CN113043278B - Mechanical arm track planning method based on improved whale searching method - Google Patents
Mechanical arm track planning method based on improved whale searching method Download PDFInfo
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- CN113043278B CN113043278B CN202110392530.5A CN202110392530A CN113043278B CN 113043278 B CN113043278 B CN 113043278B CN 202110392530 A CN202110392530 A CN 202110392530A CN 113043278 B CN113043278 B CN 113043278B
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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
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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
- B25J9/1656—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
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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
- B25J9/1679—Programme controls characterised by the tasks executed
Abstract
The invention discloses a mechanical arm track planning method based on an improved whale searching method, which comprises the following steps of 1: importing a three-dimensional model; step 2: establishing a space coordinate system of the mechanical arm six-degree-of-freedom structure body; and step 3: defining motion parameters of the three-dimensional model and acquiring a pose; and 4, step 4: establishing a mechanical arm motion time optimal model; and 5: defining a constraint condition; and 6: the track planning is carried out on the mechanical arm by using the improved whale searching method, the global optimal solution can be obtained more quickly by using the method, and the result has higher accuracy.
Description
Technical Field
The invention belongs to the field of industrial robots and computer application, and particularly relates to a mechanical arm track planning method based on an improved whale searching method.
Background
With the rapid development of modern artificial intelligence technology, the manufacturing industry is developing towards integration and automation, and industrial robots serving the mechanical field are rising rapidly. Under the intelligent large environment, the requirements on the automation degree and the precision of the industrial robot are higher and higher. However, the industrial robot body has high investment cost and low efficiency in research and development and actual test, so that a simulation experiment needs to be performed on the designed industrial robot before production to analyze whether the performance of the industrial robot meets the requirements.
The kinematics solution, the dynamics solution, the trajectory planning and the like are performed on the simulation model in sequence. More and more industrial robot trajectory planning application examples show that trajectory planning only considering continuity and smoothness cannot meet most industrial requirements, and the problems of energy consumption, efficiency, impact and the like need to be considered, so that the performance of the trajectory is improved. Therefore, constraint conditions of trajectory planning need to be provided according to different task requirements so as to achieve the purpose of trajectory optimization. Generally, an intelligent optimization method is adopted to optimize targets, but the intelligent optimization methods commonly used for track planning research have the defects of multiple parameters, complex calculation process and the like. Compared with most intelligent optimization methods, the method for searching the global optimal value by whale provided in recent years has the advantages of few parameters, simple structure and the like, but is easy to fall into a local optimal solution.
In summary, the current mechanical arm trajectory planning method cannot simultaneously meet the requirements of small calculated amount in the analysis process, accurate calculation result, high reliability and the like.
Disclosure of Invention
The invention aims at: in order to solve the problem that the existing mechanical arm track planning method cannot meet the requirements of small calculated amount in the analysis process, accurate calculation result, high reliability and the like at the same time, the invention provides the mechanical arm track planning method based on the improved whale searching method, the method greatly reduces the calculated amount, meets the requirement of high precision at the same time, and can be applied to the track planning of an industrial robot.
The technical scheme is as follows: a mechanical arm track planning method based on an improved whale searching method comprises the following steps:
step 1: acquiring parameters of all connecting rods of the mechanical arm, constructing a three-dimensional model of the mechanical arm and constructing a three-dimensional model of a main body interacting with the motion of the mechanical arm in an actual application scene;
step 2: defining a space coordinate system of each joint of the mechanical arm; wherein, each direction axis of the space coordinate system of the joint i is defined as x i 、y i 、z i A shaft; theta.theta. i Is x i-1 Axial z i-1 The shaft rotates to x i The angle of the shaft;
and step 3: setting path points between the main body and the manipulator at the tail end of the mechanical arm based on tasks to be completed by the mechanical arm under the space coordinate system in the step 2; the method comprises the steps that tasks are executed through a simulation mechanical arm, and the set pose of a mechanical arm end manipulator corresponding to each path point is obtained;
and 4, step 4: according to task requirements, defining the movement time between two adjacent path points to obtain the total time required for completing the whole task; establishing a mathematical model with optimal mechanical arm movement time based on the total time required for completing the whole task;
and 5: taking the mathematical model established in the step 4 as an objective function of the whale optimization searching method, taking the maximum value of the kinematic parameters of each joint of the mechanical arm as a constraint condition of the whale optimization searching method, and obtaining the optimal movement time by adopting the whale optimization searching method;
step 6: and planning to obtain the motion track of the mechanical arm based on the optimal motion time.
According to the method, a three-dimensional model of the mechanical arm and a three-dimensional model of a main body interacting with the movement of the mechanical arm in an actual application scene are constructed in ROBCAD software.
Further, step 2 specifically includes:
defining the intersection point of the common perpendicular line of the joints at the two ends of the mechanical arm connecting rod i +1 and the axis of the joint i as an origin, and establishing x along the common perpendicular line and pointing to the direction of the joint i +1 i Axis, establishing z along the joint i axis i Axis, determination of y by right technique i A shaft.
Further, in step 3, setting a path point between the main body and the manipulator at the end of the robot arm specifically includes:
and defining the path point which the manipulator at the tail end of the mechanical arm passes through in the complete task according to the joint motion on the mechanical arm, the speed and the acceleration of the joint motion, the joint axis and the joint motion range.
Further, in step 3, the pose is expressed as:
wherein n is x 、n y 、n z Normal unit vectors describing the coordinate system of the end operator in the x, y and z directions respectively; o x 、o y 、o z Direction unit vectors describing the coordinate system of the end effector in the x, y and z directions respectively; a is a x 、a y 、a z Respectively, a near unit vector describing the coordinate system of the end effector in the x, y and z directions; p is a radical of x 、p y 、p z Position vectors describing the end effector coordinate system in the x, y, z directions, respectively.
In the invention, the software ROBCAD directly acquires the pose of the manipulator at the tail end of the mechanical arm at the set path point.
Further, in step 4, the mathematical model for optimizing the motion time of the mechanical arm is represented as:
T total ＝mint 1 ′+mint′ 2 +mint′ 3 +...... (2)
wherein, t' 1 、t′ 2 、t′ 3 Respectively representing the running time of the mechanical arm between two adjacent path points.
Further, in step 5, the kinematic parameters of each joint of the mechanical arm include: angular velocity of each joint of mechanical arm
Angular acceleration of each joint of mechanical arm
And angular acceleration of joints of the arm
The constraint conditions of the whale optimization searching method are represented as follows:
wherein the content of the first and second substances,
is the maximum value of the angular velocity of each joint of the mechanical arm,
is the maximum value of the angular acceleration of each joint of the mechanical arm,
the maximum value of the angular jerk of each joint of the mechanical arm.
Further, in step 5, the whale optimization searching method comprises the following steps:
s100: initializing a non-linear convergence factor
Coefficient vector
Coefficient vector
Parameter l, parameter p, nonlinear inertial weight ω and maximum number of iterations t max (ii) a Setting the population number N and randomly generating an initial population position;
s200: calculating the fitness value of each whale individual in the population, defining the whale individual with the minimum fitness value as the current optimal individual, and using X * Representing its position vector;
s300: updating nonlinear convergence factors of individual whales
Coefficient vector
Coefficient vector
Parameter l, parameter p, nonlinear inertial weight ω;
s400: judging whether the updated parameters meet the following conditions: p < 0.5 and | A | < 1, if satisfied, updating the location of each individual whale according to the following equation:
if the updated parameters satisfy p < 0.5 and | A | > 1, updating the position of each whale individual according to the following formula, namely the shortest running time obtained by solving currently:
if the updated parameter satisfies that p is more than or equal to 0.5, updating the position of each whale individual according to the following formula, and obtaining the shortest operation time obtained by the current solution:
wherein the content of the first and second substances,
is a nonlinear convergence factor;
is a coefficient vector; l is [ -1,1]The random number of (2); p is [0,1 ]]The random number of (2);
is [0,1 ]]The random vector of (a); omega is a nonlinear inertial weight; t is t max Is the maximum iteration number; mu is a constant coefficient; b is a constant defining the shape of the logarithmic spiral.
S500: judging whether the iteration number reaches the maximum iteration number t max If not, returning to S200; if so, outputting the current optimal individual and the position vector X thereof * And obtaining the optimal exercise time. Nonlinear convergence factor in whale searching method
The convergence rate is nonlinear, and the convergence rate in the early stage is fast and the convergence rate in the later stage is relatively slow.
Has the advantages that: compared with the prior art, the invention has the following advantages:
(1) The improved whale searching method is applied to track optimization of the mechanical arm, optimal track planning of the movement time of the mechanical arm is achieved, the calculation result has higher precision, and the optimization time is shortened;
(2) The invention obtains the pose of the manipulator end corresponding to each path point through the ROBCAD software, thereby reducing the calculated amount of matrix transformation.
Drawings
FIG. 1 is a schematic view of a robotic arm;
FIG. 2 is a space coordinate system established in the embodiment;
FIG. 3 is a three-dimensional model of an embodiment;
FIG. 4 shows an exemplary embodiment of a standard-based test function F 1 (x) The improved whale optimization search and other three commonly used intelligent optimization methods are used for comparing the convergence rate;
FIG. 5 is a graph showing a standard-based test function F in the example 2 (x) The improved whale optimization search and other three commonly used intelligent optimization methods are used for comparing the convergence accuracy;
FIG. 6 shows the results of time optimization in the examples;
FIG. 7 shows the results of the trajectory planning of each joint in the example;
fig. 8 is a general flow diagram.
Detailed Description
The technical scheme of the invention is further explained by combining the attached drawings and the embodiment.
Referring to fig. 8, in the embodiment, a trajectory planning method for a mechanical arm based on an improved whale searching method is adopted to plan a trajectory of the mechanical arm for performing a task of picking raw materials; fig. 3 is a schematic diagram of a robotic arm performing the task of grasping raw material, as shown in fig. 3, the task being performed by a body comprising: the device comprises a machining center 1, a material taking point 2, a mechanical arm 3, a bin 4 and a raw material point 5; the processing center 1 and the bin 4 are respectively arranged at two sides of the mechanical arm 3, the raw material point 5 is positioned at any position of the bin 4, and the material taking point 2 is positioned at the processing center 1; the end-of-arm manipulator grips raw material at the raw material point 5, moves to the machining center, places the raw material at the material taking point 2, and then returns to the initial position, which is a one-time material taking movement.
Now, the steps of the planning method used in this embodiment will be described with reference to this task, which includes the following steps:
step 1: importing a three-dimensional model: acquiring main parameters of each connecting rod of the mechanical arm, wherein the main parameters comprise the size, the material density, the centroid position, the connection mode and the like of each connecting rod including the base, and importing three-dimensional models of the mechanical arm and other main bodies related to the mechanical arm in an actual application scene into software ROBCAD; see fig. 1;
step 2: referring to fig. 2, a spatial coordinate system of the six-DOF structural body of the robot arm is established, wherein each directional axis of the spatial coordinate system of the joint i is defined as x i 、y i 、z i A shaft; theta i Is x i-1 Axial around z i-1 The shaft rotates to x i Angle of the shaft: defining a base coordinate system {0} and space coordinate systems of joints of the mechanical arm by a standard D-H parameter method; the method specifically comprises the following steps: defining the intersection point of the common perpendicular line of the joints at the two ends of the connecting rod i +1 and the axis of the joint i as an origin, and establishing x along the common perpendicular line and pointing to the direction of the joint i +1 i Shaft, along which joint axis z is established i Axis, determining y by right-hand rule i A shaft;
and step 3: defining model motion parameters, and acquiring a pose: based on the step 2, defining path points of a movable mechanism (including joint motion, joint motion speed and acceleration, joint axis, motion range and the like) and a mechanical arm end manipulator for completing a specific task in software ROBCAD, and defining the path points passing through in sequence as P 0 、P 1 、P 2 、P 1 、P 3 、P 4 、P 3 、P 0 Wherein P is 0 At an initial position, P, of the end-of-arm manipulator 1 Is at any position on the storage bin close to the raw material point, P 2 At the location of the charging point, P 3 Is at any position on the machining center near the material taking point, P 4 Is the position of a material taking point. Simulating the process that the mechanical arm clamps raw materials in an actual application scene, moves in a machining center, and then returns to an initial position, wherein the software ROBCAD can directly acquire the pose of the mechanical arm end operator corresponding to each set path point:
and 4, step 4: time-optimal modeling: defining the motion time between two adjacent path points according to the practical application requirement, namely t' 1 、t′ 2 、t′ 3 、t′ 4 、t′ 5 、t′ 6 、t′ 7 Then the total time required to complete the entire specific task is:
T total ＝mint′ 1 +mint′ 2 +mint′ 3 +mint′ 4 +mint′ 5 +mint′ 6 +mint′ 7
and 5: defining a constraint condition: adding and researching angular velocity of each joint of mechanical arm
Angular acceleration
Sum angular jerk
And taking the maximum value of the isokinetic parameters as a constraint condition of the optimized search of the improved whale:
in the present embodiment, the constraint conditions of each joint are set as follows:
step 6: planning a track: taking the mathematical model in the step 4 as an objective function of the method, and carrying out trajectory planning on the mechanical arm based on the constraint conditions defined in the step 5 and an improved whale searching method, wherein the improved whale searching method comprises the following calculation steps:
(1) Setting the number of populations to be N =30, and randomly generating the position of an initial population; initializing parameters
l, p, ω and t max Wherein:
wherein, the first and the second end of the pipe are connected with each other,
is a nonlinear convergence factor;
is a coefficient vector; l is [ -1,1]The random number of (2); p is [0,1 ]]The random number of (2);
is [0,1 ]]A random vector of (a); omega is a nonlinear inertial weight; t is t max The maximum number of iterations is 500 in this example; mu is a constant coefficient, and the value in the embodiment is 0.01 after multiple simulation experiments.
(2) Calculating the fitness value of each whale individual (namely a search agent) in the population, selecting the whale individual with the minimum fitness value, defining the whale individual as the current optimal individual, and using X to select * Represents its position vector:
(3) Once per iteration, the relevant parameters for each search agent are updated:
l, p, ω. If p < 0.5 and | A | < 1, then the location update for each search agent is calculated as in equation (8):
otherwise, if p is less than 0.5 and | A | ≧ 1, the calculation is performed according to equation (9):
if p is greater than or equal to 0.5, the position is updated according to equation (10):
(4) And comparing the individuals in the population after the position is updated, and determining the globally optimal individual and the current position.
(5) If the iteration times reach the maximum value, namely the termination condition of the circulation part in the WOA is reached, outputting a result, namely the optimal movement time; otherwise, returning to the step (2) and continuing to calculate until the termination condition is met.
In order to verify the convergence performance of the improved whale optimization algorithm, the whale optimization algorithm is calculated based on a standard test function,and comparing the convergence performance with the convergence performance of three other commonly used intelligent optimization algorithms, and FIG. 4 shows a standard-based test function F in the embodiment 1 (x) The improved whale optimization search and other three commonly used intelligent optimization methods are used for comparing the convergence rate; standard test function F 1 (x) Expressed as:
FIG. 5 is a graph showing a standard-based test function F in the example 2 (x) The improved whale optimization search and other three commonly used intelligent optimization methods are used for comparing the convergence accuracy; standard test function F 2 (x) Expressed as:
as shown in fig. 4 and 5,. The convergence speed and the convergence precision of the improved whale optimization algorithm are superior to those of a genetic algorithm GA, a particle swarm optimization PSO and a basic whale optimization WOA.
The optimal movement time of the mechanical arm obtained by the searching method in the embodiment is shown in the following table and fig. 6, and the final result of the trajectory planning is shown in fig. 7.
The mechanical arm trajectory planning result which is obtained by the method of the embodiment and aims at time optimization meets the requirements of small calculated amount, reliable calculated result and high precision.
Claims (4)
1. A mechanical arm track planning method based on an improved whale searching method is characterized by comprising the following steps: the method comprises the following steps:
step 1: acquiring parameters of all connecting rods of the mechanical arm, constructing a three-dimensional model of the mechanical arm and constructing a three-dimensional model of a main body interacting with the motion of the mechanical arm in an actual application scene;
step 2: defining a space coordinate system of each joint of the mechanical arm;
and 3, step 3: setting path points between the main body and the manipulator at the tail end of the mechanical arm based on tasks to be completed by the mechanical arm under the space coordinate system in the step 2; the method comprises the steps that tasks are executed through a simulation mechanical arm, and the set pose of a mechanical arm end manipulator corresponding to each path point is obtained;
and 4, step 4: according to task requirements, defining the movement time between two adjacent path points to obtain the total time required for completing the whole task; establishing a mathematical model with optimal mechanical arm movement time based on the total time required for completing the whole task;
and 5: taking the mathematical model established in the step 4 as an objective function of the whale optimization searching method, taking the maximum value of the kinematic parameter of each joint of the mechanical arm as a constraint condition of the whale optimization searching method, and obtaining the optimal movement time by adopting the whale optimization searching method;
and 6: planning to obtain the motion track of the mechanical arm based on the optimal motion time;
the mathematical model for optimizing the motion time of the mechanical arm is represented as follows:
T total ＝min t′ 1 +min t' 2 +min t' 3 +……(2)
wherein, t' 1 、t' 2 、t' 3 Respectively representing the operation time of the mechanical arm between two adjacent path points;
the kinematic parameters of each joint of the mechanical arm comprise: angular velocity of each joint of mechanical arm
Angular acceleration of each joint of mechanical arm
And angular acceleration of joints of the arm
The constraint conditions of the whale optimization searching method are represented as follows:
wherein the content of the first and second substances,
is the maximum value of the angular velocity of each joint of the mechanical arm,
is the maximum value of the angular acceleration of each joint of the mechanical arm,
the maximum value of the angular acceleration of each joint of the mechanical arm;
the whale optimization searching method comprises the following steps:
s100: initializing a non-linear convergence factor
Coefficient vector
Parameter l, parameter p, nonlinear inertia weight omega and maximum iteration number t max (ii) a Setting a population quantity N and randomly generating an initial population position;
s200: calculating the fitness value of each whale individual in the population, defining the whale individual with the minimum fitness value as the current optimal individual, and using X * Representing its position vector;
s300: updating the nonlinear convergence factor of each whale individual
Coefficient vector
Parameter l, parameter p, nonlinear inertial weight ω;
s400: judging whether the updated parameters meet the following conditions: p is less than 0.5 and | A | is less than 1; if the calculated shortest running time is met, the position of each whale individual is updated according to the following formula:
if the updated parameters satisfy p < 0.5 and | A | ≧ 1, the location of each individual whale is updated according to the following equation:
if the updated parameter satisfies that p is more than or equal to 0.5, updating the position of each whale individual according to the following formula:
wherein the content of the first and second substances,
is a nonlinear convergence factor;
is a coefficient vector; l is [ -1,1]The random number of (2); p is [0,1 ]]The random number of (2);
is [0,1 ]]The random vector of (a); omega is a nonlinear inertial weight; t is t max Is the maximum number of iterations;
s500: judging whether the iteration number reaches the maximum iteration number t max If not, returning to S200; if so, outputting the current optimumIndividuals and their location vectors X * And obtaining the optimal exercise time.
2. The mechanical arm trajectory planning method based on the improved whale searching method as claimed in claim 1, wherein the mechanical arm trajectory planning method comprises the following steps: the step 2 specifically comprises:
defining the intersection point of the common perpendicular line of the joints at the two ends of the mechanical arm connecting rod i +1 and the axis of the joint corresponding to the connecting rod i as an origin, and establishing x along the common perpendicular line and in the direction of the joint corresponding to the connecting rod i +1 i A shaft establishing z along the joint axis corresponding to the link i i Axis, determining y by right hand rule i A shaft.
3. The mechanical arm trajectory planning method based on the improved whale searching method as claimed in claim 1, wherein the mechanical arm trajectory planning method comprises the following steps: in step 3, the setting of the path point between the main body and the manipulator at the end of the mechanical arm specifically includes:
the path points that the end-of-arm manipulator passes when completing the task are defined in the software ROBCAD.
4. The mechanical arm trajectory planning method based on the improved whale search method as claimed in claim 1, wherein the mechanical arm trajectory planning method comprises the following steps: in step 3, the pose is expressed as:
wherein n is x 、n y 、n z Normal vectors describing the coordinate system of the end effector in the x, y and z directions respectively; o. o x 、o y 、o z Orientation vectors describing the coordinate system of the end effector in the x, y and z directions respectively; a is x 、a y 、a z Respectively, describing the approach vectors of the coordinate system of the end operator in the x direction, the y direction and the z direction; p is a radical of formula x 、p y 、p z Position vectors describing the end effector coordinate system in the x, y, z directions, respectively.
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