CN115609580B - A method for suppressing flexible vibration of space manipulator - Google Patents
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- B—PERFORMING OPERATIONS; TRANSPORTING
- B25—HAND TOOLS; PORTABLE POWER-DRIVEN TOOLS; MANIPULATORS
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- B25J9/00—Programme-controlled manipulators
- B25J9/16—Programme controls
- B25J9/1656—Programme controls characterised by programming, planning systems for manipulators
- B25J9/1669—Programme controls characterised by programming, planning systems for manipulators characterised by special application, e.g. multi-arm co-operation, assembly, grasping
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Abstract
本发明涉及一种空间机械臂柔性振动抑制方法，步骤包括：离散获得末端运动轨迹；设置零空间项系数和优化算法参数；在速度层面和加速度层面，构建包含零空间项的空间机械臂末端轨迹与关节轨迹间的逆运动学关系；构建在上述关节轨迹运动驱动下的柔性机械臂动力学运动模型，描述机械臂末端柔性振动；通过机械臂末端柔性振动计算，获取机械臂末端柔性振动幅值,与优化前的机械臂末端柔性振动幅值进行比较，判断是否满足柔性振动抑制的要求。本发明基于多项式末端轨迹差值和最小范数法逆运动学关系，实现了将期望末端轨迹转换为含零空间项的关节运动轨迹。
The present invention relates to a method for suppressing flexible vibration of a space manipulator, the steps of which include: discretely obtaining the end motion trajectory; setting the coefficient of the zero space term and the optimization algorithm parameters; constructing the inverse kinematics relationship between the end trajectory of the space manipulator and the joint trajectory containing the zero space term at the velocity level and the acceleration level; constructing a dynamic motion model of the flexible manipulator driven by the joint trajectory motion to describe the flexible vibration of the end of the manipulator; obtaining the amplitude of the flexible vibration of the end of the manipulator through the flexible vibration calculation of the end of the manipulator, and comparing it with the amplitude of the flexible vibration of the end of the manipulator before optimization to determine whether the requirements for flexible vibration suppression are met. The present invention realizes the conversion of the desired end trajectory into the joint motion trajectory containing the zero space term based on the polynomial end trajectory difference and the minimum norm method inverse kinematics relationship.
Description
Technical Field
The invention relates to a flexible vibration suppression method for a space manipulator, and belongs to the technical field of robots.
Background
The space mechanical arm has the characteristics of light weight, large structural size, obvious joint flexibility and the like, is a complex flexible multi-body system with strong coupling and high nonlinearity, and is one of the important problems to be solved urgently when the positioning precision of the mechanical arm system is effectively improved and the elastic vibration is reduced, and the research of the problem is widely focused by a plurality of students at home and abroad.
Under the condition that other equipment is not added, the main method for suppressing the flexible vibration at present is to optimally design the mechanical arm by adding vibration suppressing equipment or shaping input signals (weight cost or calculation resource cost). The existing method utilizes an input signal with special frequency to complete vibration suppression, is completely decoupled with mechanical arm dynamics characteristics, has poor robustness and large calculation resource consumption, and is difficult to realize quick expansion application.
Disclosure of Invention
The invention solves the technical problems of overcoming the defects of the prior art and providing a space manipulator flexible vibration suppression method which is used for suppressing the flexible vibration of a manipulator under the conditions that the weight of the robot or the manipulator is limited and the computing resources in a control system are limited.
The solution of the invention is as follows:
a flexible vibration suppression method for a space manipulator comprises the following steps:
s1, dispersing to obtain a terminal motion track, performing difference dispersion on the desired terminal track through a penta polynomial function according to the desired terminal position, and decomposing to obtain a terminal motion track X in a time domain;
S2, setting a zero space term coefficient and an optimization algorithm parameter;
S3, initializing and calculating joint motion tracks, and constructing inverse kinematics relation between the tail end track of the space manipulator containing a zero space item and the joint track at a speed level and an acceleration level;
S4, constructing a dynamic model of the flexible mechanical arm, constructing a dynamic motion model of the flexible mechanical arm under the driving of the joint track motion, and describing the flexible vibration of the tail end of the mechanical arm;
S5, obtaining the flexible vibration amplitude of the tail end of the mechanical arm through flexible vibration calculation of the tail end of the mechanical arm, comparing the flexible vibration amplitude of the tail end of the mechanical arm with the flexible vibration amplitude of the tail end of the mechanical arm before optimization, and judging whether the requirement of flexible vibration inhibition is met.
Further, in S1,
Where t represents the current movement time, t f represents the total planning time, and r 0 and r f represent the initial and desired end positions of the robot arm end, respectively.
Further, the end speedThe method can be solved as follows:
Further, tip acceleration The method can be solved as follows:
Further, in S3, according to the minimum norm method, the inverse kinematics relationship between the end track and the joint track of the spatial manipulator including the null space term is constructed as follows:
In the formula, In order to achieve the angular velocity of the joint,The joint angular acceleration is given, J is the jacobian matrix of the mechanical arm,J + is the pseudo-inverse of J, J +＝JT(JJT)-1, and I is the identity matrix, which are derivatives of the Jacobian matrix.
Further, the joint movement track θ is:
Δt is the calculation step size.
Further, in S4, the flexible vibration of the end of the mechanical arm is described as:
wherein q is a generalized coordinate, an articulation angle θ is selected, Second derivative of generalized coordinatesM is a system quality matrix, C is a constraint equation and is related to a generalized coordinate Q and time t, C q is a partial differential matrix of the constraint equation to the generalized coordinate Q, lambda is a Lagrangian multiplier, F is an elastic force matrix and is related to the generalized coordinate Q, and Q is a generalized external force matrix and is related to the generalized coordinate Q.
Further, the flexible vibration is δ max＝max(|Xact-X|),Xact is the actual end position under the current motion trajectory.
Further, in S5,
5.1 If the flexible vibration control requirements are met,
The system optimization model is expressed as:
Wherein, AndRespectively isAndLower and upper boundaries of (2).
Each generation of particle swarm algorithm generates a zero-space term coefficientAndIf the minimum flexible vibration delta max under the current algebra calculated according to the dynamics equation is smaller than the expected value delta limit, the optimization is finished, and the zero-space term coefficient of the current speed layer is calculatedAnd acceleration levelNamely, the optimal solution is theta,The final and optimal joint movement track can be obtained correspondingly;
5.2 if the residual vibration control requirement is not met, if the flexible vibration delta max calculated according to the dynamic equation is larger than the expected value delta limit, continuing to carry out iterative solution.
Further, the continuous iteration solving method comprises the following steps:
5.2.1 updating population optima and individual optima:
Individual optimization Updated to minimize delta max under the current generationAndPopulation optimization gbest (t) is updated to be the smallest under all generationsAnd
5.2.2 Updating the zero-space term coefficients:
updating the coefficients of the null space term according to the particle swarm algorithm containing the contraction factor AndThe update formula is:
representing before update AndThe value of the sum of the values,Representing updatedAndA value; in order to update the rate of change of the particles before updating, The new generation of zero space term coefficient is regenerated for the updated particle change speed with the upper and lower limits of [ -1,1]And
5.2.3 Updating the joint movement track:
according to updated The inverse kinematics relation is re-utilized to calculate and obtain new theta,I.e. the updated motion profile.
5.2.4 Updating and calculating the flexible vibration of the tail end of the mechanical arm:
Using the newly obtained joint motion trail theta, Recalculating the motion flexible vibration of the mechanical arm;
if the residual vibration control requirement is not satisfied, repeating the steps 5.2.1 to 5.2.4 until the requirement is satisfied, wherein the obtained theta, The optimal motion track is the optimal motion track, and the track simultaneously meets the requirement of the tail end motion.
Compared with the prior art, the invention has the beneficial effects that:
(1) The method is based on the inverse kinematics relation of the polynomial end track difference and the minimum norm method, and realizes the conversion of the expected end track into the joint motion track containing the zero space item;
(2) According to the invention, the particle swarm optimization algorithm containing the contraction factors is adopted to carry out iterative optimization on the joint motion track containing the zero space item, so that the joint motion track meeting the minimum flexible vibration requirement is obtained, and the resource consumption is low.
Drawings
FIG. 1 is a block diagram of the overall algorithm of the present invention;
FIG. 2 is a flowchart of the shrink factor particle swarm algorithm of the present invention;
FIG. 3 is a graph showing the variation of the optimum objective function (residual vibration amplitude) of the present invention;
FIG. 4 shows the original planned trajectory and the optimized trajectory of the end point of the present invention.
Detailed Description
The invention is further illustrated below with reference to examples.
As shown in fig. 1, in the mechanical arm end trajectory motion planning, first, the end trajectory is subjected to difference value dispersion by a polynomial function of five times, and the end motion trajectory X in the time domain is obtained by decomposition:
where t f represents the planning time, and r 0 and r f represent the initial and desired end positions of the robot arm end, respectively.
The tip speed can be solved as:
In the mechanical arm kinematics calculation process, a certain mapping relation exists between the tail end speed and each joint angular speed, namely an inverse kinematics relation. According to a minimum norm method, constructing inverse kinematics relation between the tail end track of the space manipulator and the joint track, wherein the tail end track comprises a zero space item, at a speed level and an acceleration level:
In the formula, AndRespectively are orthogonal toAndZero space terms of (2) Is an arbitrary vector, i.e., is a zero-space term coefficient. The null-space term produces a change in configuration to the robotic arm without affecting the speed of the tip. By integrating the velocity, a discrete joint angle curve is obtained that contains 2 coefficients of the null space term.
According to a first Lagrangian equation, constructing a dynamic motion model of the flexible mechanical arm under the driving of the joint track motion, and describing the residual vibration of the tail end of the mechanical arm:
In the formula, Q is generalized coordinate, joint angle and angular speed can be selected, M is mass matrix, C is constraint equation, F is elastic force matrix, and Q is external force matrix.
To increase the convergence rate, a particle swarm algorithm with a contraction factor is designed, as shown in fig. 2, and the speed and position of each particle are changed according to the following formula:
Where c 1 and c 2 are learning factors, r 1 and r 2 are any value between [ -1,1], χ is called a shrink factor, defined as:
The summarized optimization model may be expressed as:
Wherein, AndRespectively isAndLower and upper boundaries of (2).
By using the inverse kinematics relation containing the zero space item and the particle swarm algorithm containing the contraction factor, the specific optimization iteration times are set, as shown in fig. 3, the joint velocity and joint acceleration analysis solution under the minimum flexible vibration state can be respectively obtained, and then the joint motion track analysis solution is obtained in a differential mode:
according to fig. 3, when the iteration number is 20, the flexible vibration is reduced to be less than 50% of the initial state, and the requirement on the computing resource is low. By taking the joint movement track as the input condition of the flexible mechanical arm movement, the mechanical arm movement track meeting the minimum flexible vibration can be obtained without changing the expected tail end movement track, as shown in figure 4.
The method is based on the inverse kinematics relation of the polynomial end track difference and the minimum norm method, and realizes the conversion of the expected end track into the joint motion track containing the zero space item;
according to the invention, the particle swarm optimization algorithm containing the contraction factors is adopted to carry out iterative optimization on the joint motion track containing the zero space item, so that the joint motion track meeting the minimum flexible vibration requirement is obtained.
Although the present invention has been described in terms of the preferred embodiments, it is not intended to be limited to the embodiments, and any person skilled in the art can make any possible variations and modifications to the technical solution of the present invention by using the methods and technical matters disclosed above without departing from the spirit and scope of the present invention, so any simple modifications, equivalent variations and modifications to the embodiments described above according to the technical matters of the present invention are within the scope of the technical matters of the present invention.
Claims (6)
1. The flexible vibration suppression method for the space manipulator is characterized by comprising the following steps of:
dispersing to obtain a terminal motion track, carrying out difference dispersion on the expected terminal track through a penta polynomial function according to the expected terminal position, and decomposing to obtain a terminal motion track X in a time domain;
Setting a zero space item coefficient and an optimization algorithm parameter;
initializing and calculating joint motion tracks, and constructing inverse kinematics relation between the tail end track of the space manipulator containing a zero space item and the joint track at a speed level and an acceleration level;
Constructing a dynamic model of the flexible mechanical arm, constructing a dynamic motion model of the flexible mechanical arm under the driving of the joint track motion, and describing the flexible vibration of the tail end of the mechanical arm;
The flexible vibration amplitude of the tail end of the mechanical arm is obtained through flexible vibration calculation of the tail end of the mechanical arm, and compared with the flexible vibration amplitude of the tail end of the mechanical arm before optimization, whether the requirement of flexible vibration inhibition is met is judged;
according to a minimum norm method, constructing an inverse kinematics relation between a tail end track and a joint track of a space manipulator comprising a zero space item, wherein the inverse kinematics relation is as follows:
In the formula, In order to achieve the angular velocity of the joint,The joint angular acceleration is given, J is the jacobian matrix of the mechanical arm,Is that
The derivative of the Jacobian matrix, J + is the pseudo-inverse of J, J +＝JT(JJT)-1, I is the identity matrix,For the end velocity to be the end velocity,Is the end acceleration;
The method is characterized in that the joint movement track theta is as follows:
Δt is the calculation step;
The method for judging whether the requirement of flexible vibration suppression is met is as follows:
(5.1) if the flexible vibration control requirement is satisfied,
The system optimization model is expressed as:
Wherein, AndRespectively isAndLower and upper boundaries of (2);
Each generation of particle swarm algorithm generates a zero-space term coefficient AndIf the minimum flexible vibration delta max under the current algebra calculated according to the dynamics equation is smaller than the expected value delta limit, the optimization is finished, and the zero-space term coefficient of the current speed layer is calculatedAnd acceleration levelNamely, the optimal solution is theta,The final and optimal joint movement track can be obtained correspondingly;
(5.2) if the residual vibration control requirement is not met, if the flexible vibration delta max calculated according to the dynamic equation is larger than the expected value delta limit, continuing to carry out iterative solution;
The continuous iteration solving method comprises the following steps:
(5.2.1) updating population optima and individual optima:
Individual optimization Updated to minimize delta max under the current generationAndPopulation optimization gbest (t) is updated to be the smallest under all generationsAnd
(5.2.2) Updating the null space term coefficients:
updating the coefficients of the null space term according to the particle swarm algorithm containing the contraction factor AndThe update formula is:
representing before update And
The value of the sum of the values,Representing updatedAndA value;
Value values; in order to update the rate of change of the particles before updating, The new generation of zero space term coefficient is regenerated for the updated particle change speed with the upper and lower limits of [ -1,1]And
(5.2.3) Updating the joint movement track:
according to updated The inverse kinematics relation is re-utilized to calculate and obtain new theta, The updated motion trail;
(5.2.4) updating the flexible vibration of the tail end of the computing mechanical arm:
Using the newly obtained joint motion trail theta, Recalculating the motion flexible vibration of the mechanical arm;
if the residual vibration control requirement is not satisfied, repeating the steps 5.2.1 to 5.2.4 until the requirement is satisfied, wherein the obtained theta,
The optimal motion track is the optimal motion track, and the track simultaneously meets the requirement of the tail end motion.
2. The method for suppressing flexible vibration of a space manipulator according to claim 1, wherein the tip movement trace
Where t represents the current movement time, t f represents the total planning time, and r 0 and r f represent the initial and desired end positions of the robot arm end, respectively.
3. The method for suppressing flexible vibration of a space manipulator according to claim 2, wherein the tip speed isThe method can be solved as follows:
4. the method for suppressing flexible vibration of a space manipulator according to claim 2, wherein the tip acceleration is The method can be solved as follows:
5. the method for suppressing flexible vibration of a space manipulator according to claim 1, wherein describing the flexible vibration of the manipulator end is:
wherein q is a generalized coordinate, an articulation angle θ is selected, Second derivative of generalized coordinatesM is a system quality matrix, C is a constraint equation and is related to a generalized coordinate Q and time t, C q is a partial differential matrix of the constraint equation to the generalized coordinate Q, lambda is a Lagrangian multiplier, F is an elastic force matrix and is related to the generalized coordinate Q, and Q is a generalized external force matrix and is related to the generalized coordinate Q.
6. The method for suppressing flexible vibration of a space manipulator according to claim 5, wherein the flexible vibration is δ max＝max(Xact-X),Xact as an actual end position under a current motion trajectory.
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