CN116577981B - Control distribution method for omni-directional driving underwater robot propelled by magnetic coupling vector - Google Patents
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Abstract
The invention provides a control distribution method of an omni-directional driving underwater robot propelled by a magnetic coupling vector, which describes the control distribution problem of a multi-vector propeller as a convex optimization problem under the constraint of a nonlinear inequality, and can calculate the control distribution of nonlinear physical characteristics of the omni-directional driving underwater robot propelled by the magnetic coupling vector; meanwhile, the problem of optimal control distribution is solved by using an augmentation Lagrangian penalty function method, the limit that the control quantity exceeds thrust saturation can be overcome, and the operation instantaneity and the control precision can be effectively ensured.
Description
Technical Field
The invention relates to the technical field of underwater robots, in particular to a magnetic coupling vector propulsion omni-directional driving underwater robot control distribution method.
Background
The underwater robot can work for a long time in an extreme water environment which is difficult for divers to reach, and helps humans explore the unknown world. With the continuous progress of autonomous navigation, motion control, target detection and identification, sensor and data fusion and other technologies, the underwater robot plays an important role in the fields of hydrologic environment monitoring, hydropower station dam body detection, underwater facility inspection and the like.
Aiming at the requirements of underwater operation tasks, the underwater robot not only needs to have high freedom of movement to realize three-dimensional space path following, but also needs to have flexible maneuverability to adjust the pose of the robot in real time, so that the camera device carried on the machine body can conveniently carry out fine observation on an underwater target in the optimal pose. Therefore, underwater robots with omni-directional drive are attracting more and more attention. The control distribution is a common method for processing redundant control of the overdrive underwater robot, and the upper control command is mapped to the corresponding propeller, so that the synthetic thrust of all the propellers is reduced to the control requirement as much as possible. In the motion control of an underwater robot, the control allocation is reconfigured, which may make the controller design modular.
The existing reconstruction control distribution method utilizes a mathematical quadratic programming method to solve the control distribution problem, is similar to the patent in the expression form of an objective function, and adopts L2 norm to describe the control distribution precision and the propeller energy consumption. However, in terms of describing constraint conditions of the propeller, the quadratic programming can only solve the problem of linear constraint, but for the magnetically coupled vector propeller, physical constraint has typical nonlinear characteristics, so that a mathematical quadratic programming method cannot be used. Meanwhile, the novel intelligent distribution method based on the particle swarm algorithm, the ant colony algorithm, the genetic algorithm and the like can be used for processing non-convex and non-smooth optimization models because the gradient information of the objective function is not relied on. However, the intelligent allocation method has huge calculation amount, generally has higher requirements on a hardware platform, and often cannot meet the application requirements of real-time allocation.
Disclosure of Invention
The invention aims to provide a control and distribution method of an omni-directional driving underwater robot propelled by a magnetic coupling vector, which solves the problem of a control and distribution calculation method of non-linear physical characteristics of the omni-directional driving underwater robot propelled by the magnetic coupling vector.
The embodiment of the invention is realized by the following technical scheme: a magnetic coupling vector propulsion omni-directional driving underwater robot control distribution method comprises the following steps:
step S1, taking a mathematical quadratic form for controlling the distribution precision and the energy consumption expenditure of the propeller as an optimization target to establish an objective function for controlling the distribution problem;
s2, expressing the thrust output of the magnetic coupling propeller under the constraint of the maximum reconstruction angle as a thrust reachable set, and under the limitation of the saturated thrust and the vector thrust maximum reconstruction angle, the propeller reachable set becomes a constraint condition for controlling the distribution optimization problem, and further, the constraint condition for controlling the distribution problem is induced by the thrust reachable set of the single propeller;
step S3: describing the control allocation problem as a convex optimization problem with nonlinear constraint conditions according to the formulas of the step S1 and the step S2, and correspondingly establishing a formula;
step S4: adopting an augmented Lagrangian penalty function method, after a Lagrangian multiplier takes constraint conditions as penalty items into an objective function, equivalently converting a convex optimization problem in the original objective function into a minimized unconstrained optimization problem, and correspondingly establishing a formula;
step S5: further adding a penalty factor item on the basis of the original objective function, and continuously correcting the Lagrangian multiplier to smooth the objective function so as to obtain an updated Lagrangian multiplier formula;
further, the objective function of the control allocation problem is:
wherein the first term in the formula (1) represents control allocation error and the second term represents pushThe energy consumption of the feeder is high; the positive definite matrix Q is a limiting parameter, and represents that energy expenditure is reduced to be a secondary target relative to an optimization problem taking improved control distribution precision as a primary target; τ c Representing generalized force instruction output by an upper controller, B is a propeller layout matrix of the underwater robot, and u= [ u ] 1 ,u 2 ,u 3 ] T Representing thrust vectors assigned to the respective propellers;
further, the constraint conditions of the control distribution problem which can be summarized by the thrust of the single propeller are as follows:
wherein u is max Represents the maximum thrust, theta, of the propeller max Representing the maximum reconstruction angle of the propeller, and defining u once without considering the forward and reverse rotation of the propeller ix Is non-negative;
further, the convex optimization problem of the nonlinear constraint condition is:
further, the minimized unconstrained optimization problem is:
further, the objective function of smoothing by continuously correcting the lagrangian multiplier is:
the update formula of the Lagrangian multiplier is:
the technical scheme of the invention has at least the following advantages and beneficial effects: firstly, describing the control distribution problem of the multi-vector propeller as a convex optimization problem under the constraint of a nonlinear inequality, and carrying out control distribution calculation aiming at the physical constraint of the nonlinear characteristic of the magnetic coupling vector propeller; secondly, an objective function of the control distribution problem comprises two factors of error and energy consumption, and the main and secondary of solving and optimizing are clear: the method takes the minimized control error as a main task, and minimizes the energy consumption of the system on the basis; and thirdly, solving the optimal control distribution problem by using an augmented Lagrangian penalty function method, so that the limit that the control quantity exceeds the thrust saturation can be overcome, and the operation instantaneity and the control precision can be effectively ensured.
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In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings that are needed in the embodiments will be briefly described below, it being understood that the following drawings only illustrate some embodiments of the present invention and therefore should not be considered as limiting the scope, and other related drawings may be obtained according to these drawings without inventive effort for a person skilled in the art.
Fig. 1 is a schematic structural diagram of an omni-directional driving underwater robot propelled by a magnetic coupling vector according to a magnetic coupling vector control distribution method of the omni-directional driving underwater robot propelled by a magnetic coupling vector according to an embodiment of the present invention;
fig. 2 is a schematic diagram of a thrust reachable set of a single vector propeller of the omni-directional driving underwater robot control distribution method of magnetic coupling vector propulsion provided by the embodiment of the invention;
fig. 3 is a schematic diagram of an application step of an augmented lagrangian algorithm of a control and distribution method of an omni-directional driving underwater robot propelled by a magnetic coupling vector according to an embodiment of the present invention.
Detailed Description
For the purpose of making the objects, technical solutions and advantages of the embodiments of the present invention more apparent, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention, and it is apparent that the described embodiments are some embodiments of the present invention, but not all embodiments of the present invention. The components of the embodiments of the present invention generally described and illustrated in the figures herein may be arranged and designed in a wide variety of different configurations.
Thus, the following detailed description of the embodiments of the invention, as presented in the figures, is not intended to limit the scope of the invention, as claimed, but is merely representative of selected embodiments of the invention. All other embodiments, which can be made by those skilled in the art based on the embodiments of the invention without making any inventive effort, are intended to be within the scope of the invention.
Examples
The embodiment provides a control and distribution method for an omni-directional driving underwater robot propelled by magnetic coupling vectors, as shown in fig. 1, because a single magnetic coupling vector propeller of the omni-directional driving underwater robot propelled by the magnetic coupling vectors has three degrees of freedom, the underwater robot has the capability of flexible movement and omni-directional control under the driving of the three magnetic coupling vector propellers. The omni-directional driving underwater robot control distribution method based on magnetic coupling vector propulsion takes the L2 norm of minimized control distribution error and propeller energy consumption as an optimization target, and under the nonlinear constraint of maximum reconstruction angle and thrust output saturation of the magnetic coupling vector propeller, an optimal distribution solution can be obtained from the whole world by adopting an augmentation Lagrange penalty function method. The present invention will illustrate the control allocation method from both mathematical model building and solving methods.
The method mainly comprises the following steps:
firstly, taking a mathematical quadratic form of control allocation precision and propeller energy consumption expenditure as an optimization target to establish an objective function of a control allocation problem, as shown in a formula (1):
the first term in the equation represents the control allocation error and the second term represents the propeller energy consumption overhead. Wherein the positive definite matrix Q is a limiting parameter, representing the phaseFor the optimization problem with the control allocation accuracy improvement as a primary target, the energy overhead reduction is a secondary target. τ c Representing generalized force instruction output by an upper controller, B is a propeller layout matrix of the underwater robot, and u= [ u ] 1 ,u 2 ,u 3 ] T Representing the thrust vector assigned to the corresponding propeller.
Each vector propeller i has a thrust vector u of the underwater robot in its coordinate system i ＝[u ix ,u iy ,u iz ] T . In addition, the magnetically coupled thrusters are constrained by a maximum reconstruction angle, and the thrust output under constraint may be expressed as a set of thrust reachability. Under the limitation of the maximum reconstruction angle of the saturated thrust and the vector thrust, the reachable set of the propeller becomes a constraint condition for controlling the distribution optimization problem. Constraints governing the distribution problem can be generalized by the achievable thrust of a single propeller i:
wherein u is max Represents the maximum thrust, theta, of the propeller max Representing the maximum reconstruction angle of the propeller. The three-dimensional view of the thrust reachable set of a single propeller, as shown in FIG. 2, is defined here once without regard to the forward and reverse rotation of the propeller, u ix Is non-negative.
According to equations (1) and (2), the control allocation problem can be described as a convex optimization problem with nonlinear constraints, and expressed as:
secondly, solving a control allocation problem of the multi-vector propeller based on an augmented Lagrangian penalty function method:
the constraint condition of the underwater robot for controlling the distribution problem has a nonlinear characteristic under the drive of the magnetic coupling vector propeller. In order to balance the solving precision and the operation complexity, an augmented Lagrangian penalty function method is adopted. When Lagrangian multiplier lambda i After the constraint condition is taken as a punishment term into the objective function, the convex optimization problem in the original objective function can be equivalently converted into an unconstrained optimization problem for minimizing L (u), wherein
If u is a feasible solution, the output thrust meets the constraint condition c ij Not less than 0, maximum value is lambda ij The value taken at=0, i.e. L (u), is equal to f (u) in this case, simplifying the original inequality constraint optimization problem; when u is not a viable solution, i.e. the thrust output does not fully satisfy the constraint: presence of c ij <0, will correspond to lambda ij Is set to be an arbitrarily large positive number, other lambda ij The value is set to 0 to ensure that L (u) approaches positive infinity in this case.
As can be seen from the formula (4), the feasible solution causes the objective function L (u) to be discontinuous on the propeller reachable set boundary, so the scheme further adds the penalty factor term sigma on the basis of the original objective function k Smoothing the objective function by continuously correcting the lagrangian multiplier:
the update formula of the Lagrangian multiplier is:
so far, the convex optimization problem under the nonlinear inequality constraint can completely obtain the global optimal solution by an augmented Lagrangian penalty function method.
The specific implementation steps are shown in fig. 3. The method is realized in a magnetically coupled vector-propelled underwater robot prototype, and has corresponding experimental simulation for verification.
It is worth mentioning that the invention firstly describes the problem of multi-vector propeller control distribution as a convex optimization problem under the constraint of a nonlinear inequality, and can control distribution calculation aiming at the physical constraint of the nonlinear characteristics of the magnetic coupling vector propeller; secondly, an objective function of the control distribution problem comprises two factors of error and energy consumption, and the main and secondary of solving and optimizing are clear: the method takes the minimized control error as a main task, and minimizes the energy consumption of the system on the basis; and thirdly, solving the optimal control distribution problem by using an augmented Lagrangian penalty function method, so that the limit that the control quantity exceeds the thrust saturation can be overcome, and the operation instantaneity and the control precision can be effectively ensured.
The above is only a preferred embodiment of the present invention, and is not intended to limit the present invention, but various modifications and variations can be made to the present invention by those skilled in the art. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention should be included in the protection scope of the present invention.
Claims (1)
1. The method for controlling and distributing the omni-directional driving underwater robot propelled by the magnetic coupling vector is characterized by comprising the following steps:
step S1, taking a mathematical quadratic form for controlling the distribution precision and the energy consumption expenditure of the propeller as an optimization target to establish an objective function for controlling the distribution problem;
the objective function of the control allocation problem is:
(1)
wherein, the first term in the formula (1) represents control distribution precision, and the second term represents propeller energy consumption cost; wherein the positive definite matrixDefining parameters representing the reduction of energy overhead as a secondary objective relative to the optimization problem with improved control allocation accuracy as a primary objective; />Generalized force instruction representing upper controller output, < ->Is a propeller layout matrix of the underwater robot,representing thrust vectors assigned to the respective propellers;
s2, expressing the thrust output of the magnetic coupling propeller under the constraint of the maximum reconstruction angle as a thrust reachable set, and under the limitation of the saturated thrust and the vector thrust maximum reconstruction angle, the propeller reachable set becomes a constraint condition for controlling the distribution optimization problem, and further, the constraint condition for controlling the distribution problem is induced by the thrust reachable set of the single propeller;
the constraint conditions of the control distribution problem which can be summarized by the thrust of the single propeller are as follows:
(2)
wherein the method comprises the steps ofIndicating maximum thrust of the propeller, +.>Representing the maximum reconstruction angle of the propeller and once again irrespective of the forward and reverse rotation of the propeller, defining +.>Is non-negative;
step S3: describing the control allocation problem as a convex optimization problem with nonlinear constraint conditions according to the formulas of the step S1 and the step S2, and correspondingly establishing a formula;
the convex optimization problem of the nonlinear constraint condition is as follows:
(3)；
step S4: adopting an augmented Lagrangian penalty function method, after a Lagrangian multiplier takes constraint conditions as penalty items into an objective function, equivalently converting a convex optimization problem in the original objective function into a minimized unconstrained optimization problem, and correspondingly establishing a formula;
the minimized unconstrained optimization problem is:
(4)；
wherein the method comprises the steps ofIs a Lagrangian multiplier;
if u is a feasible solution, the output thrust meets the constraint conditionMaximum value is->Get from the place, i.e.)>In this case equal to +.>The problem of constraint optimization of the original inequality is simplified; when u is not a viable solution, i.e. the thrust output does not fully satisfy the constraint: there is->Will correspond +.>Set to an arbitrarily large positive number, others +.>The value is set to 0 to ensure +.>Approaching infinity in this case;
step S5: further adding a penalty factor item on the basis of the original objective function, and continuously correcting the Lagrangian multiplier to smooth the objective function so as to obtain an updated Lagrangian multiplier formula;
the objective function of smoothing by continuously correcting the Lagrangian multiplier is:
(5)；
wherein,is a punishment parameter;
the updating formula of the Lagrangian multiplier is as follows:
(6)；
the convex optimization problem under the nonlinear inequality constraint is obtained through an augmented Lagrangian penalty function method, and the method comprises the following specific implementation steps:
starting: inputting the desired generalized force τ c
The first step: initialization ofk=0Lagrange multiplierλ k ij Penalty parameterConstraint and precision violation constantsη * ，ε * Threshold valueη k ，ε k ；
And a second step of: solving forCorresponding u k+1 ；
And a third step of: judging whether or not to meet；
The third step is satisfied, the optimal allocation u is output k ；
If the third step is not satisfied, performing a fourth step;
fourth step:
and if the fourth step is satisfied, judging the conditionAnd->Whether or not it is true, if so, outputting the optimal allocation u k Otherwise, it is->Updating Lagrangian multiplier according to formula (6)>Updating the threshold η k ，ε k Then, a second step is carried out;
if the fourth step is not satisfied,the Lagrangian multiplier is unchanged, and the threshold eta is updated k ，ε k The second step is performed.
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