CN109352656A - A kind of multi-joint mechanical arm control method with time-varying output constraint - Google Patents
A kind of multi-joint mechanical arm control method with time-varying output constraint Download PDFInfo
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- B—PERFORMING OPERATIONS; TRANSPORTING
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- B—PERFORMING OPERATIONS; TRANSPORTING
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Abstract
The invention discloses a kind of multi-joint mechanical arm control method with time-varying output constraint, specific steps include: the multi-joint mechanical arm kinetic model and desired pursuit path that (1) is established under time-varying output constraint；(2) transfer function that the system with time-varying output constraint is converted to abandoned new system is established；(3) former mechanical arm system, is converted to new mechanical arm system by the transfer function obtained according to step (2)；(4) tracking error signal of mechanical arm system after converting is defined；(5) for the neural network control device of the mechanical arm system design stability after conversion.The present invention can be totally unknown in system parameter and realizes that the exact trajectory of mechanical arm tracks in the case where having time-varying output constraint, and ensures the satisfaction of time-varying output constraint.
Description
Technical Field
The invention relates to the field of automation, in particular to a multi-joint mechanical arm control method with time-varying output constraint.
Background
The rapid development of science and technology provides assistance for further application and popularization of mechanical arms, and the multi-joint mechanical arm is the most widely applied automatic mechanical equipment and is widely applied to the fields of industrial manufacturing, military, medical treatment, entertainment, even space exploration and the like. In practical applications, various constraints exist in the robot arm control system, such as input saturation, limited task space, limited speed, and the like. Once these constraints are violated, they may cause a decrease in the performance of the robotic arm system, even resulting in damage to the system and a threat to the safety of the personnel associated with the robotic arm system. With the further development of science and technology, the concept of human-computer interaction is proposed, more and more robots will work around human beings in the future, and therefore the design of the controller for the mechanical arm system with the specified constraint has important theoretical significance and practical application value. However, in most of the current researches, mainly the stability and control accuracy of the robot system are studied, and the design of the controller considering the output constraint is insufficient. By adopting the existing recursion design method, most research results can only solve the problem of mechanical arm control with constant output constraint, and the upper and lower boundaries of limited output are set more loosely, so that the conservative property of the algorithm is increased, and the practicability of the algorithm is limited.
The multi-joint mechanical arm is used as a time-varying and coupled multi-input multi-output complex nonlinear system, the motion control of the multi-joint mechanical arm is extremely complex, and in the actual control design process, the parameters of the mechanical arm are often unknown or the parameter measurement has large errors, so that a controller design tool aiming at an unknown parameter model is needed. The artificial neural network utilizes the approximability of the neural network, and the unknown dynamic model of the mechanical arm system is approximated by the neural network, so that the aim of accurate control can be achieved under the condition that unknown parameters exist in the system. The selection of the topological structure of the neural network and the adjustment of the weight of the neural network have strict theoretical analysis methods, so the neural network is widely applied to the control of the mechanical arm.
Disclosure of Invention
The invention aims to overcome the defects of the prior art and provides a multi-joint mechanical arm control method with time-varying output constraint. The invention can realize high-precision tracking control of the multi-joint mechanical arm with time-varying output constraint under the condition that parameters are completely unknown. The invention converts a system with time-varying output constraint into a new system without constraint by establishing a system conversion method, solves the problem of unknown parameters of the mechanical arm by adopting a neural network, and establishes an adaptive neural network controller for the converted nonlinear system by combining a back-stepping method to realize track tracking control. The invention realizes rapid and stable tracking control while ensuring the time-varying output constraint of the mechanical arm.
The purpose of the invention can be realized by the following technical scheme:
a multi-joint mechanical arm control method with time-varying output constraint comprises the following specific steps:
(1) establishing a multi-joint mechanical arm dynamic model and an expected tracking track under the time-varying output constraint;
(2) establishing a conversion function for converting a system with time-varying output constraints into a new system without constraints;
(3) converting the original mechanical arm system into a new mechanical arm system according to the conversion function obtained in the step (2);
(4) defining a tracking error signal of the converted mechanical arm system;
(5) and designing a stable self-adaptive neural network controller for the converted mechanical arm system.
Specifically, in step (1), the multi-joint mechanical arm dynamic model under the time-varying output constraint is a mechanical arm dynamic model with strong nonlinear coupling, and is represented as:
wherein, X1＝q，τ denotes the control moment, M (X)1) Representing an inertia matrix, Cm(X1,X2) Representing a centripetal force matrix, G (X)1) Represents a universal gravitation vector, JT(X1) Jacobian matrix representing the mechanical arm, F (X)2) Representing the friction force vector, f (t) representing the disturbance terms from the human and the outside world; m (X)1),Cm(X1,X2),G(X1),F(X2),JT(X1) And f (t) are unknown; the time-varying output constraint of a robotic arm is expressed as:
further, the established mechanical arm dynamic model takes the angular displacement of the joint of the mechanical arm and the angular displacement of the joint as state variables, and is expressed as follows:
wherein q is [ q ]1q2... qn]TRepresenting angular displacement, qd＝[qd1qd2... qdn]TRepresenting a given output trace, e ═ e1e2... en]TWhich is indicative of the output tracking error,andq＝[q 1 q 2...q n]respectively representing an upper bound and a lower bound of a time-varying output constraint of the robot arm, n representing a number of joints of the rigid robot arm having the time-varying output constraint,and ηi(t) are all intermediate variables.
Specifically, in the step (2), the constraint of time-varying output is converted into the constraint of tracking error of the mechanical arm output angle, and then a conversion function is designed to convert the mechanical arm system with the constraint into a new mechanical arm system without the constraint.
Designing a new state variable siAnd one about siAnd ηiStrictly monotonically increasing smooth function Q ofi(si,ηi) Expressed as:
only need siBounded, i.e., the output can be made to satisfy a time-varying output constraint.
Further, the strictly monotonically increasing smooth function and the transition state variable are specifically expressed as:
wherein,representing a transition variable siDerivative with respect to time.
Specifically, in the step (3), the converted new system obtained according to the specific conversion function is represented as:
wherein,the derivative of the intermediate variable of the transition is represented, and H and R are represented as:
specifically, in the step (4), the tracking error of the converted arm system is expressed as:
z1＝[z11,z12,...,z1n]T＝[s1,s2,...,sn]T
z2＝[z21,z22,...,z2n]T＝X2-α
wherein z is1,z2α is a virtual control quantity, expressed as:
wherein k is1＝diag{k11,k12,...,k1nIndicates a parameter matrix to be set.
Specifically, in the step (5), the designed multi-joint mechanical arm adaptive neural network controller with time-varying output constraints is represented as:
wherein k is2＝diag{k21,k22,...,k2nDenotes a parameter matrix of one setting,representing a local RBF neural network for approximating unknown dynamics in a closed-loop system,representing the Gaussian basis function, N being the number of nodes in the neural network, ξjN denote different nodes in space, called the center point of the gaussian function, ηjN denotes a center width,represents the input of the neural network and,and an estimation vector representing the weight of the used RBF neural network.
Further, the weight update rate of the neural network is as follows:
wherein,representing a constant, σ, that can be set artificially, representing the learning ratei> 0 represents a small constant that can be set artificially.
Compared with the prior art, the invention has the following beneficial effects:
1. the control method provided by the invention does not need the system parameters of the mechanical arm, and can carry out high-performance tracking control on the mechanical arm under the condition that the system has external unknown disturbance without damaging time-varying output constraint.
2. According to the invention, by establishing a system conversion method, the multi-joint mechanical arm with time-varying output constraint is converted into a new system without constraint, and the conservative type of the design of a control scheme is reduced.
3. The controller in the invention can ensure that the mechanical arm meets the time-varying output constraint condition under any given known time-varying output constraint, and solves the possible out-of-range problem of the conventional adaptive neural network controller facing the time-varying output constraint.
Drawings
FIG. 1 is a schematic view of a link plane robot arm according to an embodiment of the present invention.
Fig. 2 is a control method of a multi-joint robot arm with time-varying output constraints according to an embodiment of the present invention.
FIG. 3 is a simulation diagram of the tracking of the angular displacement of the mechanical arm joint in the embodiment of the invention.
FIG. 4 is a simulation diagram of the tracking of the angular displacement of the mechanical arm joint in the embodiment of the invention.
FIG. 5 is a graph of the error between the angular displacement of a joint and a given track of the angular displacement in an embodiment of the present invention.
FIG. 6 is a graph showing the variation of the transition variable in the embodiment of the present invention.
FIG. 7 is a simulation of robot arm control inputs in an embodiment of the present invention.
FIG. 8 is a simulation of robot arm control inputs in an embodiment of the present invention.
Detailed Description
The present invention will be described in further detail with reference to examples and drawings, but the present invention is not limited thereto.
Examples
In the present embodiment, the robot is a two-link planar robot, and the specific structure is shown in fig. 1.
Fig. 2 is a specific flowchart of a multi-joint robot arm control method with time-varying output constraints, which specifically includes the following steps:
(1) establishing a multi-joint mechanical arm dynamic model and an expected tracking track under the time-varying output constraint;
the two-link mechanical arm consists of 2 links, and an angular displacement sensor and a speed sensor are arranged at each joint point of each link to measure the angular position and the angular speed of the joint. The kinetic model of the two-link planar manipulator is represented as:
wherein, X1＝q，The angular displacement vector of the joint is q ═ q1,q2]TThe angular velocity vector of the joint isRepresents the friction term, τ represents the control moment, m (q) represents the inertia matrix,representing a centripetal force matrix, G (q) representing a gravity vector; j (q) represents the manipulator Jacobian matrix, f (t) represents the unknown perturbation, M (q),G(q),J(q),are not known.
In this embodiment, the given reference trajectory is represented as:
Xd1＝[sin(t),cos(t)]T
further setting a time-varying output constraint expressed as:
q(t)＝[-0.1×2-0.8-0.04+sin(t) -0.495×2-1.2t-0.03+cos(t)]T
in this embodiment, it is necessary to guarantee the time-varying output constraintAnd then, the track tracking control of the two-connecting-rod plane mechanical arm is realized.
M(q),G(q),J(q),The representation mode is as follows:
wherein q is1，q2Respectively representing the angular displacement of the joint 1 and the joint 2; m is1，m2Respectively representing the mass of the connecting rod 1 and the connecting rod 2; l1，l2Respectively showing the lengths of the connecting rod 1 and the connecting rod 2; i is1,I2Respectively representing the inertia of the connecting rod 1 and the connecting rod 2; g represents the gravitational acceleration;
in this embodiment, the relevant parameters of the system are specifically:
l1＝0.36m,l2＝0.32m,m1＝2.2Kg,m2＝0.86Kg,g＝9.8m/s2
I1＝64.25×10-3kgm2,I2＝22.42×10-3kgm2
the friction term is expressed as:
the disturbance term from the environment is expressed as:
f(t)＝[sin(t)+1 cos(t)+0.5]T
(2) establishing a conversion function for converting a system with time-varying output constraints into a new system without constraints;
designing a new state variable siAnd one about siAnd ηiStrictly monotonically increasing smooth function Q ofi(si,ηi) The strictly monotonically increasing smooth function and the transition state variable are specifically expressed as:
wherein,representing a transition variable siDerivative with respect to time, ei,ηi,The specific expression is as follows:
(3) converting the original mechanical arm system into a new mechanical arm system according to the conversion function obtained in the step (2); the new system after conversion, obtained from the specific conversion function, is represented as:
wherein,the derivative of the intermediate variable of the transition is represented, and H and R are represented as:
(4) defining a tracking error signal of the converted mechanical arm system;
in this embodiment, since the dynamics model of the mechanical arm is completely unknown, a neural network is usedApproaching the unknown dynamics of the closed loop system.
Input of neural networkAnd has the following components:
wherein k is1＝diag{k11,k12Denotes the designed feedback gain parameter.
(5) And designing a stable self-adaptive neural network controller for the converted mechanical arm system.
The designed multi-joint mechanical arm adaptive neural network controller with time-varying output constraint is represented as follows:
wherein k is2＝diag{k21,k22Denotes a control gain matrix which is used to control the gain, representing a local RBF neural network for approximating unknown dynamics, S, in a closed-loop systemi(Z)＝[si1(||Z-ξ1||),…,siN(||Z-ξN||)]T，Representing the Gaussian basis function, N representing the number of Gaussian basis functions in the neural network, ξjN denote different nodes in space, called the center point of the gaussian function, ηjN denotes a center width,represents the input of the neural network and,and the estimation vector of the used RBF neural network weight is represented, and N represents the number of nodes of the neural network.
Further, the weight update rate of the neural network is as follows:
wherein,representing a constant, σ, that can be set artificially, representing the learning ratei> 0 represents a small constant that can be set artificially.
In this embodiment, the system initial conditions are:
X(0)＝[0,1；0,0]
the controller parameters are as follows: initial value of weight of neural networkThe number of nodes N4096, Γ diag {70}, η ═ 0.7, δ ═ 0.01, k1＝diag{80 40}，k2＝diag{88 86}。
FIG. 3 shows angular displacement q of a robot arm joint1Simulation diagram of the tracking situation of (1). FIG. 4 shows angular displacement q of the joint of the robot arm2Simulation diagram of the tracking situation of (1). FIG. 5 shows angular displacement q of a joint1,q2With given tracking angular displacement trajectory qd1,qd2Error map between. It can be seen from fig. 3, 4 and 5 that under the designed controller, the mechanical arm can achieve a good output trajectory tracking effect, and the output of the mechanical arm can meet a given time-varying output constraint condition. FIG. 6 shows a conversion variable s of tracking error of angular displacement of a designed joint1,s2Variation diagram of (1), error conversion variable s1,s2The bounding property of (2) also ensures that the time-varying output constraint is satisfied. FIG. 7 is a robot arm control input u1A simulation diagram of (1). FIG. 8 is a robot arm control input u2A simulation diagram of (1).
The above embodiments are preferred embodiments of the present invention, but the present invention is not limited to the above embodiments, and any other changes, modifications, substitutions, combinations, and simplifications which do not depart from the spirit and principle of the present invention should be construed as equivalents thereof, and all such changes, modifications, substitutions, combinations, and simplifications are intended to be included in the scope of the present invention.
Claims (9)
1. A multi-joint mechanical arm control method with time-varying output constraint is characterized by comprising the following specific steps:
(1) establishing a multi-joint mechanical arm dynamic model and an expected tracking track under the time-varying output constraint;
(2) establishing a conversion function for converting a system with time-varying output constraints into a new system without constraints;
(3) converting the original mechanical arm system into a new mechanical arm system according to the conversion function obtained in the step (2);
(4) defining a tracking error signal of the converted mechanical arm system;
(5) and designing a stable self-adaptive neural network controller for the converted mechanical arm system.
2. The method for controlling a multi-joint mechanical arm with time-varying output constraints as claimed in claim 1, wherein in step (1), the dynamic model of the multi-joint mechanical arm under the time-varying output constraints is a dynamic model of the mechanical arm with strong nonlinear coupling, and is represented as:
wherein, X1＝q，q＝[q1q2... qn]TRepresenting angular displacement, τ control moment, M (X)1) Representing an inertia matrix, Cm(X1,X2) Representing a centripetal force matrix, G (X)1) Represents a universal gravitation vector, JT(X1) Jacobian matrix representing the mechanical arm, F (X)2) Representing the friction force vector, f (t) representing the disturbance terms from the human and the outside world; m (X)1),Cm(X1,X2),G(X1),F(X2),JT(X1) And f (t) are unknown; the time-varying output constraint of a robotic arm is expressed as:
3. the method for controlling the multi-joint mechanical arm with the time-varying output constraint as claimed in claim 2, wherein the established mechanical arm dynamic model takes the mechanical arm joint angular displacement and the joint angular displacement as state variables, and is expressed as:
wherein q is [ q ]1q2... qn]TRepresenting angular displacement, qd＝[qd1qd2... qdn]TRepresenting a given output trace, e ═ e1e2... en]TWhich is indicative of the output tracking error,andq＝[q 1 q 2...q n]respectively representing an upper bound and a lower bound of a time-varying output constraint of the robot arm, n representing a number of joints of the rigid robot arm having the time-varying output constraint,and ηi(t) are all intermediate variables.
4. The method for controlling a multi-joint robot arm with time-varying output constraints as claimed in claim 1, wherein in the step (2), a new state variable s is designediAnd one about siAnd ηiStrictly monotonically increasing smooth function Q ofi(si,ηi) Expressed as:
wherein e ═ e1e2... en]TWhich is indicative of the output tracking error,andq＝[q 1 q 2...q n]respectively representing an upper bound and a lower bound of a time-varying output constraint of the robot arm, n representing a number of joints of the rigid robot arm having the time-varying output constraint,and ηi(t) are all intermediate variables;
only need siBounded, i.e., the output can be made to satisfy a time-varying output constraint.
5. The multi-joint mechanical arm control method with the time-varying output constraint as claimed in claim 4, wherein the strict monotone increasing smooth function and the transition state variable are specifically expressed as follows:
wherein,representing a transition variable siDerivative with respect to time.
6. The method for controlling a multi-joint mechanical arm with time-varying output constraints as claimed in claim 1, wherein in the step (3), the converted new system obtained according to the specific conversion function is represented as:
wherein,the derivative of the intermediate variable of the transition is represented, and H and R are represented as:
wherein,q＝[q1q2... qn]Trepresenting angular displacement, M (q) representing an inertia matrix,representing centripetal force matrix, G (q) representing gravity vector, JT(q) represents a jacobian matrix of the robot arm, f (t) represents disturbance terms from humans and the outside, and e ═ e [ e ]1e2... en]TWhich is indicative of the output tracking error, and ηi(t) are all intermediate variables.
7. The multi-joint robot arm control method with time-varying output constraints as claimed in claim 1, wherein in the step (4), the tracking error of the converted robot arm system is expressed as:
z1＝[z11,z12,...,z1n]T＝[s1,s2,...,sn]T
z2＝[z21,z22,...,z2n]T＝X2-α
wherein z is1,z2Representing the error variables for the back-step design process in the new system,α is a virtual control quantity, expressed as:
wherein k is1＝diag{k11,k12,...,k1nDenotes a parameter matrix to be set, qd＝[qd1qd2... qdn]TRepresenting a given output trace.
8. The method for controlling a multi-joint manipulator with time-varying output constraints as claimed in claim 1, wherein in the step (5), the designed multi-joint manipulator adaptive neural network controller with time-varying output constraints is represented as:
wherein k is2＝diag{k21,k22,...,k2nDenotes a parameter matrix of one setting,representing a local RBF neural network, Si(Z)＝[si1(||Z-ξ1||),…,siN(||Z-ξN||)]T,Representing the Gaussian basis function, N representing the number of Gaussian basis functions in the neural network, ξjN denote different nodes in space, called the center point of the gaussian function, ηjN denotes a center width,represents the input of the neural network and,estimated vector, z, representing the applied RBF neural network weights1,z2Indicating the error variable in the new system, α is the virtual control quantity.
9. The method according to claim 8, wherein the weight update rate of the neural network is:
wherein,representing a constant, σ, that can be set artificially, representing the learning ratei> 0 represents a small constant that can be set artificially.
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| CN113927592A (en) * | 2021-08-24 | 2022-01-14 | 盐城工学院 | Mechanical arm force and position hybrid control method based on self-adaptive reduced-order sliding mode algorithm |
| CN115139301A (en) * | 2022-07-07 | 2022-10-04 | 华南理工大学 | Mechanical arm motion planning method based on topological structure adaptive neural network |
| CN116690561A (en) * | 2023-05-30 | 2023-09-05 | 渤海大学 | Self-adaptive optimal backstepping control method and system for single-connecting-rod mechanical arm |
| CN116690561B (en) * | 2023-05-30 | 2024-01-23 | 渤海大学 | Self-adaptive optimal backstepping control method and system for single-connecting-rod mechanical arm |
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