CN112000014B - Control method for model prediction and inversion of control mechanical arm - Google Patents

Control method for model prediction and inversion of control mechanical arm Download PDF

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CN112000014B
CN112000014B CN202010915976.7A CN202010915976A CN112000014B CN 112000014 B CN112000014 B CN 112000014B CN 202010915976 A CN202010915976 A CN 202010915976A CN 112000014 B CN112000014 B CN 112000014B
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谭天乐
尹俊雄
赵万良
周恒杰
石然
吕弢
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Shanghai Aerospace Control Technology Institute
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Abstract

The invention discloses a model prediction and inversion control method of a mechanical arm, which predicts the state information of a platform and the mechanical arm in the (k + n) th control period according to the state information measured in the current k period, and reversely deduces the control input of the platform and the control input of the mechanical arm in the k-k + n-1 period based on the generalized inverse matrix theory. Based on the deviation information of the current state and the historical state, the compensation control input of the current k-th control period platform and the mechanical arm is reversely deduced so as to weaken the state deviation caused by factors such as external interference, uncertain parameters and the like. The sum of the kth control cycle input, derived from the predicted state deviation, and the compensation control input, derived from the current and historical state deviations, is used as the control input to be applied to the platform and the robotic arm for the kth control cycle. Therefore, the synchronous control of the platform attitude and the track tracking of the mechanical arm joint with higher precision is realized, and the anti-interference capability on parameters and external disturbance is stronger.

Description

Model prediction and inversion control method for control mechanical arm
Technical Field
The invention relates to the field of robots, in particular to a model prediction and inversion control method for a mechanical arm.
Background
The mechanical arm has the characteristics of time variation, nonlinearity and strong coupling, and has wide application prospects in various fields of industry, commerce, military, aerospace and the like. For example, the robot is used for carrying, spraying and assembling on an industrial production line; the military field is used for replacing human soldiers to complete various battle tasks such as detection, weapon vehicle use, target removal and the like; the medical field is used for completing operations and the like automatically or remotely; the aerospace field is used for assisting the activities of astronauts, assisting the intersection and butt joint of spacecrafts, carrying materials, completing the assembly, maintenance, fuel filling and other tasks with important significance. Many application fields put increasing demands on the control precision of the mechanical arm. In the field of space manipulation, the attitude control of a manipulation platform is also very important.
With the development of computer technology, a complex control algorithm of the mechanical arm based on the model can be realized, so that the control precision and the response speed of the mechanical arm with multiple degrees of freedom are higher and higher. At present, methods such as PID control, fuzzy control, sliding mode variable structure control, self-adaptive control and neural network control of a mechanical arm have the problems of poor control precision/stability, low robustness on interference load and mechanical arm body parameters, large influence of artificial subjective factors of controller design and the like in different degrees, and the design is usually carried out from the stability point of view, so that the problems of good dynamic performance and steady-state performance and the like are difficult to ensure at the same time.
Disclosure of Invention
The invention aims to provide a model prediction and inversion control method for a mechanical arm, and the purpose of ensuring the mechanical arm to have better dynamic performance and steady-state performance is achieved.
In order to achieve the above purpose, the invention is realized by the following technical scheme:
a model prediction and inversion control method for a mechanical arm comprises the following steps:
and step S1, acquiring the state information of the control platform and the state information of the mechanical arm obtained by current k control period measurement.
And step S2, respectively predicting according to the state information of the control platform and the state information of the mechanical arm to obtain the predicted state information of the control platform and the predicted state information of the mechanical arm in the (k + n) th control period, wherein n is more than or equal to 1.
And step S3, acquiring the expected state information of the control platform and the expected state information of the mechanical arm in the k + n control period. And subtracting the expected state information of the control platform from the predicted state information of the control platform to obtain state deviation information of the control platform. And subtracting the expected state information of the mechanical arm from the predicted state information of the mechanical arm to obtain state deviation information of the mechanical arm.
And step S4, reversely deducing the control action sequence of the control platform and the control action sequence of the mechanical arm in the k-th to k + n-1-th control periods respectively based on the generalized inverse matrix theory.
And step S5, deducing the compensation control input of the operation platform and the mechanical arm in the current kth control period according to the state deviation information of the control platform and the state deviation information of the mechanical arm to obtain the compensation control quantity of the operation platform and the compensation control quantity of the mechanical arm.
Step S6, calculating the control quantity of the control platform in the kth control period according to the control action sequence of the control platform, and summing the control quantity of the control platform and the compensation control quantity of the operation platform to obtain a control output instruction of the control platform in the kth control period; and correspondingly inputting the control output command of the control platform in the kth control period to a force and moment executing mechanism of the control platform.
Calculating to obtain the control quantity of the mechanical arm in the kth control period according to the control action sequence of the mechanical arm, and summing the control quantity of the mechanical arm and the compensation control quantity of the mechanical arm to obtain a control output instruction of the mechanical arm in the kth control period; and correspondingly inputting the control output instruction of the mechanical arm in the kth control period to the mechanical arm joint servo motor.
Preferably, the method further comprises the following steps: and updating the kth control period to be the (k +1) th control period, repeating the step S1 to the step S6, and so on until the control process is finished.
Preferably, the step S2 includes: s2.1, establishing a state prediction equation of the control platform:
Figure BDA0002665025220000031
in the formula (I), the compound is shown in the specification,
Figure BDA0002665025220000032
I6is a 6-dimensional unit array, O6×6Is a zero matrix, k denotes the count of control periods, T denotes the control period, Mbeq(k) Representing the equivalent mass matrix of the manipulation platform at the kth control cycle, Fbeq(k) When the kth control period is represented, an equivalent nonlinear term of the control platform is controlled; tau isb(k) The three-axis control force and moment of the control platform in the kth control period are represented and are column vectors of 6 multiplied by 1; x (k) represents the state information of the control platform measured in the current k control period,
Figure BDA0002665025220000033
and the predicted state information of the control platform in the (k +1) th control period is shown.
Predicting the predicted state information of the control platform in the future k + n control period according to the control platform state information X (k) measured in the current k control period
Figure BDA0002665025220000034
The following were used:
Figure BDA0002665025220000035
in the formula (I), the compound is shown in the specification,
Figure BDA0002665025220000036
Figure BDA0002665025220000037
Figure BDA0002665025220000038
I12is a 12-dimensional identity matrix;
s2.2, establishing a state prediction equation of the mechanical arm:
Figure BDA0002665025220000039
in the formula (I), the compound is shown in the specification,
Figure BDA00026650252200000310
In1is n1Dimensional array, n1The number of joints of the mechanical arm, k represents the control period count, T represents the control period,
Figure BDA0002665025220000041
indicates the predicted state information of the robot arm at the (k +1) th control cycle,
Figure BDA0002665025220000042
indicating the mechanical arm state information measured in the current k control period, taua(k) The control moment of each joint of the mechanical arm in the kth control cycle is represented as n1X 1 column vector; maeq(k) The equivalent mass matrix of the mechanical arm in the kth control period is represented as n1×n1A matrix of (a); faeq(k) Is an equivalent nonlinear term of the mechanical arm in the k control period, which is n1X 1 in the column direction; g (k) is the gravitational moment of force of the kth control period, which is n1X 1 column vector.
The predicted state information of the robot arm in the k + n control cycle is predicted from the robot arm state information x' (k) measured in the current k control cycle
Figure BDA0002665025220000043
Figure BDA0002665025220000044
In the formula (I), the compound is shown in the specification,
Figure BDA0002665025220000045
Figure BDA0002665025220000046
Figure BDA0002665025220000047
I2n1is 2n1And (5) dimension unit array. Preferably, the step S3 includes: the state deviation information of the control platform in the k + n control period under the condition of no control input in the k-k + n-1 control period
Figure BDA0002665025220000048
The following were used:
Figure BDA0002665025220000049
in the formula, Xr(k + n) represents the expected state information of the steering platform for the (k + n) th control cycle.
Predicting the state deviation information of the mechanical arm in the (k + n) th control period under the condition that no control input exists in the (k + n) th control period
Figure BDA00026650252200000410
Comprises the following steps:
Figure BDA00026650252200000411
x 'in the formula'r(k + n) represents the expected state information of the robot arm for the (k + n) th control cycle.
Preferably, the step S4 includes: s4.1, making the state deviation information of the control platform in the k + n control period
Figure BDA00026650252200000412
And when the control period is zero, solving the control action sequence of the control platform in the k-to-k + n-1 control period according to the generalized inverse matrix theory as follows:
Figure BDA0002665025220000051
in the formula (I), the compound is shown in the specification,
Figure BDA0002665025220000052
is Bd3If n is 1, Bd3The column is full of rank and is,
Figure BDA0002665025220000053
if n is not less than 2, Bd3The row is of full rank and the column is,
Figure BDA0002665025220000054
I1representing identity matrices of respective dimensions; gamma ray1Representing an arbitrary vector.
Under the control action of the control action sequence of the control platform, the control platform can reach the expected state information X of the control platform in the (k + n) th control periodr(k+n)。
S4.2, making state deviation information of the mechanical arm
Figure BDA0002665025220000055
And if the control action sequence is zero, solving the control action sequence of the mechanical arm in the k-to-k + n-1 control period according to the generalized inverse matrix theory as follows:
Figure BDA0002665025220000056
in the formula (I), the compound is shown in the specification,
Figure BDA0002665025220000057
is Bd4If n is 1, Bd4The column is full of rank and the rank,
Figure BDA0002665025220000058
if n is not less than 2, Bd4The full rank of the row is the sum of the ranks,
Figure BDA0002665025220000059
I2an identity matrix representing the respective dimension; gamma, gamma2Representing an arbitrary vector.
Under the control action of the control action sequence of the mechanical arm, the mechanical arm can reach the expected state information x of the mechanical arm in the (k + n) th control periodr′(k+n)。
Preferably, the step S5 includes: step S5.1, compensation control quantity tau 'of the operation platform'b(k) The following:
Figure BDA00026650252200000510
in the formula, Kc1For a 12-dimensional positive-definite diagonal compensation coefficient matrix for adjusting the degree of compensation, Δ X (i) ═ Xr(i) -x (i) state deviation information of the manipulation stage for the ith control cycle.
S5.2, the compensation control quantity of the mechanical arm is as follows:
Figure BDA0002665025220000061
in the formula, Kc2Is a 2 n-dimensional positive definite diagonal compensation coefficient matrix, Δ x '(i) ═ x'r(i) -x' (i) is the state deviation information of the robot arm at the ith control cycle.
Preferably, the step S6 includes: step S6.1, the manipulation at the kth control cycle
Control output command tau of platformbf(k) The following were used:
τbf(k)＝τb(k)+τ′b(k)；
s6.2, control output instruction tau of the mechanical arm in the kth control periodaf(k) The following:
τaf(k)＝τ′a(k)+τa(k)。
compared with the prior art, the invention has at least one of the following advantages:
(1) the invention has the advantages of high state tracking precision, high response speed and stronger robustness to system parameters and external disturbance. The control moment has the characteristic of minimum norm, and control energy is saved.
The invention is based on the kinetic equation of the mechanical arm, and inverses the control force and the moment of the control platform and the control moment of the mechanical arm joint according to the state transfer equation of the discrete form, the control platform and the mechanical arm state which are measured in real time, the planned control platform and the mechanical arm expected state. According to the state deviation of the control platform and the mechanical arm, the compensation control input is directly solved according to the dynamic principle, and the robustness is high. The method adjusts the control input in real time according to the predicted state deviation of the platform and the mechanical arm and the actual state deviation information, is a control method for accurately and quantitatively controlling the controlled quantity, and has the characteristics of parameter self-adaption and accurate and quantitative control of the controller. In addition, the control method is suitable for motion control of the mechanical arm with the fixed base on the ground and motion control of the mechanical arm in space, the solved control torque has the characteristics of least square and minimum norm, and the energy is saved while the control precision is improved.
(2) The method is simple and effective, and the parameters are convenient to adjust.
The controller parameters of the invention are related to the system control period, the quality matrix and the nonlinear item which are solved by the inverse dynamics brought by the relevant states of the measured platform and the mechanical arm. Therefore, the controller parameters have the characteristic of time-varying self-adaption. The expected track can be tracked by the platform position posture and the mechanical arm joint angle only by properly setting the compensation coefficient matrix, and the dynamic and steady performance is better.
Drawings
Fig. 1 is a schematic flow chart of a method for model prediction and inversion control of a robot according to an embodiment of the present invention.
Detailed Description
The following describes the model prediction and inversion control method for a robot arm according to the present invention in detail with reference to fig. 1 and the detailed description. The advantages and features of the present invention will become more apparent from the following description. Any modification of the structure, change of the ratio or adjustment of the size of the structure, without affecting the function and the purpose of the invention, should fall within the scope of the technical disclosure of the present invention.
It is noted that, herein, relational terms such as first and second, and the like may be used solely to distinguish one entity or action from another entity or action without necessarily requiring or implying any actual such relationship or order between such entities or actions. Also, the terms "comprises," "comprising," or any other variation thereof, are intended to cover a non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements does not include only those elements but may include other elements not expressly listed or inherent to such process, method, article, or apparatus. Without further limitation, an element defined by the phrase "comprising an … …" does not exclude the presence of other identical elements in a process, method, article, or apparatus that comprises the element.
As shown in fig. 1, the present embodiment provides a model prediction and inversion control method for a spatial manipulator, including:
step S1, acquiring control platform state information x (k) and mechanical arm state information x' (k) measured in the current kth control period.
Step S2, respectively predicting according to the control platform state information X (k) and the mechanical arm state information x' (k), and obtaining the predicted state information of the control platform in the k + n control period
Figure BDA0002665025220000071
And predicted state information of the robot arm
Figure BDA0002665025220000072
Wherein n is more than or equal to 1.
Step S3, obtaining the expected state information X of the control platform in the k + n control periodr(k + n) and expected state information x 'of the robot arm'r(k+n)。
The expected state information X of the control platform is converted into the expected state information Xr(k + n) and predicted state information of the manipulation platform
Figure BDA0002665025220000073
Making difference to obtain state deviation information of the control platform
Figure BDA0002665025220000074
Expected state information x 'of the mechanical arm'r(k + n) and predicted state information of the robot arm
Figure BDA0002665025220000081
Making difference to obtain the state deviation information of the mechanical arm
Figure BDA0002665025220000082
And step S4, reversely deducing the control action sequence of the control platform and the control action sequence of the mechanical arm in the k-th to k + n-1-th control periods respectively based on the generalized inverse matrix theory.
Step S5, deriving the compensation control input of the operation platform and the mechanical arm in the current kth control cycle according to the state deviation information (including current and historical state deviation information) of the operation platform and the state deviation information (including current and historical state deviation information) of the mechanical arm, and obtaining the compensation control quantity of the operation platform and the compensation control quantity of the mechanical arm.
Step S6, calculating the control quantity of the control platform in the kth control period according to the control action sequence of the control platform, and summing the control quantity of the control platform and the compensation control quantity of the operation platform to obtain a control output instruction of the control platform in the kth control period; and correspondingly inputting the control output command of the control platform in the kth control period to a force and moment executing mechanism of the control platform.
Calculating to obtain the control quantity of the mechanical arm in the kth control period according to the control action sequence of the mechanical arm, and summing the control quantity of the mechanical arm and the compensation control quantity of the mechanical arm to obtain a control output instruction of the mechanical arm in the kth control period; and correspondingly inputting the control output instruction of the mechanical arm in the kth control period to the mechanical arm joint servo motor.
This embodiment still includes: and updating the kth control period to be the (k +1) th control period, repeating the step S1 to the step S6, and so on until the control process is finished.
In a continuous time system, establishing a kinetic equation of the mechanical arm according to a Newton-Eulerian method, a Lagrange method or a Kennel method;
according to a multi-body dynamics modeling method such as a Lagrange method, a Newton-Euler method or a Kane method, a dynamics equation of a space control platform and the mechanical arm can be established, and the dynamics equation is finally obtained as follows:
Figure BDA0002665025220000091
in the formula (I), the compound is shown in the specification,
Figure BDA0002665025220000092
in order to control the position and attitude angle vector of the platform, q is the joint angle column vector of the n-dimensional mechanical arm, and n is the joint number of the mechanical arm. Mb(x) Is a function of the quality matrix of the 6 multiplied by 6 dimensional platform (control platform) and the pose of the platform, which is abbreviated as Mb；Ma(q) the mass matrix of the manipulator in dimensions n x n as a function of the manipulator joint angle, i.e. related to the manipulator configuration, abbreviated as Ma；Mc(x, q) is a coupling part of the 6 Xn arm and the platform quality matrix, is related to both the platform pose and the mechanical arm joint angle, and is abbreviated as Mc；
Figure BDA0002665025220000093
A non-linear term for a 6 x 1 dimensional platform, which can be abbreviated as Fb，
Figure BDA0002665025220000094
Is an n x 1 dimensional nonlinear term of the mechanical arm, which can be abbreviated as Fa；τbThe three axes of the platform control forces and moments, which are 6 x 1 column vectors. Tau isaThe control moment of each joint of the mechanical arm is n multiplied by 1 column vectors. The mass matrix and the nonlinear term can be obtained by substituting a dynamic equation into the measured joint angle and angular velocity of the mechanical arm according to the position, attitude angle, velocity and attitude angular velocity of the platform which are actually measured. Equation (1) ignores the influence of gravity due to the microgravity environment in space.
Further finishing the formula (1), the obtained platform decoupling form and the mechanical arm decoupling form are shown as follows:
Figure BDA0002665025220000095
in the formula (2), Mbeq、MaeqRespectively are equivalent mass matrixes of the platform and the mechanical arm. Fbeq、FaeqEquivalent nonlinear terms for the platform and the robotic arm, respectively.
The specific representation is as follows:
Figure BDA0002665025220000096
in particular, if the mass characteristics of the arm and the load in the application of the robot arm to a fixed base or space are much smaller than those of the platform, then only the dynamics of the arm and the load itself are considered, and in equation (3),
Figure BDA0002665025220000097
in this case, only the mechanical arm body portion is subjected to subsequent control design, and the platform can be regarded as unchanged in position and posture.
The step S2 includes:
s2.1, establishing a pose prediction equation of the control platform as
Figure BDA0002665025220000101
In the formula (5), T represents a control period,
Figure BDA0002665025220000102
x (k) represents the measurement state of the control platform in the kth control period,
Figure BDA0002665025220000103
the predicted state of the (k +1) th control cycle is represented, and the prediction equation in the form of state space is obtained by sorting and is shown as an equation (6):
Figure BDA0002665025220000104
in the formula (6), the reaction mixture is,
Figure BDA0002665025220000105
I6is a 6-dimensional unit array, O6×6Is a zero matrix; k denotes the count of control cycles, T denotes the control cycle (the duration of one control cycle T entered in the specific calculation), Mbeq(k) Equivalent mass matrix representing the steering platform at the kth control cycle, Fbeq(k) Representing an equivalent nonlinear term of the control platform in the kth control period; tau isb(k) The three-axis control force and moment of the control platform in the kth control period are represented and are column vectors of 6 multiplied by 1; x (k) represents the control platform state information measured in the current kth control periodIn order to solve the above-mentioned problems,
Figure BDA0002665025220000106
and the predicted state information of the control platform in the (k +1) th control period is shown.
Predicting the predicted state information of the control platform in the future k + n control period according to the control platform state information X (k) measured in the current k control period
Figure BDA0002665025220000107
When the prediction domain n is not large and the states of the platform and the mechanical arm slowly change, the visual matrix Bd1、SbIf the value is constant, that is, the value of the kth control cycle, then:
Figure BDA0002665025220000108
in the formula (I), the compound is shown in the specification,
Figure BDA0002665025220000109
Figure BDA00026650252200001010
Figure BDA0002665025220000111
I12is a 12-dimensional identity matrix;
s2.2, establishing a joint state prediction equation of the mechanical arm. With the joint angle and joint angular velocity of the arm as state variables, i.e.
Figure BDA0002665025220000112
Where q is a joint position vector and q is,
Figure BDA0002665025220000113
is a joint velocity vector.
Using Taylor expansion of
Figure BDA0002665025220000114
In the formula (I), the compound is shown in the specification,
Figure BDA0002665025220000115
q (k) represents a joint angle vector measured at the k-th control cycle,
Figure BDA0002665025220000116
representing the predicted joint angle of the (k +1) th control cycle, and obtaining a discrete state space equation of the mechanical arm by combining the formula (2)
Figure BDA0002665025220000117
In the formula (I), the compound is shown in the specification,
Figure BDA0002665025220000118
Inis an n-dimensional unit array, n is the number of mechanical arm joints, T represents a control period (when calculation is carried out, the time length of one control period T is input) k represents the control period count,
Figure BDA0002665025220000119
represents predicted state information of the robot arm at the k +1 th control cycle, x' (k) represents state information of the robot arm measured at the current k th control cycle, and τa(k) The control moment of each joint of the mechanical arm in the kth control period is represented as n multiplied by 1 column vectors; maeq(k) Matrix representing equivalent masses of the arm, Faeq(k) An equivalent nonlinear term of the mechanical arm in the kth control cycle; the joint angle attitude vector q in the formula (8),
Figure BDA00026650252200001110
Can be measured in real time, and the quality matrix Maeq(k) Nonlinear term Faeq(k) Inverse dynamics iterations that can be based on equations (1) and (3)And (4) calculating.
Predicting the predicted state information of the mechanical arm in the k + n control period according to the mechanical arm state information x' (k) measured in the current k control period
Figure BDA00026650252200001111
When the prediction domain n is not large and the states of the platform and the mechanical arm slowly change, the matrix B can be considered asd2、GpIs a constant value. Then there are:
Figure BDA0002665025220000121
in the formula (I), the compound is shown in the specification,
Figure BDA0002665025220000122
Figure BDA0002665025220000123
Figure BDA0002665025220000124
I2n1is 2n1And (5) dimension unit array.
It will be appreciated that in steps S2.1 and S2.2, the choice of the states of the platform and the robot arm, or the prediction method used, will result in a different element in the formula. Any prediction equations of the form of equation (6) and equation (9) are also within the scope of the present patent claims.
The step S3 includes:
step S3.1, if the expected state (the expected state information of the control platform) of the (k + n) th control period is Xr(k + n), the state deviation information of the operation platform (state deviation value of the operation platform) in the k + n control period under the condition that no control input exists in the k-k + n-1 control period
Figure BDA0002665025220000125
As follows below, the following description will be given,
Figure BDA0002665025220000126
s3.2, if the joint state (the expected state information of the mechanical arm or the expected state value of the mechanical arm) of the mechanical arm in the (k + n) th control period is xr' (k + n) in the control cycle of the robot arm, the state deviation information of the robot arm predicted in the k + n control cycle when there is no control input in the k to k + n-1 control cycles
Figure BDA0002665025220000127
Is composed of
Figure BDA0002665025220000128
The step S4 includes:
s4.1, making the state deviation information of the control platform in the k + n control period
Figure BDA0002665025220000129
The control action sequence of the control platform in the k-to-k + n-1 control period is solved to be zero according to the generalized inverse matrix theory
Figure BDA00026650252200001210
In the formula (I), the compound is shown in the specification,
Figure BDA00026650252200001211
is Bd3In the generalized inverse of (1), if n is 1, Bd3The column is full of rank and the rank,
Figure BDA00026650252200001212
if n is greater than or equal to 2, Bd3The row is of full rank and the column is,
Figure BDA00026650252200001213
I1、γ1respectively units of corresponding dimensionsMatrices and arbitrary vectors. By aligning different vectors (vectors) gamma1The path of the platform state change can be optimized and selected on the premise of reaching the expected state.
Under the control of equation (13), the control platform will reach the desired state X of the control platform in the (k + n) th control periodr(k+n)。
S4.2, making state deviation information of the mechanical arm
Figure BDA0002665025220000131
The control action sequence of the mechanical arm for solving the k to k + n-1 control period is zero according to the generalized inverse matrix theory
Figure BDA0002665025220000132
In the formula (14), the compound represented by the formula (I),
Figure BDA0002665025220000133
is Bd4In the generalized inverse of (1), if n is 1, Bd4The column is full of rank and is,
Figure BDA0002665025220000134
if n is not less than 2, Bd4The full rank of the row is the sum of the ranks,
Figure BDA0002665025220000135
I2、γ2respectively, identity matrix and arbitrary vector of corresponding dimension. By means of a pair vector gamma2The selection of the robot arm can realize the optimization of the joint path of the robot arm on the premise of reaching the expected state, such as the avoidance of singularity and the like.
Under the control of equation (14), the robot will reach the desired state x of the robot in the k + n control periodr′(k+n)。
The step S5 includes:
s5.1, considering the state deviation caused by unmodeled dynamics, parameter uncertainty and external interference of the platform, and utilizing the current and history obtained by measurementObtaining state deviation information from the state, and inverting the compensation control input (the compensation control amount tau of the operating platform)b' (k)) is
Figure BDA0002665025220000136
In formula (15), Kc1A diagonal compensation coefficient matrix is determined for the 12-dimension positive matrix to adjust the degree of compensation. Δ X (i) ═ Xr(i) And X (i) is a state deviation value (current and historical state deviation information of the control platform) of the ith control period, wherein the value range of i is 1-k.
S5.2, considering state deviation caused by unmodeled dynamics, parameter uncertainty and external disturbance, obtaining current and historical state deviation information by using the measured mechanical arm state, and inverting a compensation control instruction, wherein the compensation control quantity of the mechanical arm is
Figure BDA0002665025220000137
In formula (16), Kc2Is a 2 n-dimensional positive definite diagonal compensation coefficient matrix, Δ x '(i) ═ x'r(i) And x' (i) is the state deviation value of the mechanical arm in the ith control cycle.
The step S6 includes:
s6.1, finally outputting a control output instruction tau of the control platform in the kth control period for the control force and the moment of the platformbf(k) Control amount τ of steering the stage for kth control period calculated for equation (13)b(k) And the compensated control quantity tau 'of the steering platform obtained by calculating the formula (15)'b(k) Is the sum of
τbf(k)＝τb(k)+τ′b(k) (17)
Outputting a control output instruction tau of the control platformbf(k) And force and moment actuators output to the control platform.
S6.2, outputting the kth control cycle for the control torque of the mechanical arm jointControl output instruction tau of the mechanical arm in timeaf(k) The control amount τ of the robot arm for the k-th control period calculated for equation (14)a(k) And (16) calculating the compensation control quantity tau 'of the mechanical arm'a(k) Is the sum of
τaf(k)＝τ′a(k)+τa(k) (18)
Outputting a control output instruction tau of the mechanical armaf(k) And outputting the data to a mechanical arm joint servo motor.
The step S7 includes: the measurement information of the respective state quantities of the stage and the robot arm is updated, and the k-th control cycle in step S1 is updated to the k + 1-th control cycle. And repeating the process and entering the next control period.
Therefore, the present embodiment provides a model prediction and inversion control method for a robot arm, which predicts state information of a platform and the robot arm in a (k + n) th control period according to state information measured in a current (k) th control period and according to dynamics and kinematics characteristics of the robot arm from the viewpoint of system controllability, and reversely deduces control input of a manipulation platform and control input of the robot arm in the (k-k + n-1) th control period based on a generalized inverse matrix theory. Based on the current and historical state deviation information, the compensation control input of the current kth control period platform and the mechanical arm is reversely deduced so as to weaken the state deviation caused by factors such as external interference, uncertain parameters and the like. The sum of the kth control cycle control input and the compensation control input, which is obtained from the predicted state deviation, is used as the control input to be applied to the stage and the robot arm for the kth control cycle. Therefore, the synchronous control of the attitude of the platform and the track tracking of the mechanical arm joint with higher precision is realized, and the anti-interference capability on parameters and external disturbance is stronger.
To facilitate understanding of the present embodiment, the following description takes a control cycle as an example: the method specifically comprises the following steps: the process of step S1 is the same as that of the above embodiment, and step S2 predicts the predicted state information of the robot arm and the manipulation platform in the (k +1) th control cycle based on the discrete state transfer equation (formula 6 and formula 9) of the robot arm, the joint angle and angular velocity of the robot arm, the attitude angle and angular velocity of the platform, and the position and velocity of the platform, which are currently measured:
predicting state information of the control platform in the (k +1) th control period in the future by using the control platform state information X (k) measured in the current kth control period
Figure BDA0002665025220000151
This is the formula (6).
According to the above formula (11), if the expected state of the operation platform in the (k +1) th control cycle is Xr(k +1), under the condition that no control input is input in the kth control period, the predicted state deviation of the control platform in the kth +1 control period
Figure BDA0002665025220000152
Comprises the following steps:
Figure BDA0002665025220000153
predicting the mechanical arm joint state of the (k +1) th control period according to the mechanical arm joint state x' (k) measured in the current kth control period
Figure BDA0002665025220000154
This is formula (9).
According to the formula (12), if the expected mechanical arm joint state of the k +1 th control cycle is x'r(k +1), in the case where there is no control input in the k-th control period, the predicted state deviation of the robot arm in the k + 1-th control period
Figure BDA0002665025220000155
Is composed of
Figure BDA0002665025220000156
According to the results of the formula (19) and the formula (20), inverting to obtain the control moment of the mechanical arm joint, the control force and the moment instruction sequence of the position and the posture of the control platform in the kth control period;
make the predicted state deviation of the control platform
Figure BDA0002665025220000157
To zero, the sequence of the control actions of the platform in the k-th control period is solved according to the generalized inverse matrix theory and the above equation (13)
Figure BDA0002665025220000158
In the formula (I), the compound is shown in the specification,
Figure BDA0002665025220000159
is Bd1Is expressed as a generalized inverse of
Figure BDA00026650252200001510
This solution is a special solution for the least squares, minimum norm, of the state deviation of equation (13).
Under the control of equation (21), the manipulation platform will reach the desired state X of the manipulation platform in the (k +1) th control cycler(k+1)。
Make the predicted state deviation of the mechanical arm
Figure BDA00026650252200001511
To zero, according to the generalized inverse matrix theory and the above equation (14), the sequence of mechanical arm control actions for solving k periods is
Figure BDA0002665025220000161
In the formula (22), the reaction mixture is,
Figure BDA0002665025220000162
is Bd2The generalized inverse of (1). This solution is a special solution of the least squares, minimum norms, on the robot joint state deviation of equation (14).
Under the control of formula (22), theThe mechanical arm reaches the expected state information x 'of the mechanical arm in the k +1 control period'r(k+1)。
And then, compensating the external disturbance and the unmodeled part by using the current and historical state deviation information of the mechanical arm and the platform, and performing inversion to obtain the control moment of the mechanical arm joint compensated in the kth control period and the control force and moment of the platform pose.
Step S5.1, considering the state deviation caused by unmodeled dynamics, parameter uncertainty and external interference of the platform, obtaining the current and historical state deviation information of the operation platform by utilizing measurement, and inverting a compensation control input (the compensation control quantity tau 'of the operation platform)'b(k) Is) as
Figure BDA0002665025220000163
In formula (23), Kc1A diagonal compensation coefficient matrix is determined for the 12-dimension positive matrix to adjust the degree of compensation. Δ X (i) ═ Xr(i) X (i) is a state deviation value of the ith control cycle (state deviation information of the control platform), and can be calculated by formula (11).
S5.2, taking state deviation caused by unmodeled dynamics, parameter uncertainty and external disturbance into consideration, obtaining current and historical state deviation information of the mechanical arm by utilizing measurement, and inverting a compensation control instruction, wherein the compensation control quantity of the mechanical arm is
Figure BDA0002665025220000164
In the formula (24), Kc2Is a 2 n-dimensional positive definite diagonal compensation coefficient matrix, Δ x '(i) ═ x'r(i) And x' (i) is the state deviation value of the mechanical arm in the ith control cycle, and can be calculated by the formula (12).
The step S6 includes:
s6.1, finally outputting a control output instruction tau of the control platform in the kth control period for the control force and the moment of the platformbf(k) Is represented by the formula (A)13) Calculated control quantity tau of the operation platform of the kth control periodb(k) And (15) calculating the compensation control quantity tau 'of the control platform'b(k) Is the sum of
τbf(k)＝τb(k)+τ′b(k) (25)
Outputting a control output instruction tau of the control platformbf(k) And force and moment actuating mechanisms output to the control platform.
S6.2, finally outputting the control output command tau of the mechanical arm in the kth period to the control torque of the mechanical arm jointaf(k) The control amount τ of the robot arm for the kth control period calculated by equation (14)a(k) And a compensation control quantity tau 'of the mechanical arm calculated by formula (16)'a(k) Is the sum of
τaf(k)＝τ′a(k)+τa(k) (26)
Outputting a control output instruction tau of the mechanical armaf(k) And outputting the data to a mechanical arm joint servo motor.
S7, measuring and updating the states of the platform and the mechanical arm, updating the kth control period to the (k +1) th control period, and entering the step S3.
For the fixed base mechanical arm, the dynamics of the platform part does not need to be considered, and the joint motion control of the mechanical arm body is controlled according to the steps. The integrated control strategy of the platform and the mechanical arm has the characteristics of high control precision, strong robustness on model parameters and disturbance torque and power consumption saving required by control.
The embodiment provides an inversion control method for a mechanical arm, and starts from the aspect of system controllability, the motion states of a platform and the mechanical arm after a k + n control period are predicted according to the dynamic characteristics of the mechanical arm, and a compensated platform control force, a compensated control torque and a compensated control torque of the mechanical arm in the k control period are obtained through reverse deduction according to the predicted motion states of the platform and the mechanical arm. The method realizes stronger robustness to external moment disturbance and higher tracking precision of the platform position posture and the joints of the mechanical arm.
While the present invention has been described in detail with reference to the preferred embodiments, it should be understood that the above description should not be taken as limiting the invention. Various modifications and alterations to this invention will become apparent to those skilled in the art upon reading the foregoing description. Accordingly, the scope of the invention should be limited only by the attached claims.

Claims (7)

1. A model prediction and inversion control method for a mechanical arm is characterized by comprising the following steps:
step S1, acquiring the state information of the control platform and the state information of the mechanical arm obtained by current kth control period measurement;
step S2, respectively predicting according to the state information of the control platform and the state information of the mechanical arm to obtain the predicted state information of the control platform and the predicted state information of the mechanical arm in the (k + n) th control period, wherein n is more than or equal to 1;
step S3, obtaining the expected state information of the manipulation platform and the expected state information of the robot arm in the (k + n) th control cycle,
the expected state information of the control platform and the predicted state information of the control platform are compared
Figure FDA0003541012380000011
Performing difference to obtain state deviation information of the control platform;
subtracting the expected state information of the mechanical arm from the predicted state information of the mechanical arm to obtain state deviation information of the mechanical arm;
step S4, reversely deducing the control action sequence of the control platform and the control action sequence of the mechanical arm in the k-k + n-1 control period based on the generalized inverse matrix theory;
step S5, deducing the compensation control input of the control platform and the mechanical arm in the current kth control period according to the state deviation information of the control platform and the state deviation information of the mechanical arm to obtain the compensation control quantity of the control platform and the compensation control quantity of the mechanical arm;
step S6, calculating the control quantity of the control platform in the kth control period according to the control action sequence of the control platform, and summing the control quantity of the control platform and the compensation control quantity of the control platform to obtain a control output instruction of the control platform in the kth control period; correspondingly inputting the control output command of the control platform in the kth control period to a force and moment executing mechanism of the control platform;
calculating to obtain the control quantity of the mechanical arm in the kth control period according to the control action sequence of the mechanical arm, and summing the control quantity of the mechanical arm and the compensation control quantity of the mechanical arm to obtain a control output instruction of the mechanical arm in the kth control period; and correspondingly inputting the control output instruction of the mechanical arm in the kth control period to the mechanical arm joint servo motor.
2. The method for model prediction and inversion control of a robotic arm of claim 1, further comprising: and updating the kth control period to be the (k +1) th control period, repeating the step S1 to the step S6, and so on until the control process is finished.
3. The method for model prediction and inversion control of a robot arm according to claim 1, wherein the step S2 comprises:
s2.1, establishing a state prediction equation of the control platform:
Figure FDA0003541012380000021
in the formula (I), the compound is shown in the specification,
Figure FDA0003541012380000022
I6is a 6-dimensional unit array, O6×6Is a zero matrix, k represents the control periodPeriod count, T denotes control period, Mbeq(k) Equivalent mass matrix representing the steering platform at the kth control cycle, Fbeq(k) Representing an equivalent nonlinear term of the control platform in the kth control period; tau isb(k) The three-axis control force and moment of the control platform in the kth control period are represented and are column vectors of 6 multiplied by 1; x (k) represents the state information of the control platform measured in the current kth control period,
Figure FDA0003541012380000023
representing the predicted state information of the control platform in the (k +1) th control period;
predicting the predicted state information of the control platform in the future (k + n) th control period according to the control platform state information X (k) measured in the current (k) th control period
Figure FDA0003541012380000024
The following:
Figure FDA0003541012380000031
in the formula (I), the compound is shown in the specification,
Figure FDA0003541012380000032
Figure FDA0003541012380000033
Figure FDA0003541012380000034
Sbis a constant value;
I12is a 12-dimensional identity matrix;
s2.2, establishing a state prediction equation of the mechanical arm:
Figure FDA0003541012380000035
in the formula (I), the compound is shown in the specification,
Figure FDA0003541012380000036
In1is n1Dimensional array, On1×n1Is a zero matrix; n is1The number of joints of the robot arm, k represents a control period count, T represents a control period,
Figure FDA0003541012380000037
represents predicted state information of the robot arm at the k +1 th control cycle, x' (k) represents state information of the robot arm measured at the current k th control cycle, and τa(k) The control moment of each joint of the mechanical arm in the k control cycle is represented as n1X 1 column vector; maeq(k) The equivalent mass matrix of the mechanical arm in the kth control period is represented as n1×n1A matrix of (a); faeq(k) Is an equivalent nonlinear term of the mechanical arm in the k control period, which is n1X 1 in the column direction; g (k) is the gravitational moment of force of the kth control period, which is n1X 1 column vector;
the predicted state information of the robot arm in the k + n control cycle is predicted from the robot arm state information x' (k) measured in the current k control cycle
Figure FDA0003541012380000038
Figure FDA0003541012380000039
In the formula (I), the compound is shown in the specification,
Figure FDA00035410123800000310
Figure FDA00035410123800000311
Figure FDA00035410123800000312
I2n1is 2n1And (5) dimensional unit array.
4. The method for model prediction and inversion control of a robot arm according to claim 3, wherein the step S3 comprises:
under the condition of no control input in the k-th to k + n-1 th control period, the state deviation information of the control platform in the k + n th control period
Figure FDA0003541012380000041
The following were used:
Figure FDA0003541012380000042
in the formula, Xr(k + n) desired state information of the manipulation platform representing a k + n-th control period;
predicting the state deviation information of the mechanical arm in the k + n control period under the condition of no control input in the k-k + n-1 control period
Figure FDA0003541012380000043
Comprises the following steps:
Figure FDA0003541012380000044
in formula (II), x'r(k + n) represents desired state information of the robot arm for the (k + n) th control cycle.
5. The model prediction and inversion control method of a robot arm according to claim 4, wherein the step S4 includes:
step S4.1, order the k + n control periodState deviation information of the control platform
Figure FDA0003541012380000045
And when the control period is zero, solving the control action sequence of the control platform in the k-to-k + n-1 control period according to the generalized inverse matrix theory as follows:
Figure FDA0003541012380000046
in the formula (I), the compound is shown in the specification,
Figure FDA0003541012380000047
is Bd3If n is 1, Bd3The column is full of rank and the rank,
Figure FDA0003541012380000048
if n is not less than 2, Bd3The full rank of the row is the sum of the ranks,
Figure FDA0003541012380000049
I1an identity matrix representing a corresponding dimension; gamma ray1Represents an arbitrary vector; under the control action of the control action sequence of the control platform, the control platform can reach the expected state information X of the control platform in the (k + n) th control periodr(k+n)；
S4.2, enabling state deviation information of the mechanical arm
Figure FDA00035410123800000410
And if the control action sequence is zero, solving the control action sequence of the mechanical arm in the k-th to k + n-1 th control period according to the generalized inverse matrix theory as follows:
Figure FDA0003541012380000051
in the formula (I), the compound is shown in the specification,
Figure FDA0003541012380000052
is Bd4In the generalized inverse of (1), if n is 1, Bd4The column is full of rank and the rank,
Figure FDA0003541012380000053
if n is not less than 2, Bd4The full rank of the row is the sum of the ranks,
Figure FDA0003541012380000054
I2an identity matrix representing the respective dimension; gamma ray2Represents an arbitrary vector;
the mechanical arm reaches the expected state information x 'of the mechanical arm in the k + n control period under the control action of the control action sequence of the mechanical arm'r(k+n)。
6. The method for model prediction and inversion control of a robot arm according to claim 5, wherein the step S5 comprises:
step S5.1, compensating control quantity tau 'of the control platform'b(k) The following were used:
Figure FDA0003541012380000055
in the formula, Kc1For a 12-dimensional matrix of positive definite diagonal compensation coefficients, for adjusting the degree of compensation, Δ X (i) ═ Xr(i) -x (i) state deviation information of the manipulation stage for the ith control period;
and S5.2, the compensation control quantity of the mechanical arm is as follows:
Figure FDA0003541012380000056
in the formula, Kc2Is a 2 n-dimensional positive definite diagonal compensation coefficient array, Δ x '(i) ═ x'r(i) -x' (i) is the state deviation information of the robot arm at the ith control cycle.
7. The method for model prediction and inversion control of a robot arm according to claim 6, wherein the step S6 comprises:
s6.1, control output instruction tau of the control platform in the kth control periodbf(k) The following:
τbf(k)＝τb(k)+τ′b(k)；
s6.2, control output instruction tau of the mechanical arm in the kth control periodaf(k) The following were used:
τaf(k)＝τ′a(k)+τa(k)。
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