CN117001660A - Parameter learning and synchronous control method for redundancy mechanical arm - Google Patents
Parameter learning and synchronous control method for redundancy mechanical arm Download PDFInfo
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- CN117001660A CN117001660A CN202310850722.5A CN202310850722A CN117001660A CN 117001660 A CN117001660 A CN 117001660A CN 202310850722 A CN202310850722 A CN 202310850722A CN 117001660 A CN117001660 A CN 117001660A
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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
- B25J9/1628—Programme controls characterised by the control loop
- B25J9/1643—Programme controls characterised by the control loop redundant control
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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
- B25J9/1628—Programme controls characterised by the control loop
- B25J9/163—Programme controls characterised by the control loop learning, adaptive, model based, rule based expert control
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Abstract
The invention provides a parameter learning and synchronous control method of a redundant mechanical arm, which belongs to the technical field of mechanical arm control and comprises the following steps: s1: establishing a physical parameter estimation iterative formula of the redundancy mechanical arm and acquiring an estimated physical parameter vector; s2: establishing a speed layer control formula of the end effector according to the estimated physical parameter vector; s3: performing inverse kinematics analysis of a speed layer on the motion planning of the redundancy mechanical arm, and establishing a quadratic optimization scheme; s4: converting the quadratic form optimization scheme into quadratic programming; s5: solving by using a quadratic programming solver; s6: and controlling the redundancy mechanical arm according to the solving result. The invention can accurately learn the physical parameters of the redundant manipulator, and synchronously control the redundant manipulator based on the estimated physical parameter information, so that the manipulator has self-adaptability and high efficiency in the execution process.
Description
Technical Field
The invention relates to a parameter learning and synchronous control method for a redundant manipulator, belongs to the technical field of manipulator control, and is particularly suitable for parameter learning and synchronous control of the redundant manipulator.
Background
A redundant manipulator is a manipulator that has more degrees of freedom than the task space dimension. Compared with the common mechanical arm, the robot arm has higher flexibility and self-adaptive capacity, and can realize the functions of obstacle avoidance, path planning optimization and the like by utilizing the redundant degrees of freedom, thereby more efficiently completing given tasks. With the continuous development and progress of robot technology, the redundant manipulator has become one of important technologies in the fields of industrial automation and artificial intelligence, and has a wide application prospect. However, most redundant robot arm control algorithms are currently designed and implemented primarily based on known physical parameters. In some special scenarios, the redundant manipulator needs to be modified to meet different task requirements, which can change the physical parameters of the manipulator. For example, robotic arms in medical procedures often require replacement of end effectors having specific shapes, sizes, and materials to perform delicate and complex tasks; in search and rescue scenarios, the robotic arm may be equipped with a telescopic link to accommodate different building and terrain environments. In these scenarios, redundant robot arm control algorithms based on known physical parameters have difficulty in accurately controlling the robot arm.
Although the redundant mechanical arm has more degrees of freedom and flexibility, and can better meet the complex task demands, more kinematic parameters are needed to describe the structural information. When the physical parameters of the redundant manipulator are changed, the changed physical parameters can be determined through a traditional off-line calibration process. However, this calibration process is cumbersome, time consuming, and prone to errors. Therefore, it is needed to design an efficient parameter learning and synchronous control method to improve the control accuracy and task efficiency of the redundant manipulator, reduce the failure rate, and shorten the debugging time.
Disclosure of Invention
In view of this, the invention provides a method for learning and synchronously controlling parameters of a redundant manipulator, which can effectively learn physical parameters of the manipulator by using state information of the manipulator, and realize synchronous control based on the learned physical parameters, thereby improving the self-adaptive capacity of the redundant manipulator system.
In order to achieve the above purpose, the present invention provides the following technical solutions:
a parameter learning and synchronous control method of a redundant manipulator comprises the following steps:
s1: establishing a physical parameter estimation iteration formula of the redundant manipulator according to a parameterized equation of the position and the speed of the end effector of the redundant manipulator, and further obtaining an estimated physical parameter vector of the redundant manipulator;
s2: establishing a speed layer control formula of the end effector according to the jacobian matrix parameterization formula and the estimated physical parameter vector of the redundant manipulator in the step S1;
s3: according to a speed layer control formula of the end effector in the step S2, performing speed layer inverse kinematics analysis on the motion planning of the redundant manipulator, and establishing a quadratic optimization scheme;
s4: converting the quadratic form optimization scheme in the step S3 into a quadratic form;
s5: solving the quadratic programming in the step S4 by using a quadratic programming solver;
s6: and (5) controlling the redundancy mechanical arm according to the solving result obtained in the step (S5).
Further, the parameterized equation for the end effector position in step S1 is p (θ, φ) =H2, whereThe position of the end effector of the mechanical arm is redundancy; />The joint angle of the redundant mechanical arm; a is more than or equal to 7, and the number of degrees of freedom of the redundant mechanical arm is represented; />The physical parameter vector is the physical parameter vector of the redundancy mechanical arm; the matrix H is defined asParameterized equation for the position of the end effector, the time derivative of which yields the parameterized equation for the speed>Wherein->The speed of the end effector of the mechanical arm is redundancy; />Is the time derivative of the jacobian matrix H and +.> The joint speed of the ith joint of the redundant manipulator;
further, according to the parameterized equation of the end effector position and speed, the iterative equation of the physical parameter estimation of the redundant manipulator is established as
Wherein,representation matrix->A state interfered by the additional noise; s is(s) i Representing zero mean co-distributed random noise applied at the ith joint velocity of the redundant manipulator; />For the redundant mechanical arm estimation physical parameter vector, its time derivative is +.>Is a convergence parameter; />Is a design parameter; the superscript T denotes a transpose operation of the vector or matrix; the physical parameter estimation iterative formula of the redundancy mechanical arm can acquire an estimated physical parameter vector of the redundancy mechanical arm by utilizing the position and speed information of the end effector.
Further, the jacobian parameterization formula described in step S2 can be specifically described asWherein->Jacobian representing the position of the redundant manipulator end effector with respect to joint angle; matrix M i (θ) is defined as +.>φ i An i-th element representing a physical parameter vector phi; further, using the estimated physical parameter vector of the redundant manipulator, the end effector's velocity layer control formula can be expressed as +.>Wherein->Estimated physical parameter vector representing redundancy manipulator +.>Is the i-th element of (a); />The joint angular velocity of the mechanical arm is redundancy;representing design parameters; />Indicating a desired end effector position; />Indicating a desired end effector speed.
Further, the second time in step S3The type optimization scheme can be expressed as follows: the designed minimized performance index is a quadratic function of the joint angular speed of the redundant manipulator and is constrained by a speed layer control formula of the end effector and joint physical constraint; i.e. minimizing performance index asConstraint is->Andwherein (1)>Is a positive diagonal matrix; />For the performance index to be optimized, ψ is a joint angular velocity feasible region set of the redundant manipulator.
Further, the quadratic optimization scheme described in step S4 is converted into a quadratic programming, specifically, the vector u is introduced to replace the original variableThe quadratic optimization scheme is rewritten as follows: the minimum performance index is u T Ωu/2+w T u, provided that au=c and u - ≤u≤u + Wherein->u + And u - And respectively representing the upper limit and the lower limit of the feasible region of the angular velocity of the joint of the redundant manipulator.
Further, in step S5, the quadratic programming is solved by a quadratic programming solver, so as to obtain an optimal solution for the parameter learning and the synchronous control of the redundant manipulator.
Further, step S6 is specifically to convert the quadratic programming result solved by the solver into a control signal required by the corresponding motor drive of the redundant manipulator through the control relationship, so as to drive the redundant manipulator to realize the control task.
The invention has the beneficial effects that: the invention provides a parameter learning and synchronous control method for a redundant manipulator, which establishes a physical parameter estimation iterative formula of the redundant manipulator, can effectively learn physical parameters, and simultaneously controls the redundant manipulator based on an estimated physical parameter vector, thereby having more adaptability and high efficiency.
Drawings
For further description of the objects and technical solutions of the present invention, the present invention is illustrated by the following drawings:
FIG. 1 is a flow chart of a method for parameter learning and synchronization control of a redundant manipulator;
FIG. 2 is a diagram of a motion process of a redundant manipulator according to an embodiment of the present invention, with coordinate axes in meters;
FIG. 3 is a graph of joint angular velocity with time (in seconds) on the abscissa and angular velocity (in radians/seconds) on the ordinate, according to an embodiment of the present invention;
FIG. 4 is a graph of position error of an end effector in x, y and z directions, with time (in seconds) on the abscissa and error magnitude (in meters) on the ordinate, according to an embodiment of the present invention;
FIG. 5 is a graph of the variation of estimated physical parameters during a task according to an embodiment of the present invention, the abscissa is time (in seconds), and the ordinate is the magnitude of the estimated physical parameters (in meters);
FIG. 6 shows the learning error of physical parameters, the abscissa is time (in seconds), and the ordinate is the magnitude of the error (in meters).
Detailed Description
The present invention will be described in detail below with reference to the accompanying drawings and examples in order to make the objects and technical solutions of the present invention more clear. Examples: assuming a control scenario of one redundancy robot (a Franka Emika Panda robot with seven degrees of freedom), the actual physical parameter Φ= [0.333,0.316,0.0825,0.0825,0 ] of the redundancy robot is set.384，0.088，0.1070] T (unit: meters) is unknown, known: the degree of freedom of the redundant manipulator and the dimension of the physical parameter vector are both 7, and the initial angle of each joint of the redundant manipulator is theta (0) = [0, -pi/4, 0, -3 pi/4, 0, pi/2, 0] T (unit: radian), the upper and lower limits of the joint angular velocity of the redundant manipulator are u + ＝u - ＝[0.5，0.5，0.5，0.5，0.5，0.5，0.5] T (in radian/second), the execution task is set to be the Chinese knot track tracking task within 10 seconds. Aiming at the scene, the invention provides a parameter learning and synchronous control method of a redundant mechanical arm, which comprises the following steps in combination with fig. 1:
s1: establishing a physical parameter estimation iteration formula of the redundant manipulator according to a parameterized equation of the position and the speed of the end effector of the redundant manipulator, and further obtaining an estimated physical parameter vector of the redundant manipulator;
the parameterized equation of the end effector position is p (θ, φ) =H2, whereThe position of the end effector of the mechanical arm is redundancy; />The joint angle of the redundant mechanical arm; />The physical parameter vector is the physical parameter vector of the redundancy mechanical arm; matrix H is defined as +.>Parameterized equation for the position of the end effector, the time derivative of which yields the parameterized equation for the speed>Wherein->The speed of the end effector of the mechanical arm is redundancy;is the time derivative of the jacobian matrix H and +.> The joint speed of the ith joint of the redundant manipulator;
further, according to the parameterized equation of the end effector position and speed, a physical parameter estimation iterative equation of the redundant manipulator is established as
Wherein,representation matrix->A state interfered by the additional noise; s is(s) i Representing zero mean independent co-distributed random noise applied to the ith joint speed of the redundant manipulator; />For the redundant mechanical arm estimation physical parameter vector, its time derivative is +.>Is a convergence parameter; />Is a design parameter; the superscript T denotes a transpose operation of the vector or matrix; the iterative formula for estimating the physical parameters of the redundant manipulator can utilize the position and speed signals of the end effectorAnd obtaining an estimated physical parameter vector of the redundant manipulator.
In the present embodiment of the present invention,the initial value of (5) is set to [0.300,0.294,0.049,0.0720,0.338,0.041,0.177 ]] T (unit: m), η is set to 50000, α is set to 1, noise s i Is set to less than 0.05.
Step S2: and (3) establishing a speed layer control formula of the end effector according to the jacobian matrix parameterization formula and the estimated physical parameter vector of the redundant manipulator in the step S1.
The jacobian parameterization formula can be specifically described asWherein the method comprises the steps ofJacobian representing the position of the redundant manipulator end effector with respect to joint angle; the matrix Mi (θ) is defined as +.>φ i An i-th element representing a physical parameter vector phi; further, using the estimated physical parameter vector of the redundant manipulator, the end-effector speed layer control formula can be expressed asWherein->Estimated physical parameter vector representing redundancy manipulator +.>Is the i-th element of (a); />The joint angular velocity of the mechanical arm is redundancy; />Representing design parameters; />Indicating a desired end effector position; />Indicating a desired end effector speed.
In this embodiment, β is set to 5.
Step S3: according to a speed layer control formula of the end effector in the step S2, performing speed layer inverse kinematics analysis on the motion planning of the redundant manipulator, and establishing a quadratic optimization scheme;
the designed minimized performance index is a quadratic function of the joint angular speed of the redundant manipulator and is constrained by a speed layer control formula of the end effector and joint physical constraint; i.e. minimizing performance index asConstraint is->And->Wherein (1)>Is a positive diagonal matrix; />For the performance index to be optimized, ψ is a joint angular velocity feasible region set of the redundant manipulator.
In this embodiment, Ω is set as an identity matrix, and w is set as a zero vector.
Step S4: and (3) converting the quadratic optimization scheme in the step S3 into a quadratic programming.
Specifically, the vector u is introduced to replace the original variableThe quadratic optimization scheme is rewritten as follows: the minimum performance index is u T Ωu/2+w T u, provided that au=c and u - ≤u≤u + Wherein->u + And u - And respectively representing the upper limit and the lower limit of the feasible region of the angular velocity of the joint of the redundant manipulator.
Step S5: and (3) solving the quadratic programming in the step S4 by using a quadratic programming solver.
In the embodiment, a Karush-Kuhn-Tucker condition and a dual space method are used, so that the quadratic programming problem is equivalent to a projection equation set solving problem. The specific projection equation set is
Wherein,is a Lagrangian coefficient; delta > 0 is a coefficient controlling the convergence speed, set to 0.001 in this example; p (P) ψ (. Cndot.) is a projection function, specifically described as +.>Wherein->And u i Respectively represent the vector u + ，u - And the ith element of u; and then solving the quadratic programming problem through the solver.
Step S6: and converting the quadratic programming result solved by the solver into a control signal required by the corresponding motor drive of the redundant manipulator through a control relation, thereby driving the redundant manipulator to realize a control task.
In the embodiment, simulation experiments are carried out by utilizing MATLAB software so as to verify the correctness and superiority of the method. Specific experimental results are shown in fig. 2, 3, 4, 5 and 6.
Further, it can be seen from fig. 2 that the redundancy manipulator successfully completes the given chinese junction trajectory tracking task.
It can be seen from fig. 3 that the joint velocity starts at 0 rad/sec throughout the task execution and that the individual joint values change smoothly and steadily.
From FIG. 4, it can be seen that the trace tracking error of the redundant manipulator end-effector is at 10 -4 The order of magnitude of meters represents the accuracy of the control aspect of the invention.
From fig. 5, it can be seen that the estimated physical parameter quickly converges to a true value around 0 seconds, embodying the effectiveness of the present invention in learning the physical parameter.
It can be seen from fig. 6 that the learning error of the physical parameter is converged rapidly within 0.2 seconds and converged to 10 after 2 seconds -4 The order of meters represents the accuracy of the invention in learning physical parameters.
Finally, it is noted that the above-mentioned preferred embodiments are only intended to illustrate rather than limit the invention, and that, although the invention has been described in detail by means of the above-mentioned preferred embodiments, it will be understood by those skilled in the art that various changes in form and details may be made therein without departing from the scope of the invention as defined by the appended claims.
Claims (5)
1. The parameter learning and synchronous control method of the redundant mechanical arm is characterized by comprising the following steps of:
s1: establishing a physical parameter estimation iteration formula of the redundant manipulator according to a parameterized equation of the position and the speed of the end effector of the redundant manipulator, and further obtaining an estimated physical parameter vector of the redundant manipulator;
the parameterized equation of the end effector position is p (θ, φ) =H2, whereThe position of the end effector of the mechanical arm is redundancy; />The joint angle of the redundant mechanical arm; a is more than or equal to 7, and the number of degrees of freedom of the redundant mechanical arm is represented; />The physical parameter vector is the physical parameter vector of the redundancy mechanical arm; matrix H is defined as +.>Parameterized equation for the position of the end effector, the time derivative of which yields the parameterized equation for the speed>Wherein->The speed of the end effector of the mechanical arm is redundancy; matrix->Is the time derivative of matrix H and the joint angular velocity of the ith joint of the redundant manipulator;
according to the parameterized equation of the position and the speed of the end effector, the iterative equation of the physical parameter estimation of the redundant manipulator is established as
Wherein,representation matrix->A state interfered by the additional noise; s is(s) i Representing zero mean co-distributed random noise applied to the ith joint angular velocity of the redundant manipulator; />For the redundant mechanical arm estimation physical parameter vector, its time derivative is +.> Is a convergence parameter; />Is a design parameter; the superscript T denotes a transpose operation of the vector or matrix; the physical parameter estimation iterative formula of the redundancy mechanical arm can acquire an estimated physical parameter vector of the redundancy mechanical arm by utilizing the position and speed information of the end effector;
s2: establishing a speed layer control formula of the end effector according to the jacobian matrix parameterization formula and the estimated physical parameter vector of the redundant manipulator in the step S1;
s3, performing inverse kinematics analysis on the velocity layer of the motion planning of the redundant manipulator according to the velocity layer control formula of the end effector in the step S2, and establishing a quadratic optimization scheme;
s4: converting the quadratic form optimization scheme in the step S3 into a quadratic form;
s5: solving the quadratic programming in the step S4 by using a quadratic programming solver;
s6: and (5) controlling the redundancy mechanical arm according to the solving result obtained in the step (S5).
2. The method for learning and synchronizing parameters of a redundant manipulator according to claim 1, wherein the jacobian parameterization formula in step S2 is specifically described asWherein the method comprises the steps ofJacobian representing the position of the redundant manipulator end effector with respect to joint angle; matrix M i (θ) is defined as +.>φ i An i-th element representing a physical parameter vector phi; further, using the estimated physical parameter vector of the redundant manipulator, the end-effector speed layer control formula may be expressed asWherein->Estimated physical parameter vector for redundancy manipulator +.>Is the i-th element of (a); />The joint angular velocity of the mechanical arm is redundancy; />Is a design parameter; />For a desired end effector position; />Indicating a desired end effector speed.
3. The method for parameter learning and synchronization control of a redundant manipulator according to claim 1, wherein the quadratic optimization scheme in step S3 may be represented as follows: the designed minimized performance index is a quadratic function of the joint angular speed of the redundant manipulator and is constrained by a speed layer control formula of the end effector and joint physical constraint; i.e. minimizing performance index asConstraint is->And->Wherein,is a positive diagonal matrix; />For the performance index to be optimized, ψ is a joint angular velocity feasible region set of the redundant manipulator.
4. The method for parameter learning and synchronization control of a redundant manipulator according to claim 1, wherein the quadratic optimization scheme in step S4 is converted into oneThe secondary programming is to introduce a vector u to replace the original variableThe quadratic optimization scheme is rewritten as follows: the minimum performance index is u T Ωu/2+w T u, provided that au=c and u - ≤u≤u + Wherein-> u + And u - And respectively representing the upper limit and the lower limit of the feasible region of the angular velocity of the joint of the redundant manipulator.
5. The method for parameter learning and synchronous control of a redundant manipulator according to claim 1, wherein step S6 is specifically to convert a quadratic programming result solved by a solver into a control signal required by a motor drive of the redundant manipulator, so as to drive the redundant manipulator to realize a control task.
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