CN112157650A - Vehicle-mounted mechanical arm dynamics modeling and control method - Google Patents
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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
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- B25J9/1602—Programme controls characterised by the control system, structure, architecture
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- 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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Abstract
The invention discloses a vehicle-mounted mechanical arm dynamics modeling and control method, which comprises the following steps of establishing a motion equation; step two, establishing a transmission system; the establishment of the motion equation comprises analyzing the influence of each motion equation from six aspects of gravity equation, inertia matrix, scientific matrix, payload, base force and dynamic operability, the establishment of the transmission system is to analyze the influence of the friction force on the motion equation, the establishment of the motion equation is to firstly input the type of research, namely a Puma560 robot, the robot is at the standard pose, the joint speed and the acceleration are 0, the robot is at the static state at the moment, the action of the moments is assumed to enable the robot to keep balance under the action of gravity, and the moments are calculated under the condition without the gravity to obtain a matrix of 10 multiplied by 6: under the condition that the robot is in a standard pose, the robot has the characteristics of strong practicability and simple and convenient adjustment.
Description
Technical Field
The invention relates to the technical field of vehicle-mounted mechanical arms, in particular to a vehicle-mounted mechanical arm dynamics modeling and control method.
Background
The development and application of robot call play a very important role in the recent modern industrial development history of the world, and the robot technology has achieved a long development and huge achievement from the production of the first industrial robot in the united states in 1959 to the present.
At home, automatic welding of a spatial intersecting curve mainly has two forms, namely, a universal welding industrial robot is adopted, the universal welding industrial robot can complete automatic welding tasks of complex curves such as the spatial intersecting curve and the like, but cannot be used for field operation. And secondly, a special automatic semi-automatic welding machine based on a profiling technology is adopted. Some researchers in China recently research the spatial coherence curve profiling welding control technology and initially popularize and apply the technology. However, due to the limitation of the profiling technology, when processing curves with different specifications and different forms, the profiling cam must be replaced, and complex adjustment must be carried out when the cam is replaced every time, so that the operation is difficult, and the practicability is poor. Therefore, a vehicle-mounted mechanical arm dynamics modeling and control method which is strong in design practicability and simple and convenient to adjust is necessary.
Disclosure of Invention
The invention aims to provide a vehicle-mounted mechanical arm dynamics modeling and control method to solve the problems in the background technology.
In order to solve the technical problems, the invention provides the following technical scheme: the vehicle-mounted mechanical arm dynamics modeling method comprises the steps of firstly, establishing a motion equation; step two, establishing a transmission system; the establishment of the motion equation comprises analyzing the influence of each motion equation from six aspects of a gravity equation, an inertia matrix, a formula matrix, a payload, a base force and dynamic operability, and the establishment of the transmission system is to analyze the influence of the friction force on the motion equation.
According to the above technical solution, in the establishment of the motion equation, the type of research is first input, which is the Puma560 robot, the robot is in the standard pose at this time, the joint velocity and the acceleration are 0, here, the robot is now in the stationary state, it is assumed that the actions of these moments are such that the robot can still keep balance under the action of gravity, and the moments are calculated under the condition of no gravity, so as to obtain a matrix of 10 × 6: under the condition that the robot is in a standard pose, the joint 1 rotates at the speed of 2rad/s, and the acceleration of other joints is 0. The joint moment is no longer 0 at this time.
According to the technical scheme, when the influence of the gravity equation is established, the gravload method is used, the gravity acceleration is set as the earth gravity acceleration in the SerialLink object, in order to reduce joint moment, the gravity is changed into the gravity of the moon, then the gravity is changed into the earth value and is set to be right side up, the moment when the arm is vertically upward is calculated, and the torque required by the motor is estimated by using the result.
According to the technical scheme, when the influence of the inertia matrix is established, the inertia matrix is a function related to the pose of the mechanical arm, and the matrix is a symmetric matrix. M11 and M22 in this matrix represent the waist joint and shoulder joint of the robot, respectively, which are large because the motions of these joints are related to the motions of the large arm and small arm of the robot arm, and Mij Mji, i ≠ j in the matrix, which represents the coupling from the acceleration of joint i to joint j, and by changing the pose of the robot arm and the angles of the joints 2 and 3, it is derived how the elements in the inertia matrix can be changed along with the change of the robot configuration.
According to the technical scheme, when the scientific matrix is established to influence, the scientific matrix C represents the functional relation between the joint coordinates and the joint speed, all joints on the robot body rotate at the speed of 1rad/s in the standard pose, and the scientific matrix at the moment is calculated.
According to the above technical solution, when establishing payload impact, there are two factors determining the maximum payload: firstly, the mass of the tail end of the robot increases the rotational inertia of the joint of the robot and simultaneously reduces the acceleration and the dynamic performance; secondly, the weight of the tail end of the robot can increase the gravity needing joint support, the moment for acceleration of the joint can be reduced due to the increased gravity moment component, the dynamic performance of the robot is reduced, the maximum effective load of the Puma560 robot is 2.5 kilograms, a weight of 2.5 kilograms is added to the tail end of the robot, the center of mass of the effective load deviates 150 millimeters along the direction of the Z axis of the coordinate axis, the inertia under the standard pose is calculated, and the proportion coefficient of the gravity load increase on the joint is obtained by comparing the inertia with the inertia when no load is added.
According to the above technical solution, when the base force influence is established, the moving robot applies a force rotation amount to the base, the force rotation amount is an optional parameter of the rne method, the force rotation amount is applied to the base to keep the base balanced, and the moments around the x axis and the y axis are calculated.
According to the technical scheme, when the influence of dynamic operability is established, only translational acceleration is considered under a standard pose, so that the translational acceleration is a matrix Mx with the upper left corner being 3 multiplied by 3, a three-dimensional ellipsoid is drawn, the radius of the ellipsoid is obtained and is the square root of a special value of the matrix, and the ratio of the minimum radius to the maximum radius is calculated.
According to the technical scheme, when the friction force analysis influences a motion equation, the static friction moment and the dynamic friction moment are calculated according to the coulomb friction coefficient, the gear transmission ratio and the viscous friction coefficient by using the dynamic parameters of the first connecting rod of the Puma560 robot.
The vehicle-mounted mechanical arm dynamics control method comprises the following specific steps: step one, forward kinematics simulation; secondly, controlling independent joints of the robot; step three, testing a position control loop; step four, rigid body power compensation; and step five, flexible transmission.
According to the above technical solution, in the above step one, the listed differential equations are rearranged to obtain:
this represents the acceleration of the joint, in the research through Matlab, the acceleration of the joint is calculated by using an acell method in a SerialLink object, this function is packaged in a Robot module of Simulink, then a Simulink model sl _ ztorque of a Puma560 Robot in a zero joint moment state is opened, the simulation is run, the motion of the Robot is represented in the form of animation, and the change of the joint angle at different times is drawn by using software:
in the second step, taking the shoulder joint of Puma560 as an example, the function:
a power model of the motor is described. The laplace transform of the above equation:
sJΩ(s)+BΩ(s)＝KmKau(s), transforming the above formula to obtain:
obtaining the effective inertia:
taking the average value of 2kg/m2 to obtain the total inertia of 372 x 106kg/m2, using a controller based on the actual speed and the required speed error, operating the simulator, adding a disturbance moment, re-editing the test and re-operating the test to obtain a speed ring with the increased disturbance moment, in a Simulink model, by setting the value of Ki, the system is better when the gains are 1 and 10 through trial and error;
in the third step, the position ring is responsible for keeping the position of the joint, the position ring simultaneously provides the speed requirement for the speed ring, a tester is also established for testing the position control ring, the position requirement comes from an LSPB track generator, in order to realize better tracking performance under the condition of individual speed, the controller needs to be optimized by adjusting gain, the tracking error and the error performance of the controller are obtained when Kp is 40, then a time response curve with front feedback is observed, and the tracking error is found according to the image;
in the fourth step, the joint angle, the joint speed, the joint acceleration, the moment of inertia and the coupling moment of the joint are added into a control algorithm, and the four steps are mainly carried out by two methods: feedforward control and calculation moment control, using Simulink to test the controller/firstly establishing an object, loading a feedforward controller model, and operating the controller, the change of the robot configuration can be found to be very slow; firstly creating an object by using Simulink, then removing Coulomb friction, then loading a calculation torque controller, generating an expected joint angle and joint speed by a jtraj module, expressing initial and final joint angles by parameters of the joint angle and the joint speed, and running simulation to obtain a tracking error;
in the fifth step, the Simulink model is utilized, and the angles of the motor and the connecting rod are measured by a simple two-rod flexible manipulator, so that the system is effectively controlled.
Compared with the prior art, the invention has the following beneficial effects: in the invention, the raw materials are mixed,
(1) the method is an important precondition for researching the robot by analyzing the kinematics of the robot, wherein the kinematics comprises the geometry of the robot moving relative to a fixed coordinate system, and the kinematics analysis, the trajectory planning and the task execution of the control robot are carried out on the robot under a specific working environment; the process of robot kinematics modeling can be deduced according to the rotation and translation transformation between adjacent joints and connecting rods, and the inverse of kinematics is solved. The inverse solution of the robot shows the motion condition of the terminal pose in the reachable working space, the efficiency can be improved, the influence of the joint speed on the terminal linear speed and the terminal angular speed can be understood more visually, the robot function of a robot Toolbo in MATLAB is adopted, the path planning of the solution can be carried out, the optimal solution is realized, the influence of each interference item on the change of the robot pose when the pose of the robot changes is obtained, and a method for eliminating the interference item as much as possible is provided.
Drawings
The accompanying drawings, which are included to provide a further understanding of the invention and are incorporated in and constitute a part of this specification, illustrate embodiments of the invention and together with the description serve to explain the principles of the invention and not to limit the invention. In the drawings:
FIG. 1 is a diagram of the change of gravity load along with the position and posture of a robot when an inertia matrix is established according to the invention;
FIG. 2 is a diagram of the pose change of the robot along with the gravitational moments of the joints 2 and 3 when an inertia matrix is established according to the invention;
FIG. 3 is a diagram of a spatial acceleration ellipsoid of a robot under the influence of dynamic maneuverability of the present invention;
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
Referring to fig. 1-3, the present invention provides the following technical solutions: the vehicle-mounted mechanical arm dynamics modeling method comprises the steps of firstly, establishing a motion equation; step two, establishing a transmission system; the establishment of the motion equation comprises analyzing the influence of each motion equation from six aspects of a gravity equation, an inertia matrix, a formula matrix, a payload, a base force and dynamic operability, and the establishment of the transmission system is to analyze the influence of friction force on the motion equation;
in the establishment of the equation of motion, the type under study, Puma560 robot, is first input, the robot is in the standard pose, the joint velocity and the acceleration are 0, the robot is now in the static state, the moments are calculated under the condition without gravity, and a 10 × 6 matrix is obtained, assuming that the moments act to keep the robot balanced under the action of gravity: under the condition that the robot is in a standard pose, the joint 1 rotates at the speed of 2rad/s, and the acceleration of other joints is 0. The joint moment is no longer 0 at this time;
when the influence of the gravity equation is established, a gravload method is used, the gravity acceleration is set as the earth gravity acceleration in a SerialLink object, in order to reduce joint moment, the gravity is changed into the gravity of the moon, then the gravity is changed into the earth value and is set to be right side up, the moment when the arm is vertically upward is calculated, and the torque required by the motor is estimated by using the result;
when the influence of the inertia matrix is established, the inertia matrix is a function of the pose of the mechanical arm, the matrix is a symmetric matrix, M11 and M22 in the matrix respectively represent the waist joint and the shoulder joint of the robot, the two values are larger because the motions of the joints are related to the motions of the large arm and the small arm of the mechanical arm, Mij-Mji, i ≠ j in the matrix represents the coupling from the acceleration of the joint i to the joint j, and how the elements in the inertia matrix can be changed along with the change of the pose of the robot is obtained by changing the pose of the mechanical arm and the angles of the joints 2 and 3;
when a scientific matrix is established to influence, the scientific matrix C represents the functional relation between the joint coordinates and the joint speed, all joints on the robot rotate at the speed of 1rad/s under the standard pose, and the scientific matrix at the moment is calculated;
when establishing payload impact, there are two factors that determine the maximum payload: firstly, the mass of the tail end of the robot increases the rotational inertia of the joint of the robot and simultaneously reduces the acceleration and the dynamic performance; secondly, the weight of the tail end of the robot can increase a gravity needing joint support, the moment for acceleration of the joint can be reduced by the component of the increased gravity moment, so that the dynamic performance of the robot is reduced, the maximum effective load of the Puma560 robot is 2.5 kilograms, a weight of 2.5 kilograms is added to the tail end of the robot, the center of mass of the effective load deviates 150 millimeters along the direction of the Z axis of the coordinate axis, the inertia under the standard pose is calculated, and the proportion coefficient of the gravity load increase on the joint is obtained by comparing the inertia with the inertia when no load is added;
when the base force influence is established, the moving robot applies a force rotation amount to the base, the force rotation amount is an optional parameter of the rne method, the force rotation amount is applied to the base to keep the base balanced, and the moments around the x axis and the y axis are calculated; when the influence of dynamic operability is established, only translational acceleration is considered under a standard pose, so that the matrix Mx is a 3 multiplied by 3 matrix Mx at the upper left corner, a three-dimensional ellipsoid is drawn, the radius of the ellipsoid is obtained and is the square root of a special value of the matrix, and the ratio of the minimum radius to the maximum radius is calculated;
when the friction force analysis influences the motion equation, calculating static friction moment and dynamic friction moment according to coulomb friction coefficient, gear transmission ratio and viscous friction coefficient by using the dynamic parameters of the first connecting rod of the Puma560 robot;
the vehicle-mounted mechanical arm dynamics control method comprises the following specific steps: step one, forward kinematics simulation; secondly, controlling independent joints of the robot; step three, testing a position control loop; step four, rigid body power compensation; step five, flexible transmission is performed;
in the step oneRearranging the listed differential equations yields:
this represents the acceleration of the joint, in the research through Matlab, the acceleration of the joint is calculated by using an acell method in a SerialLink object, this function is packaged in a Robot module of Simulink, then a Simulink model sl _ ztorque of a Puma560 Robot in a zero joint moment state is opened, the simulation is run, the motion of the Robot is represented in the form of animation, and the change of the joint angle at different times is drawn by using software:
in the second step, taking the shoulder joint of Puma560 as an example, the function:
a power model of the motor is described. The laplace transform of the above equation:
sJΩ(s)+BΩ(s)＝KmKau(s), transforming the above formula to obtain:
obtaining the effective inertia:
taking the average value of 2kg/m2 to obtain the total inertia of 372 x 106kg/m2, using a controller based on the actual speed and the required speed error, operating the simulator, adding a disturbance moment, re-editing the test and re-operating the test to obtain a speed ring with the increased disturbance moment, in a Simulink model, by setting the value of Ki, the system is better when the gains are 1 and 10 through trial and error;
in the third step, the position ring is responsible for keeping the position of the joint, the position ring simultaneously provides the speed requirement for the speed ring, a tester is also established for testing the position control ring, the position requirement comes from an LSPB track generator, in order to realize better tracking performance under the condition of individual speed, the controller needs to be optimized by adjusting gain, the tracking error and the error performance of the controller are obtained when Kp is 40, then a time response curve with front feedback is observed, and the tracking error is found according to the image;
in the fourth step, the joint angle, the joint speed, the joint acceleration, the moment of inertia and the coupling moment of the joint are added into a control algorithm, and the four steps are mainly carried out by two methods: feedforward control and calculation moment control, using Simulink to test the controller/firstly establishing an object, loading a feedforward controller model, and operating the controller, the change of the robot configuration can be found to be very slow; firstly creating an object by using Simulink, then removing Coulomb friction, then loading a calculation torque controller, generating an expected joint angle and joint speed by a jtraj module, expressing initial and final joint angles by parameters of the joint angle and the joint speed, and running simulation to obtain a tracking error;
in the fifth step, the Simulink model is utilized, and the angles of the motor and the connecting rod are measured by a simple two-rod flexible manipulator, so that the system is effectively controlled.
It is noted that, herein, relational terms such as first and second, and the like may be used solely to distinguish one entity or action from another entity or action without necessarily requiring or implying any actual such relationship or order between such entities or actions. Also, the terms "comprises," "comprising," or any other variation thereof, are intended to cover a non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements does not include only those elements but may include other elements not expressly listed or inherent to such process, method, article, or apparatus.
Finally, it should be noted that: although the present invention has been described in detail with reference to the foregoing embodiments, it will be apparent to those skilled in the art that changes may be made in the embodiments and/or equivalents thereof without departing from the spirit and scope of the invention. Any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in the protection scope of the present invention.
Claims (9)
1. The vehicle-mounted mechanical arm dynamics modeling method is characterized by comprising the following steps: comprises that
Step one, establishing a motion equation; step two, establishing a transmission system; the establishment of the motion equation comprises analyzing the influence of each motion equation from six aspects of a gravity equation, an inertia matrix, a formula matrix, a payload, a base force and dynamic operability, and the establishment of the transmission system is to analyze the influence of the friction force on the motion equation.
2. The modeling method for dynamics of vehicle-mounted mechanical arm according to claim 1, characterized in that: in the establishment of the motion equation, firstly, the type of research is input, which is a Puma560 robot, the robot is in a standard pose at this time, the joint speed and the acceleration are 0, the robot is in a static state at this time, the moments are calculated under the condition that the gravity is absent, and a matrix of 10 × 6 is obtained on the assumption that the moments have the effect that the robot can still keep balance under the action of gravity: under the condition that the robot is in a standard pose, the joint 1 rotates at the speed of 2rad/s, and the acceleration of other joints is 0. The joint moment is no longer 0 at this time.
3. The modeling method for dynamics of vehicle-mounted mechanical arm according to claim 2, characterized in that: when the influence of the gravity equation is established, the gravload method is used, the gravity acceleration is set as the earth gravity acceleration in the SerialLink object, the gravity is changed into the gravity of the moon in order to reduce the joint moment, then the gravity is changed into the earth value and is set to be right side up, the moment when the arm is vertically upward is calculated, and the torque required by the motor is estimated by using the result.
4. The modeling method for dynamics of vehicle-mounted mechanical arm according to claim 3, characterized in that: when the influence of the inertia matrix is established, the inertia matrix is a function of the pose of the mechanical arm, the matrix is a symmetric matrix, M11 and M22 in the matrix respectively represent the waist joint and the shoulder joint of the robot, the two values are larger because the motions of the joints are related to the motions of the large arm and the small arm of the mechanical arm, Mij-Mji, i ≠ j in the matrix represents the coupling from the acceleration of the joint i to the joint j, and how the elements in the inertia matrix can be changed along with the change of the pose of the robot is obtained by changing the pose of the mechanical arm and the angles of the joints 2 and 3.
5. The modeling method for dynamics of vehicle-mounted mechanical arm according to claim 4, characterized in that: when the scientific matrix is established to influence, the scientific matrix C represents the functional relation between the joint coordinates and the joint speed, all joints on the robot body rotate at the speed of 1rad/s under the standard pose, and the scientific matrix at the moment is calculated.
6. The modeling method for dynamics of vehicle-mounted mechanical arm according to claim 5, characterized in that: when establishing the payload impact, there are two factors that determine the maximum payload: firstly, the mass of the tail end of the robot increases the rotational inertia of the joint of the robot and simultaneously reduces the acceleration and the dynamic performance; secondly, the weight of the tail end of the robot can increase a gravity needing joint support, the moment for acceleration of the joint can be reduced by the component of the increased gravity moment, so that the dynamic performance of the robot is reduced, the maximum effective load of the Puma560 robot is 2.5 kilograms, a weight of 2.5 kilograms is added to the tail end of the robot, the center of mass of the effective load deviates 150 millimeters along the direction of the Z axis of the coordinate axis, the inertia under the standard pose is calculated, and the proportion coefficient of the gravity load increase on the joint is obtained by comparing the inertia with the inertia when no load is added;
when the base force influence is established, the moving robot applies a force rotation amount to the base, the force rotation amount is an optional parameter of the rne method, the force rotation amount is applied to the base to keep the base balanced, and the moments around the x axis and the y axis are calculated;
when the influence of dynamic operability is established, only translational acceleration is considered under a standard pose, so that the matrix Mx is a 3 x 3 matrix at the upper left corner, a three-dimensional ellipsoid is drawn, the radius of the ellipsoid is obtained and is the square root of a special value of the matrix, and the ratio of the minimum radius to the maximum radius is calculated.
7. The modeling method for dynamics of vehicle-mounted mechanical arm according to claim 6, characterized in that: and when the friction force analysis influences the motion equation, calculating the static friction moment and the dynamic friction moment according to the coulomb friction coefficient, the gear transmission ratio and the viscous friction coefficient by using the dynamic parameters of the first connecting rod of the Puma560 robot.
8. The vehicle-mounted mechanical arm dynamics control method comprises the following specific steps: step one, forward kinematics simulation; secondly, controlling independent joints of the robot; step three, testing a position control loop; step four, rigid body power compensation; and step five, flexible transmission.
9. The vehicle-mounted mechanical arm dynamics control method according to claim 8, characterized in that: in the first step, the listed differential equations are rearranged to obtain:
in the second step, taking the shoulder joint of Puma560 as an example, the function:
in the third step, the position ring is responsible for keeping the position of the joint, the position ring simultaneously provides the speed requirement for the speed ring, a tester is also established for testing the position control ring, the position requirement comes from an LSPB track generator, in order to realize better tracking performance under the condition of individual speed, the controller needs to be optimized by adjusting gain, the tracking error and the error performance of the controller are obtained when Kp is 40, then a time response curve with front feedback is observed, and the tracking error is found according to the image;
in the fourth step, the joint angle, the joint speed, the joint acceleration, the moment of inertia and the coupling moment of the joint are added into a control algorithm, and the four steps are mainly carried out by two methods: feedforward control and calculation moment control, using Simulink to test the controller/firstly establishing an object, loading a feedforward controller model, and operating the controller, the change of the robot configuration can be found to be very slow; firstly creating an object by using Simulink, then removing Coulomb friction, then loading a calculation torque controller, generating an expected joint angle and joint speed by a jtraj module, expressing initial and final joint angles by parameters of the joint angle and the joint speed, and running simulation to obtain a tracking error;
in the fifth step, the Simulink model is utilized, and the angles of the motor and the connecting rod are measured by a simple two-rod flexible manipulator, so that the system is effectively controlled.
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