CN117140504A - N-link mechanical arm control method based on incremental model predictive control - Google Patents
N-link mechanical arm control method based on incremental model predictive control Download PDFInfo
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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
- B25J9/1628—Programme controls characterised by the control loop
- B25J9/163—Programme controls characterised by the control loop learning, adaptive, model based, rule based expert control
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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
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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
- B25J9/1628—Programme controls characterised by the control loop
- B25J9/1633—Programme controls characterised by the control loop compliant, force, torque control, e.g. combined with position control
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Abstract
The invention discloses an N-link mechanical arm control method based on incremental model predictive control, which comprises the following steps: s1, establishing a Lagrange dynamics model of an N-link mechanical arm system, and performing approximate sampling discretization on the Lagrange dynamics model; s2, an incremental model prediction controller is established to predict the future state or output of the system, and an optimization problem is solved in a limited time interval; and S3, applying the optimized first-step control input to the system, and repeatedly carrying out the optimization process in the backward translation range of the model, so as to realize the control of the N-link mechanical arm system. Simulation results show that under the condition of known external disturbance, the incremental model predictive control can better control the steady motion of the two-link mechanical arm, and the two-link mechanical arm reaches the expected position under the condition of meeting the constraint condition. Compared with the prior art, the method solves the problems that PID process parameters are difficult to adjust, overshoot is too large and constraint cannot be met.
Description
Technical Field
The invention belongs to the technical field of space mechanical arm control, and particularly relates to an N-link mechanical arm control method based on incremental model predictive control.
Background
With the rapid development of the world aerospace industry, the exploration of space is continued deeply, and a large number of space tasks such as building of space stations, maintenance of space equipment, care of scientific experiment loads and the like are needed to be completed in the future. Due to the specificity of the space environment and the limitations of the current technology level, these tasks have not been accomplished entirely by astronauts. The space manipulator has the operation capability of adapting to space environments such as microgravity, high-low temperature alternation, high radiation and the like, and the space manipulator is adopted to assist or replace astronauts to finish some space operation tasks, so that the space manipulator has important significance in the aspects of economy and safety, and has become an important research direction in the field of space technology research.
The mechanical arm is a multi-input multi-output system, has the adverse characteristics of high nonlinearity, strong dynamic coupling, parameter perturbation, unknown interference and the like, and the conventional mechanical arm control system adopts a PID (Proportion integration-differentiation) control method. The design methods of the existing PID controllers are mainly divided into two types, namely a traditional PID design method and an intelligent PID control method.
The design of the traditional PID mainly uses some measurable intermediate states or outputs of a system as feedback, and realizes tracking of the outputs by adjusting the inputs through the PID parameters calculated in advance, but the design has the problems of overshoot, jitter and the like in a nonlinear scene, so the design cannot be used in a plurality of aerospace fields with high precision requirements.
The intelligent PID control method is generally used for a multi-input multi-output nonlinear control system. The existing intelligent PID control method mainly comprises a fuzzy self-adaptive PID controller, a neural network PID and the like. The fuzzy self-adaptive PID controller utilizes fuzzy logic and optimizes the parameters of PID in real time according to a certain fuzzy rule, so that the defect that the parameters of the traditional PID cannot be adjusted in real time is overcome, the sliding mode buffeting phenomenon of the mechanical arm can be effectively reduced, the dynamic performance and the anti-interference capability are better, and the method is difficult to meet the constraint condition and the performance index requirement. Neural networkWith arbitrary nonlinear expression capability, the parameter k can be established through learning the system performance P 、k i 、k d The self-tuning PID controller has better robustness and the ability to compensate for nonlinear hysteresis problems than the fuzzy PID control. However, the design of the neural network PID controller requires a large amount of training data, and the quality of the network fitting directly influences the performance of the controller.
Disclosure of Invention
The invention aims to provide an N-link mechanical arm control method based on incremental model predictive control, which mainly solves the problems that PID process parameters in a PID controller are difficult to adjust, overshoot is too large and constraint cannot be met in the prior art.
In order to achieve the above purpose, the technical scheme adopted by the invention is as follows:
an N-bar mechanical arm control method based on incremental model predictive control comprises the following steps:
s1, establishing a Lagrangian dynamics model of an N-link mechanical arm system, performing first-order Taylor expansion on the Lagrangian dynamics model, and performing approximate sampling discretization on the Lagrangian dynamics model through a Shannon sampling theorem;
s2, an incremental model prediction controller is established to predict the future state or output of the system, and an optimization problem is solved in a limited time interval to optimize the state;
and S3, applying the optimized first-step control input to the system, and repeatedly carrying out the optimization process in the backward translation range of the model, so as to realize the control of the N-link mechanical arm system.
Further, in the step S1, the discrete dynamics model is:
where x represents a system state quantity, u represents a system input quantity, c (k) is a linearized constant, y represents a system output quantity, and a d ,B d ,C d For state space system matrix；
Performing differential operation on two sides of the formula (1) to obtain:
x(k+1)-x(k)＝A d [x(k)-x(k-1)]+B d [u(k)-u(k-1)]+Δc (2)
the state differential variable Δx and the control input differential variable Δu are defined as:
Δx(k+1)＝x(k+1)-x(k)
Δx(k)＝x(k)-x(k-1)
Δu(k)＝u(k)-u(k-1) (3)
Δc＝c(k)-c(k-1)
then formula (2) can be written as:
Δx(k+1)＝A d Δx(k)+B d Δu(k)+Δc (4)
the method comprises the following steps:
further, in the incremental model predictive controller in the step S2, the incremental model predictive control algorithm tracks the reference trajectory by minimizing the cost function while satisfying the constraint condition; i.e. at time t, the actual sampling time is KT, the cost function depends on the tracking error e (k) =y d (k) -r (k) and control input u d (k) Wherein r (k) is a reference track, an output prediction Np step is defined, and an input prediction Np step is controlled; then there are:
written as (6)
E k ＝Tx d (k)+T x Δx d (k)+HΔU k +S (7)
Wherein s=fΔc-r k Is constant, the quantization index of the controller performance, namely the cost function is defined as
Wherein Q and R are respectively an error weight diagonal matrix and an input vector diagonal matrix; bringing formula (7) into (8) to obtain:
with matrix P and vector f, the cost function can be written as:
further, in the step S2, the optimization problem, that is, the quadratic programming problem expression is:
s.t. X min ≤V(T k Δx d (k)+T x x d (k)+H x ΔU k +S x )≤X max (11)
U min ≤∑ΔU k ≤U max 。
compared with the prior art, the invention has the following beneficial effects:
based on a dynamic equation of the mechanical arm, the invention considers the input quantity of a design state space by adopting an incremental model predictive control method because of various state constraints and motor limitations of the actual mechanical arm, and finally converts the incremental design of the control quantity in the linear discrete system into the optimization solution of the QP problem. Simulation results show that under the condition of known external disturbance, the incremental model predictive control can better control the steady motion of the two-link mechanical arm, and the two-link mechanical arm reaches the expected position under the condition of meeting the constraint condition. Compared with the prior art, the problems that PID process parameters are difficult to adjust, overshoot is too large and constraint cannot be met are avoided.
Drawings
FIG. 1 is a schematic diagram of model predictive control in accordance with the present invention.
FIG. 2 is a schematic diagram of a two-bar linkage mechanical arm according to an embodiment of the present invention.
FIG. 3 is a graph showing the results of the joint angle tracking according to the embodiment of the present invention.
Fig. 4 is a graph showing the results of the joint angular velocity tracking in the embodiment of the present invention.
FIG. 5 is a graph showing the results of the input torque of the joint according to the embodiment of the present invention.
FIG. 6 is a diagram showing the result of the angle tracking error in the embodiment of the present invention.
Detailed Description
The invention will be further illustrated by the following description and examples, which include but are not limited to the following examples.
Examples
According to the N-link mechanical arm control method based on incremental model predictive control, firstly, a Lagrange dynamics model of an N-link mechanical arm system is established, and due to the characteristics of nonlinearity and continuity, the Lagrander dynamics model is required to be linearized by carrying out first-order Taylor expansion on a jacobian matrix, and then the Lagrange dynamics model is approximately sampled and discretized by a shannon sampling theorem. Finally, as the actual multi-degree-of-freedom mechanical arm responds to the state through the driving moment of the joint motor, the output moment of the motor is not suddenly changed, but continuously changes relative to the output moment at the last moment, and the optimal change quantity of the control moment can be well calculated by adopting the incremental model predictive control.
As shown in fig. 1, in the incremental model prediction control, a model prediction controller predicts the future state or output of a system using a specific model, solves an optimization problem in a limited time interval, and applies the optimized first-step control input to the system, so that the optimization process is repeatedly performed in a backward translation range.
In the present invention, a discrete kinetic model is considered as follows:
where x represents a system state quantity, u represents a system input quantity, c (k) is a linearized constant, y represents a system output quantity, and a d ,B d ,C d Is a state space system matrix.
By performing differential operation on both sides of the formula (1), it is possible to obtain:
x(k+1)-x(k)＝A d [x(k)-x(k-1)]+B d [u(k)-u(k-1)]+Δc(2)
the state differential variable Δx and the control input differential variable Δu are defined as:
Δx(k+1)＝x(k+1)-x(k)
Δx(k)＝x(k)-x(k-1)
Δu(k)＝u(k)-u(k-1) (3)
Δc＝c(k)-c(k-1)
then formula (2) can be written as:
Δx(k+1)＝A d Δx(k)+B d Δu(k)+Δc (4)
the method comprises the following steps:
the incremental model predictive control algorithm tracks the reference trajectory by minimizing the cost function while meeting constraints. I.e. at time t, the actual sampling time is kT, the cost function depends on the tracking error e (k) =y d (k) -r (k) and control input u d (k) Wherein r (k) is a reference track, an output prediction Np step is defined, and an input prediction Np step is controlled; then there are:
written as (6)
E k ＝Tx d (k)+T x Δx d (k)+HΔU k +S (7)
Wherein s=fΔc-r k Constant, a quantitative index of controller performanceI.e. the cost function is defined as
Wherein Q and R are respectively an error weight diagonal matrix and an input vector diagonal matrix; bringing formula (7) into (8) to obtain:
with matrix P and vector f, the cost function can be written as:
the optimization problem, namely the quadratic programming problem expression is as follows:
s.t. X min ≤V(T k Δx d (k)+T x x d (k)+H x ΔU k +S x )≤X max (11)
U min ≤∑ΔU k ≤U max 。
in order to verify the feasibility and control effect of the control method, a two-link rigid mechanical arm is used as a control object, and numerical simulation and verification are carried out in MATLAB. It is known from the definition of the European space that it can only move in a two-dimensional plane and that the robot arm end has only position information. FIG. 2 is a schematic illustration of a two-bar mechanical arm. The arm parameter settings are shown in tables 1 and 2.
Table 1: mechanical arm model parameters
| (symbol) | Value of | (symbol) | Value of |
| m 1 | 2kg | m 2 | 2kg |
| l 1 | 0.5m | l 2 | 0.5m |
| I 1 | 0.125kg·m 2 | I 2 | 0.125kg·m 2 |
Wherein m is the mass of the connecting rod, l is the length of the connecting rod, and I is the rotational inertia of the connecting rod.
Table 2: mechanical arm model constraint
Wherein tau is the input torque of the joint motor, q is the joint angle,is the angular velocity of the joint.
Hypothesis type(11) State weight matrix q=200i for QP problem in 4 Input weight matrix r=0.01i 2 (I is a unit array), the gravity coefficient is g=9.8n/kg, and tracking is performed when the end position of the mechanical arm is a preset constant value. Assume that the reference track is that the joint angle of the two-connecting-rod mechanical arm is [1,1]Is set to be [0,0]The joint angular velocity is also [0,0]The relevant constraints are shown in table 2.
In the simulation case of disturbance known, the external moment disturbance is set as tau d =0.1 sin (0.2pi t) +0.05 (N). At a sampling interval T of 0.05s, predicting a time domain N p When 10, the track following effect of the expression (11) is shown in fig. 3 to 6.
From the figure, under the action of external known additive disturbance, the joint angles and the angular velocities of the mechanical arm connecting rods 1 and 2 can be quickly converged to the vicinity of the reference state quantity, the motor input torque u gradually tends to be stable, and the state error does not show a divergence result and a larger buffeting phenomenon. Meanwhile, in the whole tracking process, preset constraint conditions are met.
Based on a dynamic equation of the two-degree-of-freedom mechanical arm, the method of incremental model predictive control is considered to design the input quantity of a state space due to various state constraints and motor limitations of the actual mechanical arm, and finally, the design of the control quantity in the linear discrete system is converted into the optimization solution of the QP problem. Simulation results show that under the condition of known external disturbance, the incremental model predictive control can better control the steady motion of the two-link mechanical arm, and the two-link mechanical arm reaches the expected position under the condition of meeting the constraint condition. Compared with the prior art, the problems that PID process parameters are difficult to adjust, overshoot is too large and constraint cannot be met are avoided.
The above embodiment is only one of the preferred embodiments of the present invention, and should not be used to limit the scope of the present invention, but all the insubstantial modifications or color changes made in the main design concept and spirit of the present invention are still consistent with the present invention, and all the technical problems to be solved are included in the scope of the present invention.
Claims (4)
1. The N-link mechanical arm control method based on the incremental model predictive control is characterized by comprising the following steps of:
s1, establishing a Lagrangian dynamics model of an N-link mechanical arm system, performing first-order Taylor expansion on the Lagrangian dynamics model, and performing approximate sampling discretization on the Lagrangian dynamics model through a Shannon sampling theorem;
s2, an incremental model prediction controller is established to predict the future state or output of the system, and an optimization problem is solved in a limited time interval to optimize the state;
and S3, applying the optimized first-step control input to the system, and repeatedly carrying out the optimization process in the backward translation range of the model, so as to realize the control of the N-link mechanical arm system.
2. The method for controlling an N-bar linkage mechanical arm based on incremental model predictive control according to claim 1, wherein in the step S1, the discrete dynamics model is:
where x represents a system state quantity, u represents a system input quantity, c (k) is a linearized constant, y represents a system output quantity, and a d ,B d ,C d Is a state space system matrix;
performing differential operation on two sides of the formula (1) to obtain:
x(k+1)-x(k)＝A d [x(k)-x(k-1)]+B d [u(k)-u(k-1)]+Δc(2)
the state differential variable Δx and the control input differential variable Δu are defined as:
Δx(k+1)＝x(k+1)-x(k)
Δx(k)＝x(k)-x(k-1)
Δu(k)＝u(k)-u(k-1) (3)
Δc＝c(k)-c(k-1)
then formula (2) can be written as:
Δx(k+1)＝A d Δx(k)+B d Δu(k)+Δc (4)
the method comprises the following steps:
3. the method according to claim 2, wherein in the incremental model predictive controller in step S2, the incremental model predictive control algorithm tracks the reference trajectory by minimizing the cost function while satisfying the constraint condition; i.e. at time t, the actual sampling time is kT, the cost function depends on the tracking error e (k) =y d (k) -r (k) and control input u d (k) Wherein r (k) is a reference track, an output prediction Np step is defined, and an input prediction Np step is controlled; then there are:
written as (6)
E k ＝Tx d (k)+T x Δx d (k)+HΔU k +S (7)
Wherein s=fΔc-r k Is constant, the quantization index of the controller performance, namely the cost function is defined as
Wherein Q and R are respectively an error weight diagonal matrix and an input vector diagonal matrix; bringing formula (7) into (8) to obtain:
with matrix P and vector f, the cost function can be written as:
4. the method for controlling an N-link manipulator based on incremental model predictive control according to claim 3, wherein in the step S2, the optimization problem, that is, the quadratic programming problem expression is:
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Citations (6)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US20100268353A1 (en) * | 2007-12-21 | 2010-10-21 | Crisalle Oscar D | Systems and Methods for Offset-Free Model Predictive Control |
| US20130158680A1 (en) * | 2011-12-20 | 2013-06-20 | Pratt & Whitney | Hybrid Control System |
| CN107662211A (en) * | 2017-10-16 | 2018-02-06 | 西北工业大学 | A kind of robot for space forecast Control Algorithm based on quanta particle swarm optimization |
| CN109571528A (en) * | 2018-12-29 | 2019-04-05 | 南京工程学院 | Activation lacking mechanical finger and finger tips trajectory predictions method |
| CN111158349A (en) * | 2020-01-15 | 2020-05-15 | 浙江大学 | Unmanned vehicle model prediction control method based on multi-step linearization strategy |
| CN112000014A (en) * | 2020-09-03 | 2020-11-27 | 上海航天控制技术研究所 | Control method for model prediction and inversion of control mechanical arm |
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Patent Citations (6)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US20100268353A1 (en) * | 2007-12-21 | 2010-10-21 | Crisalle Oscar D | Systems and Methods for Offset-Free Model Predictive Control |
| US20130158680A1 (en) * | 2011-12-20 | 2013-06-20 | Pratt & Whitney | Hybrid Control System |
| CN107662211A (en) * | 2017-10-16 | 2018-02-06 | 西北工业大学 | A kind of robot for space forecast Control Algorithm based on quanta particle swarm optimization |
| CN109571528A (en) * | 2018-12-29 | 2019-04-05 | 南京工程学院 | Activation lacking mechanical finger and finger tips trajectory predictions method |
| CN111158349A (en) * | 2020-01-15 | 2020-05-15 | 浙江大学 | Unmanned vehicle model prediction control method based on multi-step linearization strategy |
| CN112000014A (en) * | 2020-09-03 | 2020-11-27 | 上海航天控制技术研究所 | Control method for model prediction and inversion of control mechanical arm |
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