CN111730594A - Decentralized control method and system for face-to-face collision of modular robot - Google Patents

Decentralized control method and system for face-to-face collision of modular robot Download PDF

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CN111730594A
CN111730594A CN202010528464.5A CN202010528464A CN111730594A CN 111730594 A CN111730594 A CN 111730594A CN 202010528464 A CN202010528464 A CN 202010528464A CN 111730594 A CN111730594 A CN 111730594A
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state space
friction
model
torque
space expression
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董博
门小东
张振国
周帆
李元春
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Changchun University of Technology
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Changchun University of Technology
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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
    • B25J9/1602—Programme controls characterised by the control system, structure, architecture
    • B25J9/1605—Simulation of manipulator lay-out, design, modelling of manipulator
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B25—HAND TOOLS; PORTABLE POWER-DRIVEN TOOLS; MANIPULATORS
    • B25J—MANIPULATORS; CHAMBERS PROVIDED WITH MANIPULATION DEVICES
    • B25J9/00—Programme-controlled manipulators
    • B25J9/08—Programme-controlled manipulators characterised by modular constructions
    • 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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  • Engineering & Computer Science (AREA)
  • Robotics (AREA)
  • Mechanical Engineering (AREA)
  • Automation & Control Theory (AREA)
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  • Feedback Control In General (AREA)

Abstract

The invention relates to a decentralized control method and a decentralized control system for face-to-face collision of a modular robot, wherein the decentralized control method comprises the following steps: determining a torque based on a model of harmonic drive compliance and friction; establishing a dynamic model for each module subsystem in the robot; carrying out decoupling separation uncertainty through a state space expression based on a dynamic model to obtain a state space expression after decoupling separation; converting the decoupled and separated state space expression to obtain a converted state space expression; respectively compensating unknown terms, model uncertain terms and coupling terms in the converted state space expression by adopting an RBF neural network based on the converted state space expression; constructing a decentralized controller of the modular robot system based on the unknown item, the model uncertainty item and the coupling item; and controlling the robot based on the decentralized controller of the modular robot system. The invention can effectively improve the performance of the modular robot and weaken buffeting influence.

Description

Decentralized control method and system for face-to-face collision of modular robot
Technical Field
The invention relates to the field of automatic control, in particular to a method and a system for decentralized control of face-to-face collision of a modular robot.
Background
The modular robot is composed of joint modules with interfaces of uniform standards, the modules can be freely added and deleted to be combined into different configurations according to different working environments and tasks, and control parameters of other modules of the robot do not need to be adjusted. Due to the advantages of flexible configuration, convenient assembly and the like, the modular robot is often applied to dangerous and uncertain environment operations such as space exploration, disaster rescue, high and low temperature and the like. Therefore, the robot system will inevitably be affected by the uncertain environment. Therefore, a suitable control system is required to ensure the robustness and accuracy of the modular robot in the face of an external collision.
In addition to the modular nature, in order to achieve high-precision robot control, it is also common for the robot to control under conditions of random delay, input dead zone, input saturation, visual servoing, etc. In addition, joint torque feedback technology has also received wide attention from the robot community as an effective way to improve the control accuracy of robots. There are a number of disadvantages to using joint torque sensors, which may impair the robustness, reliability and simplicity of the robot. In order to avoid the problems, the invention provides a torque estimation method based on a harmonic drive model.
Based on the modularized design idea, the components of the modularized robot are designed to have standardized mechanical and electrical interfaces so as to facilitate free assembly and communication between different modules, the ideal modularized robot not only meets the modularized characteristic on the mechanical structure, but also needs to be modularized on a controller, namely, each robot module is controlled by a control system of the robot module and is independent of each other, the work of each module control subsystem is not influenced by the control subsystems of other modules, and when the configuration of the robot changes, the control system can also automatically adjust control parameters to adapt to the configuration change of the robot. Decentralized control is widely applied to the design of modular robot control systems as an advanced control strategy based on the demand. Under the condition of only adopting the dynamic information of the local joint modules, the distributed control strategy can provide structural flexibility for the robot system, so that each joint module can be recombined into a plurality of robot configurations to meet the task requirements under different working environments, and the control parameters of the robot system do not need to be readjusted.
The invention provides a distributed control method for the outside-facing collision of a modular robot based on moment estimation, aiming at a class of modular robot systems. Meanwhile, the invention adds the idea of self-adaptive dynamic collision compensation into the decentralized control, so that the system can return to the expected track as soon as possible under the condition of a large-force collision, and the moment is ensured to be in the rated range of the system, thereby not influencing the normal work of the system.
Disclosure of Invention
The invention aims to provide a distributed control method and a system for the outward-facing collision of a modular robot, which can enable the system to return to an expected track as soon as possible under the condition of a large-force collision and ensure that the normal work of the system is not influenced when the moment is in a rated range.
In order to achieve the purpose, the invention provides the following scheme:
a decentralized control method for a modular robot to face an external collision, the control method comprising:
determining a joint torque based on a model of harmonic drive compliance and friction;
establishing a dynamic model for each module subsystem in the robot;
carrying out decoupling separation uncertainty through a state space expression based on the dynamic model to obtain a state space expression after decoupling separation;
converting the decoupled and separated state space expression to obtain a converted state space expression;
respectively compensating unknown terms, model uncertain terms and coupling terms in the converted state space expression by adopting an RBF neural network based on the converted state space expression;
building a decentralized controller of the modular robot system based on the unknown item, the model uncertainty item and the coupling item;
and controlling the robot based on the decentralized controller of the modular robot system.
Optionally, the following formula is specifically adopted for determining the torque of the model based on the compliance and friction of the harmonic drive:
τfi＝τfci-τupi
Figure BDA0002534491660000031
wherein, taufciA determination part for joint moment estimation; tau isupiFor moment output disturbance, it is an uncertain item of modeling; tau iswiIs the torque of the wave generator and is equal to the torque of the motor; tau isfiIs the output torque of the flexspline, cfi、kfi0、cwiAnd kwi0Is a undetermined constant, γiIs the reduction ratio of the harmonic drive.
Optionally, the following formula is specifically adopted for establishing the dynamic model for each module subsystem in the robot:
Figure BDA0002534491660000032
wherein the corner mark "I" denotes the ith subsystem, ImiIs the moment of inertia of the motor, gammaiRepresenting a reduction ratio of the gear;
Figure BDA0002534491660000033
respectively representing the position, the speed and the acceleration of the ith joint; tau isiIn order to control the torque, the torque is controlled,
Figure BDA0002534491660000034
for the concentrated friction of the harmonic device and the friction of the motor, the expression is as follows:
Figure BDA0002534491660000035
wherein the content of the first and second substances,
Figure BDA0002534491660000036
representing position dependent friction and other friction due to modeling errors,
Figure BDA0002534491660000037
a parameter uncertainty representing the friction torque,
Figure BDA0002534491660000038
a friction matrix representing the dependence of the speed,
Figure BDA0002534491660000039
and
Figure BDA00025344916600000310
an estimate representing a friction parameter;
Figure BDA00025344916600000311
for non-linear functions of velocity and acceleration, the expression is as follows:
Figure BDA00025344916600000312
wherein the content of the first and second substances,
Figure BDA00025344916600000313
a parameter representing a constant variable is represented by,
Figure BDA00025344916600000314
representing a time variable parameter.
Optionally, the decoupling separation uncertainty is performed through a state space expression based on the kinetic model, and the state space expression after the decoupling separation is obtained specifically adopts the following formula:
Figure BDA00025344916600000315
wherein, Bi＝(Imiγi)-1∈R+It is shown that,
Figure BDA00025344916600000316
and
Figure BDA00025344916600000317
represents an estimate of a friction parameter,
Figure BDA0002534491660000041
representing position dependent friction and other friction due to modeling errors.
Figure BDA0002534491660000042
The speed-dependent friction matrix of the friction matrix,
Figure BDA0002534491660000043
a parameter uncertainty representing the friction torque,
Figure BDA0002534491660000044
a parameter representing a constant variable is represented by,
Figure BDA0002534491660000045
representing a time variable parameter, di(qi) Is the disturbance torque term.
Optionally, converting the decoupled state space expression to obtain a converted state space expression specifically includes:
defining a state vector of a system
Figure BDA0002534491660000046
And a control input ui＝τi∈R 1×11, 2.., n, the state space equation for the ith joint subsystem is expressed as:
Figure BDA0002534491660000047
wherein the content of the first and second substances,
Figure BDA0002534491660000048
representing the accurately modeled and measurable part of the subsystem dynamics,
Figure BDA0002534491660000049
Figure BDA00025344916600000410
the overall model uncertainty is represented, including frictional force model errors and external uncertainty disturbances.
Optionally, the respectively compensating the unknown term, the model uncertainty term, and the coupling term in the converted state space expression by using the RBF neural network based on the converted state space expression specifically includes:
constructing a robust neural network decentralized controller;
a decentralized controller compensates for unknown terms, model uncertainty terms, and coupling terms in the transformed state space expression based on the robust neural network.
Optionally, the following formula is specifically adopted by the decentralized controller for constructing the modular robot system based on the unknown item, the model uncertainty item, and the coupling item:
Figure BDA00025344916600000411
wherein, tauiIndicating control force, τfciFor the determination of the joint moment estimation, gammaiFor reduction ratio of harmonic gearing, uic1Part for the accurate modeling of a compensation system, uir2For compensation of the uncertainty of the frictional force modeling and for external impacts for a robust control term, uin3As control items of neural networks, ImiRepresenting the moment of inertia of the motor, aiIndicating acceleration error，
Figure BDA0002534491660000051
The velocity of the i-th joint is indicated,
Figure BDA0002534491660000052
and
Figure BDA0002534491660000053
represents an estimate of a friction parameter,
Figure BDA0002534491660000054
designed to compensate for non-parametric uncertainties,
Figure BDA0002534491660000055
and
Figure BDA0002534491660000056
respectively to compensate for the parameter uncertainty,
Figure BDA0002534491660000057
is an ideal weight W of the neural networkziEstimated value of phizi(|ri|) is the basis function of the neural network.
The present invention additionally provides a decentralized control system for a face-to-face collision of a modular robot, the control system comprising:
a torque estimation module to determine a torque based on a model of harmonic drive compliance and friction;
the dynamic model establishing module is used for establishing a dynamic model for each module subsystem in the robot;
the decoupling and separating module is used for carrying out decoupling and separating uncertainty through a state space expression based on the dynamic model to obtain a state space expression after decoupling and separating;
the conversion module is used for converting the state space expression after the decoupling and the separation to obtain a converted state space expression;
a compensation module, configured to respectively compensate an unknown item, a model uncertainty item, and a coupling item in the converted state space expression by using an RBF neural network based on the converted state space expression;
a decentralized controller building module for building decentralized controllers of the modular robot system based on the unknown items, the model uncertainty items and the coupling items;
and the execution module is used for controlling the robot based on the distributed controller of the modularized robot system.
Optionally, the torque estimation module specifically adopts the following formula:
τfi＝τfci-τupi
Figure BDA0002534491660000058
wherein, taufciA determination part for joint moment estimation; tau isupiFor moment output disturbance, it is an uncertain item of modeling; tau iswiIs the torque of the wave generator and is equal to the torque of the motor; tau isfiIs the output torque of the flexspline, cfi，kfi0，cwiAnd kwi0Is a undetermined constant, γiIs a reduction ratio.
Optionally, the dynamic model building module specifically adopts the following formula:
Figure BDA0002534491660000061
wherein the corner mark "I" denotes the ith subsystem, ImiIs the moment of inertia of the motor, gammaiRepresenting a reduction ratio of the gear;
Figure BDA0002534491660000062
respectively representing the position, the speed and the acceleration of the ith joint; tau isiIn order to control the torque, the torque is controlled,
Figure BDA0002534491660000063
concentrated friction for harmonic devices and friction for electric motorsThe expression is as follows:
Figure BDA0002534491660000064
wherein, bfi、fci、fsiAnd fτiAre the parameters of the friction force model and,
Figure BDA0002534491660000065
representing position dependent friction and other friction due to modeling errors;
Figure BDA0002534491660000066
for non-linear functions of velocity and acceleration, the expression is as follows:
Figure BDA0002534491660000067
wherein z ismi，zqj。zqkRespectively, unit vectors, τ, along the i, j, k joint rotation axisfciIs an estimate of the joint torque, di(qi) In order to be the term of the disturbance torque,
Figure BDA0002534491660000068
transpose the vector for the unit of the i-th joint axis of rotation,
Figure BDA0002534491660000069
and
Figure BDA00025344916600000610
respectively, the velocity of the k, j-th joint.
According to the specific embodiment provided by the invention, the invention discloses the following technical effects:
the invention estimates the joint moment feedback value by modeling the harmonic transmission device. Meanwhile, the invention adds the idea of self-adaptive dynamic collision compensation into the decentralized control, so that the system can return to the expected track as soon as possible under the condition of a large-force collision, and the moment is ensured to be in the rated range of the system, thereby not influencing the normal work of the system.
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In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings needed to be used in the embodiments will be briefly described below, and it is obvious that the drawings in the following description are only some embodiments of the present invention, and it is obvious for those skilled in the art to obtain other drawings without inventive exercise.
Fig. 1 is a flowchart of a decentralized control method for a modular robot to face an external collision according to an embodiment of the present invention;
FIG. 2 is a schematic structural diagram of a modular robot according to an embodiment of the present invention;
FIG. 3 is a block diagram of a harmonic drive in accordance with an embodiment of the present invention;
FIG. 4 is a schematic diagram of the kinematic relationship of the harmonic drive of the embodiment of the present invention;
FIG. 5 is a schematic diagram of the kinematic relationship of harmonic drive based on compliance according to an embodiment of the present invention;
FIG. 6 is a schematic diagram of the present invention in view of the kinematic relationship between the wave generator and the compliance of the flexspline;
FIG. 7 is a schematic diagram of the kinematic relationship inside the joints of the modular robot according to the embodiment of the present invention;
FIG. 8 is an experimental setup for verifying the effectiveness of the present invention according to an embodiment of the present invention;
FIG. 9 is a torque estimation deviation curve of the experimental shutdown 1 and the rapid movement of the joint 2 according to the embodiment of the present invention;
FIG. 10 is a graph of control torque for the experimental shutdown 1 and the rapid movement of the joint 2 according to the embodiment of the present invention;
FIG. 11 is a graph of joint position error for the experimental shutdown 1 and the joint 2 in rapid motion according to an embodiment of the present invention;
FIG. 12 is a graph of the moment estimation deviation for slow motion of the experimental shutdown 1 and joint 2 according to an embodiment of the present invention;
FIG. 13 is a graph of control torque for slow motion of the experimental shutdown 1 and joint 2 according to an embodiment of the present invention;
FIG. 14 is a graph of the position error of the joint for slow motion of the experimental shutdown 1 and joint 2 according to the embodiment of the present invention;
fig. 15 is a schematic structural diagram of a distributed control system for a modular robot in a face-to-face collision according to an embodiment of the present invention.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
The invention aims to provide a distributed control method and a system for the outward-facing collision of a modular robot, which can enable the system to return to an expected track as soon as possible under the condition of a large-force collision and ensure that the normal work of the system is not influenced when the moment is in a rated range.
In order to make the aforementioned objects, features and advantages of the present invention comprehensible, embodiments accompanied with figures are described in further detail below.
The modular mechanical arm based on the robust neural network control algorithm is formed by connecting joints and connecting rods end to end, wherein each joint comprises a direct-current brush motor, an incremental encoder, a harmonic reducer, a torque sensor and a rigid coupling part. The direct current brush motor in the joint is used as a driving device of a mechanical arm system, the incremental encoder is installed at the tail end of the motor and used for measuring the position change of the motor, the harmonic reducer is installed at the output end of the motor and used for reducing the speed of the motor and increasing the output torque, and the torque sensor is installed at the output end of the harmonic reducer and then connected with the connecting rod and used for measuring the output torque of the joint.
Firstly, a dynamics model of a modularized robot system is established by analyzing dynamics relation of each module of the robot, then a robust neural network control algorithm based on learning is designed, the control method not only keeps the fault-tolerant capability of the robust control method, but also can quickly and stably control the robot after the robot is newly configured, and various uncertainties in establishment of the robot model are approached through the neural network and compensated. Finally, the control algorithm realizes the accurate control of the modular robot. The specific method comprises the following steps:
fig. 1 is a flowchart of a distributed control method for a modular robot to face an external collision according to an embodiment of the present invention, and fig. 2 is a schematic structural diagram of a modular robot according to an embodiment of the present invention, as shown in fig. 1 and fig. 2, the method includes:
step 101: a joint torque based on a model of harmonic drive compliance and friction is determined.
The schematic structural diagram of the modular robot is shown in fig. 2. Wherein each rotary joint is composed of the following parts: a direct current brush motor is used as a driver of the joint module to drive the robot joint module to normally operate; an incremental encoder mounted at the motor end of the joint module for measuring the rotational displacement of the motor when the robot is in operation; an absolute encoder installed at the link end of the joint module for measuring the rotational displacement of the joint when the robot is in normal operation; the harmonic transmission device is used as a reducer of the motor and plays a role in matching rotating speed and transmitting torque between the motor and the actuating mechanism, and the harmonic transmission device mainly comprises a wave generator, a flexible gear and a rigid gear. Firstly, an ideal harmonic drive model is established, then the wave generator and the harmonic drive model of the compliance and friction of the flexible gear are considered on the basis of the ideal harmonic drive model, and the joint torque value is estimated on the basis of the harmonic drive model.
(1) Basic ideal model of harmonic drive
As shown in fig. 4, which is a schematic diagram of the internal structure motion relationship of the harmonic drive device, the mathematical relationship among the wave generator, the rigid gear and the flexible gear in the joint can be obtained as follows:
θwi＝(γi+1)θci-γiθfi(1)
ωwi＝(γi+1)ωci-γiωfi(2)
in the above formula, γiRepresenting the reduction ratio, theta, of the harmonic drivewi,θci,θfiRespectively showing the rotation angles, omega, of the wave generator, the rigid gear and the flexible gearwi,ωci,ωfiThe angular velocities of rotation, respectively, and the ideal static mechanical equilibrium relationship can be expressed as:
Figure BDA0002534491660000091
wherein, tauwiIs the input torque of the wave generator, i.e. the motor output torque. Tau isfiIs the output torque of the flexible gear, namely the joint torque. Theta ci0, irrespective of the moment τ on the rigid wheelci. Therefore, the equations (1), (2) and (3) can be simplified to the ideal linear relationship:
θwi＝-γiθfi(4)
ωwi＝-γiωfi(5)
Figure BDA0002534491660000092
the harmonic device fundamental model described above treats it as a fully rigid, ideal gear reduction system with ideal linear relationships between its input and output. However, in practical applications, the input and output of the harmonic drive measured by the sensor do not satisfy a linear relationship, and these non-linear properties may exist in non-linear friction torque, torsional deformation of parts and kinematic errors in the harmonic drive. Given an ideal kinematic relationship describing the harmonic drive motion and torque constraint performance, the remaining effects can be expressed in combination with frictional forces, deformation and kinematic error attributes.
(2) Model based on harmonic transmission device flexibility and friction
While the ideal model of the harmonic drive is described above and it is proposed that the input and output do not follow an ideal linear relationship due to the structure of the harmonic drive itself, a model based on the compliance and friction of the harmonic drive flexspline is described below, as shown in fig. 5, and the kinematic relationship can be expressed in the form of equations (7), (8):
θwi＝-γiθfIi(7)
ωwi＝-γiωfIi(8)
wherein, thetafIiAngle, omega, representing the gear position of the flexsplinefIiIndicating the angular velocity of the flexspline rotation. The torque transmission relationship of the harmonic device can be expressed as:
Figure BDA0002534491660000101
wherein, taufriIs the friction torque.
Because the flexible gear is made of a special soft metal material in the harmonic drive device and is tightly sleeved on the elliptical wave generator to make the flexible gear form an ellipse with the wave generator, if the flexibility of the flexible gear is considered, the flexible gear can be twisted and deformed when running, so that a certain position deviation delta theta exists between the input angle and the output angle of the harmonic drive deviceiThis positional deviation can be expressed as:
Δθi＝θfOi-θfIi(10)
wherein, thetafOiRepresenting the angle of the flexspline output. An encoder can be generally arranged at the motor end of the robot joint to measure the rotation angle of the motor, namely the input angle theta of the wave generatorwIiThen another encoder is arranged at the output end of the joint to measure the output angle theta of the flexible gearfOi. Calculating the torsional deformation delta theta according to the transmission relation by the measured angle information of the input end and the output end of the harmonic transmission devicei：
Figure BDA0002534491660000102
In the model described above, the angular deviation of the input and output of the harmonic drive due to torsional deformation caused by compliance of the flexspline is taken into account, as well as the frictional effects in torque transmission. And therefore more accurate than the basic model. It has also been shown in some experimental studies that wave generators in harmonic drives have angular input to output deviations. Therefore, a model considering the flexibility of the harmonic drive flexible gear and the wave generator at the same time needs to be established, and a model considering the flexibility of the harmonic drive flexible gear and the wave generator at the same time is established below.
Fig. 6 defines the flexspline twist and the wave generator twist, respectively:
Δθfi＝θfOi-θfIi(12)
Δθwi＝θwOi-θwIi(13)
in expressions (12) and (13), it is noted that only the input position (motor rotation angle) θ of the wave generatorwIiAnd flexspline output position (joint angle) θfOiAre measurable by a motor-end incremental encoder and a link-end absolute encoder, respectively. These measured position information can be used to calculate the total torsion angle of the harmonic device of the i-th joint using the following relationship, so that the total torsion angle of the harmonic device is:
Figure BDA0002534491660000111
add and subtract the term θ from the above equationfIiAnd
Figure BDA0002534491660000112
the total twist angle of the harmonic device can be finally obtained:
Figure BDA0002534491660000113
wherein the content of the first and second substances,
Figure BDA0002534491660000114
to representKinematic error, represented by the measured output of the flexspline minus the desired output:
Figure BDA0002534491660000115
(3) moment estimation based on harmonic transmission device flexibility model:
in order to obtain a joint torque estimation value with higher precision, the torque deviation and the kinematic error of the harmonic transmission device need to be considered, an error model is established to compensate the error of the harmonic device, and as shown in fig. 7, the form of the error model is defined as follows:
Figure BDA0002534491660000116
wherein the content of the first and second substances,
Figure BDA0002534491660000117
is a kinematic error of the wave generator,
Figure BDA0002534491660000118
is the kinematic error of the flexspline.
From the typical stiffness and hysteresis behavior of a harmonic device, it can be concluded that the local spring rate of the flexspline of the harmonic device increases with increasing flexspline torque. Therefore, by defining the elastic coefficient k of the flexible gear partfiComprises the following steps:
Figure BDA0002534491660000119
due to the symmetric nature of the stiffness of the harmonic device, its local elastic coefficient can be approximated as:
kfi＝kfi0(1+(cfiτfi)2) (19)
wherein k isfi0And cfiIs a undetermined constant. If k isfi0Not equal to 0, the flexspline torsion can be calculated by the relations (18) and (19) as follows:
Figure BDA0002534491660000121
furthermore, at rated torque, the deformation range of the harmonic device drops sharply to zero, which means that the stiffness of the wave generator increases sharply. To replicate this hysteresis shape of the stiffness characteristic, the local elastic coefficient of the wave generator is modeled as:
Figure BDA0002534491660000122
wherein k iswi0And cwiIs a undetermined constant. If k iswi0Not equal to 0, the torsion angle of the wave generator can be calculated by the following relationship:
Figure BDA0002534491660000123
therefore, the total torsion angle of the harmonic device can be obtained by bringing equations (20) and (22) into equation (15):
Figure BDA0002534491660000124
deforming the above equation, the joint moment is equal to the flexspline output of the harmonic device, we finally get the joint moment estimated value, which can be estimated as follows:
Figure BDA0002534491660000125
wherein, taufciIs part of the joint torque estimation, the torque output disturbance τupiConsidered as an uncertainty of the modeling, which will be compensated for in subsequent sections. Wave generator moment tauwiApproximately equal to the torque of the motor.
Step 102: and establishing a dynamic model for each module subsystem in the robot.
In the reference robot modeling method with the torque sensor, for the whole system of a modular robot based on torque estimation, each module forms an independent subsystem, a dynamic model is established for each module subsystem, and the torque estimation value obtained in the formula (24) is brought into the reference dynamic model to obtain the expression of the ith subsystem:
Figure BDA0002534491660000131
in the formula (25), the subscript "I" denotes the ith subsystem, ImiIs the moment of inertia of the motor, gammaiRepresenting a reduction ratio of the gear;
Figure BDA0002534491660000132
respectively representing the position, the speed and the acceleration of the ith joint;
Figure BDA0002534491660000133
mainly including the concentrated friction of harmonic devices and the friction of the motor, the friction term can be expressed as a type of function with respect to joint position and velocity, which is expressed as follows:
Figure BDA0002534491660000134
wherein, bfi、fci、fsiAnd fτiAre the parameters of the friction force model and,
Figure BDA0002534491660000135
representing position dependent friction and other friction due to modeling errors. Suppose fsiAnd fτiThe nominal values are close to their actual values. Thus Beck influence
Figure BDA0002534491660000136
Can be at nominal parameters
Figure BDA0002534491660000137
Is linearized so the higher order terms
Figure BDA0002534491660000138
Can be ignored as follows:
Figure BDA0002534491660000139
by substituting formula (27) into formula (26), friction torque
Figure BDA00025344916600001310
Can be approximated as:
Figure BDA00025344916600001311
wherein the content of the first and second substances,
Figure BDA00025344916600001312
a parameter uncertainty representing the friction torque,
Figure BDA00025344916600001313
and
Figure BDA00025344916600001314
representing an estimate of a friction parameter.
Figure BDA00025344916600001315
Is defined in the form:
Figure BDA00025344916600001316
Figure BDA00025344916600001317
an item is defined as:
Figure BDA00025344916600001318
wherein z ismizqjzqkRespectively unit vectors, z, along the rotation axes of the i, j, k-th jointsmi，zqj。zqkAre respectively alongUnit vector of i, j, k-th joint rotation axis, taufciIs an estimate of the joint torque, di(qi) In order to be the term of the disturbance torque,
Figure BDA00025344916600001319
transpose the vector for the unit of the i-th joint axis of rotation,
Figure BDA00025344916600001320
and
Figure BDA00025344916600001321
respectively, the velocity of the k, j-th joint. To facilitate IDC analysis between the joint modules,
Figure BDA00025344916600001322
and
Figure BDA00025344916600001323
can be rewritten as:
Figure BDA0002534491660000141
Figure BDA0002534491660000142
wherein the content of the first and second substances,
Figure BDA0002534491660000143
wherein the content of the first and second substances,
Figure BDA0002534491660000144
is a unit vector zmiAnd zqjThe dot product of (a) is,
Figure BDA0002534491660000145
is an alignment error. In a similar manner to that described above,
Figure BDA0002534491660000146
is a unit vector zmiAnd zqk×zqjThe dot product of (a) is,
Figure BDA0002534491660000147
is an alignment error. In addition, di(qi) It is the disturbance torque term, which is caused by an external impact.
Step 103: and carrying out decoupling separation uncertainty through a state space expression based on the dynamic model to obtain a state space expression after decoupling separation.
Step 104: and converting the decoupled and separated state space expression to obtain a converted state space expression.
Rewriting the kinematic model of the i-th joint subsystem according to the kinematic model obtained in equation (25) to obtain:
Figure BDA0002534491660000148
wherein, Bi＝(Imiγi)-1∈R+Defining a state vector of the system
Figure BDA0002534491660000149
And a control input ui＝τi∈R 1×11, 2.. times, n, as can be seen from the relation (33), the state space equation of the i-th joint subsystem can be expressed as:
Figure BDA00025344916600001410
wherein the content of the first and second substances,
Figure BDA0002534491660000151
IDC terms representing the accurately modeled and measurable part of the subsystem dynamics
Figure BDA0002534491660000152
Figure BDA0002534491660000153
Representing overall model uncertainty, including frictional model errors and external uncertaintyAnd (4) interference.
Specifically, the model uncertainty analysis is as follows:
with reference to model expression (30), IDC terms are represented as
Figure BDA0002534491660000154
And
Figure BDA0002534491660000155
most model uncertainties are due to joint friction and disturbance torque, which exist in
Figure BDA0002534491660000156
di(qi) In (1). Note that IDC and model uncertainty obey the following properties:
attribute 1: vector zmizqjzqkThe product between is bounded, i.e.
Figure BDA0002534491660000157
Figure BDA0002534491660000158
Also, when a robot is stable, its velocity and acceleration must be bounded, so from the IDC expressions (31), (32), it can be concluded that the terms are stable if the j and k joints (j, k < i)
Figure BDA0002534491660000159
And
Figure BDA00025344916600001510
is bounded and satisfies a relationship
Figure BDA00025344916600001511
And
Figure BDA00025344916600001512
where ρ isUiAnd ρViKnown as a well-known boundary.
Note 1: when a joint is expressed as in Attribute 1After j and k stabilize, term
Figure BDA00025344916600001513
And
Figure BDA00025344916600001514
is bounded, meaning that the bottom joint i-1 is stable when the ith joint is controlled. Based on this property, a modular robot can apply a decentralized control strategy to stabilize joints one level after the other.
Note 2: unlike the current study, which considers cross-coupling terms including Copenforces, centrifugal forces and gravitational forces to be associated with the entire robot, in this study, the joint moments τ are duefciThe full load moment in the ith joint subsystem space can be reflected, so the IDC term contains only the coupling dynamics of the bottom joint (from the base joint to the ith joint). This greatly reduces the magnitude of the IDC and simplifies the complexity of the dynamics model.
Attribute 2: based on the friction model (26) and its approximate expression (27), because of the parameter bfifcifsifτiAnd their estimates are bounded, parameter uncertainty
Figure BDA00025344916600001515
Are also bounded, i.e.
Figure BDA00025344916600001516
Where ρ isFil＝[ρFi1ρFi2ρFi3ρFi4]TIs a known normal vector. Thus, it can be concluded that the upper bound of the friction modeling error can be defined as
Figure BDA00025344916600001517
Attribute 3: item of friction
Figure BDA00025344916600001518
Is bounded
Figure BDA00025344916600001519
Where ρ isfpiIs a known constant which is determined by the position q of the jointiAnd velocity
Figure BDA00025344916600001520
And (4) limitation.
Attribute 4: definition of disturbance torque term di(qi) Is a function of the position of the robot joint, and is bounded, its upper bound di(qi)≤ρdi。
Step 105: and respectively compensating unknown terms, model uncertain terms and coupling terms in the converted state space expression by adopting an RBF neural network based on the converted state space expression.
Step 106: building a decentralized controller of the modular robotic system based on the unknown item, the model uncertainty item, and the coupled item.
1. Design of robust neural network controller
First, from the state space equation obtained in equation (34), the total control torque is defined for each joint subsystem:
Figure BDA0002534491660000161
wherein u isiRepresenting the control input of the ith joint to be determined, assuming a desired trajectory q for the ith jointidIs second order constrained bounded, defining for the controller the following:
Figure BDA0002534491660000162
wherein λ isiFor any constant, defining u by respectively compensating each item in the dynamic model of the reference modular robotiThe following were used:
ui＝uic1+uir2+uin3, (37)
wherein the content of the first and second substances,
Figure BDA0002534491660000163
and parts for accurately modeling the compensation system comprise the rotational inertia of the motor and the friction moment. u. ofir2Is a robust control term that compensates for the uncertainty of the friction modeling and the uncertainty portion of the disturbance torque term. u. ofin3Are neural network control terms, each of which is used to compensate IDC terms
Figure BDA0002534491660000164
2. Decentralized controller uncertainty compensation control based on robust neural network
Uncertainty compensation is performed for each term mentioned in equation (37). The compensation of the precise modeling part is completed firstly, and the compensation design of the friction torque and the disturbance torque needs to be completed. Modeling uncertainty for friction force of ith joint subsystem
Figure BDA0002534491660000165
In combination with the variable parameter model uncertainty compensator,
Figure BDA0002534491660000166
is decomposed into:
Figure BDA0002534491660000171
wherein the content of the first and second substances,
Figure BDA0002534491660000172
is an unknown constant vector of the vector,
Figure BDA0002534491660000173
is a variable and is limited by:
Figure BDA0002534491660000174
the control design method based on decomposition designs an adaptive compensation control item to compensate the uncertainty of constant parameters
Figure BDA0002534491660000175
And a robust control term for compensation
Figure BDA0002534491660000176
The controller is designed in the following form:
Figure BDA0002534491660000177
wherein the content of the first and second substances,
Figure BDA0002534491660000178
designed to compensate for non-parametric uncertainties
Figure BDA0002534491660000179
And disturbance torque term di(qi). Item(s)
Figure BDA00025344916600001710
And
Figure BDA00025344916600001711
respectively for compensating for parameter uncertainties
Figure BDA00025344916600001712
And
Figure BDA00025344916600001713
since the friction compensation is the same for each key, the control term for the ith joint
Figure BDA00025344916600001714
And
Figure BDA00025344916600001715
is defined as:
Figure BDA00025344916600001716
Figure BDA00025344916600001717
Figure BDA00025344916600001718
wherein the content of the first and second substances,
Figure BDA00025344916600001719
is a positive control parameter.
First of all finish uic1Compensation sum u for accurately modeled partir2The compensation design of friction torque and disturbance torque needs to be designed, and then a neural network control item u needs to be designedin3For compensating for system model uncertainty, i.e., IDC term. The neural network has excellent ability to learn any function, and plays an important role in the classical control theory because the neural network can avoid complex mathematical analysis due to the self-learning ability. The controller based on the RBF neural network can effectively improve the control precision, robustness and adaptability of the system. IDC item because of modular robot
Figure BDA00025344916600001720
For highly non-linear functions, an RBF neural network is used to approximate the IDC term and compensate for it.
Knowing an uncertainty from Attribute 1
Figure BDA00025344916600001721
Being bounded, the modular robotic system uncertainty based on the RBF neural network can be expressed as:
Figure BDA0002534491660000181
wherein, WziIs an ideal weight value of the neural network, and is defined
Figure BDA0002534491660000182
Is WziIs determined by the estimated value of (c),
Figure BDA0002534491660000183
to estimate the error, phizi(|ri|) is a basis function of the neural network,
Figure BDA0002534491660000184
is composed of
Figure BDA0002534491660000185
Their expressions are:
Figure BDA0002534491660000186
Figure BDA0002534491660000187
from the neural network expression (45), the control law u can be designedin3The IDC term is compensated, and the control law is in the form:
Figure BDA0002534491660000188
the estimated values of the weights are updated with the following adaptive law:
Figure BDA0002534491660000189
finally, in combination (35), (37), (40) and (47), the decentralized controller design of the modular robot system is as follows:
Figure BDA00025344916600001810
step 107: and controlling the robot based on the decentralized controller of the modular robot system.
Experimental study
In order to study the effectiveness of the proposed robust neural network decentralized control method, when the method is oriented to external collision, two expected tracking tracks of fast motion and slow motion are adopted for comparison, and a 2-degree-of-freedom modular robot experimental platform is established, as shown in fig. 8. The 2-degree-of-freedom modular robot consists of two groups of joint modules and connecting rods, wherein each joint module comprises a direct-current brush motor manufactured by Maxon company, the model of the direct-current brush motor is 218014, the maximum output torque is 190Nm, and the rotational inertia is 118g/cm 2; a harmonic drive is connected with the output of the motor and is used for a speed reducer, and the speed reduction ratio is 101: 1; an incremental encoder manufactured by Maxon company is arranged at the motor end, and the model is as follows: HEDL-5540-A11 with an accuracy of 500count/rev, which is used for measuring the displacement of the motor end; an absolute encoder, model DS-70-64-3SH-S0, manufactured by Netzer, having 19 bits of accuracy, was mounted at the end of the link to collect absolute position data of the end of the link. A linear power amplifier (PLA) manufactured by Quanser company is adopted to drive a motor of a joint module and a QPIDe data acquisition card are adopted to acquire data of each sensor for robot control.
The expected tracking trajectories of joint 1 and joint 2 in the slow case are defined as:
Figure BDA0002534491660000191
the desired tracking trajectories for joint 1 and joint 2 in the fast case are defined as:
Figure BDA0002534491660000192
the parameters of the robot used in the experiment are given in the following table:
TABLE 1 controller parameter settings
Figure BDA0002534491660000193
As shown in fig. 9-14, it can be seen from the experimental curves that the control method can better track the expected trajectory no matter the robot moves fast or slowly, and when the robot is collided by the outside, the control method achieves higher control accuracy due to the learning and compensation of the model uncertainty, thereby obtaining better trajectory tracking effect. Based on the robust neural network control method provided by the patent, the output torque of the motor is smoother.
Fig. 15 is a schematic structural diagram of a distributed control system for a modular robot to face an external collision according to an embodiment of the present invention, and as shown in fig. 15, the system includes: a moment estimation module 201, a dynamic model building module 202, a decoupling separation module 203, a conversion module 204, a compensation module 205, a decentralized controller construction module 206 and an execution module 207.
Wherein the torque estimation module 201 is configured to determine a torque based on a model of harmonic drive compliance and friction;
the dynamics model establishing module 202 is used for establishing a dynamics model for each module subsystem in the robot;
the decoupling and separating module 203 is used for carrying out decoupling and separating uncertainty through a state space expression based on the dynamic model to obtain a state space expression after decoupling and separating;
the conversion module 204 is configured to convert the decoupled state space expression to obtain a converted state space expression;
the compensation module 205 is configured to respectively compensate the unknown term, the model uncertainty term, and the coupling term in the converted state space expression by using an RBF neural network based on the converted state space expression;
a decentralized controller building module 206 for building decentralized controllers of the modular robotic system based on the unknown items, model uncertainty items, and coupled items;
the execution module 207 is used to control the robot based on the decentralized controller of the modular robot system.
The invention provides a modular robot decentralized control method based on moment estimation. The uncertainty of the frictional force modeling in the robot model and the disturbance moment item caused by external collision are compensated by a robust control method, and the uncertainty IDC item of the robot is approximated and compensated by a neural network control algorithm. Because the uncertainty of the modular robot is accurately compensated, the performance of the modular robot can be effectively improved by applying the control method, and the buffeting influence is weakened.
The embodiments in the present description are described in a progressive manner, each embodiment focuses on differences from other embodiments, and the same and similar parts among the embodiments are referred to each other. For the system disclosed by the embodiment, the description is relatively simple because the system corresponds to the method disclosed by the embodiment, and the relevant points can be referred to the method part for description.
The principles and embodiments of the present invention have been described herein using specific examples, which are provided only to help understand the method and the core concept of the present invention; meanwhile, for a person skilled in the art, according to the idea of the present invention, the specific embodiments and the application range may be changed. In view of the above, the present disclosure should not be construed as limiting the invention.

Claims (10)

1. A decentralized control method for a face-to-face collision of a modular robot, characterized in that the control method comprises:
determining a joint torque based on a model of harmonic drive compliance and friction;
establishing a dynamic model for each module subsystem in the robot;
carrying out decoupling separation uncertainty through a state space expression based on the dynamic model to obtain a state space expression after decoupling separation;
converting the decoupled and separated state space expression to obtain a converted state space expression;
respectively compensating unknown terms, model uncertain terms and coupling terms in the converted state space expression by adopting an RBF neural network based on the converted state space expression;
building a decentralized controller of the modular robot system based on the unknown item, the model uncertainty item and the coupling item;
and controlling the robot based on the decentralized controller of the modular robot system.
2. A distributed control method of a modular robot face-to-face collision as claimed in claim 1, characterized in that the determination of the moment based on a model of harmonic drive compliance and friction uses in particular the following formula:
τfi＝τfci-τupi
Figure FDA0002534491650000011
wherein, taufciA determination part for joint moment estimation; tau isupiFor moment output disturbance, it is an uncertain item of modeling; tau iswiIs the torque of the wave generator and is equal to the torque of the motor; tau isfiIs the output torque of the flexspline, cfi、kfi0、cwiAnd kwi0Is a undetermined constant, γiIs the reduction ratio of the harmonic drive.
3. A distributed control method for a modular robot face-to-face collision as claimed in claim 1, wherein the building of the dynamic model for each module subsystem in the robot specifically employs the following formula:
Figure FDA0002534491650000012
wherein the corner mark "I" denotes the ith subsystem, ImiIs the moment of inertia of the motor, gammaiRepresenting a reduction ratio of the gear; q. q.si,
Figure FDA0002534491650000021
Respectively representing the position, the speed and the acceleration of the ith joint; tau isiIn order to control the force rejection,
Figure FDA0002534491650000022
for harmonic devicesThe friction force and the friction force of the motor are expressed as follows:
Figure FDA0002534491650000023
wherein the content of the first and second substances,
Figure FDA0002534491650000024
representing position dependent friction and other friction due to modeling errors; ,
Figure FDA0002534491650000025
a parameter uncertainty representing the friction torque,
Figure FDA0002534491650000026
a friction matrix representing the dependence of the speed,
Figure FDA0002534491650000027
and
Figure FDA0002534491650000028
represents an estimate of a friction parameter,
Figure FDA0002534491650000029
for non-linear functions of velocity and acceleration, the expression is as follows:
Figure FDA00025344916500000210
wherein the content of the first and second substances,
Figure FDA00025344916500000211
a parameter representing a constant variable is represented by,
Figure FDA00025344916500000212
representing a time variable parameter.
4. The decentralized control method for the face-to-face collision of the modular robot according to claim 1, wherein the decoupling separation uncertainty is performed through a state space expression based on the dynamic model, and the state space expression after the decoupling separation is obtained specifically adopts the following formula:
Figure FDA00025344916500000213
wherein, Bi＝(Imiγi)-1∈R+It is shown that,
Figure FDA00025344916500000214
and
Figure FDA00025344916500000215
estimated value representing friction force parameter
Figure FDA00025344916500000216
Designed to compensate for non-parametric uncertainties,
Figure FDA00025344916500000217
representing position dependent friction and other friction due to modeling errors,
Figure FDA00025344916500000218
expressed as a speed-dependent friction matrix,
Figure FDA00025344916500000219
a parameter uncertainty representing the friction torque,
Figure FDA00025344916500000220
a parameter representing a constant variable is represented by,
Figure FDA00025344916500000221
representing a time variable parameter, di(qi) Is composed ofA disturbance torque term.
5. The decentralized control method for the face-to-face collision of the modular robot according to claim 1, wherein the converting the decoupled state space expression to obtain the converted state space expression specifically comprises:
defining a state vector of a system
Figure FDA00025344916500000222
And a control input ui＝τi∈R1×11, 2.., n, the state space equation for the ith joint subsystem is expressed as:
Figure FDA0002534491650000031
wherein the content of the first and second substances,
Figure FDA0002534491650000032
representing the accurately modeled and measurable part of the subsystem dynamics,
Figure FDA0002534491650000033
Figure FDA0002534491650000034
the overall model uncertainty is represented, including frictional force model errors and external uncertainty disturbances.
6. The decentralized control method for external-facing collision of a modular robot according to claim 1, wherein the respectively compensating for the unknown term, the model uncertainty term, and the coupling term in the transformed state space expression using the RBF neural network based on the transformed state space expression specifically comprises:
constructing a robust neural network decentralized controller;
a decentralized controller compensates for unknown terms, model uncertainty terms, and coupling terms in the transformed state space expression based on the robust neural network.
7. The method of claim 1, wherein the decentralized controller for constructing the modular robot system based on the unknown term, the model uncertainty term, and the coupling term uses the following formula:
Figure FDA0002534491650000035
wherein, tauiIndicating control force, τfciA determination part representing an estimate of the joint moment, gammaiRepresents the reduction ratio of the harmonic device, uic1Part for the accurate modeling of a compensation system, uir2For compensation of the uncertainty of the frictional force modeling and for external impacts for a robust control term, uin3As control items of neural networks, ImiRepresenting the moment of inertia of the motor, aiAn error in the acceleration is indicated and,
Figure FDA0002534491650000036
the velocity of the i-th joint is indicated,
Figure FDA0002534491650000037
and
Figure FDA0002534491650000038
represents an estimate of a friction parameter,
Figure FDA0002534491650000039
designed to compensate for non-parametric uncertainties,
Figure FDA00025344916500000310
and
Figure FDA00025344916500000311
respectively for compensating for parametersThe items are determined such that,
Figure FDA0002534491650000041
is an ideal weight W of the neural networkziEstimated value of phizi(|ri|) is the basis function of the neural network.
8. A modular robot decentralized control system for a face-to-face collision, characterized in that the control system comprises:
a torque estimation module to determine a torque based on a model of harmonic drive compliance and friction;
the dynamic model establishing module is used for establishing a dynamic model for each module subsystem in the robot;
the decoupling and separating module is used for carrying out decoupling and separating uncertainty through a state space expression based on the dynamic model to obtain a state space expression after decoupling and separating;
the conversion module is used for converting the state space expression after the decoupling and the separation to obtain a converted state space expression;
a compensation module, configured to respectively compensate an unknown item, a model uncertainty item, and a coupling item in the converted state space expression by using an RBF neural network based on the converted state space expression;
a decentralized controller building module for building decentralized controllers of the modular robot system based on the unknown items, the model uncertainty items and the coupling items;
and the execution module is used for controlling the robot based on the distributed controller of the modularized robot system.
9. The system of claim 8, wherein the moment estimation module is further configured to use the following equation:
τfi＝τfci-τupi
Figure FDA0002534491650000042
wherein, taufciA determination part for joint moment estimation; tau isupiFor moment output disturbance, it is an uncertain item of modeling; tau iswiIs the torque of the wave generator and is equal to the torque of the motor; tau isfiIs the output torque of the flexspline, cfi，kfi0，cwiAnd kwi0Is a undetermined constant, γiIs the reduction ratio of the harmonic drive.
10. The system of claim 8, wherein the kinetic modeling module is further configured to apply the following equation:
Figure FDA0002534491650000051
wherein the corner mark "I" denotes the ith subsystem, ImiIs the moment of inertia of the motor, gammaiRepresenting a reduction ratio of the gear; q. q.si,
Figure FDA0002534491650000052
Respectively representing the position, the speed and the acceleration of the ith joint; tau isiIn order to control the force rejection,
Figure FDA0002534491650000053
for the concentrated friction of the harmonic device and the friction of the motor, the expression is as follows:
Figure FDA0002534491650000054
wherein, bfi、fci、fsiAnd fτiAre the parameters of the friction force model and,
Figure FDA0002534491650000055
indicating position dependent frictionForces and other frictional forces due to modeling errors;
Figure FDA0002534491650000056
for non-linear functions of velocity and acceleration, the expression is as follows:
Figure FDA0002534491650000057
wherein z ismi，zqj。zqkRespectively, unit vectors, τ, along the i, j, k joint rotation axisfciIs an estimate of the joint torque, di(qi) In order to be the term of the disturbance torque,
Figure FDA0002534491650000058
transpose the vector for the unit of the i-th joint axis of rotation,
Figure FDA0002534491650000059
and
Figure FDA00025344916500000510
respectively, the velocity of the k, j-th joint.
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Application publication date: 20201002