CN106625666B - Control method and device of redundant mechanical arm - Google Patents
Control method and device of redundant mechanical arm Download PDFInfo
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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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Abstract
The embodiment of the invention discloses a control method and a control device for a redundant mechanical arm. The method comprises the following steps: acquiring current point information and target point information of the redundant mechanical arm; determining a track function corresponding to the motion track of the redundant mechanical arm moving from the current point to the target point according to the current point information and the target point information; establishing an equation corresponding to the track function by taking the redundancy space vector as an independent variable; and solving an equation corresponding to the track function according to a target approach method to obtain the position and the speed of each joint in the redundant mechanical arm corresponding to the motion track. By adopting the technical scheme, the embodiment of the invention can reduce the search space of the multi-objective optimization problem of the redundant mechanical arm on the premise of obtaining the global optimal solution meeting the design objective, avoid the occurrence of the dimension explosion problem in the multi-objective solution process, simplify the required calculated amount in the control process of the redundant mechanical arm and improve the reaction speed of the redundant mechanical arm.
Description
Technical Field
The invention relates to the technical field of robots, in particular to a control method and device of a redundant mechanical arm.
Background
In recent years, with the improvement of artificial intelligence technology and mechanical control technology and the improvement of the complexity of tasks performed by robots, redundant robot arms (robot arms with more than 6 joints) are increasingly applied to robots to complete various complex tasks.
When the redundant mechanical arm executes a specific task in a Cartesian space, infinite solutions exist in a joint space, and in specific application, a group of optimal solutions can be generally selected according to optimization indexes such as joint speed, joint torque or barrier distance to determine the moving process of the redundant mechanical arm. When a robot executes a more complex task, multiple targets of a redundant mechanical arm are generally required to be optimized simultaneously, and at present, methods commonly used for multi-target optimization can be classified into a weighted function method and a pareto frontier method. However, although the weighting function method can use the weighting coefficient to weight the optimization target so as to convert the multi-target optimization problem into the single-target optimization problem, the method is difficult to judge the influence of the change of the weighting coefficient on the optimization result, only one solution can be obtained each time, the value of the weighting coefficient needs to be changed continuously, the calculation steps are complicated, and certain limitations exist; the calculation complexity of the pareto frontier method is increased sharply along with the increase of the degree of freedom of the mechanical arm, and when the number of joints of the redundant mechanical arm is large, the method also has the problems of complicated calculation and complex steps.
Disclosure of Invention
In view of this, embodiments of the present invention provide a control method and device for a redundant robot arm, so as to solve the technical problems of complex calculation and complex steps of a multi-target solution method in the prior art.
In a first aspect, an embodiment of the present invention provides a method for controlling a redundant manipulator, including:
acquiring current point information and target point information of the redundant mechanical arm;
determining a track function corresponding to the motion track of the redundant mechanical arm moving from the current point to the target point according to the current point information and the target point information;
establishing an equation corresponding to the track function by taking the redundancy space vector as an independent variable;
and solving an equation corresponding to the track function according to a target approach method to obtain the position and the speed of each joint in the redundant mechanical arm corresponding to the motion track.
In a second aspect, an embodiment of the present invention further provides a control apparatus for a redundant manipulator, including:
the information acquisition unit is used for acquiring the current point information and the target point information of the redundant mechanical arm;
the track unit is connected with the information acquisition unit and used for determining a track function corresponding to a motion track of the redundant mechanical arm moving from the current point to the target point according to the current point information and the target point information;
the redundancy processing unit is connected with the track unit and used for establishing an equation corresponding to the track function by taking the redundancy space vector as an independent variable; and solving an equation corresponding to the track function according to a target approach method to obtain the position and the speed of each joint in the redundant mechanical arm corresponding to the motion track.
According to the technical scheme for controlling the redundant mechanical arm, the current point information and the target point information of the redundant mechanical arm are obtained, a track function corresponding to a motion track of the redundant mechanical arm moving from the current point to the target point is determined according to the obtained current point information and the obtained target point information, an equation corresponding to the track function is established by taking a redundant space vector as an independent variable, and the equation is solved by a target approach method to obtain the position and the speed of each joint in the redundant mechanical arm corresponding to the motion track. By adopting the technical scheme, the embodiment of the invention can reduce the search space of the multi-objective optimization problem of the redundant mechanical arm on the premise of obtaining the global optimal solution meeting the design objective, avoid the occurrence of the dimension explosion problem in the multi-objective solution process, simplify the required calculated amount in the control process of the redundant mechanical arm and improve the reaction speed of the redundant mechanical arm.
Drawings
Other features, objects and advantages of the invention will become more apparent upon reading of the detailed description of non-limiting embodiments made with reference to the following drawings:
fig. 1 is a schematic flowchart illustrating a control method for a redundant robot arm according to an embodiment of the present invention;
fig. 2 is a schematic flowchart of a control method for a redundant robot arm according to a second embodiment of the present invention;
FIG. 3 is a schematic diagram of a coordinate system of a nine-degree-of-freedom redundant robot arm according to a second embodiment of the present invention
Fig. 4 is a block diagram of a control device of a redundant robot arm according to a third embodiment of the present invention.
Detailed Description
The present invention will be described in further detail with reference to the accompanying drawings and examples. It is to be understood that the specific embodiments described herein are merely illustrative of the invention and are not limiting of the invention. It should be further noted that, for the convenience of description, only some but not all of the relevant aspects of the present invention are shown in the drawings.
Example one
The embodiment of the invention provides a control method of a redundant mechanical arm. The method can be carried out by a control device of the redundant robot arm, wherein the device can be implemented by hardware and/or software and can be integrated in a control module for controlling the robot. Fig. 1 is a schematic flowchart of a control method for a redundant robot arm according to an embodiment of the present invention, as shown in fig. 1, the method includes:
and S110, acquiring current point information and target point information of the redundant mechanical arm.
In this embodiment, the current point information and the target point information of the redundant manipulator may be the current point information and the target point information of the end of the redundant manipulator, or may be the current point information and the target point information of each joint of the redundant manipulator, which is not limited herein. In consideration of the practicability of the current point information and the target point information, optionally, the current point information of the redundant mechanical arm may include current point information of the end of the mechanical arm and current point information of each joint of the redundant mechanical arm, and the target point information may include target point information of the end of the mechanical arm. The current point information (target point information) may include information such as position coordinates, angle coordinates, linear velocity, angular velocity, linear acceleration, and/or angular acceleration of the end of the robot arm or each joint of the robot arm at the current (target) position.
For example, when the current point information of the redundant mechanical arm is obtained, the current point information of the redundant mechanical arm can be directly obtained through a sensor or a calculation result at the previous moment is adopted as the current point information of the redundant mechanical arm; when the target point information of the redundant mechanical arm is obtained, the target point information to which the tail end of the redundant mechanical arm needs to move can be obtained through calculation according to the current point information of the tail end of the redundant mechanical arm and the motion trail information of the tail end of the redundant mechanical arm. Taking the current point information as an angle coordinate, an angular velocity and an angular acceleration as an example, the angular information and the angular velocity information of a certain joint of the redundant mechanical arm at the current position can be obtained by an encoder arranged at the joint, and the angular acceleration information can be obtained by differential operation; alternatively, the target point information of each joint of the robot arm calculated at the previous time may be directly called as the current point information of each joint of the robot arm at the current time.
And S120, determining a track function corresponding to the motion track of the redundant mechanical arm moving from the current point to the target point according to the current point information and the target point information.
In this embodiment, the trajectory function corresponding to the motion trajectory of the redundant mechanical arm moving from the current point to the target point may include a trajectory function corresponding to the motion trajectory of each joint of the redundant mechanical arm when the end of the redundant mechanical arm moves from the current point to the target point, and the trajectory function of each joint of the redundant mechanical arm may be one or more, that is, the trajectory function corresponding to the motion trajectory of each joint of the redundant mechanical arm may be described as a whole by using one total trajectory function, or may be described in a form that the motion trajectory of each joint corresponds to one or more trajectory functions. It should be noted that the trajectory function corresponding to the motion trajectory of each joint of the redundant robot arm may include an equality and/or an inequality, for example, the trajectory function of a certain joint of the redundant robot arm may include a correspondence between the position coordinate, the velocity, and/or the acceleration of the joint and other variables (such as the position coordinate, the velocity, and/or the acceleration of the end of the robot arm), and may further include a value range of the position coordinate, the moving velocity, and/or the moving angular velocity of the joint when the redundant robot arm normally moves, and the like, which is not limited herein.
Specifically, when determining a track function corresponding to a motion track of the redundant mechanical arm moving from a current point to a target point, a track function at the end of the redundant mechanical arm may be determined according to current point information and target point information at the end of the redundant mechanical arm, then a relationship between a motion track of each joint and a motion track at the end of the redundant mechanical arm may be determined according to a connection relationship between the end of the redundant mechanical arm and each joint, and then a track function for each shutdown of the redundant mechanical arm may be determined according to the track function at the end of the redundant mechanical arm.
And S130, establishing an equation corresponding to the track function by taking the redundancy space vector as an independent variable.
Specifically, the corresponding relationship between the redundancy vector and variables such as position coordinates, speed or acceleration of each joint may be determined, and then the independent variables such as position coordinates, speed or acceleration in the trajectory function corresponding to each joint may be replaced with the redundancy space vector according to the corresponding relationship, so as to establish an equation corresponding to the trajectory function in which each joint of the redundant manipulator takes the redundancy space vector as the independent variable. The redundancy space vector may be any vector of a redundancy vector space, and the redundancy vector space may be an existing vector space or a custom space, which is not limited herein.
S140, solving an equation corresponding to the track function according to a target approach method to obtain the position and the speed of each joint in the redundant mechanical arm corresponding to the motion track.
In this embodiment, after the position and the velocity of each joint of the redundant robot arm are obtained, the acceleration of each joint of the redundant robot arm can be further obtained as needed. For example, when there is a finite set of solutions to the equation corresponding to the trajectory function of a certain joint of the redundant manipulator, all solutions to the equations may be obtained, and then a set of solutions to the equations may be selected according to actual needs or according to a set selection rule to obtain a target position of the joint at a next time and simultaneously determine a moving speed and an acceleration of the joint when the joint moves from a current position to the target position. When an infinite set of solutions exist in an equation corresponding to a track function of a certain joint of the redundant mechanical arm, one set of solutions of the equation can be obtained at will, and a target position of the joint at the next moment, and a moving speed and an acceleration of the joint moving from the current position to the target position can be obtained through the set of solutions; it is also possible to first set the constraint condition of the equation solution, then solve the equation that meets the constraint condition, and guide the movement process of the joint from the current time to the next time with the set of solutions, which is not limited herein. In order to ensure that each joint of the redundant mechanical arm can efficiently move, reduce the output torque and motion of each joint, avoid singularity and avoid the limit of joint motion, preferably, the position, the speed and the acceleration of each joint in the redundant mechanical arm corresponding to the motion track can be obtained according to the solution of an equation meeting constraint conditions.
The control method for the redundant manipulator provided by the embodiment of the invention comprises the steps of obtaining current point information and target point information of the redundant manipulator, determining a track function corresponding to a motion track of the redundant manipulator moving from a current point to a target point according to the obtained current point information and the target point information, establishing an equation corresponding to the track function by taking a redundant space vector as an argument, and solving the equation by a target proximity method to obtain the position and the speed of each joint in the redundant manipulator corresponding to the motion track. By adopting the technical scheme, the searching space of the multi-objective optimization problem of the redundant mechanical arm can be reduced on the premise of obtaining the global optimal solution meeting the design objective, the problem of dimension explosion in the multi-objective solving process is avoided, the required calculated amount in the control process of the redundant mechanical arm is simplified, and the reaction speed of the redundant mechanical arm is improved.
Example two
Fig. 2 is a schematic flow chart illustrating a control method for a redundant robot arm according to a second embodiment of the present invention. The present embodiment is optimized on the basis of the foregoing embodiment, and further, the acquiring current point information and target point information of the redundant manipulator includes: acquiring the speed of the tail end of the redundant mechanical arm at the target point; and mapping the joint angle, the joint angular velocity and the joint angular acceleration of the redundant mechanical arm to a redundant space according to the velocity of the tail end of the redundant mechanical arm at the current target point.
Further, the determining, according to the current point information and the target point information, a trajectory function corresponding to a motion trajectory of the redundant manipulator moving from the current point to the target point includes: and determining an optimized objective function and constraint conditions corresponding to the motion trail of the redundant manipulator moving from the current point to the target point according to an inverse kinematics equation.
Further, the solving an equation corresponding to the trajectory function according to a target proximity method to obtain the position and the speed of each joint in the redundant manipulator corresponding to the motion trajectory includes: in a redundancy space, solving an equation corresponding to the track function through an auxiliary vector and a single-target optimization algorithm according to an optimization target function, a minimum target value corresponding to an optimization target, a corresponding constraint condition and a preset weighting coefficient to obtain the position and the speed of each joint in the redundant manipulator corresponding to the motion track.
Accordingly, as shown in fig. 2, the method for controlling a redundant robot arm according to the present embodiment includes:
and S210, acquiring the speed of the tail end of the redundant mechanical arm at the target point.
Preferably, the acquiring the speed of the end of the redundant mechanical arm at the current point includes: and determining the speed of the tail end of the redundant mechanical arm at the next sampling point according to the pose of the tail end of the redundant mechanical arm at the current point and the pose of the tail end of the redundant mechanical arm at the next sampling point in the motion trail. The pose of the tail end of the redundant mechanical arm refers to the position and the pose of the redundant mechanical arm, the position can be represented by position coordinates, and the pose can be represented by angles. For example, information such as angular velocity and/or angular acceleration of the redundant mechanical arm at the current point can be obtained according to an encoder installed at the tail end of the redundant mechanical arm, or information such as angular velocity and/or angular acceleration of the tail end of the redundant mechanical arm at the current point can be directly obtained according to a calculation result of the redundant mechanical arm at the last moment, and then the angular velocity of the redundant mechanical arm at the next sampling point can be obtained according to the angle of the redundant mechanical arm at the current point and the angle of the redundant mechanical arm at the next sampling point, so that the velocity of the redundant mechanical arm at the next sampling point can be obtained.
And S220, mapping the joint angle, the joint angular velocity and the joint angular acceleration of the redundant mechanical arm to a redundant space according to the velocity of the tail end of the redundant mechanical arm at the target point.
For example, the relationship between the end velocity of the redundant manipulator and the angular velocity of the joints of the redundant manipulator (i.e., the trajectory function of each joint of the redundant manipulator with the angular velocity as an independent variable) can be expressed as:
wherein,is the speed of the end of the robot arm,vi(i ═ x, y, z) denotes linear velocity, ωi(i ═ θ, Ψ, Φ) represents an angular velocity;is the angular velocity of the joint of the mechanical arm,n is the degree of freedom of the redundant mechanical arm, wherein the N is 6+ r, and r is more than 1; j is an element of R6×NIs a Jacobian matrix.
Let α be any r (r ═ n-6 > 1) columns in the jacobian matrix J, such that the remaining 6 columns constitute the nonsingular matrix J*Then equation (1) can be rewritten as:
thus, any joint angular velocity satisfying the formula (2)Can be further rewritten as:
wherein,is a special solution satisfying the formula (3),is a homogeneous solution of formula (3), and
order toWherein, i is 1,2, …, r, αjIs column j of matrix α;is a column matrix and its pre-r (r ═ N-6) behavior is 0;is a column matrix, and its i-th row is 1, and the other rows in the first r-th row except the i-th row are 0. Defining redundancy space vector k ═ k (k)1,…,kr)TFor any vector in the redundancy vector space, there are:
assuming angular velocityExpressed in S (k), the angle theta is expressed in P (k), and the angle is acceleratedDegree of rotationExpressed by A (k), the angular velocity of the redundant mechanical arm jointCan be expressed as a function of the redundancy space vector k:
the expression of the redundant manipulator joint angle theta with respect to the redundant space vector k is as follows:
angular acceleration of redundant mechanical arm jointThe expression for the redundancy space vector k is:
wherein, theta0Is the angle of the joint at the previous moment,and delta t is the angular velocity of the joint at the last moment and is the sampling step length.
And S230, determining an optimized objective function and constraint conditions corresponding to the motion track of the redundant manipulator moving from the current point to the target point according to an inverse kinematics equation.
In this embodiment, redundant machinesThe optimization objective function and the constraint condition corresponding to the motion trajectory of the arm moving from the current point to the target point can be flexibly set as required, for example, the moving range of the redundant arm can be limited to avoid an obstacle, or the bending angle of the redundant arm is limited to avoid that each joint reaches the motion limit thereof, and the like. In consideration of the practicability of each constraint condition, optionally, the optimization objective function includes that the joint motion amplitude of the redundant mechanical arm is minimum or the redundant mechanical arm is minimally affected by the corresponding gear clearance; the constraint conditions include: and constraining the joint speed of the redundant mechanical arm within a preset speed range or constraining the joint angle of the redundant mechanical arm within a preset angle range. For example, the optimized objective function with the minimum redundant manipulator joint motion amplitude may be:the optimal objective function for the redundant manipulator with minimal impact on the corresponding gear clearance may be:the constraint condition for constraining the joint speed of the redundant mechanical arm within the preset speed range can be as follows:the constraint condition for constraining the joint angle of the redundant mechanical arm within the preset angle range may be: thetamin≤θ≤θmax。
And S240, establishing an equation corresponding to the track function by taking the redundancy space vector as an independent variable.
In this embodiment, the optimization objective function and the constraint equation of the redundant manipulator trajectory may be established based on the redundant space, and both the optimization objective function and the constraint equation of the redundant manipulator may be expressed as expressions using the joint angle, the joint angular velocity, and/or the joint angular acceleration as arguments, so that the optimization objective function and the constraint equation using the redundant space vector k as arguments may be obtained by substituting the above expressions (7), (8), and (9) into the expressions. For example, the optimization objective function for the minimum joint motion amplitude may be further expressed as an equation for a redundant space vector k:
the optimized objective function for a robotic arm that is minimally affected by the corresponding gear backlash may be further expressed as an equation for a redundant space vector k:
the constraint on the joint angular velocity limit can be further expressed as an equation with the redundant space vector k as argument:
the constraints on joint angle limits can be further expressed as an equation with the redundant space vector k as an argument:
and S250, solving an equation corresponding to the track function through an auxiliary vector and a single-target optimization algorithm according to an optimization target function, a minimum target value corresponding to an optimization target, a corresponding constraint condition and a preset weighting coefficient in a redundancy space to obtain the position and the speed of each joint in the redundant manipulator corresponding to the motion track.
For example, a single-objective optimization algorithm for solving the equation corresponding to the trajectory function may be flexibly determined according to the requirement, and is not limited herein. Preferably, the single-target optimization algorithm includes: Newton-Euler algorithm, Nelder-Mead simplex algorithm, interior point algorithm, genetic algorithm, and/or Pattern Search algorithm.
Pareto frontier is a solution set of multi-objective optimization problems, defined as follows: on the multi-objective feasible region omega, there is a point x*E.g., x ∈ omega, if there is no point, then f (x) ≦ f (x)*) If this is true, and at least one point x 'e.g. omega exists such that the strict inequality f (x') > f (x)*) Is established, then x*Is a pareto optimal solution. Taking a dual-objective optimization problem as an example, the equation corresponding to the trajectory function is as follows:
in the above formula, f (x) { f1(x) f2(x) The "is the optimization objective function,for the minimum target value corresponding to the optimization objective function, a is the matrix constraint, b is the vector constraint, ω is the weighting coefficient vector, and γ is the auxiliary vector. The weighting coefficient vector omega can be set by a user or a developer according to needs, and the auxiliary vector gamma is used for converting the original multi-objective optimization problem into a single-objective optimization problem.
In this embodiment, an interior point method may be used to solve the equation (12) to obtain an optimal solution of the equation, and then the angle, the angular velocity, and the angular velocity corresponding to the optimal solution of each joint of the redundant mechanical arm are obtained through the equations (7), (8), and (9), so as to obtain the position and the velocity of each joint of the redundant mechanical arm at the next time.
Taking a nine-degree-of-freedom redundant manipulator as an example (assuming that the D-H coordinates of the nine-degree-of-freedom redundant manipulator are shown in fig. 3, and the D-H parameter table of the link of the nine-degree-of-freedom redundant manipulator is shown in table 1), the process of solving the position and speed of each joint of the redundant manipulator may be:
TABLE 1
| θi | di(mm) | αi | ai(mm) | Range of |
| 0 | d1 | 90° | 0 | 1550≤d1≤8276 |
| θ2 | 0 | 0 | a2＝2200 | -90≤θ2≤90 |
| θ3 | 0 | -90° | 0 | -90≤θ3≤90 |
| θ4 | d4＝2800 | 90° | a4＝-375 | -180≤θ4≤180 |
| θ5 | 0 | -90° | a5＝-a4＝375 | -180≤θ5≤180 |
| θ6 | d4＝2800 | 90° | 0 | -180≤θ6≤180 |
| θ7 | 0 | -90° | 0 | -90≤θ7≤90 |
| θ8 | d8＝1650 | 90° | 0 | -90≤θ8≤90 |
| θ9 | 0 | 0 | ah＝350 | -90≤θ9≤90 |
First, the velocity of the end of the redundant robot arm is converted into the coordinate system of the link 3 as reference:
then, a wrist coordinate system is defined. In consideration of simplicity of calculation, a wrist coordinate system may be defined according to structural characteristics of the redundant manipulator, wherein specific coordinates and directions of the wrist coordinate system may be flexibly set as required, and are not limited herein. For example, a coordinate system of the wrist may be defined as a coordinate system parallel to the coordinate system of the end of the redundant robot arm, and the origin coincides with the origin of the coordinate system of the link 8, and when the velocities of the wrist and the end of the redundant robot arm are referenced to the coordinate system of the link 3, the following relationship exists between the angular velocity and the linear velocity:
3ωw＝3ωh (15)
3vw＝3vh-3Rw(wωh×wPh)＝3vh-3ωh×3Ph＝3vh-3ωh×ah 3xh (16)
wherein,3ωwis the angular velocity in the wrist coordinate system referenced to the connecting rod 3 coordinate system;3ωhis a connecting rod 3 coordinate system as a referenceAngular velocity in the redundant arm end coordinate system under consideration;3vwis the linear velocity in the wrist coordinate system with reference to the connecting rod 3 coordinate system;3vhthe linear velocity in the coordinate system of the tail end of the redundant mechanical arm is taken as the reference of the coordinate system of the connecting rod 3;3xhis the value of the unit vector in the Z direction in the redundant robot arm end coordinate system with reference to the link 3 coordinate system:
in the above formula, ciRepresents cos (. theta.) ofi)，siDenotes sin (θ)i)，cijRepresents cos (. theta.) ofi+θj)，sijDenotes sin (θ)i+θj)。
Definition of3JwTo relate angular velocity of jointsVelocity of wristThe Jacobian matrix of (D) then has:
the Jacobian matrix can be found by the vector product method as follows:
3Jw＝[J1 J2 J3 J4 J5 J6 J7 J8 J9] (19)
wherein,
in this embodiment, any three rows in the formula (19) may be represented as α, J*For the remaining columns other than the three columns comprising α5、J6And J7As α, the remaining columns (J)1、J2、J3、J4、J8And J9) Composition J*The following can be obtained by the formula (5):
wherein,
J21＝a2s3-d6c5-d4-a5s5-d7c5c7+d7s5c6s7，
J23＝a2c3+a4c4+a5c4c5-d6c4s5-d7c4s5c7+d7s4s6s7-d7c4c5c6s7，
J31＝-d4-d7(c5c7-s5c6s7)-d6c5-a5s5，
J33＝a4c4+d7(s7(s4s6-c4c5c6)-c4s5c7)+a5c4c5-d6c4s3，
J41＝d7(s7(c4s6+s4c5c6)+s4s5c7)-a4s4-a5s4c5+d6s4s5，
J42＝d7(s7(s4s6-c4c5c6)-c4s5c7)+a4c4+a5c4c5-d6c4s5，
J84＝s7(s4s6-c4c5c6)-c4s5c7，
J85＝-s7(c4s6+s4c5c6)-s4s5c7，
J86＝c5c7-s5c6s7，
J94＝c8(s4c6+c4c5s6)-s8(c7(s4s6-c4c5c6))+c4s5s7，
J95＝s8(c7(s4s6+s4c5c6))-s4s5s7-c8(c4c6-s4c5s6)，
J96＝s8(c5s7-s5c6c7)+c8s5s6。
order toAndfrom formula (20):
wherein,is a matrixThe ith element of (1).
From formula (6):
wherein, α ═ J (J)5 J6 J7)。
Thus, the following formulae (21) to (26)(j ═ 1,2,3,4,8 and 9) uses(i-5, 6 and 7, j-1, 2,3,4,8 and 9) instead, the following formulae (21) to (26) are used(k ═ 1,2,3,4,5 and 6) with-Jik(i-5, 6 and 7, k-1, 2,3,4,5 and 6) instead of (i-5, 6 and 7) can be obtainedAndthe value of (c). To be provided withFor example, in the formulae (21) to (26)(j ═ 1,2,3,4,8 and 9) uses(j ═ 1,2,3,4,8, and 9) instead, one can obtain:
from formulae (21) to (26)(k ═ 1,2,3,4,5 and 6) with-J5k(k ═ 1,2,3,4,5, and 6) instead, we can obtain:
from the formula (19)Thus, it is possible to obtain:
wherein,is a matrixThe ith element of (1). The same can be obtained:
wherein,
angular velocity of jointRepresented as a redundancy vector (k)5,k6,k7) Function of (c):
by substituting equation (28) for equation (8), a redundancy vector (k) for the joint angle θ can be obtained5,k6,k7) As a function of the argument:
wherein, theta0Is the current joint angle and Δ t is the sampling step.
The equations that the formula (28) is substituted into the formula (10-1) and the formula (29) is substituted into the formula (10-2) can obtain the minimum joint motion amplitude and the minimum influence of the mechanical arm on the corresponding gear clearance are respectively as follows:
wherein Hi(θ(k5,k6,k7) Is a link transformation matrix0Ti(θ(k5,k6,k7) Second row and fourth column of elements):
0Ti(θ(k5,k6,k7))＝0T1(d1)·1T2(θ2)L i-1Ti(θi),(i＝1,L,9) (32)
wherein,i-1Ti(θi) Is the Denavit-Hartenberg matrix:
wherein d isi、αiAnd aiIs the parameter Denavit-Hartenberg, and the specific values are shown in Table 1.
The constraint conditions that the joint angular velocity limit and the joint angle limit can be obtained by substituting formula (28) for formula (11-1) and formula (29) for formula (11-2) are as follows:
from formula (33):
from equation (34), the matrix a and vector b in equation (12) can be further derived as follows:
thus, the multi-objective optimization problem can be translated into:
the redundancy vector (k) can be obtained from the equations (30), (31) and (35)5,k6,k7) Of the redundancy vector (k)5,k6,k7) The optimal values of the optimal values are substituted into the formula (28) and the formula (29), so that the angular speed and the angle of each joint of the redundant mechanical arm at the next sampling point can be obtained, and the position and the speed of each joint of the redundant mechanical arm can be obtained.
The control method of the redundant manipulator provided by the second embodiment of the invention comprises the steps of obtaining the speed of the tail end of the redundant manipulator at a target point, mapping the joint angle, the joint angular speed and the joint angular acceleration of the redundant manipulator to a redundant space according to the speed of the tail end of the redundant manipulator at the target point, determining an optimized objective function and a constraint condition corresponding to the motion track of the redundant manipulator moving from the current point to the target point according to an inverse kinematics equation, establishing an equation corresponding to the motion track by taking a redundant space vector as an argument, and solving the equation corresponding to the track function through an auxiliary vector and a single-objective optimization algorithm to obtain the position and the speed of each joint in the redundant manipulator corresponding to the motion track. By adopting the technical scheme, the mathematical module of the multi-objective constraint optimization problem is established, a theoretical basis can be provided for solving the multi-objective optimization problem, on the premise that a global optimal solution meeting a design objective is obtained, the search space of the multi-objective optimization problem of the redundant manipulator is reduced, the problem of dimension explosion in the multi-objective solution process is avoided, the calculated amount required in the control process of the redundant manipulator is simplified, and the reaction speed of the redundant manipulator is improved.
EXAMPLE III
The third embodiment of the invention provides a control device of a redundant mechanical arm. The device can be realized by hardware and/or software, is generally integrated in a control module for controlling the robot, and can realize the control of the redundant mechanical arm by executing the control method of the redundant mechanical arm. Fig. 4 is a block diagram showing a configuration of a control apparatus for a redundant robot arm according to the present embodiment, and as shown in fig. 4, the apparatus includes:
an information obtaining unit 410, configured to obtain current point information and target point information where the redundant manipulator is located;
a track unit 420, connected to the information obtaining unit, configured to determine, according to the current point information and the target point information, a track function corresponding to a motion track of the redundant manipulator moving from the current point to the target point;
a redundancy processing unit 430 connected to the trajectory unit, configured to establish an equation corresponding to the trajectory function with a redundancy space vector as an argument; and solving an equation corresponding to the track function according to a target approach method to obtain the position and the speed of each joint in the redundant mechanical arm corresponding to the motion track.
The control device for the redundant manipulator provided by the third embodiment of the invention obtains the current point information and the target point information of the redundant manipulator through the information obtaining unit, determines a track function corresponding to a motion track of the redundant manipulator moving from the current point to the target point according to the obtained current point information and the target point information through the track unit, establishes an equation corresponding to the track function by using a redundant space vector as an argument through the redundant processing unit, and solves the equation through a target approximation method to obtain the position and the speed of each joint in the redundant manipulator corresponding to the motion track. By adopting the technical scheme, the embodiment of the invention can reduce the search space of the multi-objective optimization problem of the redundant mechanical arm on the premise of obtaining the global optimal solution meeting the design objective, avoid the occurrence of the dimension explosion problem in the multi-objective solution process, simplify the required calculated amount in the control process of the redundant mechanical arm and improve the reaction speed of the redundant mechanical arm.
Further, the information obtaining unit 410 is specifically configured to: acquiring the speed of the tail end of the redundant mechanical arm at the target point; and mapping the joint angle, the joint angular velocity and the joint angular acceleration of the redundant mechanical arm to a redundant space according to the velocity of the tail end of the redundant mechanical arm at the target point.
Further, the obtaining the velocity of the redundant robotic arm tip at the current point comprises: and determining the speed of the tail end of the redundant mechanical arm at the next sampling point according to the pose of the tail end of the redundant mechanical arm at the current point and the pose of the tail end of the redundant mechanical arm at the next sampling point in the motion trail.
Further, the trajectory unit 420 is specifically configured to determine, according to an inverse kinematics equation, an optimized objective function and a constraint condition corresponding to a motion trajectory of the redundant manipulator moving from the current point to the target point.
Further, the optimization objective function comprises that the joint motion amplitude of the redundant mechanical arm is minimum or the influence of the redundant mechanical arm on the corresponding gear clearance is minimum; the constraint conditions include: and constraining the joint speed of the redundant mechanical arm within a preset speed range or constraining the joint angle of the redundant mechanical arm within a preset angle range.
Further, the solving an equation corresponding to the trajectory function according to a target proximity method to obtain the position and the speed of each joint in the redundant manipulator corresponding to the motion trajectory includes: in a redundancy space, solving an equation corresponding to the track function through an auxiliary vector and a single-target optimization algorithm according to an optimization target function, a minimum target value corresponding to an optimization target, a corresponding constraint condition and a preset weighting coefficient to obtain the position and the speed of each joint in the redundant manipulator corresponding to the motion track.
Further, the single-target optimization algorithm includes: Newton-Euler algorithm, Nelder-Mead simplex algorithm, interior point algorithm, genetic algorithm, and/or Pattern Search algorithm.
The control device for the redundant manipulator provided by the embodiment can execute the control method for the redundant manipulator provided by any embodiment of the invention, and has the corresponding functional modules and beneficial effects of executing the control method for the redundant manipulator. For details that are not described in detail in this embodiment, reference may be made to a control method of a redundant robot arm according to any embodiment of the present invention.
It is to be noted that the foregoing is only illustrative of the preferred embodiments of the present invention and the technical principles employed. It will be understood by those skilled in the art that the present invention is not limited to the particular embodiments described herein, but is capable of various obvious changes, rearrangements and substitutions as will now become apparent to those skilled in the art without departing from the scope of the invention. Therefore, although the present invention has been described in greater detail by the above embodiments, the present invention is not limited to the above embodiments, and may include other equivalent embodiments without departing from the spirit of the present invention, and the scope of the present invention is determined by the scope of the appended claims.
Claims (6)
1. A control method of a redundant manipulator is characterized by comprising the following steps:
acquiring current point information and target point information of the redundant mechanical arm;
determining a track function corresponding to a motion track of the redundant mechanical arm moving from a current point to a target point according to an inverse kinematics equation, wherein the track function comprises an optimization objective function and a constraint condition, the optimization objective function comprises that the joint motion amplitude of the redundant mechanical arm is minimum or the influence of the redundant mechanical arm on a corresponding gear gap is minimum, and the constraint condition comprises that the joint speed of the redundant mechanical arm is constrained within a preset speed range or the joint angle of the redundant mechanical arm is constrained within a preset angle range;
establishing an equation corresponding to the track function by taking the redundancy space vector as an independent variable;
in a redundancy space, solving an equation corresponding to the track function through an auxiliary vector and a single-target optimization algorithm according to an optimization target function, a minimum target value corresponding to an optimization target, a corresponding constraint condition and a preset weighting coefficient to obtain the position and the speed of each joint in the redundant manipulator corresponding to the motion track.
2. The method according to claim 1, wherein the acquiring current point information and target point information of the redundant robot arm comprises:
acquiring the speed of the tail end of the redundant mechanical arm at the target point;
and mapping the joint angle, the joint angular velocity and the joint angular acceleration of the redundant mechanical arm to a redundant space according to the velocity of the tail end of the redundant mechanical arm at the target point.
3. The method of controlling a redundant robotic arm of claim 2, wherein said obtaining a velocity of the redundant robotic arm tip at the current point comprises:
and determining the speed of the tail end of the redundant mechanical arm at the next sampling point according to the pose of the tail end of the redundant mechanical arm at the current point and the pose of the tail end of the redundant mechanical arm at the next sampling point in the motion trail.
4. The method of controlling a redundant robotic arm of claim 1, wherein the single objective optimization algorithm comprises: Newton-Euler algorithm, Nelder-Mead simplex algorithm, interior point algorithm, genetic algorithm, or Pattern Search algorithm.
5. A control apparatus for a redundant robot arm, comprising:
the information acquisition unit is used for acquiring the current point information and the target point information of the redundant mechanical arm;
the track unit is connected with the information acquisition unit and used for determining a track function corresponding to a motion track of the redundant mechanical arm moving from a current point to a target point according to an inverse kinematics equation, wherein the track function comprises an optimization objective function and a constraint condition, the optimization objective function comprises the minimum joint motion amplitude of the redundant mechanical arm or the minimum influence of the redundant mechanical arm on a corresponding gear gap, and the constraint condition comprises the constraint of the joint speed of the redundant mechanical arm in a preset speed range or the constraint of the joint angle of the redundant mechanical arm in a preset angle range;
the redundancy processing unit is connected with the track unit and used for establishing an equation corresponding to the track function by taking the redundancy space vector as an independent variable; in a redundancy space, solving an equation corresponding to the track function through an auxiliary vector and a single-target optimization algorithm according to an optimization target function, a minimum target value corresponding to an optimization target, a corresponding constraint condition and a preset weighting coefficient to obtain the position and the speed of each joint in the redundant manipulator corresponding to the motion track.
6. The control device of a redundant robotic arm according to claim 5, wherein the information acquisition unit is specifically configured to: acquiring the speed of the tail end of the redundant mechanical arm at the current point; and mapping the joint angle, the joint angular velocity and the joint angular acceleration of the redundant mechanical arm to a redundant space according to the speed of the tail end of the redundant mechanical arm at the current point.
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