CN108287469B - Mechanical arm optimal obstacle avoidance control method and device based on artificial potential field gravitation factor - Google Patents
Mechanical arm optimal obstacle avoidance control method and device based on artificial potential field gravitation factor Download PDFInfo
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Abstract
The invention relates to an optimal mechanical arm obstacle avoidance control method and device based on an artificial potential field gravitation factor, wherein the method comprises the following steps: 1) setting initial values of an initialized model position and a gravity factor; 2) calculating the attraction and the repulsion applied to the tail end of the mechanical arm by adopting an artificial potential field algorithm; 3) based on the initialized model position and step 2), acquiring a path point set at the tail end of the mechanical arm by utilizing the attraction force and the repulsion force; 4) acquiring the shortest distance between a point in a mechanical arm tail end path point set and the center position of an obstacle and the tail end termination position of a mechanical arm, and acquiring the shortest obstacle avoidance path model description based on model constraint conditions; 5) and constructing an obstacle avoidance path objective function based on the shortest obstacle avoidance path model description, and iteratively solving a zero value of the obstacle avoidance path objective function by adopting an optimization method to obtain a set of the optimal path points of the mechanical arm. Compared with the prior art, the method has the advantages of good instantaneity and robustness and the like, can adapt to the change of the position and the size of the obstacle, and realizes optimal obstacle avoidance.
Description
Technical Field
The invention belongs to a mechanical arm path planning method, and particularly relates to an optimal mechanical arm obstacle avoidance control method and device based on an artificial potential field gravitation factor.
Background
With the development of industrial robots, the production technology thereof is gradually improved, and the cost is relatively reduced, so that the threshold for enabling bionic robots (such as mechanical arms) like human beings to enter the lives of people is lower and lower. For example, the pleasantness and dexterity of mechanical arms such as iwa of KUKA company, jaco of Kinova company, Saywer of Rethin robotics company and the like make the beautiful desire of making social life, work and the like more flexible and intelligent more likely. The service mechanical arm is slowly changed from an industrial robot, a robot used and replaced between a human and a robot into a robot which is blended into the production and living environment of the human and can be harmoniously cooperated with the human. Therefore, how to enable the mechanical arm to safely and conveniently cooperate with human is an important problem worthy of attention, and the mechanical arm safety obstacle avoidance is a foundation and research hotspot for achieving man-machine integration.
The artificial potential field method is a local path planning method firstly proposed by Khatib, and the basic idea is that the robot moves in the environment as a robot moves in a virtual artificial stress field, an obstacle generates repulsion to a mobile robot, a target point generates attraction to the mobile robot, and the resultant force of the repulsion and the attraction is used as force for controlling the robot to move to the target point. Since the target point is designed as the global minimum point of the resultant force, the robot can theoretically reach the target point under the action of the resultant force, but the target is not reachable and the local minimum value is not a problem. The literature 'Wangyun, Zhu Lei, Wang military administration, six-degree-of-freedom mechanical arm obstacle avoidance path planning based on a navigation potential function method, university of Beijing science and engineering, 2015,35(2):186 + 191' solves the problem of local minimum trap of the traditional artificial potential field method by combining a geometric method and an artificial potential field method. An inverse kinematics method is used for path planning of the whole machine, however, the method needs to be used for screening from 8 sets of inverse solutions, and is low in efficiency and poor in real-time performance. The technical scheme includes that the method comprises the following steps of ' Wangjunlong, Zhangliang, Naja, Jing bin and the like, ' mechanical arm obstacle avoidance path planning of an artificial potential field method is improved, computer engineering and application, 2013,49(21):266 plus 270 ' are adopted, and when the artificial potential field method falls into a local minimum value, the problem is solved by adding a virtual obstacle to change the whole artificial potential field. The implementation of the method must obtain a group of 'reasonable' joint angle solutions through other methods, but the 'reasonable' solutions are difficult to select in real-time application. There are many published documents on how to improve the local defects of the artificial potential field method in the aspect of obstacle avoidance of the mobile robot, and there is no similar document disclosed for realizing the change capable of adapting to the position and the size of an obstacle by using an artificial potential field gravity factor and meeting the requirement of avoiding the obstacle at the tail end of the mechanical arm in the optimal state. Therefore, the optimal obstacle avoidance method of the mechanical arm based on the artificial potential field gravitation factor is designed, the mechanical arm has multiple obstacle avoidance paths for obstacles with different positions and sizes, and the method has important significance on how to obtain the optimal obstacle avoidance path.
Disclosure of Invention
The invention aims to overcome the defects of the prior art and provide an optimal obstacle avoidance control method of a mechanical arm based on an artificial potential field gravitation factor.
The purpose of the invention can be realized by the following technical scheme:
an optimal mechanical arm obstacle avoidance control method based on an artificial potential field gravity factor comprises the following steps:
1) setting initial values of an initialized model position and a gravity factor;
2) according to the step 1), calculating the attraction and the repulsion applied to the tail end of the mechanical arm by adopting an artificial potential field algorithm;
3) based on the initialized model position and the step 2), acquiring a path point set at the tail end of the mechanical arm by utilizing the attraction force and the repulsion force;
4) acquiring the shortest distance between a point in the mechanical arm tail end path point set and the center position of an obstacle and the tail end termination position of the mechanical arm, and acquiring the shortest obstacle avoidance path model description based on model constraint conditions;
5) and constructing an obstacle avoidance path objective function based on the shortest obstacle avoidance path model description, and iteratively solving the minimum zero value of the obstacle avoidance path objective function by adopting an optimization method to obtain a set of the optimal path points of the mechanical arm.
Further, the initialized model position λ is represented as:
λ＝{ρ0,Xo(x,y),Xg(x,y),Xt(x,y)}
where ρ is0Is a repulsive potential field action range constant, Xo(X, y) is the center position of the obstacle, Xg(X, y) is the target point location, Xt(x, y) is the robot arm end initial position.
Further, the gravity factor κfIs defined as:
κf＝ka/(ka+kb)
wherein k isaIs the coefficient of gravitational potential field, kbIs the repulsive force potential field coefficient.
Further, in the step 3), a set P of path points of the end of the robot arm is obtainedtrajExpressed as:
Ptraj＝Γ(t,κf,λ)
i.e. PtrajAnd t, kfλ, where t is the time of the end of the arm movement, κfFor the gravity factor, λ is the initialized model position, and Γ (·) is the relationship function.
Further, the obstacle avoidance path objective function L (k)f) The method specifically comprises the following steps:
L(κf)＝f2(κf)+g2(κf)
wherein the intermediate function f (κ)f)、g(κf) Defined by the shortest obstacle avoidance path model description:
dminthe shortest distance between the point in the mechanical arm tail end path point set and the center position of the obstacle,
is the end position of the mechanical arm, r is the radius of the circumscribed circle of the barrier, Xg(x, y) is the target point location.
The invention also provides a mechanical arm optimal obstacle avoidance control device based on the artificial potential field gravitation factor, which comprises the following components:
the initialization module is used for acquiring the initial values of the initialization model position and the gravity factor;
the artificial potential field solving module is used for calculating the attraction and the repulsion suffered by the tail end of the mechanical arm by adopting an artificial potential field algorithm according to the position of the initialized model and the attraction factor;
the path solver is used for acquiring a path point set at the tail end of the mechanical arm according to the initialized model position and the attractive force and the repulsive force acquired by the artificial potential field solving module;
the shortest obstacle avoidance path model description module is used for acquiring the shortest distance between a point in the mechanical arm tail end path point set and the center position of an obstacle and the mechanical arm tail end termination position, and acquiring the optimal path model description based on model constraint conditions;
and the shortest path solver is used for constructing an obstacle avoidance path objective function based on the shortest obstacle avoidance path model description, and iteratively solving the minimum zero value of the obstacle avoidance path objective function by adopting an optimization method to obtain a set of the optimal path points of the mechanical arm.
Further, in the initialization module, the initialization model position λ is represented as:
λ＝{ρ0,Xo(x,y),Xg(x,y),Xt(x,y)}
where ρ is0Is a repulsive potential field action range constant, Xo(X, y) is the center position of the obstacle, Xg(X, y) is the target point location, Xt(x, y) is the robot arm end initial position.
Further, in the initialization module, the gravity factor kfIs defined as:
κf＝ka/(ka+kb)
wherein k isaIs the coefficient of gravitational potential field, kbIs the repulsive force potential field coefficient.
Further, in the path solver, an obtained set P of path points of the end of the mechanical armtrajExpressed as:
Ptraj＝Γ(t,κf,λ)
i.e. PtrajAnd t, kfλ, where t is the time of the end of the arm movement, κfFor the gravity factor, λ is the initialized model position, and Γ (·) is the relationship function.
Further, in the shortest path solver, an obstacle avoidance path objective function L (κ)f) The method specifically comprises the following steps:
L(κf)＝f2(κf)+g2(κf)
wherein the intermediate function f (κ)f)、g(κf) Defined by the shortest obstacle avoidance path model description:
dminthe shortest distance between the point in the mechanical arm tail end path point set and the center position of the obstacle,
is the end position of the mechanical arm, r is the radius of the circumscribed circle of the barrier, Xg(x, y) is the target point location.
Compared with the prior art, the invention has the following beneficial effects:
firstly, the optimal obstacle avoidance algorithm of the mechanical arm is simple, large amount of complex calculation is not needed, the real-time performance is better, the obstacle avoidance path is shortest, and the energy consumption is least.
Second, the present invention constructs and solves the gravity factor κfAnd the most obstacle avoidance path of the robot can be more intuitively and effectively researched.
Thirdly, the invention carries out deep research on the parameters of the artificial potential field method to construct the gravity factor kappafThe method is applied to the problem of planning the optimal obstacle avoidance path of the mechanical arm, the obstacle avoidance path objective function is constructed, the optimal path planning is carried out aiming at different obstacle sizes and positions, the optimal obstacle avoidance path of the mechanical arm is realized, the real-time performance is better, and the mechanical arm can be safely, conveniently and jointly cooperated with human beings with low consumption.
Fourthly, the optimal obstacle avoidance method for the mechanical arm can effectively improve the safety performance, the service life and the like of the mechanical arm.
Fifthly, the optimal obstacle avoidance method for the mechanical arm has good road robustness and high obstacle avoidance success rate.
Drawings
FIG. 1 is a control flow diagram of the present invention;
FIG. 2 is a diagram of an industrial SCARA plane two-degree-of-freedom mechanical arm obstacle avoidance model;
FIG. 3 is a schematic diagram of an embodiment of an optimal path feature with an obstacle radius of 0.4;
FIG. 4 is a schematic diagram of an embodiment of an optimal path feature with an obstacle radius of 0.44;
FIG. 5 is a schematic diagram of an optimal path characteristic with a center of the second obstacle being (0.6,0.54) according to the second embodiment;
FIG. 6 is a schematic diagram of an optimal path characteristic with a center of circle of a second obstacle of (0.6 ) according to an embodiment;
fig. 7 is a schematic diagram of the change of the joint angle of the mechanical arm of the optimal obstacle avoidance path (r is 0.4 and 0.44).
Detailed Description
The invention is described in detail below with reference to the figures and specific embodiments. The present embodiment is implemented on the premise of the technical solution of the present invention, and a detailed implementation manner and a specific operation process are given, but the scope of the present invention is not limited to the following embodiments.
As shown in fig. 1, the present invention provides an optimal obstacle avoidance control method for a mechanical arm based on an artificial potential field gravity factor, which includes the following steps:
1) initial values for the initialized model position and gravity factor are set. The initialized model position λ is expressed as:
λ＝{ρ0,Xo(x,y),Xg(x,y),Xt(x,y)}
where ρ is0Is a repulsive potential field action range constant, Xo(X, y) is the center position of the obstacle, Xg(X, y) is the target point location, Xt(x, y) is the robot arm end initial position.
The gravity factor kappafIs defined as:
κf＝ka/(ka+kb)
wherein k isaIs the coefficient of gravitational potential field, kbIs the repulsive force potential field coefficient. When attraction potential field coefficient kaThe larger the proportion is, the larger is κfThe larger the arc is, the smaller the radian of the obstacle avoiding path at the tail end of the mechanical arm is, and k isa/kbK at infinityfThe extreme value is 1; otherwise, the radian of the obstacle-avoiding path at the tail end of the mechanical arm is increased, and k isa/kbInfinite hour kfThe extreme value is 0. By passingDefining the gravity factor kfAnd the optimal obstacle avoidance path of the robot can be more intuitively and effectively researched.
2) According to the step 1), calculating the gravitation F borne by the tail end of the mechanical arm by adopting an artificial potential field algorithmaatAnd repulsive force Frep。
3) Acquiring a mechanical arm tail end path point set P based on the initialized model position and the attractive force and the repulsive force acquired in the step 2)trajExpressed as:
Ptraj＝Γ(t,κf,λ)
i.e. PtrajAnd t, kfλ, where t is the time of the end of the arm movement, κfFor the gravity factor, λ is the initialized model position, and Γ (·) is the relationship function.
4) And acquiring the shortest distance between a point in the mechanical arm tail end path point set and the center position of the obstacle and the mechanical arm tail end termination position, and acquiring the shortest obstacle avoidance path model description based on model constraint conditions.
The shortest obstacle avoidance path model is described as:
wherein d isminSet P of motion path points at the end of a robot armtrajCenter of neutral obstacle XoShortest distance of (x, y): dmin＝Φmin(κf,λ)；
The end position for a point at the end of the arm is expressed as:
when d isminAnd r represents that the tail end of the mechanical arm and the outer circle of the obstacle are in a tangent state, and a unique solution exists, wherein the critical state is the shortest path of the mechanical arm for avoiding the obstacle.
The constrained motion path eventually converges to the target point.
5) Constructing an obstacle avoidance path objective function based on the shortest obstacle avoidance path model description, and iteratively solving the minimum zero value of the obstacle avoidance path objective function by adopting an optimization method to satisfy L (kappa)f) Obtaining a set of optimal path points for the robotic arm, 0
And the gravity factor optimal solution at that time
The optimal solution meets the requirement of avoiding the barrier of the tail end of the mechanical arm in the optimal state.
The obstacle avoidance path objective function L (k)f) The method specifically comprises the following steps:
L(κf)＝f2(κf)+g2(κf)
wherein the intermediate function f (κ)f)、g(κf) Defined by the shortest obstacle avoidance path model description:
dminthe shortest distance between the point in the mechanical arm tail end path point set and the center position of the obstacle,
is the end position of the mechanical arm, r is the radius of the circumscribed circle of the barrier, Xg(x, y) is the target point location.
As shown in fig. 1, the apparatus for implementing the optimal obstacle avoidance control method for the mechanical arm based on the artificial potential field gravitation factor includes an initialization module, an artificial potential field solving module, a path solver, a shortest obstacle avoidance path model module, and a shortest obstacle avoidance path solver, where the shortest obstacle avoidance path description module includes a model state solver and a shortest obstacle avoidance path model description.
The embodiment takes a two-degree-of-freedom mechanical arm as an example, but the method is not limited to be applied to the robot. As shown in fig. 2, the two-degree-of-freedom mechanical arm obstacle avoidance model is an industrial SCARA plane. Defining the circle circumscribing the barrier area is done to simplify describing the barrier. Before executing a movement instruction, the robot carries out online calculation planning according to the information of the position of the obstacle and the position of the target, and the optimal obstacle avoidance path movement is realized.
Determining the action range constant rho of repulsive force potential field for obstacles with any position and size0Then, the change of the motion path of the tail end of the mechanical arm is determined by the gravitational potential field coefficient kaCoefficient of repulsive potential field kbRatio (k) ofa/kb) Determine ρ0May be equal to the distance between the obstacle position and the target point position. Therefore, the method applies the artificial potential field method to the planning of the optimal obstacle avoidance path of the mechanical arm, has good real-time performance, can adapt to the change of the position and the size of the obstacle, and meets the requirement of the end of the mechanical arm on obstacle avoidance in the optimal state.
Example one
First, as shown in fig. 3 and 4, a schematic diagram of an optimal path characteristic of a situation of a size change of an obstacle according to an embodiment of the present invention is shown, where a represents an obstacle point, b represents a target point, and c represents a movement path. Establishing the radii of the two obstacles as 0.4 and 0.44 respectively, fixing the central point positions (0.6 and 0.6) of the obstacles, the central point positions (0.9 and 0.2) of the target points and the initial central positions (0.2 and 0.2) of the tail ends of the mechanical arms, and determining the function range constant rho of the repulsive potential field0Equal to the distance of the obstacle from the target point of 0.5.
Secondly, after initializing the model state model position lambda through the first step, then giving kappafIs 1.
Thirdly, calculating through an artificial potential field algorithm to obtain the gravitational force F borne by the tail end of the mechanical armaatAnd repulsive force Frep。
Fourthly, calculating the artificial potential field algorithm by utilizing a path solver to obtain the gravitational force F borne by the tail end of the mechanical armaatRepulsive force FrepInitializing the position of the model, and solving a set P of path points at the tail end of the mechanical armtraj＝Γ(t,κf,λ)。
Fifthly, solving a set P of path points of the tail ends of the mechanical arms according to the fourth steptraj＝Γ(t,κfλ), model state solver in the shortest obstacle avoidance path model solves for multiple dmin,
The value of (c).
Sixthly, obtaining the description of the shortest obstacle avoidance path model by combining the model constraint conditions
And an objective function L (k) of the obstacle avoidance pathf)＝f2(κf)+g2(κf) The shortest path solver is used to solve for L (kappa) by iterative optimization (gradient descent is used in this example, but the optimization method is not limited to this method)f) Minimum value of zero, satisfies L (k)f) And (5) finally obtaining a set of optimal path points of the mechanical arm as 0
The optimal path is as shown in fig. 3 and 4, and the optimal solution is as follows when the radius is 0.4
The optimal solution at a radius of 0.44 is
Example two
First, as shown in fig. 5 and fig. 6, which are schematic diagrams illustrating optimal path characteristics under the condition of changing the center positions of two obstacles according to the embodiment of the present invention, the center positions of the two obstacles are determined to be (0.6,0.56) and (0.6 ), the radius of the fixed obstacle is 0.41, the center position of the target point is (0.9,0.2), and the starting center position of the end of the robot arm is (0.2 ). Determining the function range constant rho of repulsive force potential field0Equal to the distance between the obstacle and the target point.
Secondly, after initializing the model state model position lambda through the first step, then giving kappafIs 1.
Thirdly, artificial vigor is performedCalculating by field algorithm to obtain the gravitational force F applied to the tail end of the mechanical armaatAnd repulsive force Frep。
Fourthly, calculating the artificial potential field algorithm by utilizing a path solver to obtain the gravitational force F borne by the tail end of the mechanical armaatRepulsive force FrepInitializing the position of the model, and solving a set P of path points at the tail end of the mechanical armtraj＝Γ(t,κf,λ)。
Fifthly, solving a set P of path points of the tail ends of the mechanical arms according to the fourth steptraj＝Γ(t,κfλ), model state solver in the shortest obstacle avoidance path model solves for multiple dmin,
The value of (c).
Sixthly, obtaining the description of the shortest obstacle avoidance path model by combining the model constraint conditions
And an objective function L (k) of the obstacle avoidance pathf)＝f2(κf)+g2(κf) Iterative optimization is adopted to solve L (kappa)f) Minimum value of zero, satisfies L (k)f) And (0) finally obtaining a set of shortest path points of the mechanical arm
The optimal path is as shown in fig. 5 and 6, and the optimal solution is (0.6,0.56) when the center position of the obstacle is (c)
The optimal solution with the center position of the obstacle being (0.6 ) is
In the first embodiment and the second embodiment, the optimal obstacle avoidance path of the tail end of the mechanical arm for obstacles with different circle center positions and radiuses is discussed. And for different tail end paths, carrying out example solving analysis on joint paths of the mechanical arm aiming at a plane model based on the industrial SCARA robot, wherein the joint paths are obtained by inverse kinematics calculation of the robot.
The optimal obstacle avoidance path of the end of the robot in the first embodiment is selected as an example, where the radius r of the obstacle is 0.4 and 0.44, the center position is (0.6 ), the target point is (0.9,0.2), and the starting position of the end of the robot is (0.2 ). The lengths of the large arm and the small arm of the planar two-degree-of-freedom mechanical arm model shown in FIG. 2 are 0.4m and 0.35m respectively. And setting the origin of the obstacle avoidance model coordinate system to be (-0.5, 0.3) of the mechanical arm coordinate system, so that the mechanical arm can complete the obstacle avoidance movement task within the movement space range. The tail end of the mechanical arm can accurately track the optimal obstacle avoidance path by controlling the two joint motors of the mechanical arm.
In the first embodiment, when the radius of the obstacle is 0.4 and 0.44, the repulsive potential field action range constant ρ is set0The optimal mechanical arm obstacle avoidance control method based on the artificial potential field gravity factor can calculate the corresponding optimal gravity factor
1 and 0.9075 respectively, to obtain the optimal obstacle avoidance path of the tail end of the mechanical arm.
As shown in fig. 3, when the radius of the obstacle is r equal to 0.4, the obstacle does not block the linear movement of the end of the robot arm to the target point. As shown in fig. 4, when r is 0.44, the end path of the robot arm moves along the x-axis first, and then starts to move in the negative y-axis direction to reach the target point while avoiding the obstacle.
The two cases of the change of the mechanical arm joint angle obtained by the inverse kinematics calculation of the robot are shown in fig. 7, which shows the large arm joint angle q1And the angle q of the forearm joint2The dotted line r is 0.4, the small arm joint of the mechanical arm is increased and then decreased, and the large arm joint is decreased and then increased, so that the linear motion of the tail end of the mechanical arm is realized. When the arm starts to move, the articulation is substantially the same in both cases. When r is 0.44, the end of the mechanical arm is in t epsilon [0.2,1 ∈]In the time period, the small arm joint of the mechanical arm is increased by more angles than the condition that r is equal to 0.4, and simultaneously the large arm is reduced by more anglesThe reason for this is that the arc path appears at the end of the mechanical arm when r is 0.44, so that the mechanical arm needs to swing more angles to realize obstacle avoidance.
In the horizontal two-degree-of-freedom mechanical arm of the two embodiments, experimental results show that when the radius of an obstacle is increased, the optimal solution is obtained
The radian of the path at the tail end of the mechanical arm is gradually reduced, the shortest path for avoiding the obstacle is kept, and the mechanical arm is finally stopped at the position of the target center point. Pass pair k before the robot performs a motion taskfSolving an optimal solution to realize an optimal path aiming at obstacles with different radiuses; maintaining repulsive potential field coefficient k when the obstacle position moves upwardbConstant, gravitational potential field coefficient kaGradually becoming larger, the optimal solution
The curvature of the end path of the mechanical arm becomes smaller gradually, but the smooth path can still be kept, and the end path reaches and stops at the target central point position under the shortest path. In the actual mechanical arm obstacle avoidance experiment, k can be changedfThe optimal obstacle avoidance path adapting to the moving obstacle is realized.
The mechanical arm optimal obstacle avoidance control method based on the artificial potential field gravitation factor applies the artificial potential field method to mechanical arm optimal obstacle avoidance path planning, is not only suitable for mechanical arms with two degrees of freedom in a horizontal plane, but also suitable for obstacle avoidance of other multi-degree-of-freedom industrial robots, and is also suitable for obstacle avoidance of a 3D space robot.
The foregoing detailed description of the preferred embodiments of the invention has been presented. It should be understood that numerous modifications and variations could be devised by those skilled in the art in light of the present teachings without departing from the inventive concepts. Therefore, the technical solutions available to those skilled in the art through logic analysis, reasoning and limited experiments based on the prior art according to the concept of the present invention should be within the scope of protection defined by the claims.
Claims (8)
1. An optimal mechanical arm obstacle avoidance control method based on an artificial potential field gravitation factor is characterized by comprising the following steps:
1) setting initial values of an initialized model position and a gravity factor;
2) according to the step 1), calculating the attraction and the repulsion applied to the tail end of the mechanical arm by adopting an artificial potential field algorithm;
3) based on the initialized model position and the step 2), acquiring a path point set at the tail end of the mechanical arm by utilizing the attraction force and the repulsion force;
4) acquiring the shortest distance between a point in the mechanical arm tail end path point set and the center position of an obstacle and the tail end termination position of the mechanical arm, and acquiring the shortest obstacle avoidance path model description based on model constraint conditions;
5) constructing an obstacle avoidance path objective function based on the shortest obstacle avoidance path model description, and iteratively solving a zero value of the obstacle avoidance path objective function by adopting an optimization method to obtain a set of optimal path points of the mechanical arm;
the gravity factor kappafIs defined as:
κf＝ka/(ka+kb)
wherein k isaIs the coefficient of gravitational potential field, kbIs the repulsive force potential field coefficient.
2. The optimal obstacle avoidance control method for the mechanical arm based on the artificial potential field gravity factor as claimed in claim 1, wherein the initialized model position λ is expressed as:
λ＝{ρ0,Xo(x,y),Xg(x,y),Xt(x,y)}
where ρ is0Is a repulsive potential field action range constant, Xo(X, y) is the center position of the obstacle, Xg(X, y) is the target point location, Xt(x, y) is the robot arm end initial position.
3. The artificial potential field-based gravitational cause of claim 1The optimal obstacle avoidance control method for the mechanical arm is characterized in that in the step 3), the obtained tail end path point set P of the mechanical armtrajExpressed as:
Ptraj＝Γ(t,κf,λ)
i.e. PtrajAnd t, kfλ, where t is the time of the end of the arm movement, κfFor the gravity factor, λ is the initialized model position, and Γ (·) is the relationship function.
4. The optimal obstacle avoidance control method for mechanical arm based on artificial potential field gravitation factor as claimed in claim 1, wherein the obstacle avoidance path objective function L (k;)f) The method specifically comprises the following steps:
L(κf)＝f2(κf)+g2(κf)
wherein the intermediate function f (κ)f)、g(κf) Defined by the optimal path model description:
dminthe shortest distance between the point in the mechanical arm tail end path point set and the center position of the obstacle,
is the end position of the mechanical arm, r is the radius of the circumscribed circle of the barrier, Xg(x, y) is the target point location.
5. The utility model provides an optimum obstacle avoidance control device of arm based on artifical potential field gravitation factor which characterized in that includes:
the initialization module is used for acquiring the initial values of the initialization model position and the gravity factor;
the artificial potential field solving module is used for calculating the attraction and the repulsion suffered by the tail end of the mechanical arm by adopting an artificial potential field algorithm according to the position of the initialized model and the attraction factor;
the path solver is used for acquiring a path point set at the tail end of the mechanical arm according to the initialized model position and the attractive force and the repulsive force acquired by the artificial potential field solving module;
the shortest obstacle avoidance path description module is used for acquiring the shortest distance between a point in the mechanical arm tail end path point set and the center position of an obstacle and the tail end termination position of the mechanical arm, and acquiring the shortest obstacle avoidance path model description based on model constraint conditions;
the shortest path solver is used for constructing an obstacle avoidance path objective function based on the shortest obstacle avoidance path model description, and an optimization method is adopted to iteratively solve the zero value of the obstacle avoidance path objective function to obtain a set of the optimal path points of the mechanical arm;
in the initialization module, the gravity factor kfIs defined as:
κf＝ka/(ka+kb)
wherein k isaIs the coefficient of gravitational potential field, kbIs the repulsive force potential field coefficient.
6. The optimal obstacle avoidance control device for the mechanical arm based on the artificial potential field gravity factor as claimed in claim 5, wherein in the initialization module, an initialization model position λ is expressed as:
λ＝{ρ0,Xo(x,y),Xg(x,y),Xt(x,y)}
where ρ is0Is a repulsive potential field action range constant, Xo(X, y) is the center position of the obstacle, Xg(X, y) is the target point location, Xt(x, y) is the robot arm end initial position.
7. The optimal obstacle avoidance control device for the mechanical arm based on the artificial potential field gravitation factor as claimed in claim 5, wherein the set of path points P at the end of the mechanical arm obtained in the shortest path solvertrajExpressed as:
Ptraj＝Γ(t,κf,λ)
i.e. PtrajAnd t, kfλ, where t is the time of the end of the arm movement, κfIs a gravitational factor, λ is initialThe modeled positions, Γ (·), are the relationship functions.
8. The optimal obstacle avoidance control device for mechanical arm based on artificial potential field gravitation factor as claimed in claim 5, wherein in the shortest path solver, an obstacle avoidance path objective function L (k;)f) The method specifically comprises the following steps:
L(κf)＝f2(κf)+g2(κf)
wherein the intermediate function f (κ)f)、g(κf) Defined by the shortest obstacle avoidance path model description:
dminthe shortest distance between the point in the mechanical arm tail end path point set and the center position of the obstacle,
is the end position of the mechanical arm, r is the radius of the circumscribed circle of the barrier, Xg(x, y) is the target point location.
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