CN110682286B - Real-time obstacle avoidance method for cooperative robot - Google Patents

Real-time obstacle avoidance method for cooperative robot Download PDF

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CN110682286B
CN110682286B CN201910452401.3A CN201910452401A CN110682286B CN 110682286 B CN110682286 B CN 110682286B CN 201910452401 A CN201910452401 A CN 201910452401A CN 110682286 B CN110682286 B CN 110682286B
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mechanical arm
obstacle avoidance
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CN110682286A (en
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徐智浩
周雪峰
唐观荣
李帅
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Institute of Intelligent Manufacturing of Guangdong Academy of Sciences
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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
    • B25J9/1666—Avoiding collision or forbidden zones

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Abstract

The invention discloses a real-time obstacle avoidance method for a cooperative robot, which comprises the steps of establishing an obstacle avoidance model in advance, constructing an inequality drawing for describing real-time obstacle avoidance of the robot, selecting a speed minimum norm as a redundancy resolution scheme, designing a motion control mode of a mechanical arm, modeling physical constraints of the mechanical arm, modeling an obstacle avoidance problem of the mechanical arm, optimally solving the obstacle avoidance problem model of the mechanical arm to obtain joint angular speed control quantity of the mechanical arm of the robot, sending the joint angular speed control quantity to a mechanical arm controller, and controlling the mechanical arm to avoid obstacles. The method does not need off-line planning; the proposed obstacle avoidance algorithm can realize obstacle avoidance of static and dynamic obstacles, does not influence the operation to be executed by an end effector of the obstacle avoidance algorithm, and is carried out in parallel without contradiction; the proposed obstacle avoidance algorithm can simultaneously avoid the physical overrun of the mechanical arm, namely the joint angle and the angular speed do not exceed the actual limits.

Description

Real-time obstacle avoidance method for cooperative robot
Technical Field
The invention relates to the field of robot control, in particular to a real-time obstacle avoidance method for a cooperative robot.
Background
With the development of science and technology, a new generation of robots represented by cooperative robots have been widely used in the fields of industry, agriculture, medical treatment, companion, and the like. Different from the traditional industrial robot, the cooperative robot and the human coexist in the same space, so that the robot has good real-time obstacle avoidance capability, can avoid static and dynamic obstacles in real time in a complex multi-edge environment, and ensures the safety of the robot. Most obstacle avoidance algorithms aiming at the robot are mostly concentrated on the mobile robot at present, and as the structure of the mechanical arm is more complex, the obstacle avoidance problem of the whole body needs to be considered in the obstacle avoidance process, the difficulty of algorithm design is greatly increased, and the obstacle avoidance algorithm applied to the mobile robot in the prior art is difficult to apply to a mechanical arm system.
At present, the obstacle avoidance method aiming at the mechanical arm is mostly based on an artificial potential field method, wherein the target position of the robot generates a similar attraction effect on the end effector, and meanwhile, the obstacle generates a similar repulsion effect on the robot. However, this type of method generally has a local minimum problem. Moreover, for a mechanical arm with redundant degrees of freedom such as a cooperative robot, an obstacle avoidance strategy is not designed according to the redundant characteristic of the degrees of freedom.
Disclosure of Invention
The invention aims to overcome the defects of the prior art and provides a real-time obstacle avoidance method for a cooperative robot, which is suitable for a mechanical arm with redundant freedom.
In order to achieve the purpose, the technical scheme of the invention is as follows:
a cooperative robot real-time obstacle avoidance method comprises the following steps:
uniformly selecting a group of key points A on each connecting rod of the body of the mechanical armiAnd defines a radius d1So as to be at point AiIs the center of a sphere d1Set a of spheres of radius ═ { a ═ ai1., α } can completely surround the body of the robot arm;
acquiring image information of the position of the obstacle, and simplifying the acquired images of the mechanical arm and the position of the obstacle into a key point BjSo that point B is formedjIs the center of a sphere d2Set B ═ B consisting of a series of spheres of radiusiI 1.. b } can completely surround the obstacle;
inequality description | A for constructing and describing real-time obstacle avoidance of robotiBjL ≧ d, where d ═ d1+d2+ Δ d, Δ d > 0 is the distance margin and the inequality description is rewritten as an inequality description of the velocity layer:
definition D ═ aiBjI-d, the inequality of the velocity layer is:
Figure GDA0002449891890000011
wherein
Figure GDA0002449891890000017
Figure GDA0002449891890000013
Is that
Figure GDA0002449891890000014
A unit vector of (a); j. the design is a squareaiIs a key point A on the mechanical armiA corresponding Jacobian matrix; g (| D |) is a function of class k;
Figure GDA0002449891890000016
is a set of real numbers.
Selecting the minimum speed norm as a redundancy analysis scheme, and optimizing the joint angular speed norm
Figure GDA0002449891890000021
Let xd(t)、
Figure GDA0002449891890000022
Respectively, a desired position and velocity, x (t) being a current position of the end effector of the robot arm, such that the angular velocity of the joint of the robot arm
Figure GDA0002449891890000023
Satisfying the following formula so that the tail end execution of the mechanical arm moves according to a preset track
Figure GDA0002449891890000024
Wherein J (theta) is a Jacobian matrix of the mechanical arm, k is a normal number, theta,
Figure GDA0002449891890000025
respectively the joint angle and the angular velocity of the mechanical arm;
the obstacle avoidance problem modeling for constructing the mechanical arm is as follows:
min
Figure GDA0002449891890000026
s.t.
Figure GDA0002449891890000027
Figure GDA0002449891890000028
θmin≤θ(t)≤θmax(3d)
Figure GDA0002449891890000029
wherein,
Figure GDA00024498918900000212
θmin，
Figure GDA00024498918900000211
the lower bound and the upper bound of the joint angle and the angular speed of the mechanical arm are respectively;
and (4) carrying out optimization solution on the obstacle avoidance problem model of the mechanical arm to obtain the joint angular velocity control quantity of the mechanical arm of the robot, sending the joint angular velocity control quantity to a mechanical arm controller, and controlling the mechanical arm to avoid the obstacle.
Compared with the prior art, the invention has the beneficial effects that:
1. the method is a real-time obstacle avoidance method, and does not need to carry out off-line planning;
2. the proposed obstacle avoidance algorithm can realize obstacle avoidance of static and dynamic obstacles, does not influence the operation to be executed by an end effector of the obstacle avoidance algorithm, and is carried out in parallel without contradiction;
3. the proposed obstacle avoidance algorithm can simultaneously avoid the physical overrun of the mechanical arm, namely the joint angle and the angular speed do not exceed the actual limits;
4. the proposed function g (| D |) is a class of functions rather than a specific function, can be selected according to actual conditions, and has better flexibility.
Drawings
FIG. 1 is a schematic diagram of a mechanical arm obstacle avoidance mechanism;
FIG. 2 is a schematic diagram of a planar four degree-of-freedom robot;
FIGS. 3a-3d are diagrams of the avoidance of dynamic obstacles by the robot arm;
fig. 4a-4d are simulation graphs.
Detailed Description
The present invention will be described in further detail with reference to the accompanying drawings and detailed description.
Example (b):
the real-time obstacle avoidance method for the cooperative robot provided by the embodiment mainly comprises the following steps:
obstacle avoidance model construction
The obstacle avoidance schematic of the mechanical arm is shown in fig. 1. Because the mechanism information of the mechanical arm is consistent, a group of key points A can be uniformly selected on each connecting rod of the body of the mechanical armiAnd defines a radius d1So as to be at point AiIs the center of a sphere d1A set of a series of spheres of radius can completely surround the body of the robot arm; as shown on the left side of fig. 1; similarly, a group B is selected by acquiring the image information of the obstacle avoidance objectjAnd radius d2To wrap the obstacle; in order to avoid collision, a certain margin delta d is selected to be more than 0, and a safety distance d is defined as d1+d2+ Δ d, if all A's are made during the operation of the robotiAnd BjAll can make | AiBjAnd | ≧ d, collision can be avoided.
(II) mixing the inequality | AiBj| ≧ d describes the velocity layer:
definition D ═ aiBjI-d, the inequality of the velocity layer is:
Figure GDA0002449891890000031
wherein
Figure GDA0002449891890000032
Is that
Figure GDA0002449891890000033
A unit vector of (a); j. the design is a squareaiIs a key point A on the mechanical armiA corresponding Jacobian matrix; g (| D |) is a function of class k,
Figure GDA00024498918900000316
is a set of real numbers.
(III) defining the minimum speed norm as the redundancy analysis scheme
Setting an optimization index of
Figure GDA0002449891890000034
The energy consumption condition of the mechanical arm is described, if the speed of the mechanical arm is higher, the value is higher, the energy consumption is higher, and otherwise, the value is lower.
(IV) designing a motion controller of the mechanical arm:
let xd(t)、
Figure GDA0002449891890000035
For the desired position and velocity of the end effector of the robot arm, x (t), respectively, and the current position of the end effector, the PD controller is designed such that the angular velocity of the joints of the robot arm
Figure GDA0002449891890000036
The following formula is satisfied, so that the tail end execution of the mechanical arm can run according to a preset track
Figure GDA0002449891890000037
Wherein J (theta) is a Jacobian matrix of the mechanical arm, k is a normal number, theta,
Figure GDA0002449891890000038
respectively the joint angle and the angular velocity of the mechanical arm.
(V) modeling the physical constraints of the robotic arm
Mainly comprises joint angle amplitude limiting and angular velocity amplitude limiting. Definition of thetamin，
Figure GDA0002449891890000039
The lower and upper bounds of the mechanical arm joint angle and angular velocity, respectively, then the physical constraint is written as: thetamin≤θ(t)≤θmax，
Figure GDA00024498918900000310
And (VI) comprehensively considering the steps from two to five, and modeling the obstacle avoidance problem of the mechanical arm as follows:
min
Figure GDA00024498918900000311
s.t.
Figure GDA00024498918900000312
Figure GDA00024498918900000313
θmin≤θ(t)≤θmax(3d)
Figure GDA00024498918900000314
wherein
Figure GDA00024498918900000317
Is a set of real numbers.
And (seventhly) calculating the control quantity (namely the angular velocity instruction of the joint) in real time by adopting a recurrent neural network as follows:
Figure GDA0002449891890000041
Figure GDA0002449891890000042
Figure GDA0002449891890000043
wherein, oa >0，
Figure GDA0002449891890000049
Are dual variables.
Figure GDA0002449891890000044
The calculation method comprises the following steps: for each row of elements, if the element is greater than zero, then no modification is made, if the element is less than 0, then the element is made to be 0,
Figure GDA00024498918900000410
is a set of real numbers.
And sending the joint angular velocity control quantity of the robot arm obtained by solving to a manipulator controller, and controlling the manipulator to avoid the obstacle.
In the practical application process, as the method is mainly carried out on the mechanical arm controller, the method mainly comprises two stages:
an initialization stage:
initializing controller parameters k, α, oa, and obtaining preset mechanical arm key point information AiAnd its corresponding Jacobian matrix JaiThe expression of (1); key point of obstacle BiA safety distance d. The preset task information of the tail end of the mechanical arm is as follows: x is the number ofd(t)、
Figure GDA0002449891890000045
Initializing a dual variable λ1(0)＝0，λ2(0) Mechanical arm physical constraint of 0: thetamin，θmax，
Figure GDA0002449891890000046
The algorithm flow is as follows:
1. real-time measurement of an obstacle B by means of a measuring unit such as a cameraiAnd calculating the real-time speed thereof;
2. reading current state information of the mechanical arm: the number of the theta's is,
Figure GDA0002449891890000047
3. calculating the key point A by using thetaiCorresponding position, calculate JoAnd B; and updating lambda according to equation (4c)2
4. Obtaining the real-time position x of the mechanical arm end effector, and updating lambda according to the formula (4b)1
5. The joint angular velocity (i.e., the control command) is calculated from equation (4 a).
The method is further verified and explained below with reference to a simulation example:
a planar four-degree-of-freedom robot is selected as shown in fig. 2. The left side shows the basic structure of the mechanical arm and the selection method of the key points. Wherein A is1、A3、A5、A7Are respectively positioned at the center of each connecting rod of the mechanical arm, A2、A4、A6Is located at the joint. The right side shows the D-H parameter table for the robot arm.
The controller parameters are selected from oa-0.001, α -8, k-8, d-0.1 m, with the physical constraint of θmin＝-3rad，θmax＝3rad，
Figure GDA0002449891890000048
The K-type function is chosen to be G (| D |) -, 500| D |, "oa" represents a positive control gain;
defining the tail end task track of the robot as follows: x is the number ofd＝[0.4+0.1cos(0.5t)，0.4+0.1sin(0.5t)]T
The simulation time length is 20s, and the motion trail of a dynamic obstacle in the plane is as follows: b [ -0.1+0.01t, 0.3]T，
The obstacle radius is 0.05 m. The simulation results are shown in fig. 3 and 4. Fig. 3a-d are diagrams of the avoidance of dynamic obstacles by the robot arm, where the dark trace (large circle) is an estimate of the end effector indicating that the robot arm can perform operations on a given task, and the small circle is an obstacle indicating that the robot arm can perform real-time avoidance of dynamic obstacles. Fig. 4 is a simulation curve: the tracking error of the end effector to the expected track is shown in figure (a), and it can be known that the method provided by the patent can enable the end effector to complete a given task; in the graph (b), the distance between the key point and the obstacle is not less than the preset safe distance d, which is 0.1, in the process. (c) And (d) a joint angular velocity curve of the mechanical arm. Graphs (c) (d) show that the arm does not exceed the physical limits throughout the process
Therefore, the obstacle avoidance strategy provided by the method can complete the given task at the end and simultaneously realize the real-time obstacle avoidance, and can avoid the physical limit.
The above embodiments are only for illustrating the technical concept and features of the present invention, and the purpose thereof is to enable those skilled in the art to understand the contents of the present invention and implement the present invention accordingly, and not to limit the protection scope of the present invention accordingly. All equivalent changes or modifications made in accordance with the spirit of the present disclosure are intended to be covered by the scope of the present disclosure.

Claims (2)

1. A cooperative robot real-time obstacle avoidance method is characterized by comprising the following steps:
selecting a group of key points A on each connecting rod of the body of the mechanical armiAnd defines a radius d1So as to be at point AiIs the center of a sphere d1Set a of spheres of radius ═ { a ═ aiI 1., a } can completely surround the body of the robot arm;
acquiring image information of the position of the obstacle, and simplifying the acquired images of the mechanical arm and the position of the obstacle into a key point BjSo that point B is formedjIs the center of a sphere d2Set B ═ B consisting of a series of spheres of radiusiI 1.. b } can completely surround the obstacle;
inequality description | A for constructing and describing real-time obstacle avoidance of robotiBjL ≧ d, where d ═ d1+d2+ Δ d, Δ d > 0 is the distance margin and the inequality description is rewritten as an inequality description of the velocity layer:
definition D ═ aiBjI-d, the inequality of the velocity layer is:
Figure FDA0002449891880000011
wherein
Figure FDA0002449891880000012
Figure FDA0002449891880000013
Is that
Figure FDA0002449891880000014
A unit vector of (a); j. the design is a squareaiIs a key point A on the mechanical armiA corresponding Jacobian matrix; g (| D |) is a function of class k;
Figure FDA0002449891880000015
is a set of real numbers;
selecting the minimum speed norm as a redundancy analysis scheme, and optimizing the joint angular speed norm
Figure FDA0002449891880000016
Let xd(t)、
Figure FDA0002449891880000017
Respectively the expected position and speed of the end effector of the mechanical arm, x (t) is the current position of the end effector of the mechanical arm, so that the joint angular speed of the mechanical arm
Figure FDA0002449891880000018
Satisfying the following formula so that the tail end execution of the mechanical arm moves according to a preset track
Figure FDA0002449891880000019
Wherein J (theta) is a Jacobian matrix of the mechanical arm, k is a normal number, theta,
Figure FDA00024498918800000110
respectively the joint angle and the angular velocity of the mechanical arm;
the obstacle avoidance problem modeling for constructing the mechanical arm is as follows:
Figure FDA00024498918800000111
Figure FDA00024498918800000112
Figure FDA00024498918800000113
θmin≤θ(t)≤θmax(3d)
Figure FDA00024498918800000114
wherein,
Figure FDA00024498918800000115
θmin，
Figure FDA00024498918800000116
the lower bound and the upper bound of the joint angle and the angular speed of the mechanical arm are respectively;
Figure FDA00024498918800000117
is a set of real numbers;
and (4) carrying out optimization solution on the obstacle avoidance problem model of the mechanical arm to obtain the joint angular velocity control quantity of the mechanical arm of the robot, sending the joint angular velocity control quantity to a mechanical arm controller, and controlling the mechanical arm to avoid the obstacle.
2. The real-time obstacle avoidance method for the cooperative robot as claimed in claim 1, wherein the solving method comprises:
calculating the control quantity in real time by adopting a recurrent neural network as follows:
Figure FDA0002449891880000021
Figure FDA0002449891880000022
Figure FDA0002449891880000023
wherein,
Figure FDA0002449891880000024
is a dual variable;
Figure FDA0002449891880000025
the calculation method comprises the following steps: for each row of elements, if the element is larger than zero, no modification is carried out, and if the element is smaller than 0, the element is set to be 0;
Figure FDA0002449891880000026
is a set of real numbers.
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