CN109079780B - Distributed mobile mechanical arm task layered optimization control method based on generalized coordinates - Google Patents

Distributed mobile mechanical arm task layered optimization control method based on generalized coordinates Download PDF

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CN109079780B
CN109079780B CN201810899025.8A CN201810899025A CN109079780B CN 109079780 B CN109079780 B CN 109079780B CN 201810899025 A CN201810899025 A CN 201810899025A CN 109079780 B CN109079780 B CN 109079780B
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CN109079780A (en
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方浩
吴楚
曾宪琳
陈杰
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Beijing Institute of Technology BIT
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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
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B25—HAND TOOLS; PORTABLE POWER-DRIVEN TOOLS; MANIPULATORS
    • B25J—MANIPULATORS; CHAMBERS PROVIDED WITH MANIPULATION DEVICES
    • B25J9/00—Programme-controlled manipulators
    • B25J9/16—Programme controls
    • B25J9/1656—Programme controls characterised by programming, planning systems for manipulators
    • B25J9/1664—Programme controls characterised by programming, planning systems for manipulators characterised by motion, path, trajectory planning
    • 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
    • B25J9/1679—Programme controls characterised by the tasks executed
    • B25J9/1682—Dual arm manipulator; Coordination of several manipulators

Abstract

The invention provides a distributed mobile mechanical arm task layered optimization control method based on generalized coordinates, wherein a main task is that a plurality of mobile mechanical arms carry a target object through cooperation of an end effector so that the center of the target object tracks a given reference track, a secondary task is that joint angles are controlled by the sum of maximized operation degrees of all the mechanical arms and moving bases are controlled to form a formation and obstacle avoidance, the task is divided into an optimized layer and a control layer by introducing the generalized coordinates, reasonable distribution of redundancy in the control process is realized, and the secondary task is not in conflict with the main task while the secondary task is completed. The invention can realize distributed multi-mobile-mechanical-arm cooperative control by using a completely distributed control method.

Description

Distributed mobile mechanical arm task layered optimization control method based on generalized coordinates
Technical Field
The invention relates to the technical field of multi-agent control, in particular to a distributed mobile mechanical arm task hierarchical optimization control method based on generalized coordinates.
Background
In recent years, with the urgent need of a wide range of complex tasks in the industry, multi-robot arm coordination has received wide attention in various fields. Because the traditional fixed mechanical arm has limited working space, more and more people adopt the mobile mechanical arm for mounting the fixed mechanical arm on the mobile base to realize complex cooperative tasks. The mobile mechanical arm can adapt to complex and variable tasks by utilizing a larger moving range of a mobile base and flexible operation capability of the mechanical arm, but the high redundancy and the kinematic nonlinear constraint of the mobile mechanical arm make the cooperative control of the multiple mobile mechanical arms have great difficulty.
For the mobile robot arm, the sum of the degrees of freedom of the base and the robot arm is generally not less than the dimension of a task space, so the mobile robot arm has redundancy. In the case of cooperative control of the primary task, each mobile robot arm also has redundancy to accomplish other secondary tasks, or to optimize the objective. Therefore, a task priority concept needs to be introduced, so that when primary tasks and secondary tasks exist simultaneously, the mobile mechanical arm can perform motion control according to task levels, the low-priority task is guaranteed not to influence the high-priority task, and the possible conflict problem is solved.
The degree of operation is a measure of the ability of the current state manipulator to reach any position or any direction, and can represent the degree of the current state manipulator far away from the singular configuration. When the robot arm is in a near singular area, the robot arm is intended to reach a desired position or direction, and its joint angular velocity or angular acceleration will be infinite, thereby damaging the robot arm. Meanwhile, since the multiple mobile mechanical arm systems share the same working space and generate resource conflicts when the same object is transported, the problems of obstacle avoidance and collision avoidance need to be considered. In actual engineering, it is usually required that the mobile robot arm completes secondary tasks such as maximizing the operation degree and avoiding obstacles and collisions in the process of realizing the cooperative control of the main task.
In a conventional control method, cooperative control of mobile robots is usually realized in a centralized manner to ensure precision and robustness, but the centralized manner will bring huge computational burden to a central node, so that the whole system is easily crashed due to the failure of one node, it is difficult to control a plurality of mobile robots simultaneously, and the problem of cooperative transportation, manufacturing and assembling with high requirements on flexibility in the industry cannot be solved. The distributed system has the characteristics of small communication burden, small calculation complexity, strong robustness and the like, and is often used in actual engineering.
At present, most of research on distributed multi-mobile-mechanical-arm cooperative control is carried out in a mode of combining centralized planning with distributed control, and the distributed multi-mobile-mechanical-arm cooperative control is not a completely distributed control method. A few fully distributed control methods require the design of an observer to obtain information for all moving robots, which is a significant computational burden for distributed systems. For task priority control, the main method is to design the cooperative control of the end effector as a main task in a task space, and design secondary tasks such as maximizing the operability, avoiding obstacles and collisions and the like in a null space of a Jacobian matrix.
Therefore, how to realize the task priority control problem in the multi-mobile-mechanical-arm cooperation by using a fully distributed control method and reasonably distribute redundancy under the condition of ensuring the task priority is a problem to be solved urgently.
Disclosure of Invention
In view of this, the invention provides a generalized coordinate-based task layering optimization control method for a distributed mobile manipulator, which can realize distributed multi-mobile-manipulator cooperative control by using a fully distributed control method.
The specific embodiment of the invention is as follows:
a distributed mobile mechanical arm task layered optimization control method based on generalized coordinates is characterized in that a main task is that a multi-mobile mechanical arm carries a target object through cooperation of an end effector to enable the center of the target object to track a given reference track, and a secondary task is that a joint angle is controlled by the sum of the maximized operation degrees of all the mechanical arms and a mobile base is controlled to form a formation and avoid an obstacle, and the method comprises the following steps:
step one, integrating the position x and the joint angle theta of the end effector into a vector, and defining the vector as a generalized coordinate q ═ xT,θT]TEstablishing a single mobile mechanical arm model according to the generalized coordinates;
step two, introducing relative deviation zeta, and carrying out layered processing on the main task and the secondary task in the task priority control, wherein the layered processing comprises the following steps: consistent coordinated tracking of the control layer enables q-zeta → qdAnd optimization layer with constraints such that ζ → ζ*(ii) a When the task priority cooperative control is realized, the relation between the generalized coordinate and the relative deviation satisfies q-zeta*＝qd，ζ*For optimum relative deviation, qdGiven reference trajectory vectors;
designing constraint conditions of the optimization layer, wherein the constraint conditions comprise central tracking equation constraint and target object shape equation constraint based on the optimization layer and the neighbor mechanical arms, so that the task of the optimization layer does not influence the realization of the control layer task;
defining a range constraint set of relative deviation to enable the cost function of the non-convex optimization problem to be a convex function in the range constraint set;
decomposing the central tracking equality constraint into n local constraint equality forms, wherein n is the number of the mechanical arms; defining a non-smooth penalty term, and increasing the non-smooth penalty term on the basis of a Lagrangian function to obtain an improved Lagrangian function; obtaining a projection primitive-dual dynamics updating law of an optimization layer by a projection method by utilizing the range constraint set, and solving a non-convex optimization problem with constraint conditions in a distributed mode to ensure that
Figure BDA0001758911880000041
t is time;
step six, applying the optimal relative deviation zeta obtained in the step five*Designing a control layer consistency cooperative tracking control law so that
Figure BDA0001758911880000042
And realizing distributed task priority cooperative control.
Further, the single mobile robot arm is shaped as
Figure BDA0001758911880000043
u is a controlled variable and is a control variable,
Figure BDA0001758911880000044
j (theta) is the Jacobian matrix of the mobile robot arm, Im、IkRespectively m and k dimensional unit vectors.
Further, the method for making the cost function be a convex function in the range constraint set in the fourth step is:
the cost function is composed of the sum of the operation degree maximization quadratic function and the weighted sum of the quadratic function of the formation of the moving base
Figure BDA0001758911880000045
Selecting a mobile base expected formation vector to ensure that the cost function is a convex function within the range constraint set.
Has the advantages that:
1. according to the invention, the task priority problem in the cooperative transportation of multiple mobile mechanical arms is solved through distributed hierarchical optimization control, and the reasonable distribution of redundancy is realized by defining relative deviation in an optimized layer, so that the secondary tasks such as maximizing the operation degree and avoiding obstacles by forming a mobile base are solved, and meanwhile, the secondary tasks do not conflict with the main task tracked by a transportation target center; secondly, integrating the position of the end effector and the joint angle into a vector to define the vector as a generalized coordinate, and reasonably distributing the redundancy of the mobile mechanical arm by depending on the generalized coordinate through expanding the coordinate dimension; moreover, the whole layered optimization control framework is of a distributed structure by designing a projection original-dual dynamics updating law on an optimization layer and designing a consistency cooperative tracking control law on a control layer, each mobile mechanical arm only needs to know the states of the mobile mechanical arm and neighbor nodes, global information interaction is not needed, the communication burden of the system is reduced, each mobile mechanical arm carries out operation control, a central node is not needed for carrying out overall planning, the calculation burden of the system is reduced, and the distributed structure has stronger survivability and robustness.
2. The invention establishes a new mobile mechanical arm model, converts the actual engineering problem into a layered optimization control problem based on generalized coordinates, can solve the problems of carrying target center tracking, mechanical arm posture adjustment and mobile base motion control under the same frame, ensures the unique solution of the controlled joint angle and solves the redundancy problem.
3. The invention designs a projection primitive-dual dynamics updating law by adopting an improved Lagrange function with a non-smooth penalty function, so that the central tracking coupling equality constraint in the non-convex optimization problem with the constraint condition can be used as a plurality of local equality constraints, and the primitive optimization problem is solved by a completely distributed method.
Drawings
FIG. 1 is a schematic diagram of a multi-robot cooperative handling system according to an embodiment of the present invention;
FIG. 2 is a flow chart of distributed hierarchical optimization control of multiple mobile robotic arms in an embodiment of the present invention;
FIG. 3 is a schematic view of a communication topology between multiple mobile robotic arms in an embodiment of the invention;
FIG. 4 is a schematic view of the overall motion process and obstacle position of a multi-mobile-robot arm according to an embodiment of the present invention;
FIG. 5 is a schematic diagram illustrating a process of moving the positions of the end effector of the multi-motion robotic arm according to an embodiment of the present invention;
FIG. 6 is a schematic diagram illustrating the movement process and obstacle position of the multi-mobile-robot mobile base according to an embodiment of the present invention;
FIG. 7 is a diagram illustrating the variation of the operation degree of each mobile robot according to an embodiment of the present invention;
FIG. 8 is a graph of center tracking error for a conveyed object in an embodiment of the present invention;
FIG. 9(a) is a graph of x-axis error for the position of an end effector of a mobile robotic arm in an embodiment of the present invention;
fig. 9(b) is a y-axis error plot of the position of the end effector of the mobile robotic arm in an embodiment of the present invention.
Detailed Description
The invention is described in detail below by way of example with reference to the accompanying drawings.
In the example, the mobile mechanical arm is formed by fixing the mechanical arm on the mobile base, the carrying target is an object with a given shape, the cooperative control task can be divided into a main task and a secondary task according to task priority, the main task is that the multiple mobile mechanical arms carry the target object through cooperation of the end effector to enable the center of the target object to track a given reference track, the secondary task is that the joint attitude is controlled and the mobile base enables the sum of the operation degrees of all the mechanical arms to keep a large value, and the mobile base switches the formation to adapt to a complex obstacle environment.
The invention provides a distributed mobile mechanical arm task hierarchical optimization control method based on generalized coordinates, wherein the position of an end effector and a joint angle are integrated together to be defined as generalized coordinates, the hierarchical control method is designed into two layers, the upper layer is an optimization layer, the reasonable distribution of redundancy is realized through the relative deviation corresponding to the distributed optimization generalized coordinates, the sum of the operation degrees is kept at a larger value, and a mobile base completes formation switching; the lower layer is a control layer, and the relative deviation obtained by the optimization layer is applied to the consistency formation tracking control of the generalized coordinates, so that the purpose of tracking the given reference track by the center of the transported object is realized. The flow chart is shown in fig. 2, and the steps are as follows:
the method comprises the following steps: defining generalized coordinates, and establishing a single mobile mechanical arm model.
The number of the mobile robot arms in the cooperative transportation system is set as n. Then for the ith mobile robot arm, kinematic constraints should be satisfied
xi＝ρi(θi)+pi,i＝1,…,n (1)
Wherein the content of the first and second substances,
Figure BDA0001758911880000061
is the position of the end-effector,
Figure BDA0001758911880000062
is to move the position of the base in a way that,
Figure BDA0001758911880000063
is the joint angle.
Figure BDA0001758911880000064
The method is characterized in that the nonlinear mapping from a mechanical arm joint space to a task space is realized, and m and k are dimensions of the task space and the joint space respectively. Each mobile mechanical arm can obtain the position and the joint angle of the end effector per se, has certain calculation capacity and capacity of communicating with neighbors, and at least one mobile mechanical arm can obtain the position sigma of a given reference trackdAnd velocity
Figure BDA0001758911880000065
The communication topology between the mobile mechanical arms is an undirected connected graph, and the communication topology between the mobile mechanical arms and a given reference track is a directed topology, and the schematic diagram is shown in fig. 3.
Let the moving base speed of the ith moving mechanical arm be
Figure BDA0001758911880000066
Angular velocity of the joint
Figure BDA0001758911880000067
Defining generalized coordinates qi＝[xi T,θi T]TAnd a control quantity ui＝[vi T,ωi T]T. Obtaining a model of the ith mobile mechanical arm by derivation of two sides of the step (1)
Figure BDA0001758911880000071
Wherein
Figure BDA0001758911880000072
Ji(θi) Is the Jacobian matrix of the ith mobile robot arm, Im、IkRespectively m and k dimensional unit vectors.
Step two: defining generalized coordinates qiZeta relative deviationiSo that when the task priority control task is completed, qiZeta deviation from optimumi *Satisfy the following relationship
qi-ζi *＝qd (3)
Wherein q isd＝[σd T,0k×m T]TGiven a reference trajectory vector. The task priority control task can be decomposed into a distributed optimization problem of relative deviation in the optimization layer and a tracking problem of generalized coordinates in the control layer.
Optimal relative deviation ζ of ith mobile robot for optimization layeri *Should be solved by the distributed optimization problem. For convenience of representation xi、θiAnd q isiA relation of (2), a definition matrix
Figure BDA0001758911880000073
And
Figure BDA0001758911880000074
so that the following equation holds
Figure BDA0001758911880000075
Definition xiiAnd (4) an estimated amount of the moving base formation center for the ith moving robot arm. The optimization target of the optimization layer optimization problem consists of an operation degree maximization function and a moving base formation function so as to realize the subtask requirement, and the optimization target is as follows:
Figure BDA0001758911880000076
wherein
Figure BDA0001758911880000077
For the purpose of the moving base formation function,i ξrepresenting the desired formation vector for the motion base,
Figure BDA0001758911880000078
for the operation degree maximization function, the operation degree muiSatisfy the requirement of
Figure BDA0001758911880000079
Ji(θi) Is the Jacobian matrix, mu, of the ith mobile robot armi mThe maximum value of the operation degree of the ith mobile mechanical arm.
In order to reasonably allocate redundancy and avoid conflict with the requirements of the main task, corresponding constraint conditions need to be designed, and therefore a distributed optimization problem is constructed:
Figure BDA0001758911880000081
wherein ζ is [ ζ ═ ζ [ ]1 T,…,ζn T]T，ξ＝[ξ1 T,…,ξn T]T，
Figure BDA0001758911880000082
Ωi、ΨiIs ζi、ξiJ is a neighbor of the mobile robot i,
Figure BDA0001758911880000083
and
Figure BDA0001758911880000084
is the central tracking constraint and the target object shape constraint in the main task, xii-ξ j0 is the consistency constraint of the mobile base formation center estimator.
And thirdly, reasonably selecting the expected formation vector of the mobile base to enable the cost function of the non-convex optimization problem to be a convex function in the range constraint set.
Design range constraint set omega of relative deviationi、ΨiSo that
Figure BDA0001758911880000085
At omegaiThe upper surface is concave, and the relative inner points zeta epsilon rint (omega) and zeta epsilon rint (psi) meet the Slater condition.
The cost function is composed of the weighted sum of an operation degree maximization quadratic function and a moving base formation quadratic function, wherein the quadratic function is as
Figure BDA0001758911880000086
But because of the non-linearity of g (z), the function is non-convex. For the shapes of
Figure BDA0001758911880000087
A quadratic function of the form wherein g (z) ═ g1(z),…,gr(z)]TIf it is a convex function, one of the following conditions is satisfied:
(1)gi(z) is less than or equal to 0, and g isi(z) is a concave function，i＝1,…,r；
(2)gi(z) is not less than 0 and gi(z) is a convex function, i ═ 1, …, r.
Due to the fact that
Figure BDA0001758911880000088
And
Figure BDA0001758911880000089
all are quadratic functions, and the expected formation vector of the moving base can be selected to meet the inequality condition
Figure BDA00017589118800000810
i is 1, …, n, such that the set Ω is constrained in rangei、ΨiInner part
Figure BDA00017589118800000811
Is a convex function, at the same time
Figure BDA00017589118800000812
Always true, so in the range constraint set omegaiInner part
Figure BDA00017589118800000813
Also a convex function. In summary, the cost function
Figure BDA0001758911880000091
And n is a convex function when i is 1 and ….
Designing a non-smooth penalty term to construct an improved Lagrange equation, constructing a projection primitive-dual dynamics updating law of an optimization layer, and solving a non-convex optimization problem with constraint conditions in a distributed mode.
Because the central tracking constraint is an aggregation item, the information of all the mobile mechanical arms needs to be known, and the information is difficult to process in a distributed mode, the central tracking coupling equation constraint in the non-convex optimization problem with the constraint condition is written into a form of n local constraints, and a local Lagrangian multiplier lambda is defined for the ith mobile mechanical armiSo that λ is ═ λ1 T,…,λn T]T(ii) a And define a consistent set
Figure BDA00017589118800000914
From which non-smoothness penalty terms can be designed
Figure BDA0001758911880000092
So that phi (lambda) can be taken as lambdaiA measure of the degree of conformity when
Figure BDA00017589118800000915
When phi (lambda) is 0.
For the optimization problem (6), the Lagrangian equation is
Figure BDA0001758911880000093
Wherein alpha is>0 is constant, v ═ v [ v ]1 T,…,νn T]T，η＝[η1 T,…,ηn T]T，
Figure BDA00017589118800000916
L is a Laplace matrix of the communication topology between the mobile robotic arms, defined as follows
Figure BDA0001758911880000095
In the formula, l is the number of the neighbor of the mobile mechanical arm,
Figure BDA0001758911880000096
is a neighbor set of the ith mobile robot, when the ith, j mobile robots can communicate with each other, aij＝1，
Figure BDA0001758911880000097
Otherwise, aij＝0，
Figure BDA0001758911880000098
Using non-smooth penalty terms, improved Lagrangian functions can be designed
Figure BDA0001758911880000099
By selecting constants
Figure BDA00017589118800000910
λ eventually converges to a consistent set
Figure BDA00017589118800000911
Therefore it has the advantages of
Figure BDA00017589118800000912
I.e. in a consistent set
Figure BDA00017589118800000913
The improved Lagrangian function (9) is equivalent to the original Lagrangian function (8). Whereby the projection method can be realized
Figure BDA0001758911880000101
Figure BDA0001758911880000102
Figure BDA0001758911880000103
Figure BDA0001758911880000104
Figure BDA0001758911880000105
Obtaining a projection primitive-dual dynamics update law:
Figure BDA0001758911880000106
in which P represents a projection, and the updating law (10) can be guaranteed by projecting the primitive-dual dynamics
Figure BDA0001758911880000107
So as to obtain the optimal relative deviation zeta which meets the requirements of the secondary task and does not conflict with the primary taski *。
And fifthly, applying the optimal relative deviation, designing a consistency tracking control law of a control layer, and realizing distributed task priority cooperative control.
For the control layer, q needs to be implementediZeta deviation from optimumi *Satisfies formula (3), i.e. qi-ζi *＝qdWherein q isd＝[σd T,0k×m T]T. The design consistency tracking control law is as follows
Figure BDA0001758911880000108
Wherein, beta>0 is a constant number of times, and,
Figure BDA0001758911880000109
when the ith mobile mechanical arm can obtain the position sigma of the given reference trackdAnd velocity
Figure BDA00017589118800001010
When b is greater thani1, otherwise, bi＝0。
As the undirected communication diagram is formed among the mobile mechanical arms, and at least one mobile mechanical arm can obtain the given reference track information, a given reference track is always arranged in the whole communication topologyThe directed path from the path to any moving mechanical arm exists, so that the directed spanning tree exists in the whole communication topology, thereby
Figure BDA0001758911880000111
As can be seen from the above-mentioned step,
Figure BDA0001758911880000112
thus finally qiZeta deviation from optimumi *Must satisfy qi-ζi *＝qd. Therefore, the main task of cooperatively conveying the target object through the end effector to enable the center of the target object to track a given reference track and the secondary task of controlling the joint operability and moving the base formation are realized.
The example sets up a coordinated handling system comprising three mobile robotic arms, namely n is 3, the system composition is shown in fig. 1, and the software simulation results of the example are given below to demonstrate the effectiveness of the method.
As shown in fig. 4-6, the three figures show the results of the distributed task priority hierarchical optimization control of the three mobile robots, wherein the 20 th and 45 th control mobile bases perform formation switching to avoid obstacles. Fig. 4 shows the overall motion process and the obstacle position of the multi-mobile robot arm, and fig. 5 and 6 show the end effector position and the mobile base position in detail respectively. Fig. 7 is a diagram showing changes in the operation degree of all the moving robot arms. It can be found from the figure that for a conveying system formed by the three movable mechanical arms, the cooperative conveying of the target object can be ensured, the center of the target object can track a given reference track, meanwhile, the operation degree of each movable mechanical arm can be optimized to be far greater than 0, and the moving base is controlled to switch the formation to achieve the purpose of avoiding obstacles.
Fig. 8 is a graph of error in tracking the center of the transported object in the embodiment of the present invention, and fig. 9(a) and 9(b) are a graph of error in the x-axis and a graph of error in the y-axis of the position of the end effector of the mobile robot arm in the embodiment of the present invention, respectively, and it can be seen that even if the formation switching occurs at the 20 th and 45 th mobile bases, the error still converges to 0 very quickly, which proves the effectiveness of the method.
In summary, the above description is only a preferred embodiment of the present invention, and is not intended to limit the scope of the present invention. Any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in the protection scope of the present invention.

Claims (3)

1. A generalized coordinate-based distributed priority hierarchical optimization control method for a mobile mechanical arm is characterized in that a main task is that multiple mobile mechanical arms carry a target object in a cooperative mode through an end effector to enable the center of the target object to track a given reference track, and a secondary task is that the joint angle is controlled by the sum of the maximized operation degrees of all the mechanical arms and the formation of mobile bases is controlled to avoid obstacles, and the generalized coordinate-based distributed priority hierarchical optimization control method is characterized by comprising the following steps:
step one, integrating the position x and the joint angle theta of the end effector into a vector, and defining the vector as a generalized coordinate q ═ xT,θT]TEstablishing a single mobile mechanical arm model according to the generalized coordinates;
step two, introducing relative deviation zeta, and carrying out layered processing on the main task and the secondary task in the task priority control, wherein the layered processing comprises the following steps: consistent coordinated tracking of the control layer enables q-zeta → qdAnd optimization layer with constraints such that ζ → ζ*(ii) a When the task priority cooperative control is realized, the relation between the generalized coordinate and the relative deviation satisfies q-zeta*＝qd，ζ*For optimum relative deviation, qdGiven reference trajectory vectors;
designing constraint conditions of the optimization layer, wherein the constraint conditions comprise central tracking equation constraint and target object shape equation constraint based on the optimization layer and the neighbor mechanical arms, so that the task of the optimization layer does not influence the realization of the control layer task;
defining a range constraint set of relative deviation to enable the cost function of the non-convex optimization problem to be a convex function in the range constraint set;
decomposing the central tracking equation into n local constraint equation forms; defining a non-smooth penalty term, increasing said non-smooth penalty term on the basis of the Lagrangian function for obtaining an improved pullA Grenarian function; obtaining a projection primitive-dual dynamics updating law by using the range constraint set through a projection method, and solving a non-convex optimization problem with constraint conditions in a distributed mode to ensure that
Figure FDA0002650512610000011
t is time;
step six, applying the optimal relative deviation zeta obtained in the step five*Designing a control layer consistency cooperative tracking control law so that
Figure FDA0002650512610000012
And realizing distributed task priority cooperative control.
2. The generalized coordinate-based distributed priority hierarchical optimization control method of a mobile robot arm according to claim 1, wherein the single mobile robot arm model is shaped as follows
Figure FDA0002650512610000021
u is a controlled variable and is a control variable,
Figure FDA0002650512610000022
j (theta) is the Jacobian matrix of the mobile robot arm, Im、IkRespectively m and k dimensional unit vectors.
3. The generalized coordinate-based distributed priority hierarchical optimization control method of the mobile mechanical arm according to claim 1, wherein the method for making the cost function be a convex function in the range constraint set in the fourth step is:
the cost function is composed of the sum of the operation degree maximization quadratic function and the weighted sum of the quadratic function of the formation of the moving base
Figure FDA0002650512610000023
The operation degree maximization quadratic function is
Figure FDA0002650512610000024
The moving base formation quadratic function is
Figure FDA0002650512610000025
i ξVector representing desired formation of moving base, ξiEstimated amount of the moving base formation center for the ith moving mechanical armiSatisfy the requirement of
Figure FDA0002650512610000026
μi mIs the maximum value of the operation degree of the ith mobile mechanical arm, rhoiNonlinear mapping from a mechanical arm joint space to a task space; definition of
Figure FDA0002650512610000027
And
Figure FDA0002650512610000028
so that q isi＝Δexi+Δaθi,
Figure FDA0002650512610000029
And selecting the expected formation vector of the mobile base by ensuring that the cost function is a convex function in the range constraint set.
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