CN111796525B - Model prediction control method based on exoskeleton robot mechanical arm - Google Patents
Model prediction control method based on exoskeleton robot mechanical arm Download PDFInfo
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- G05B13/00—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion
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Abstract
The invention discloses a model prediction control method based on an exoskeleton robot mechanical arm, and belongs to the field of exoskeleton robots. Aiming at the problem of overlarge steady-state error under the condition of time-varying disturbance and parameter uncertainty in the prior art, the invention provides a model prediction control method based on an exoskeleton robot mechanical arm, which comprises the following steps: firstly, a high-gain observer based on continuous time is provided for estimating the state and disturbance of a tracking error; then, an improved performance index is provided, which comprises a tracking error part and a control input part; and finally, obtaining a model predictive control law after the performance indexes are subjected to rolling time domain optimization. The method can meet the requirement of optimal non-offset tracking, has better steady-state performance under the condition of time-varying disturbance, and is easy to realize.
Description
Technical Field
The invention relates to the field of exoskeleton robots, in particular to a model prediction control method of a mechanical arm of an exoskeleton robot.
Background
The exoskeleton robot technology is a comprehensive technology which integrates sensing, control, information, fusion and mobile computing and provides a wearable mechanical mechanism for a person as an operator. Exoskeleton robots find substantial application in civilian, military and commercial applications, such as: the walking aid can assist people with physical disabilities to walk in the civil aspect, and can assist soldiers to fight in the military aspect, and the like. Due to the complexity of the mechanical structure of the exoskeleton robot and the influence of various parameters such as friction force, accurate values of the parameters of the exoskeleton robot are difficult to obtain.
Chinese patent application, publication No. CN105955015A, published 2016, 9, 21, discloses a fuzzy control method for exoskeleton systems. The method is designed aiming at the conditions that the traditional exoskeleton is easily influenced by the external environment when the PID control is mostly adopted, and the control effect of the system is poor. After the control model is changed, the controller can better track an expected curve compared with a PID (proportion integration differentiation) controller in fuzzy adaptive control, and has obvious advantages in the aspects of instantaneity, robustness and the like. But the fuzzy control rule of the method is complex and is not easy to realize.
The Chinese patent application, application No. CN105796286B, publication No. 2016, 7, 27, discloses a control method based on a lower limb exoskeleton robot, which adds an air bag pressure sensor on the basis of a traditional lower limb exoskeleton human intention detection sensor, and reflects the acting force of a human body and an exoskeleton by measuring a signal generated by pressing an air bag by a human thigh, so as to feed back the human body movement intention and correct the deviation of an exoskeleton control algorithm; the air bag sensor is used, and meanwhile, a flexible man-machine interface can be provided for a human body, so that the acting force of the human body and the exoskeleton robot is buffered; meanwhile, the assistance effect of the lower limb exoskeleton robot can be well evaluated by collecting the motion curve of the wearing exoskeleton human body and the force curve of the airbag sensor. The method corrects the offset by a fuzzy controller. However, the fuzzy rule of the method is complex to make and depends on expert experience, which is not favorable for implementation.
Disclosure of Invention
1. Technical problem to be solved
Aiming at the problem of overlarge steady-state error under the conditions of time-varying disturbance and parameter uncertainty in the prior art, the invention provides a model prediction control method based on an exoskeleton robot mechanical arm, which can meet the requirement of optimal non-offset tracking, ensures better dynamic stability and is easy to realize.
2. Technical scheme
The purpose of the invention is realized by the following technical scheme.
A model prediction control method based on an exoskeleton robot mechanical arm comprises the following steps:
step 1: providing an improved performance index which comprises a tracking error part and a control input part;
step 2: providing a high-gain observer based on continuous time, and estimating the state and disturbance of a tracking error;
and step 3: and (3) combining the errors and the disturbances in the step (2), and obtaining a model predictive control law after the performance indexes in the step (1) are subjected to rolling time domain optimization.
Further, in the step 1, the method comprises the following steps:
step 101, providing a mechanical arm motion control system equation of the exoskeleton robot:
wherein u is the moment generated on the actuator shaft, d is the disturbance moment on the link shaft, and q is 1 To perform angular positions on the shaft, q 2 Angular position of the connecting rod, J 1 Is the moment of inertia of the actuator, J 2 Is the moment of inertia of the connecting rod, F 1 Is the coefficient of friction of the actuator, F 2 The friction coefficient of the connecting rod, K is the elastic coefficient of the spring, N is the transmission ratio of the transmission gear, m is the mass of the connecting rod, l is the length of the connecting rod, and g is the gravity acceleration;
step 102, a dynamic tracking error equation of a mechanical arm motion system of the exoskeleton robot is given:
wherein q is 2r (t) is a reference output signal,
is a set of positive integers, b 0 Is the nominal value of b (t), which is the control gain. e (t) is the error of the actual output from the reference output, w (t) is the sum of various unknown disturbances and uncertainties, w 4 (t) contains a known reference output;
step 103, providing performance indexes of a mechanical arm motion control system equation based on the exoskeleton robot:
wherein: t: (>0) Is the prediction period; u. of r (t) is the desired steady state control input,
is the weight of the tracking error; r (R)>0) Is the weight of the controller input。
Further, in the step 2, the continuous-time based high-gain observer is:
wherein the content of the first and second substances,
and
are all generated by an observer,/ i ,σ i And τ is the adjustable observer gain.
Further, the method of estimating the tracking error system is as follows:
in step 201, a tracking error e (T + τ) at a future time is given in a prediction period T, and after taylor series expansion, the tracking error e (T + τ) can be expressed as follows:
where 0. Ltoreq. Tau. Ltoreq.T, simply by symbolizing the estimated values of the variables
Indicating that the predicted value of the variable is signed
Represents;
in step 202, the disturbance observer generates an estimate represented by
The predicted tracking error can be expressed in the form:
the control input is represented in the form:
the predicted tracking error can be expressed in the form:
wherein:
step 203, the controller input and the expected controller input at the future time are given, respectively as follows:
wherein the vector
The method is used for correcting the interference and uncertainty existing in the traditional Taylor series expansion prediction method.
Further, combining the formulas (6), (7) and (8), the performance index in the formula (3) is rewritten as follows:
wherein:
further, the process of obtaining the model predictive control law after optimizing the performance index rolling time domain is as follows:
will be represented by the formula (9)
For is to
Calculating the partial derivative to obtain:
knowing matrix
Is a positive definite matrix. Order to
The optimized control output is obtained as follows:
the model predictive control law is given in conjunction with equation (10) as follows:
wherein the gain is controlled
To meet the practical application, the estimated value
And
are generated by an observer. And the following assumptions must be satisfied: there is a known constant L ≧ 0, mE N + I.e. | w (m) (t)|≤L。
3. Advantageous effects
Compared with the prior art, the invention has the advantages that: the invention designs a continuous time model prediction control system method based on an exoskeleton robot, and by designing a model prediction control method with a nonlinear disturbance observer, optimal non-offset tracking can be realized under various disturbances. Compared with the traditional model prediction control law, the method has better steady-state performance under the condition of time-varying disturbance; meanwhile, the method provides a new performance index, and definitely analyzes the influence of the control input weight on the stability of the closed loop.
Drawings
FIG. 1 is a block diagram of a model predictive control method implementation proposed by the present invention;
FIG. 2 is a schematic view of an exoskeleton-based robotic arm;
FIG. 3 is a graph of q in the case of system uncertainty and external interference 2 The output curve of (a);
FIG. 4 is q of FIG. 3 after enlargement in 0-15 seconds 2 The output curve of (1).
Detailed Description
The invention is described in detail below with reference to the drawings and specific examples.
Examples
As shown in fig. 1, the invention discloses a model prediction control method for an exoskeleton robot mechanical arm, comprising the following steps:
step 1: the improved performance index comprises a tracking error part and a control input part, and comprises the following specific steps:
step 101, a motion control system equation of a mechanical arm of the exoskeleton robot is given:
as shown in fig. 2, in the schematic diagram of the exoskeleton robot mechanical arm, u is the moment generated on the actuator shaft, d is the disturbance moment on the link shaft, and q is 1 To perform angular position on the shaft, q 2 Angular position of the connecting rod, J 1 Is the moment of inertia of the actuator, J 2 Is the moment of inertia of the connecting rod, F 1 Is the coefficient of friction of the actuator, F 2 Is the friction coefficient of the connecting rod, K is the spring elastic coefficient, N is the transmission ratio of the transmission gear, m is the connecting rod mass, l is the connecting rod length, and g is the gravitational acceleration;
step 102, a dynamic tracking error equation of a mechanical arm motion system of the exoskeleton robot is given:
wherein q is 2r (t) is a reference output signal,
is a set of positive integers, b 0 Is the nominal value of b (t), b (t) is the control gain, e (t) is the error of the actual output from the reference output, w (t) is the sum of various unknown disturbances and uncertainties, w (t) is the sum of the various unknown disturbances and uncertainties 4 (t) contains a known reference output;
step 103, providing performance indexes of a motion control system equation based on the mechanical arm of the exoskeleton robot:
wherein T: (>0) Is the prediction period; u. u r (t) is a desired steady state control input,
Q(>0) Is a weight of the tracking error, R: (>0) Is the weight of the controller input.
And 2, step: designing a high-gain observer based on continuous time to estimate the state and disturbance of a tracking error, and specifically comprising the following steps of:
first, a continuous-time based high-gain observer is given:
wherein the content of the first and second substances,
and
are all generated by an observer,/ i ,σ i And τ is the adjustable observer gain.
Next, the method of estimating the tracking error system is as follows:
in step 201, a tracking error e (T + τ) at a future time is given in a prediction period T, and after taylor series expansion, the tracking error e (T + τ) can be expressed as follows
Where 0. Ltoreq. Tau. Ltoreq.T, simply by symbolizing the estimated values of the variables
Indicating that the predicted value of the variable is signed
Represents;
in step 202, the estimated value generated by the disturbance observer is represented as
The predicted tracking error can be expressed in the form:
the control input is represented in the form:
the predicted tracking error can be expressed in the form:
wherein:
step 203, the controller input and the expected controller input at the future time are given as follows:
wherein the vector
The method is used for correcting the interference and uncertainty existing in the traditional Taylor series expansion prediction method.
And 3, combining the errors and the disturbances in the step 2, and obtaining a model predictive control law after the performance indexes are subjected to rolling time domain optimization, wherein the method specifically comprises the following steps:
first, the performance index in the formula (3) is rewritten in the following form in combination with the formulas (6), (7), and (8):
wherein:
finally, the method for obtaining the model predictive control law after the performance indexes are optimized by the rolling time domain is as follows:
will be represented by the formula (9)
To pair
Calculating the partial derivative to obtain:
knowing matrix
Is a positive definite matrix. Order to
The optimized control output is obtained as follows:
the model predictive control law is given in conjunction with equation (10) as follows:
wherein the gain is controlled
To meet the practical application, the estimated value
And
both are generated by an observer. And the following assumptions must be satisfied: there is a known constant L ≧ 0, mE N + I.e. | w (m) (t)|≤L。
As shown in fig. 3 and 4, q in case of system uncertainty and external interference 2 The dotted line, the dashed line and the dotted line indicate that the system parameters have uncertainties of 10%, 20% and 30%, respectively, and the black line is a parameter of the actual system. It can be seen from the figure that the output can be quickly restored to the set value even in the presence of uncertainty and interference, representingThe method has excellent effect.
The invention and its embodiments have been described above schematically without limitation, and the invention can be embodied in other specific forms without departing from the spirit or essential characteristics thereof. The representation in the drawings is only one of the embodiments of the invention, the actual construction is not limited thereto, and any reference signs in the claims shall not limit the claims concerned. Therefore, if a person skilled in the art receives the teachings of the present invention, without inventive design, a similar structure and an embodiment to the above technical solution should be covered by the protection scope of the present patent. Furthermore, the word "comprising" does not exclude other elements or steps, and the word "a" or "an" preceding an element does not exclude the presence of a plurality of such elements. Several of the elements recited in the product claims may also be implemented by one element in software or hardware. The terms first, second, etc. are used to denote names, but not to denote any particular order.
Claims (2)
1. A model prediction control method based on an exoskeleton robot mechanical arm is characterized by comprising the following steps:
step 1: providing an improved performance index which comprises a tracking error part and a control input part;
step 101, providing a mechanical arm motion control system equation of the exoskeleton robot:
wherein u is the moment generated on the actuator shaft, d is the disturbance moment on the link shaft, and q 1 Angular position on the actuator shaft, q 2 Angular position of the connecting rod, J 1 Is the moment of inertia of the actuator, J 2 Is the moment of inertia of the connecting rod, F 1 Is the coefficient of friction of the actuator, F 2 Is the friction coefficient of the connecting rod, K is the spring elastic coefficient, N is the transmission ratio of the transmission gear, m is the connecting rod mass, l is the connecting rod length, and g is the gravitational acceleration;
step 102, providing a dynamic tracking error equation of the exoskeleton robot mechanical arm motion system:
wherein q is 2r (t) is a reference output signal,
is a positive integer set, b 0 Is the nominal value of b (t), b (t) is the control gain, e (t) is the error of the actual output from the reference output, w (t) is the sum of various unknown disturbances and uncertainties, w (t) is the sum of the various unknown disturbances and uncertainties 4 (t) contains a known reference output;
step 103, providing performance indexes of the motion control system equation of the exoskeleton robot mechanical arm:
wherein, T>0, is predictionPeriod, u r (t) is a desired steady state control input,
Q>0, is the weight of the tracking error, R>0, is the weight of the controller input;
and 2, step: a high-gain observer based on continuous time is provided, and the state and disturbance of a tracking error system are estimated;
the continuous-time based high-gain observer is:
wherein the content of the first and second substances,
in the formula, v 1 (t) and v k (t) is the adjustable high-gain observer gain,
and
are all generated by a high gain observer;
and 3, step 3: combining the errors and the disturbances in the step 2, and obtaining a model predictive control law after optimizing the performance index rolling time domain in the step 1; the optimization method of the performance index comprises the following steps:
combining the formulas (6), (7) and (8), the performance index in the formula (3) is rewritten as follows:
wherein the content of the first and second substances,
the method for obtaining the model predictive control law after optimization is as follows:
will be represented by the formula (9)
To pair
Calculating the partial derivative to obtain:
matrix of
Is a positive definite matrix, such that
The optimized control output is obtained as follows:
the model predictive control law is given in conjunction with equation (10) as follows:
wherein the gain [ k ] is controlled 1 k 2 k 3 k 4 ]＝(ζ 3 +hζ 4 ) -1 ζ 2 T ，
Estimated value
And
all are generated by a high gain observer and satisfy the following assumptions: there is a known constant L ≧ 0, mE N + I.e. | w (m) (t)|≤L。
2. The method for model predictive control based on exoskeleton robot mechanical arms as claimed in claim 1 wherein in step 2, the method for estimating the tracking error system is as follows:
in step 201, a tracking error e (T + τ) at a future time is given in a prediction period T, and after taylor series expansion, the tracking error e (T + τ) can be expressed as follows:
wherein tau is more than or equal to 0 and less than or equal to T, and the estimated value of the variable is signed
Indicating that the predicted value of the variable is signed
Represents;
in step 202, the disturbance observer generates an estimate represented by
The predicted tracking error can be expressed in the form:
the control input is represented in the form:
the predicted tracking error can be expressed in the form:
wherein:
step 203, the controller input and the expected controller input at the future time are given as follows:
wherein the vector
The method is used for correcting the interference and uncertainty existing in the Taylor series expansion prediction method.
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| CN111152225A (en) * | 2020-01-15 | 2020-05-15 | 北京科技大学 | Uncertain mechanical arm fixed time trajectory tracking control method with input saturation |
| CN111290273A (en) * | 2020-02-18 | 2020-06-16 | 湖州和力机器人智能科技有限公司 | Position tracking optimization control method based on exoskeleton robot flexible actuator |
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| CN109648564A (en) * | 2019-01-15 | 2019-04-19 | 西安科技大学 | A kind of control method of the multiple degrees of freedom flexible articulated mechanical arm system based on hierarchical structure MPC |
| CN111152225A (en) * | 2020-01-15 | 2020-05-15 | 北京科技大学 | Uncertain mechanical arm fixed time trajectory tracking control method with input saturation |
| CN111290273A (en) * | 2020-02-18 | 2020-06-16 | 湖州和力机器人智能科技有限公司 | Position tracking optimization control method based on exoskeleton robot flexible actuator |
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