system, M, G, C, F represent the inertial matrix of the system, G represents the gravitational force of the system, C represents the Coriolis force and centrifugal force matrix of the joint module system, and F represents the external forces of the joint module system.
As an improvement of the above technical solution, the step S2 includes the following steps:
s21: and establishing a dynamic model C of the permanent magnet synchronous motor in a magnetic field directional control mode.
S22: and determining the output torque of the harmonic speed reducer according to the transmission efficiency and the transmission ratio of the harmonic speed reducer in the joint module.
S23: substituting the friction force in the harmonic reducer and the output torque of the harmonic reducer into the dynamics model C to obtain a dynamics model B of the joint module system which is optimized for the friction force in the harmonic reducer.
As an improvement of the above technical solution, the dynamic model B of the joint module system optimized for the friction force in the harmonic reducer obtained in step S23 includes the following formula:
wherein T is D For the output torque of the speed reducer, lambda is the speed reduction ratio, eta is the transmission efficiency and T e Is the electromagnetic torque of a permanent magnet synchronous motor, T f As a friction torque in a harmonic reducer,for the moment of inertia of the permanent magnet synchronous motor, +.>The viscous friction coefficient of the permanent magnet synchronous motor.
As an improvement of the above technical solution, the step S3 includes the following steps:
s31: and determining the active constraint imposed by the joint module system according to the target task.
S32: the control force is divided into an ideal nominal constraint force and a robust control force according to the active constraint and the uncertainty factor existing in the system.
As an improvement of the above technical solution, the step S4 includes the following steps:
s41: and establishing a constraint matrix according to the active constraint of the target task.
S42: and obtaining an ideal nominal constraint force according to the constraint matrix and the UK equation.
S43: and obtaining the robust control force according to the condition of the initial condition compatibility and the influence condition of the uncertain factors in the operation of the joint module system.
As an improvement of the above technical solution, the ideal nominal constraint force obtained in the step S42 is:
wherein,for ideal nominal binding force, +.>For a nominal inertial matrix, +.>For the nominal external force set, X is a constraint coefficient matrix, b is a second-order constraint vector, c is a first-order constraint vector, and lambda is a reduction ratio.
The robust control force obtained in the step S43 is:
wherein Q is r For robust control force, u 1 To cope with initial condition incompatibility caused by uncertainty, u 2 The method is used for processing the influence condition of uncertain factors in the operation of the system on the joint module system.
As an improvement of the above-mentioned solution, the control force obtained in step S5 depends on the following formula:
wherein,to be an ideal nominal constraint force, Q r Is a robust control force.
The invention has the beneficial effects that:
by determining uncertain factors of external interference and system parameters and optimizing uncertain factors such as load torque disturbance, electromagnetic disturbance, friction of a harmonic reducer, gear clearance and the like in a magnetic field directional control mode, accurate control of a joint module system can be achieved, the anti-interference capability of the joint module of the cooperative robot is remarkably improved, and meanwhile the response speed and stability of the joint module can be improved.
Drawings
FIG. 1 is a connection state diagram of a joint module of a cooperative robot of the present invention;
FIG. 2 is a graph of step signal angle tracking trajectories and errors obtained in simulation of the present invention;
FIG. 3 is a graph of the angular tracking trace of sinusoidal signals obtained in simulation of the present invention;
FIG. 4 is a graph of the angle tracking trajectory error of the sinusoidal signal obtained in the simulation of the present invention;
FIG. 5 is a graph of the step signal angle tracking trajectory and error obtained through experimentation in the present invention;
FIG. 6 is a graph of a sinusoidal signal angle tracking trajectory obtained through experimentation in the present invention;
FIG. 7 is a graph of the angle tracking trajectory error of the sinusoidal signal obtained through experimentation in the present invention;
wherein, fig. 2, fig. 3 and fig. 4 are obtained by constructing a controller model in MATLAB/Simulink and performing simulation, and fig. 5, fig. 6 and fig. 7 are obtained by performing experiments in a rapid control prototype platform CSPACE and a joint module experimental platform.
Detailed Description
The present invention will be described in further detail with reference to the drawings and examples, in order to make the objects, technical solutions and advantages of the present invention more apparent. It should be understood that the specific embodiments described herein are for purposes of illustration only and are not intended to limit the scope of the invention.
The uncertainty factors such as load torque disturbance, electromagnetic disturbance, friction of a harmonic reducer and the like can be encountered by the cooperative robot in practical application, and the uncertainty factors easily cause the control precision of the joint module to be affected because of the high complexity of the joint module system.
In order to solve the problem, a robust control method of a joint module of a cooperative robot is provided, which comprises the following steps:
s1, establishing a general dynamic model A of the constrained joint module system according to uncertain factors in the mechanical system.
The cooperative robot mainly comprises a joint module and a serial connecting rod, wherein the joint module system is used as a power source of each joint of the cooperative robot and mainly comprises a permanent magnet synchronous motor and a harmonic reducer (shown in figure 1), is a typical motor-gear system, and the dynamic performance of the joint module has very important influence on the overall dynamic performance of the cooperative robot.
Therefore, prior to designing a controller for a constrained mechanical system, a kinetic model of the constrained joint model system must be established, including a general kinetic model a of the joint model system that takes into account uncertainty factors and constraint equations.
Specifically, the general kinetic model a is as follows:
wherein t represents the time in the collaborative robot system,represents the angle of a joint in a collaborative robotic system, < >>Represents angular velocity in a collaborative robotic system, < >>Represents angular acceleration in a collaborative robotic system, < >>R n The n-dimensional space is represented, delta (t) represents an uncertain parameter in the mechanical system, tau represents a control input of the joint module system, M represents an inertial matrix of the system, G represents a gravitational force of the system, C represents a Coriolis force and centrifugal force matrix of the joint module system, and F represents an external force of the joint module system.
After the general dynamic model a is established, the control of the joint module system needs to be optimized for these uncertainty factors, as shown in step S2.
S2, determining a dynamic model B of the joint module system which is optimized for friction force in the harmonic reducer in a magnetic field orientation control mode.
Specifically, the step S2 includes the following steps:
s21: and establishing a dynamic model C of the permanent magnet synchronous motor in a magnetic field directional control mode.
The magnetic field directional control, namely FOC, has good control capability in the whole torque and speed range, can ensure the accuracy of model establishment, and specifically, the dynamic model C of the permanent magnet synchronous motor is as follows:
wherein i is q Representing stator current on q-axis, n p Represents the pole pair number, ψ f Represents the rotor flux linkage, ω represents the rotor angular velocity,indicating angular acceleration of rotor, T e Electromagnetic torque of a permanent magnet synchronous motor, +.>Is the rotational inertia of the permanent magnet synchronous motor,viscous friction coefficient, T, of permanent magnet synchronous motor L Is the load torque of the permanent magnet synchronous motor.
Since the output shaft of the permanent magnet synchronous motor is connected to the harmonic reducer (as shown in fig. 1), and the robot joint is controlled to perform angular motion by the permanent magnet synchronous motor, the influence of the output torque of the harmonic reducer on the control of the permanent magnet synchronous motor needs to be considered on this basis, and step S22 is performed based on this.
S22: and determining the output torque of the harmonic speed reducer according to the transmission efficiency and the transmission ratio of the harmonic speed reducer in the joint module.
The permanent magnet synchronous motor controls the joints of the robot to perform angular motion by connecting an output shaft with the harmonic reducer, and the mathematical model of the permanent magnet synchronous motor is simplified and expressed as:
T D ＝ληT L (2)
Wherein T is D The output torque of the harmonic speed reducer is represented by lambda as the speed reduction ratio and eta as the transmission efficiency.
According to the above mathematical model, the output torque of the harmonic reducer is calculated, and since the harmonic reducer itself is not in a completely smooth state, and there is interference of friction factors in the process of outputting the torque, it is also necessary to optimize the friction of the harmonic reducer, and based on this, step S23 is executed.
S23: substituting the friction force in the harmonic reducer and the output torque of the harmonic reducer into the dynamics model C to obtain a dynamics model B of the joint module system which is optimized for the friction force in the harmonic reducer.
When optimizing the influence of friction force of the harmonic reducer, the moment of inertia and the viscous friction coefficient of the permanent magnet synchronous motor need to be considered, and based on the moment of inertia and the viscous friction coefficient, the method firstly causesThen will->T is as follows L The values of (2) are substituted into 1 to calculate the electromagnetic torque of the permanent magnet synchronous motor, and finally the dynamic model B of the joint module system optimized for the friction force of the harmonic reducer is obtained as follows:
wherein T is D For the output torque of the speed reducer, lambda is the speed reduction ratio, eta is the transmission efficiency and T e Is the electromagnetic torque of a permanent magnet synchronous motor, T f As a friction torque in a harmonic reducer,for the moment of inertia of the permanent magnet synchronous motor, +.>The viscous friction coefficient of the permanent magnet synchronous motor.
The calculation of the electromagnetic torque of the permanent magnet synchronous motor by the dynamics model B is primarily optimized for the friction force in the harmonic reducer, and on the basis of the calculation, the calculation needs to be optimized again for the uncertain factors in the joint module system, and for this reason, the following formulas are obtained according to the dynamics model A by rewriting M (inertia matrix of the joint module system), C (Coriolis force and centrifugal force matrix of the joint module system) and F (external force of the joint module system):
in most applications, the permanent magnet synchronous motor is usually operated in a horizontal position or slightly tilted, the influence of gravity on its movement being small, so that the influence of gravity can be neglected here, in such a way that the complexity of the model is simplified, so that the gravity is regarded here as 0, i.e. g=0, on the basis of which step S3 is further performed.
S3, dividing the control force into an ideal nominal constraint force and a robust control force according to the active constraint of the target task and the uncertain factors in the joint module system.
Specifically, the step S3 includes the following steps:
s31: and determining the active constraint imposed by the joint module system according to the target task.
Because the tasks are different, the established active constraints are different, but the active constraints can be finally expressed in a standard second-order constraint matrix form, the target task is needed to be defined first, the active constraint suffered by the current joint module system is determined according to the target task, the constraint force is determined on the basis of the target task, and the step S32 is executed on the basis.
S32: the control force is divided into an ideal nominal constraint force and a robust control force according to the active constraint and the uncertainty factor existing in the system.
The differentiation of the control forces is only a theoretical differentiation and the ideal nominal constraint force and the robust control force are not actually obtained, and step S4 is performed in order to actually represent these two forces.
S4, combining the dynamic model A with the dynamic model B to obtain ideal nominal constraint force, and determining robust control force according to uncertain factors.
Specifically, the step S4 includes the following steps:
s41: and establishing a constraint matrix according to the active constraint of the target task.
The active constraint of the target task is expressed in the form of a standard matrix, and three layers of matrixes are generally established for expression, specifically including:
zero order constraint:
first order constraint:
second order constraint:
wherein Y= [ Y ] i ] m×n For zero order constraint matrix, d= [ d ] 1 ,d 2 ,···d n ] T For zero order constraint vector, x= [ X ] i ] m×n Constraint coefficient matrix, c= [ b ] 1 ,b 2 ,···b m ] T B= [ c ] as a first-order constraint vector 1 ,c 2 ,···c m ] T Is a second order constraint vector.
S42: and obtaining an ideal nominal constraint force according to the constraint matrix and the UK equation.
The UK equation refers to the Udwadia-Kalaba equation, i.e., a constrained display motion equation.
By applying additional generalized constraint forces to the joint model system, the resulting constrained explicit equations of motion can be written as:
where Q represents a known set of external forces, which can be expressed as:Q c representing a constraint force matrix.
The exact expression given for the ideal nominal constraint in the UK equation is:
Y＝XM -1/2
Q c ＝M 1/2 Y + (b-XM -1 Q)
wherein the symbol + represents the mole-penrose generalized inverse.
Thus, the constrained explicit motion equation combined with the UK equation is:
after combining the constraint matrix of three layers with the UK equation, the ideal nominal constraint force is obtained as follows:
wherein,for ideal nominal binding force, +.>For a nominal inertial matrix, +.>For the nominal external force set, X is a constraint coefficient matrix, c is a second-order constraint vector, b is a first-order constraint vector, and lambda is a reduction ratio.
S43: and obtaining the robust control force according to the condition of the initial condition compatibility and the influence condition of the uncertain factors in the operation of the joint module system.
In the joint module system, the uncertainty factor is recorded as u for the initial condition compatibility 1 The influence of the operation of the joint module system is marked as u 2 Specific:
in the calculation u 1 When the constraint is maintained, firstly, determining the constraint maintenance error, specifically:
according to the error kept by the constraint, calculating the compatibility of the uncertain factors to the initial conditions, specifically:
wherein k is a compatible gain coefficient, P is a control parameter, ζ is a constraint maintenance error, X is a constraint coefficient matrix, and k >0, P >0.
In the calculation u 2 When first determining the uncertainty part of the inverse inertia matrix.
Wherein,is the nominal inertial matrix.
Then, according to the uncertainty part of the inverse inertia matrix, determining an uncertainty factor upper bound in the joint module system, specifically:
wherein,is the upper bound of uncertainty factor in the joint module system, P is the control parameter, ++>For an ideal nominal constraint force, X is a constraint coefficient matrix, Q is a known set of external forces, and ΔQ is the uncertainty portion of the known set of external forces.
Determining an uncertainty error convergence function according to an uncertainty factor upper bound in the joint module system, wherein the uncertainty error convergence function is specifically as follows:
determining a limit function of the joint module system under the uncertain factors according to the upper limit of the uncertain factors in the joint module system, wherein the limit function is specifically as follows:
wherein,for the limit constant +.>The value selection needs to meet the following conditions:
wherein,is a boundary matrix, which can be expressed as
Wherein,for a nominal inverse inertial matrix->
For shifting the inertia matrix>Wherein I is a unit array.
According to the limit function of the joint module system under the uncertain factors, the upper limit of the uncertain factors in the joint module system and the uncertain error convergence function, the influence condition of the uncertain factors in the operation of the joint module system is obtained, specifically:
wherein k is>0 is a compatible gain coefficient, P>0 is a control parameter, ζ is a constraint maintenance error, X is a constraint coefficient matrix,for an uncertainty error convergence function, +.>For the upper bound of uncertainty, +_>Is a boundary function of the joint module system under uncertain factors.
The obtained robust control force is represented by u 1 And u is equal to 2 The composition specifically comprises:
wherein Q is r For robust control force, u 1 To cope with initial condition incompatibility caused by uncertainty, u 2 The method is used for processing the influence condition of uncertain factors in the operation of the system on the joint module system.
After obtaining the ideal nominal constraint force and the robust control force, step S5 is performed.
S5, obtaining the control force of the joint module of the cooperative robot according to the ideal nominal constraint force and the robust control force.
The control force obtained in said step S5 depends on the following formula:
wherein,to be an ideal nominal constraint force, Q r Is a robust control force.
In order to verify the actual performance of the model, a controller model of the embodiment is built in Matlab/Simulink, and numerical simulation is carried out by taking step signals and sine signals as expected tracks, as shown in fig. 2, 3 and 4, ref represents the expected tracks, 1 represents a PID algorithm, and 2 represents the scheme provided by the invention.
In order to further verify the actual performance of the model, the embodiment performs experiments based on a rapid control prototype platform CSPACE and a joint module experiment platform, and designs a step track and sine track following experiment on the basis of numerical simulation.
The experimental platform mainly comprises a cooperation robot joint module, a position sensor, a CSPACE control box, an industrial PC (personal computer), a magnetic powder brake and the like, wherein a controller model of the embodiment is built in Matlab/Simulink software and is converted into a controller capable of running on the Matlab/Simulink, and then the controller is compiled in CCS (Compose code Studio) software and runs on the CSPACE platform, and the control result is graphically displayed in real time through the CSPACE and a computer, so that experimental variables are observed and control parameters are modified.
As shown in fig. 5, 6 and 7, ref represents a desired track, 1 represents a PID algorithm, 2 represents a scheme proposed by the present embodiment, and as can be seen from the figure, the algorithm proposed by the present invention provides higher steady-state tracking accuracy and faster transient response for the joint module of the cooperative robot.
Therefore, by adopting the method described in the embodiment, accurate control can be realized, the anti-interference capability of the joint module of the cooperative robot is obviously improved, and the response speed and stability of the system can be improved.
The above embodiments are only for illustrating the technical solution of the present invention, and are not limiting.
Claims (5)
1. The robust control method of the joint module of the cooperative robot is characterized by comprising the following steps:
s1, establishing a general dynamics model A of a constrained joint module system according to uncertain factors in a mechanical system;
s2, determining a dynamic model B of the joint module system which is optimized for the friction force in the harmonic reducer in a magnetic field directional control mode;
s3, dividing the control force into an ideal nominal constraint force and a robust control force according to the active constraint of the target task and uncertain factors in the joint module system;
s4, an ideal nominal constraint force is obtained by combining the dynamic model A with the dynamic model B, and a robust control force is determined according to uncertain factors;
s5, obtaining the control force of the joint module of the cooperative robot according to the ideal nominal constraint force and the robust control force;
the step S2 includes the steps of:
s21: establishing a dynamic model C of the permanent magnet synchronous motor in a magnetic field directional control mode;
s22: determining output torque of the harmonic reducer according to the transmission efficiency and the transmission ratio of the harmonic reducer in the joint module;
s23: substituting the friction force in the harmonic reducer and the output torque of the harmonic reducer into a dynamics model C to obtain a dynamics model B of the joint module system which is optimized for the friction force in the harmonic reducer;
the step S3 includes the steps of:
s31: determining active constraint imposed by the joint module system according to the target task;
s32: dividing the control force into an ideal nominal constraint force and a robust control force according to the active constraint and uncertain factors existing in the system;
the step S4 includes the steps of:
s41: establishing a constraint matrix according to the active constraint of the target task;
s42: obtaining an ideal nominal constraint force according to the constraint matrix and the UK equation;
s43: and obtaining the robust control force according to the condition of incompatibility of the uncertain factors on the initial conditions and the condition of influence in the operation of the joint module system.
2. The robust control method of a joint module of a cooperative robot according to claim 1, wherein: the step S1 considers a general dynamic model a of uncertainty factors, including the following formula:
wherein t represents the time in the collaborative robot system,represents the angle of a joint in a collaborative robotic system, < >>Represents angular velocity in a collaborative robotic system, < >>Represents angular acceleration in a collaborative robotic system, < >>R n The n-dimensional space is represented, delta (t) represents an uncertain parameter in the mechanical system, tau represents a control input of the joint module system, M represents an inertial matrix of the system, G represents a gravitational force of the system, C represents a Coriolis force and centrifugal force matrix of the joint module system, and F represents an external force of the joint module system.
3. The robust control method of a joint module of a cooperative robot according to claim 2, wherein: the dynamic model B of the joint module system optimized for the friction force in the harmonic reducer obtained in the step S23 includes the following formula:
wherein T is D For the output torque of the speed reducer, lambda is the speed reduction ratio, eta is the transmission efficiency and T e Is the electromagnetic torque of a permanent magnet synchronous motor, T f As a friction torque in a harmonic reducer,for the moment of inertia of the permanent magnet synchronous motor, +.>The viscous friction coefficient of the permanent magnet synchronous motor.
4. The robust control method of a joint module of a cooperative robot according to claim 2, wherein:
the ideal nominal constraint force obtained in the step S42 is:
wherein,for ideal nominal binding force, +.>For a nominal inertial matrix, +.>For the nominal external force set, X is a constraint coefficient matrix, b is a second-order constraint vector, c is a first-order constraint vector, and lambda is a reduction ratio;
the robust control force obtained in the step S43 is:
wherein Q is r For robust control force, u 1 To cope with initial condition incompatibility caused by uncertainty, u 2 The method is used for processing the influence condition of uncertain factors in the operation of the system on the joint module system.
5. The robust control method of a joint module of a cooperative robot according to claim 2, wherein: the control force obtained in said step S5 depends on the following formula:
wherein,to be an ideal nominal constraint force, Q r Is a robust control force.
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