CN116880197A - Underwater robot operation track planning optimization method and optimization system based on multi-target multi-population backbone particle swarm optimization algorithm - Google Patents
Underwater robot operation track planning optimization method and optimization system based on multi-target multi-population backbone particle swarm optimization algorithm Download PDFInfo
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Abstract
The invention provides an underwater robot operation track planning optimization method based on a multi-target multi-population backbone particle swarm optimization algorithm. Step 1: establishing a mathematical model of operation planning of the double-arm underwater robot; step 2: the calculation process of the motion planning objective function is based on the mathematical model in the step 1, and a strategy of self-adapting dynamic weight change is adopted; step 3: the particle positions of the four groups are updated when the objective function is solved based on the strategy of the weight in the step 2; step 4: performing particle velocity update based on four groups based on the position update in the step 3; step 5: performing constraint multi-objective algorithm improvement based on violation tolerance coefficients based on the speed update of the step 4; step 6: and 5, realizing the operation track planning optimization of the underwater robot based on the multi-target multi-population backbone particle swarm optimization algorithm based on the improved constraint multi-target algorithm in the step. The invention mainly solves the problem of high energy consumption of the double-arm underwater robot in the operation process.
Description
Technical Field
The invention belongs to the technical field of track optimization, and particularly relates to an underwater robot operation track planning optimization method and an underwater robot operation track planning optimization system based on a multi-target multi-population backbone particle swarm optimization algorithm.
Background
In order to meet the strategic requirements of detecting and developing ocean resources and developing deep sea operation technology in China and further develop ocean national basic strategy, an underwater robot-manipulator system (Underwater Vehicle-ManipulatorSystem, UVMS) becomes an effective means for the underwater operation at the present stage. The marine resource can replace frogman to meet the requirements of deep sea operation, realize deep sea continuous operation in a large range, more effectively develop marine resources and realize the operation requirements under complex environments.
The current underwater robot has the following problems: the two arms of the underwater double-arm robot respectively generate coupling moment to the hull of the robot during operation, so that the robot needs to consume more energy to maintain self balance; the main energy is used for maintaining the normal operation of the mechanical arm when the underwater double arm works.
Secondly, the motion optimization process of the underwater robot is a constraint multi-objective function solving process, and for the constraint multi-objective function solving process in the optimization process, a backbone particle swarm optimization algorithm with fewer parameters is used by a more method. However, the traditional backbone particle swarm algorithm has the defects of easy loss of population diversity and convergence in premature ripening.
Disclosure of Invention
The invention provides an underwater robot operation track planning optimization method based on a multi-target multi-population backbone particle swarm optimization algorithm, wherein the two arms of an underwater double-arm robot respectively generate coupling moment to the hull of the robot during operation, so that the robot needs to consume more energy to maintain self balance; when the underwater double arms are operated, main energy is used for maintaining the normal operation of the mechanical arm, and the invention mainly solves the problem of high energy consumption of the double-arm underwater robot in the operation process.
The invention provides an underwater robot operation track planning optimization system based on a multi-target multi-population backbone particle swarm optimization algorithm, which is used for realizing an underwater robot operation track planning optimization method.
The invention is realized by the following technical scheme:
an underwater robot operation track planning optimization method based on a multi-target multi-population backbone particle swarm optimization algorithm comprises the following steps:
step 1: establishing a mathematical model of energy-saving operation planning of the double-arm underwater robot, wherein the operation content comprises approaching targets and combined mechanical arm operation, and respectively setting adaptive objective functions;
step 2: solving an objective function based on the mathematical model in the step 1 by adopting a strategy of self-adapting dynamic weight change;
Step 3: carrying out particle position updating of four groups based on the strategy of the weight of the step 2;
step 4: performing particle velocity update based on four groups based on the position update in the step 3;
step 5: performing constraint multi-objective algorithm improvement based on violation tolerance coefficients based on the speed update of the step 4;
step 6: and 5, realizing the operation track planning optimization of the underwater robot based on the multi-target multi-population backbone particle swarm optimization algorithm based on the improved constraint multi-target algorithm in the step.
An underwater robot operation track planning optimization method based on a multi-target multi-population backbone particle swarm optimization algorithm, wherein the step 1 specifically comprises the following steps: the two arms of the double-arm underwater robot are identical and symmetrically arranged, so that the coupling inertia matrix of the left arm of the mechanical arm is equal to the coupling inertia matrix of the right arm of the mechanical arm, and the inertia matrix of the robot base is constant, so that the objective function values are simplified, and the following (1) - (6) are carried out after optimization:
f 1 ＝S 1 +S 2 +S 3 ＝G(1)+G(2)-r+alti (1)
wherein: s is S 1 ，S 2 ，S 3 Representing the distance of advancing, laterally shifting and downward shifting of the boat body in the approaching process respectively; g represents a coordinate point at which the tail end of the mechanical arm is fixed; r and alti respectively represent p of mechanical arm kinematics x And p y A value; i i Representing the moment of inertia of the ith joint; omega i Represents the angular velocity of the ith joint; m is m i Representing the mass of the ith joint; l (L) i The length of the arm link representing the i-th joint; f represents the resistance of the connecting rod of the ith joint in water; v represents the average rotational speed of the link rotation of the ith joint; t represents the set system operation time.
Wherein: i ei Representing the moment of inertia of a virtual joint of the ith virtual combined mechanical arm; omega ei An angular velocity representing a virtual joint of the i-th virtual combined mechanical arm; m is m ei Representing the mass of the virtual joint of the ith virtual combined mechanical arm; l (L) ei The length of the link representing the virtual joint of the ith virtual combined mechanical arm; f represents the resistance of the rod of the virtual joint of the ith virtual combined mechanical arm to water; v represents the average rotation speed of the connecting rod rotation of the virtual joint of the ith virtual combined mechanical arm; t represents the operation time of the double-arm underwater robot; h b Representing an inertia matrix of the body;representing the coupled inertial matrix of the left arm and the connected base; />Representing the coupled inertial matrix of the right arm and the connected base; />The angular velocities of the joints of the left arm and the right arm of the mechanical arm are respectively represented; j (J) a ，J b Jacobian matrices representing the left and right arms of the mechanical arm, respectively.
An underwater robot operation track planning optimization method based on a multi-target multi-population backbone particle swarm optimization algorithm, wherein the strategy of self-adaptive dynamic weight change in the step 2 is specifically as follows: the new weight change strategy is as shown in (7):
wherein: f (f) avg ，f min F is the fitness value of backbone particle swarm; by adopting the self-adaptive weight coefficient changing mode, the adaptability value can be dynamically changed in the process of evolution of the backbone particle swarm algorithm, so that the particle swarm algorithm is prevented from being trapped into a local optimal value.
An underwater robot operation track planning optimization method based on a multi-target multi-population backbone particle swarm optimization algorithm, wherein the particle position updating of four populations in the step 3 specifically comprises the following steps: updating the positions of the particle swarms in the overall algorithm by adopting four backbone particle swarms; when searching, the four backbone particle swarms find out a global optimal solution while finding out respective local optimal solutions respectively, so as to ensure diversity of the population; wherein the location updates of population 1 and population 2 of backbone particle swarm are as follows:
wherein: z=1, 2, representing the location update formulas of backbone particle swarm 1 and backbone particle swarm 2, respectively;
similarly, the formula for updating the positions of backbone particle swarm 3 will be affected by basic backbone particle swarm 1 and backbone particle swarm 2, as follows:
Wherein: gamma ray 1 ，γ 2 Relative fitness values for population 1 and population 2, respectively, and γ 1 +γ 2 =1; the position updating mode is mainly characterized in that the better adaptability has larger influence on the current particles by comparing the adaptability values of the backbone particle swarm 1 and the backbone particle swarm 2, so that the evolution of the backbone particle swarm 3 is better guided;
the same way of updating the positions of backbone particle swarm population 4 is as follows:
wherein: alpha 1 ，α 2 ，α 3 Influence factors and add to 1, respectively;
the particles in the backbone particle swarm 4 share the particle information in the other three populations, so that the evolution of the multi-population backbone particle swarm algorithm is diversified, and the searching process of the particles in the backbone particle swarm 4 is finer;
in order to reduce the influence of later variation on the algorithm, the variation probability calculation formula can be designed as follows:
pm＝e at /T (11)
wherein: a represents the initial mutation probability; t represents the algebra of evolution; t represents the total algebra of the algorithmic species evolution.
An underwater robot operation track planning optimization method based on a multi-target multi-population backbone particle swarm optimization algorithm, wherein the step 4 is based on four populations of particle speed update specifically comprises the following steps: based on the algorithm using four backbone particle swarms as the population, the first two particle swarms are used as basic particle swarms in the four sub-swarm algorithm, and the speed of the particle swarm 1 has an effect on the speed update of the particle swarm 2, the particle swarm 1 and the particle swarm 2 both adopt the traditional speed and position update formulas, and the speed update is as follows:
Wherein: z represents particle swarm 1 and particle swarm 2, z=1, 2;
the update of the particle swarm 3 speed is affected by the fitness value of the particle swarm 1 and the particle swarm 2, and the update of the particle swarm 3 speed is performed as follows:
wherein: gamma ray 1 And gamma 2 Representing the fitness values of the particles in the basic particle swarm 1 and the basic particle swarm 2 respectively; gamma represents the sum of fitness values of particle swarm 1 and particle swarm 2, and is γ=γ 1 +γ 2 ；
Optimization and improvement of the speed update of the particle swarm 4, the speed update formula of the particle swarm 4 is guided by the speed update of the particle swarm 1, the particle swarm 2 and the particle swarm 3, and is as follows:
meanwhile, in order to enhance the searching capability of the particle swarm 4, the best leader in the particle swarm 4 is evolved towards the global optimal solution, so that the position updating formula in the particle swarm 4 is improved, as follows:
wherein: alpha 1 ，α 2 ，α 3 Represents the influence factor of the corresponding term, and alpha 1 +α 2 +α 3 ＝1。
An underwater robot operation track planning optimization method based on a multi-target multi-population backbone particle swarm optimization algorithm, wherein the step 5 is based on constraint multi-target algorithm improvement of violation tolerance coefficients, and specifically comprises the following steps: all constraint violation degrees are normalized as follows:
C max ＝max(c i )i＝1，2，...，N (17)
in the above formula, constraint set c is constrained by an inequality And equality constraint->Together form a constraint set C, and C max The maximum number in the whole set c is the number; obtaining the violation degree of the decision variable for each constraint condition through calculation, and finally obtaining the normalized constraint violation degree;
the degree of violation of the constraint will be calculated as follows:
wherein: t represents the algebra of the current constrained evolution; t represents the total algebra of constrained evolution.
An underwater robot operation track planning optimizing system based on multi-target multi-population backbone particle swarm optimizing algorithm comprises a double-arm underwater robot energy-saving operation planning module and a manipulator energy-saving motion optimizing module of the underwater robot,
the energy-saving operation planning module of the double-arm underwater robot is used for establishing a mathematical model of energy-saving operation planning of the double-arm underwater robot, wherein the energy-saving operation comprises the steps of approaching to fixing a virtual base and virtually combining mechanical arm operation, and respectively setting up an adaptive objective function;
the underwater robot-manipulator energy-saving motion optimization module is used for performing a strategy of self-adaptive dynamic weight change; carrying out particle position updating of four groups; carrying out particle velocity updating based on four groups; performing constraint multi-objective algorithm improvement based on violation tolerance coefficients; and the operation track planning optimization of the underwater robot based on the multi-target multi-population backbone particle swarm optimization algorithm is realized.
An electronic device comprises a processor, a communication interface, a memory and a communication bus, wherein the processor, the communication interface and the memory are communicated with each other through the communication bus;
a memory for storing a computer program;
and the processor is used for realizing the steps of the method when executing the program stored in the memory.
A computer readable storage medium having stored therein a computer program which when executed by a processor performs the above-described method steps.
The beneficial effects of the invention are as follows:
the self-adaptive inertia weight changing strategy is adopted, and the fitness value can be dynamically changed in the process of evolution of the backbone particle swarm algorithm, so that the particle swarm algorithm is prevented from being trapped into a local optimal value.
The invention adopts an improved backbone particle swarm algorithm based on a plurality of backbone particle swarm algorithms, the algorithm consists of four independent backbone particle swarms, each particle swarm searches for an optimal solution in a specific search space, and different particle swarms can cooperate with each other and improve global search performance by exchanging information. In the algorithm, each particle swarm has a local optimal solution and a global optimal solution, and each particle swarm can share the individual optimal solution and the global optimal solution of the particle swarm to other particle swarms, so that the optimal solution can be searched better.
The invention takes the first two of four independent particle swarms as basic particle swarms in an algorithm, adopts a traditional speed and position updating formula, but the speed and the position of the particle swarm 1 have the influence on the movement of the particle swarm 2. In order to strengthen information exchange among populations and accelerate algorithm convergence speed, the speed and position update of the particle swarm 3 is influenced by the adaptability of the particle swarm 1 and the particle swarm 2; in order to further accelerate the searching performance and convergence performance of the particle swarm 4, the velocity and position update formula of the particle swarm 4 is guided by the velocity and position update formulas of the particle swarms 1, 2 and 3, and evolves towards the global optimal solution.
Drawings
FIG. 1 is a schematic diagram of a dual robotic arm D-H coordinate system of the present invention.
Fig. 2 is a single arm gripping schematic of the double arm underwater robot of the present invention.
Fig. 3 is a schematic diagram of a double arm grabbing of the double arm underwater robot of the present invention.
Fig. 4 is a schematic diagram of the spatial constraint of the double-arm motion of the double-arm underwater robot of the present invention.
Fig. 5 is a flow chart of the multi-target multi-population backbone particle swarm algorithm of the present invention.
FIG. 6 is a data diagram of a simulation of a dual arm grabbing operation according to the present invention, wherein (a) is the comparison data of the improved backbone particle swarm algorithm and the genetic algorithm in calculating the coupling moment; (b) To improve the comparison data of backbone particle swarm algorithm and genetic algorithm which can be time-consuming in calculating the mechanical arm; (c) In order to simulate the time-dependent change relation of the joint angle of the mechanical arm in the planning process; (d) In order to simulate the time-dependent change relation of the joint angular velocity of the mechanical arm in the planning process; (e) In order to simulate the time-dependent change relation of the joint angular acceleration of the mechanical arm in the planning process.
Fig. 7 is a flow chart of the method of the present invention.
Detailed Description
The following description of the embodiments of the present invention will be made clearly and completely with reference to the accompanying drawings, in which it is apparent that the embodiments described are only some embodiments of the present invention, but not all embodiments. 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.
The invention has good diversity and convergence and can avoid sinking into local optimum.
The invention can solve the problem of high energy consumption of the double-arm underwater robot in the operation process.
Establishing a kinematic and dynamic mathematical model of the double-arm underwater robot;
the double-arm underwater robot is an humanoid underwater robot with two underwater mechanical arms, wherein the two mechanical arms of the double-arm underwater robot have the same structure and size and all have four degrees of freedom.
And establishing a kinematic model of the double-arm underwater robot.
The underwater robot body has six degrees of freedom when navigating underwater. The motion of the underwater robot is based on two coordinate systems of a world coordinate system and a boat body coordinate system, so that a D-H parameter method is adopted to build a kinematic model of the double mechanical arms, and the position relation of the end effector relative to the base coordinate system can be obtained.
According to the motion requirements of the underwater robot-manipulator, the kinematics of the underwater robot are divided into forward kinematics and reverse kinematics. The positive kinematics is that the ship body starts, and the target object is used as an end point for planning; and the inverse kinematics is that the ship body is planned by starting from the target object.
In order to facilitate the kinematic modeling of the underwater robot-manipulator structure, a model motion relationship of the manipulator needs to be represented by a D-H table of the underwater robot-manipulator structure column.
After the manipulator structure is listed in the D-H table, the coordinate transformation matrix between two adjacent links of the manipulator is as follows:
and establishing a transformation matrix between adjacent coordinate systems of the mechanical arm mechanism by combining the D-H table, and multiplying the coordinates of the four adjacent mechanisms from the base coordinates to the end effector by the continuous numbers of the transformation matrices of the adjacent coordinate systems to obtain the transformation matrix of the end effector relative to the base coordinate system. Based on the above principle, the positional relationship between the end effector with respect to the base coordinate system is as follows:
wherein:is a position vector of the mechanical arm end effector; />Is the attitude vector of the mechanical arm end effector, and the results are respectively:
mathematical modeling is carried out on a dynamic model of the double-arm underwater robot;
The double mechanical arms of the double-arm underwater robot adopted by the invention have three degrees of freedom after being simplified, and the whole robot has the characteristics of high degree of freedom, nonlinearity and strong coupling, so that the Lagrange method can be used for analyzing the dynamics of the mechanical arms in order to better process the energy consumption of the mechanical arms during operation and keep the stability of the boat body.
The single arm dynamics equation for a dual arm underwater robot can be expressed using a lagrangian function:
the underwater robot arm can be regarded as a rigid body, and therefore it is assumed that the homogeneous coordinate system of a point on the link i with respect to the coordinate system { i } is expressed as i And r, deriving the point to obtain the speed of the point.
Assuming the mass of the point on the connecting rod is dm, the pseudo-inertia matrix can be obtained by squaring the point derivatives of the homogeneous coordinate system as follows:
therefore, the kinetic energy of the connecting rod i can be obtained by integrating the whole connecting rod as follows:
finally, the total kinetic energy of the mechanical arm consisting of the connecting rods can be calculated as:
wherein: k (K) ai Representing the total kinetic energy of the transmission between the various links.
Then solving the total potential energy of the mechanical arm, wherein the potential energy of i on the mechanical arm connecting rod is as follows:
U i ＝∫dU i ＝∫-dm i gT i i r i ＝-m i gT i i r (30)
wherein: m is m i Representing the mass of the connecting rod i; g represents the gravity vector [ g ] x g y g z 0]。
Therefore, the total potential energy of the mechanical arm consisting of the connecting rods is calculated as:
the Lagrangian function of the mechanical arm is obtained in sum as follows:
and carrying the expression of the kinetic energy and the potential energy of the mechanical arm obtained by solving the above to a Lagrange function expression, so that a simplified mechanical arm kinetic equation can be obtained as follows:
wherein:
so far, the kinematic and dynamic mathematical modeling of the double-arm underwater robot is finished.
Establishing a single-arm grabbing operation mathematical model of the double-arm underwater robot;
when the operation planning of the mechanical arm is carried out, the energy-saving track planning of the single mechanical arm is firstly used for research. The last joint of the four operation joints of the single arm only adjusts the gesture of the tail end of the mechanical arm in the working process of the mechanical arm, and the final planning is not influenced, so that the operation process of the three joints can be further simplified.
The multi-constraint multi-objective mathematical model of single-arm fixed single-arm grasping can be expressed as:
min y，y＝f(θ)＝[f 1 (θ)，f 2 (θ)，f 3 (θ)…，f n (θ)] (37)
s.t g i (θ)≤0，i＝1，2…k i (38)
h i (θ)＝0，i＝k i+1 ，k i+2 ，…k i+n (39)
wherein: θ= [ θ ] 1 ，θ 2 …，θ n ]∈D N Representing a decision vector; d represents a decision space; y= [ f 1 (θ)，f 2 (θ)…，f n (θ)]Representing the mapping of the decision vector on the objective function; f (f) 1 (θ)，f 2 (θ)...f n (θ) represents a decision objective function of the underwater robot-manipulator operating time; g i (θ)，h i (θ) represents the inequality constraint and the equality constraint of the manipulator at the working time, respectively.
The constraint condition is set in particular to be that,
(1) Establishment of decision variables
By inquiring related data, the decision variable with low latitude can be known to have great help to the algorithm to find the optimal solution. The two-arm underwater robot system studied by the invention can mainly consider two aspects when carrying out single-arm grabbing: and (3) after approaching the operation target point, fixing the boat body and planning a single-arm operation track after fixing. The operation track planning of the mechanical arm can simplify the track planning of a three-joint underwater mechanical arm.
According to the analysis, the two processes of approaching and grabbing can be processed and solved by utilizing the data of the joint angle of the mechanical arm, and in addition, the operation track of the mechanical arm is required to be planned, so that the joint angle of the mechanical arm of the operation sheet is used as a decision variable.
(2) Establishment of objective function
The invention establishes a calculation mode mainly taking the energy consumption of a system as a main body for an objective function in a single-arm fixed single-arm operation mode based on the energy-saving operation of the double-arm underwater robot. The operation of the invention mainly consists of two parts of approaching of the double-arm underwater robot body and single-arm operation, so that corresponding objective functions can be set up for the two parts.
Aiming at the problem of approaching an operation target, as the binocular camera of the double-arm underwater robot is limited in visual field range, in the process of approaching the target, the robot mainly moves sideways and forwards and backwards in a mode of keeping a heading angle unchanged to approach the target. Because the body of the double-arm underwater robot needs to be continuously subjected to position adjustment in the approaching process, the time consumption of the boat body approaching process is required to be shorter in order to reduce the energy consumption; the shortest path for converting the objective function into the approaching motion of the hull can be assumed on the assumption of constant speed.
Aiming at the problem of single-arm operation, the time of operation of the underwater mechanical arm is mainly influenced by three aspects: torque of the mechanical arm; heavy buoyancy of the mechanical arm; and the water resistance of the mechanical arm, so that the operation energy consumption of the mechanical arm can be calculated and solved by superposition of the operation energy consumption of the three aspects.
According to the analysis, for a single-arm fixed single-arm operation mode, two performance objective function settings are selected as follows:
f 1 ＝S 1 +S 2 +S 3 ＝G(1)+G(2)-r+alti (40)
wherein: s is S 1 ，S 2 ，S 3 Representing the distance of advancing, laterally shifting and downwards shifting of the AUV in the approaching process respectively; g represents a coordinate point at which the tail end of the mechanical arm is fixed; r and alti respectively represent p of second chapter mechanical arm kinematics x And p y A value; i i Representing the moment of inertia of the ith joint; omega i Represents the angular velocity of the ith joint; m is m i Representing the mass of the ith joint; l (L) i The length of the arm link representing the i-th joint; f represents the resistance of the connecting rod of the ith joint in water; v represents the average rotational speed of the link rotation of the ith joint; t represents time.
(3) Determination of constraint terms
The establishment of constraint items needs to be established according to the specific operation condition of the system.
First, each joint of the mechanical arm operation needs to meet the constraint of the kinematic condition, namely, the angular displacement, the angular velocity and the angular acceleration of each joint cannot exceed the motion limit of each joint. Angular displacement g of each joint 0 (θ), angular velocity g 1 (θ), angular acceleration g 2 The (θ) constraint can be expressed as:
wherein: q i (Δt)，The angle, the speed and the acceleration of each mechanical arm joint at the delta t moment are respectively represented; q imax ，/>Respectively representing the angle, angular velocity and angular acceleration extreme value of each joint.
Secondly, the safety problem of the system in the whole operation needs to be considered, namely the actual operation height of the system in the whole process is larger than the minimum operation height to be maintained, namely H real ≥H min . Actual implementation of the SystemThe height can be expressed by parameters of the joint angle of the mechanical arm as:
H real ＝L 1 *cos(θ 1 )+L 2 *cos(θ 1 )*cos(θ 2 )+L 3 *cos(θ 1 )*cos(θ 2 +θ 3 ) (43)
Finally, because the invention adopts the vision system to carry out detection operation, the operation object is required to be always in the detection range of the camera at the time of carrying out single-arm operation. Assuming that the camera used in the present invention has binocular and an open angle of 90 °, this condition can be expressed as:
wherein: t (T) N2B Representing a transformation matrix from the hull moving coordinate system to the camera detecting visual coordinate system;representing the position of the target object in the camera detection visual coordinate system; />Representing the expression of the target object on a boat body moving coordinate system; r is R bino Representing the field of view detection range of the camera.
Meanwhile, in order to update the dynamic weight coefficient of the multi-backbone particle swarm algorithm, for the multi-objective optimization problem of the invention, normalization processing can be performed on two calculation results, so as to obtain a normalized function target value f to update the weight coefficient, as follows:
wherein: alpha 1 ，α 2 Representing various influence indexes; n (N) 1 ，N 2 Representing the value of an objective functionRange.
Based on the single-arm operation of the double-arm underwater robot, the equivalent differential kinematics equation of the combined underwater double-arm robot can be obtained based on the above mathematical modeling of the kinematics and dynamics of the double-arm underwater robot, and is expressed as follows:
Wherein: j (J) b Jacobian matrix of virtual base, J m Is a jacobian matrix of the virtual combined mechanical arm.
The underwater double mechanical arms required by the invention all have four joints, so J can be obtained according to the following formula b And J m ：
/>
Wherein: p is p 0end ＝p end -r 0 ，Is p 0end Is a diagonal symmetric matrix of (a). E (E) 3 Is a third order diagonal identity matrix, E 3 ＝diag{1，1，1}，θ＝[θ 1 … θ end ] T And theta is angle information of each joint angle of the virtual combined mechanical arm.
The kinetic energy and potential energy of the virtual mechanical arm are deduced from the kinetic energy and potential energy:
to sum up: unified dynamics model of virtual combined mechanical arm:
after the equivalent combination of the two-arm underwater robot system researched by the invention is carried out by using the virtual base modeling method, the system can be regarded as the grabbing operation track planning of a six-joint underwater mechanical arm with a base.
According to the above study, a multi-constraint multi-objective mathematical model working with two arms can be expressed as:
min y，y＝f(θ)＝[f 1 (θ)，f 2 (θ)，f 3 (θ)…，f n (θ)] (52)
s.t g i (θ)≤0，i＝1，2…k i (53)
h i (θ)＝0，i＝k i+1 ，k i+2 ，…k i+n (54)
the operation of the double-arm underwater robot mainly comprises two parts of fixing the virtual base and virtually combining the mechanical arm operation, so that the two parts can be respectively provided with an adaptive objective function.
For the first part of the approach to fix the virtual base, the shortest path that the hull passes through in the approach process can be used as the objective function. When the virtual base is grabbed and fixed, the energy consumption of the left arm of the mechanical arm can be considered to be optimal, and the change of the joint angle is minimum as an objective function.
Aiming at the second part of the virtual combined mechanical arm operation track planning, mainly considering the energy consumption optimization of the virtual combined mechanical arm operation process as a main target. The influence of the actual motion process on the body of the double-arm underwater robot is considered, the motion of the boat body is kept to be minimum, and the influence of the coupling action of the double arms on the body is needed to be considered. At the same time, after each of the two robotic arms has grasped a common object, the entire system must be properly coordinated to follow the motion constraints imposed by the object itself in order to transport the object to the target location.
An underwater robot operation track planning optimization method based on a multi-target multi-population backbone particle swarm optimization algorithm comprises the following steps:
step 1: establishing a mathematical model of energy-saving operation planning of the double-arm underwater robot, wherein the energy-saving operation comprises the steps of approaching to fix a virtual base and virtually combining the operation of the mechanical arm, and respectively setting up an adaptive objective function;
step 2: performing a strategy for adaptively and dynamically changing weights based on the mathematical model in the step 1;
step 3: carrying out particle position updating of four groups based on the strategy of the weight of the step 2;
step 4: performing particle velocity update based on four groups based on the position update in the step 3;
Step 5: performing constraint multi-objective algorithm improvement based on violation tolerance coefficients based on the speed update of the step 4;
step 6: and 5, realizing the operation track planning optimization of the underwater robot based on the multi-target multi-population backbone particle swarm optimization algorithm based on the improved constraint multi-target algorithm in the step.
An underwater robot operation track planning optimization method based on a multi-target multi-population backbone particle swarm optimization algorithm, specifically, in the step 1, two arms of the double-arm underwater robot are identical and symmetrically arranged, so that the coupling inertia matrix of a left arm of the mechanical arm is equal to the coupling inertia matrix of a right arm of the mechanical arm, and the inertia matrix of a robot base is constant, so that the objective function values can be simplified, and the following (1) - (6) are performed after the optimization:
f 1 ＝S 1 +S 2 +S 3 ＝G(1)+G(2)-r+alti (1)
wherein: s is S 1 ，S 2 ，S 3 Representing the distance of advancing, laterally shifting and downward shifting of the boat body in the approaching process respectively; g represents a coordinate point at which the tail end of the mechanical arm is fixed; r and alti respectively represent p of mechanical arm kinematics x And p y A value; i i Representing the moment of inertia of the ith joint; omega i Represents the angular velocity of the ith joint; m is m i Representing the mass of the ith joint; l (L) i The length of the arm link representing the i-th joint; f represents the resistance of the connecting rod of the ith joint in water; v represents the average rotational speed of the link rotation of the ith joint; t represents the set system operation time.
An underwater robot operation track planning optimization method based on a multi-target multi-population backbone particle swarm optimization algorithm,
wherein: i ei Representing the moment of inertia of a virtual joint of the ith virtual combined mechanical arm; omega ei An angular velocity representing a virtual joint of the i-th virtual combined mechanical arm; m is m ei Representing the mass of the virtual joint of the ith virtual combined mechanical arm; l (L) ei The length of the link representing the virtual joint of the ith virtual combined mechanical arm; f represents the resistance of the rod of the virtual joint of the ith virtual combined mechanical arm to water; v represents the average rotation speed of the connecting rod rotation of the virtual joint of the ith virtual combined mechanical arm; t represents the operation time of the double-arm underwater robot; h b Representing the inertia of the bodyA matrix;representing the coupled inertial matrix of the left arm and the connected base; />Representing the coupled inertial matrix of the right arm and the connected base; />The angular velocities of the joints of the left arm and the right arm of the mechanical arm are respectively represented; j (J) a ，J b Jacobian matrices representing the left and right arms of the mechanical arm, respectively.
The invention discloses an underwater robot operation track planning optimization method based on a multi-target multi-population backbone particle swarm optimization algorithm, wherein a strategy of self-adapting dynamic weight change in step 2 is specifically to solve the defect that a traditional backbone particle swarm algorithm is easy to sink into local convergence too early.
The inertia weight of the traditional backbone particle swarm algorithm is changed in a linear decreasing mode, and the traditional backbone particle swarm algorithm has a large disadvantage in the algorithm. The new weight change strategy is as follows:
wherein: f (f) avg ，f min F is the fitness value of backbone particle swarm; by adopting the self-adaptive weight coefficient changing mode, the adaptability value can be dynamically changed in the process of evolution of the backbone particle swarm algorithm, so that the particle swarm algorithm is prevented from being trapped into a local optimal value.
The invention discloses an underwater robot operation track planning optimization method based on a multi-target multi-population backbone particle swarm optimization algorithm, and the particle position update of four populations in the step 3 is specifically that the positions of the particle swarms in the whole algorithm are updated by adopting the four backbone particle swarms. When searching, the four backbone particle swarms find out a global optimal solution while finding out respective local optimal solutions respectively, so that the diversity of the population is ensured. Wherein the location updates of population 1 and population 2 of backbone particle swarm are as follows:
wherein: z=1, 2, and represents the positional update formulas of the backbone particle group 1 and the backbone particle group 2, respectively.
Similarly, the formula for updating the positions of backbone particle swarm 3 will be affected by basic backbone particle swarm 1 and backbone particle swarm 2, as follows:
Wherein: gamma ray 1 ，γ 2 Relative fitness values for population 1 and population 2, respectively, and γ 1 +γ 2 =1. The position updating mode is mainly characterized in that the better adaptability is greatly influenced on the current particles by comparing the adaptability values of the backbone particle swarm 1 and the backbone particle swarm 2, so that the evolution of the backbone particle swarm 3 is better guided.
The same way of updating the positions of backbone particle swarm population 4 is as follows:
wherein: alpha 1 ，α 2 ，α 3 The influencing factors are respectively added to 1.
The particles in the backbone particle swarm 4 share the particle information in the other three populations, so that the evolution of the multi-population backbone particle swarm algorithm is diversified, and the searching process of the particles in the backbone particle swarm 4 is finer.
In order to cope with the particle trapping local optimum in each sub-backbone particle swarm, the invention adopts mutation operation in each generation of particle swarm, the mutation operation increases the searching space searched in the early stage of the algorithm, and the mutation probability decreases in the later stage of the algorithm, thereby increasing the convergence possibility of the algorithm. In order to reduce the influence of later variation on the algorithm, the variation probability calculation formula can be designed as follows:
pm＝e at /T (11)
Wherein: a represents the initial mutation probability; t represents the algebra of evolution; t represents the total algebra of the algorithmic species evolution.
The invention discloses an underwater robot operation track planning optimization method based on a multi-target multi-population backbone particle swarm optimization algorithm, wherein step 4 is based on four-population particle speed updating, specifically, based on the four-backbone particle swarm algorithm adopted by the invention as a population, the first two particle swarms are taken as basic particle swarms in four sub-swarm algorithms, the speed of the particle swarm 1 has an influence on the speed updating of the particle swarm 2, the particle swarm 1 and the particle swarm 2 both adopt a traditional speed and position updating formula, and the speed updating is shown as follows:
wherein: z represents particle swarm 1 and particle swarm 2, z=1, 2.
In order to enhance the communication of information between populations and increase the convergence speed of the algorithm, the speed update of the particle swarm 3 is affected by the fitness value of the particle swarm 1 and the particle swarm 2, and the speed update mode of the particle swarm 3 is as follows:
wherein: gamma ray 1 And gamma 2 Respectively represent the particle positionsFitness values in the basic particle swarm 1 and the basic particle swarm 2; gamma represents the sum of fitness values of particle swarm 1 and particle swarm 2, and is γ=γ 1 +γ 2 。
In order to further accelerate the searching performance and convergence performance of the fourth particle swarm, the speed update of the particle swarm 4 is optimized and improved, and the speed update formula of the particle swarm 4 is guided by the speed update of the particle swarm 1, the particle swarm 2 and the particle swarm 3, as follows:
Meanwhile, in order to enhance the searching capability of the particle swarm 4, the best leader in the particle swarm 4 is evolved towards the global optimal solution, so that the position updating formula in the particle swarm 4 is improved, as follows:
wherein: alpha 1 ，α 2 ，α 3 Represents the influence factor of the corresponding term, and alpha 1 +α 2 +α 3 ＝1。
The step 5 is based on the constraint multi-objective algorithm improvement of violation tolerance coefficient, and specifically, aiming at the constraint multi-objective evolutionary algorithm, the method not only needs to search for feasible solutions, but also needs to search for discrete feasible solutions in the range of a non-feasible solution set, and can solve the problem by a method for constructing a non-feasible solution reserve set. Meanwhile, in order to improve the working efficiency and performance of the algorithm in a non-feasible region, the invention introduces the concept of constraint violation tolerance coefficient w, specifically, when the objective function value of a solution is larger than the constraint violation tolerance coefficient w, the solution is regarded as a non-feasible solution, otherwise the solution is regarded as a feasible solution.
The range of constraint violation of the multi-objective optimization problem is calculated according to different problems, so that the values are generally different. To change this phenomenon, the present invention normalizes all constraint violation degrees as follows:
C max ＝max(c i )i＝1，2，...，N (17)
In the above formula, constraint set c is constrained by an inequalityAnd equality constraint->Together form a constraint set C, and C max I.e. the largest number in the whole set c. And calculating to obtain the violation degree of the decision variable for each constraint condition, and finally obtaining the normalized constraint violation degree.
In order to obtain the violation degree of the constraint, the violation degree of the constraint is judged by adopting the constraint violation threshold, the violation degree of the constraint set by the invention takes a value between 0 and 1, and the violation degree is continuously adjusted along with the algebra of evolution. In the early stage of the algorithm, the constraint violation degree is larger so that more infeasible solutions participate in evolution, and as the number of iterations increases in the later stage, the value of the constraint violation degree is close to 0, so that the algorithm is more concentrated to find the optimal solution, and the convergence of the algorithm is enhanced. The violation degree of the constraint in the invention adopts the following calculation method:
wherein: t represents the algebra of the current constrained evolution; t represents the total algebra of constrained evolution.
Example two
The embodiment of the invention provides an underwater robot operation track planning optimizing system based on a multi-target multi-population backbone particle swarm optimizing algorithm, which comprises a double-arm underwater robot energy-saving operation planning module and a manipulator energy-saving motion optimizing module of the underwater robot,
The energy-saving operation planning module of the double-arm underwater robot is used for establishing a mathematical model of energy-saving operation planning of the double-arm underwater robot, wherein the energy-saving operation comprises the steps of approaching to fixing a virtual base and virtually combining mechanical arm operation, and respectively setting up an adaptive objective function;
the underwater robot-manipulator energy-saving motion optimization module is used for performing a strategy of self-adaptive dynamic weight change; carrying out particle position updating of four groups; carrying out particle velocity updating based on four groups; performing constraint multi-objective algorithm improvement based on violation tolerance coefficients; and the operation track planning optimization of the underwater robot based on the multi-target multi-population backbone particle swarm optimization algorithm is realized.
From the above, the embodiment of the invention can solve the problem of high energy consumption of the double-arm underwater robot in the operation process by establishing the mathematical model of the energy-saving operation planning of the double-arm underwater robot and the energy-saving motion optimization of the manipulator of the underwater robot, so as to realize the planning of the local operation track of the double-arm underwater robot by a method of combining a multi-target optimization and a multi-cluster backbone particle swarm algorithm which has good diversity and convergence and can avoid sinking into local optimization.
Example III
The embodiment of the invention provides an electronic device, which comprises a memory, a processor and a computer program stored in the memory and capable of running on the processor, wherein the memory is used for storing the software program and a module, and the processor executes various functional applications and data processing by running the software program and the module stored in the memory. The memory and the processor are connected by a bus. In particular, the processor implements any of the steps of the above-described embodiment by running the above-described computer program stored in the memory.
It should be appreciated that in embodiments of the present invention, the processor may be a central processing unit (Central Processing Unit, CPU), which may also be other general purpose processors, digital signal processors (Digital Signal Processor, DSPs), application specific integrated circuits (Application Specific Integrated Circuit, ASICs), off-the-shelf programmable gate arrays (Field-Programmable Gate Array, FPGAs) or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, or the like. A general purpose processor may be a microprocessor or the processor may be any conventional processor or the like.
The memory may include read-only memory, flash memory, and random access memory, and provides instructions and data to the processor. Some or all of the memory may also include non-volatile random access memory.
As can be seen from the above, the electronic device provided by the embodiment of the invention can improve the problem of high energy consumption of the double-arm underwater robot in the operation process by establishing the mathematical model for planning the energy-saving operation of the double-arm underwater robot and the energy-saving motion optimization of the manipulator of the underwater robot, so as to plan the local operation track of the double-arm underwater robot by a method which has good diversity and convergence and can avoid the combination of a plurality of backbone particle swarm algorithms which are trapped in the local optimization and the multi-objective optimization.
It should be appreciated that the above-described integrated modules/units, if implemented in the form of software functional units and sold or used as stand-alone products, may be stored in a computer-readable storage medium. Based on such understanding, the present invention may implement all or part of the flow of the method of the above embodiment, or may be implemented by instructing related hardware by a computer program, where the computer program may be stored in a computer readable storage medium, and the computer program may implement the steps of each of the method embodiments described above when executed by a processor. The computer program comprises computer program code, and the computer program code can be in a source code form, an object code form, an executable file or some intermediate form and the like. The computer readable medium may include: any entity or device capable of carrying the computer program code described above, a recording medium, a U disk, a removable hard disk, a magnetic disk, an optical disk, a computer Memory, a Read-Only Memory (ROM), a random access Memory (Random Access Memory, RAM), an electrical carrier wave signal, a telecommunications signal, a software distribution medium, and so forth. The content of the computer readable storage medium can be appropriately increased or decreased according to the requirements of the legislation and the patent practice in the jurisdiction.
The previous description of the disclosed embodiments is provided to enable any person skilled in the art to make or use the present invention. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the generic principles defined herein may be applied to other embodiments without departing from the spirit or scope of the invention. Thus, the present invention is not intended to be limited to the embodiments shown herein but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.
It will be apparent to those skilled in the art that, for convenience and brevity of description, only the above-described division of the functional units and modules is illustrated, and in practical application, the above-described functional distribution may be performed by different functional units and modules according to needs, i.e. the internal structure of the apparatus is divided into different functional units or modules to perform all or part of the above-described functions. The functional units and modules in the embodiment may be integrated in one processing unit, or each unit may exist alone physically, or two or more units may be integrated in one unit, where the integrated units may be implemented in a form of hardware or a form of a software functional unit. In addition, the specific names of the functional units and modules are only for distinguishing from each other, and are not used for limiting the protection scope of the present invention. The specific working process of the units and modules in the above system may refer to the corresponding process in the foregoing method embodiment, which is not described herein again.
It should be noted that, the method and the details thereof provided in the foregoing embodiments may be combined into the apparatus and the device provided in the embodiments, and are referred to each other and are not described in detail.
Those of ordinary skill in the art will appreciate that the elements and algorithm steps of the examples described in connection with the embodiments disclosed herein may be implemented as electronic hardware, or combinations of computer software and electronic hardware. Whether such functionality is implemented as hardware or software depends upon the particular application and design constraints imposed on the solution. Skilled artisans may implement the described functionality in varying ways for each particular application, but such implementation decisions should not be interpreted as causing a departure from the scope of the present invention.
In the embodiments provided in the present invention, it should be understood that the disclosed apparatus/terminal device and method may be implemented in other manners. For example, the apparatus/device embodiments described above are merely illustrative, e.g., the division of modules or elements described above is merely a logical functional division, and may be implemented in other ways, e.g., multiple elements or components may be combined or integrated into another system, or some features may be omitted, or not performed.
The above embodiments are only for illustrating the technical solution of the present invention, and are not limiting; although the invention has been described in detail with reference to the foregoing embodiments, it will be understood by those of ordinary skill in the art that: the technical scheme described in the foregoing embodiments can be modified or some technical features thereof can be replaced by equivalents; such modifications and substitutions do not depart from the spirit and scope of the technical solutions of the embodiments of the present invention, and are intended to be included in the scope of the present invention.
Claims (10)
1. An underwater robot operation track planning optimization method based on a multi-target multi-population backbone particle swarm optimization algorithm is characterized by comprising the following steps:
step 1: establishing a mathematical model of operation planning of the double-arm underwater robot, wherein the operation comprises approaching and combining mechanical arm operation, and respectively establishing an adaptive objective function;
step 2: solving an objective function based on the mathematical model in the step 1 by adopting a strategy of self-adapting dynamic weight change;
step 3: carrying out particle position updating of four groups based on the strategy of the weight of the step 2;
step 4: performing particle velocity update based on four groups based on the position update in the step 3;
Step 5: performing constraint multi-objective algorithm improvement based on violation tolerance coefficients based on the speed update of the step 4;
step 6: and 5, realizing the operation track planning optimization of the underwater robot based on the multi-target multi-population backbone particle swarm optimization algorithm based on the improved constraint multi-target algorithm in the step.
2. The optimization method for the operation track planning of the underwater robot based on the multi-target multi-population backbone particle swarm optimization algorithm according to claim 1, wherein the step 1 is specifically: the two arms of the two-arm underwater robot are identical and symmetrically arranged, so that the coupling inertia matrix of the left arm of the mechanical arm is equal to the coupling inertia matrix of the right arm of the mechanical arm, and the inertia matrix of the robot base is constant, so that the following objective functions of the two-arm underwater robot operation can be obtained as follows (1) - (6):
f 1 ＝S 1 +S 2 +S 3 ＝G(1)+G(2)-r+alti (1)
wherein: s is S 1 ，S 2 ，S 3 Respectively represent the boat body trendAdvancing in the approaching process, laterally shifting and downwards shifting by a distance; g represents a coordinate point at which the tail end of the mechanical arm is fixed; r and alti respectively represent p of mechanical arm kinematics x And p y A value; i i Representing the moment of inertia of the ith joint; omega i Represents the angular velocity of the ith joint; m is m i Representing the mass of the ith joint; l (L) i The length of the arm link representing the i-th joint; f represents the resistance of the connecting rod of the ith joint in water; v represents the average rotational speed of the link rotation of the ith joint; t represents the set system operation time.
3. The underwater robot operation track planning optimization method based on the multi-target multi-population backbone particle swarm optimization algorithm is characterized by comprising the following steps of:
wherein: i ei Representing the moment of inertia of a virtual joint of the ith virtual combined mechanical arm; omega ei An angular velocity representing a virtual joint of the i-th virtual combined mechanical arm; m is m ei Representing the mass of the virtual joint of the ith virtual combined mechanical arm; l (L) ei The length of the link representing the virtual joint of the ith virtual combined mechanical arm; f represents the resistance of the rod of the virtual joint of the ith virtual combined mechanical arm to water; v represents the average rotation speed of the connecting rod rotation of the virtual joint of the ith virtual combined mechanical arm; t represents the operation time of the double-arm underwater robot; h b Representing an inertia matrix of the body;representing the coupled inertial matrix of the left arm and the connected base; />Representing the coupled inertial matrix of the right arm and the connected base; />The angular velocities of the joints of the left arm and the right arm of the mechanical arm are respectively represented; j (J) a ，J b Jacobian matrices representing the left and right arms of the mechanical arm, respectively.
4. The optimization method for the operation track planning of the underwater robot based on the multi-target multi-population backbone particle swarm optimization algorithm according to claim 1, wherein the strategy for adaptively and dynamically changing the weight in the step 2 is specifically as follows: the new weight change strategy is as shown in (7):
Wherein: f (f) avg ，f min F is the fitness value of backbone particle swarm; by adopting the self-adaptive weight coefficient changing mode, the adaptability value can be dynamically changed in the process of evolution of the backbone particle swarm algorithm, so that the particle swarm algorithm is prevented from being trapped into a local optimal value.
5. The optimization method for the operation track planning of the underwater robot based on the multi-target multi-population backbone particle swarm optimization algorithm of claim 2, wherein the particle position updating of the four populations in the step 3 is specifically: updating the positions of the particle swarms in the overall algorithm by adopting four backbone particle swarms; when searching, the four backbone particle swarms find out a global optimal solution while finding out respective local optimal solutions respectively, so as to ensure diversity of the population; wherein the location updates of population 1 and population 2 of backbone particle swarm are as follows:
wherein: z=1, 2, representing the location update formulas of backbone particle swarm 1 and backbone particle swarm 2, respectively;
similarly, the formula for updating the positions of backbone particle swarm 3 will be affected by basic backbone particle swarm 1 and backbone particle swarm 2, as follows:
wherein: gamma ray 1 ，γ 2 Relative fitness values for population 1 and population 2, respectively, and γ 1 +γ 2 =1; the position updating mode is mainly characterized in that the better adaptability has larger influence on the current particles by comparing the adaptability values of the backbone particle swarm 1 and the backbone particle swarm 2, so that the evolution of the backbone particle swarm 3 is better guided;
the same way of updating the positions of backbone particle swarm population 4 is as follows:
wherein: alpha 1 ，α 2 ，α 3 Influence factors and add to 1, respectively;
the particles in the backbone particle swarm 4 share the particle information in the other three populations, so that the evolution of the multi-population backbone particle swarm algorithm is diversified, and the searching process of the particles in the backbone particle swarm 4 is finer;
in order to reduce the influence of later variation on the algorithm, the variation probability calculation formula can be designed as follows:
at
pm＝e T (11)
wherein: a represents the initial mutation probability; t represents the algebra of evolution; t represents the total algebra of the algorithmic species evolution.
6. The optimization method for the operation track planning of the underwater robot based on the multi-target multi-population backbone particle swarm optimization algorithm of claim 5, wherein the particle speed update based on four populations in the step 4 is specifically: based on the algorithm using four backbone particle swarms as the population, the first two particle swarms are used as basic particle swarms in the four sub-swarm algorithm, and the speed of the particle swarm 1 has an effect on the speed update of the particle swarm 2, the particle swarm 1 and the particle swarm 2 both adopt the traditional speed and position update formulas, and the speed update is as follows:
Wherein: z represents particle swarm 1 and particle swarm 2, z=1, 2;
the update of the particle swarm 3 speed is affected by the fitness value of the particle swarm 1 and the particle swarm 2, and the update of the particle swarm 3 speed is performed as follows:
wherein: gamma ray 1 And gamma 2 Representing the fitness values of the particles in the basic particle swarm 1 and the basic particle swarm 2 respectively; gamma represents the sum of fitness values of particle swarm 1 and particle swarm 2, and is γ=γ 1 +γ 2 ；
Optimization and improvement of the speed update of the particle swarm 4, the speed update formula of the particle swarm 4 is guided by the speed update of the particle swarm 1, the particle swarm 2 and the particle swarm 3, and is as follows:
meanwhile, in order to enhance the searching capability of the particle swarm 4, the best leader in the particle swarm 4 is evolved towards the global optimal solution, so that the position updating formula in the particle swarm 4 is improved, as follows:
wherein: alpha 1 ，α 2 ，α 3 Represents the influence factor of the corresponding term, and alpha 1 +α 2 +α 3 ＝1。
7. The method for optimizing the operation track planning of the underwater robot based on the multi-target multi-population backbone particle swarm optimization algorithm according to claim 2, wherein the improvement of the constraint multi-target algorithm based on the violation tolerance coefficient in the step 5 is specifically as follows: all constraint violation degrees are normalized as follows:
C max ＝max(c i )i＝1,2,...,N (17)
In the above formula, constraint set c is constrained by an inequalityAnd equality constraint->Together form a constraint set C, and C max The maximum number in the whole set c is the number; through meterCalculating, namely obtaining the violation degree of the decision variable for each constraint condition, and finally obtaining the normalized constraint violation degree;
the degree of violation of the constraint will be calculated as follows:
wherein: t represents the algebra of the current constrained evolution; t represents the total algebra of constrained evolution.
8. The optimization system for the operation track planning of the underwater robot based on the multi-target multi-population backbone particle swarm optimization algorithm according to any one of claims 1 to 7, wherein the optimization system comprises a double-arm underwater robot energy-saving operation planning module and a manipulator energy-saving motion optimization module of the underwater robot;
the energy-saving operation planning module of the double-arm underwater robot is used for establishing a mathematical model of energy-saving operation planning of the double-arm underwater robot, wherein the energy-saving operation comprises the steps of approaching to fixing a virtual base and virtually combining mechanical arm operation, and respectively setting up an adaptive objective function;
the underwater robot-manipulator energy-saving motion optimization module is used for performing a strategy of self-adaptive dynamic weight change; carrying out particle position updating of four groups; carrying out particle velocity updating based on four groups; performing constraint multi-objective algorithm improvement based on violation tolerance coefficients; and the operation track planning optimization of the underwater robot based on the multi-target multi-population backbone particle swarm optimization algorithm is realized.
9. The electronic equipment is characterized by comprising a processor, a communication interface, a memory and a communication bus, wherein the processor, the communication interface and the memory are communicated with each other through the communication bus;
a memory for storing a computer program;
a processor for carrying out the method steps of any one of claims 1-7 when executing a program stored on a memory.
10. A computer-readable storage medium, characterized in that the computer-readable storage medium has stored therein a computer program which, when executed by a processor, implements the method steps of any of claims 1-7.
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