CN113478476B - Method for planning path of mechanical arm - Google Patents
Method for planning path of mechanical arm Download PDFInfo
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- CN113478476B CN113478476B CN202110616257.XA CN202110616257A CN113478476B CN 113478476 B CN113478476 B CN 113478476B CN 202110616257 A CN202110616257 A CN 202110616257A CN 113478476 B CN113478476 B CN 113478476B
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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 invention belongs to the technical field of robot control, and particularly relates to a planning method for a path of a mechanical arm. The planning method for the path of the mechanical arm enables the mechanical arm to move in a relatively optimal mode. The main process is to construct a cost function of the path, randomly generate the path, optimize the path by using a nonlinear optimization method and solve extremum, and select the optimal path in each group to input the mechanical arm. The path planning method provided by the invention has the advantages that the movement of the mechanical arm of the robot has short movement distance, long distance from an unworkable area, small maximum speed and acceleration and the like, the path planning of the mechanical arm is reasonable and reliable, and the efficiency and the safety of the robot for completing tasks are improved.
Description
Technical Field
The invention belongs to the technical field of robot control, and particularly relates to a planning method for a path of a mechanical arm.
Background
In the motion process of the robot, the path planning of the mechanical arm is one of the most important control algorithms, and with the improvement of the motion requirement of the robot, the requirements of simultaneously carrying out high-efficiency movement, avoiding the kinematic singular points of the mechanical arm and the like become one of the most important problems of the current path planning of the mechanical arm. Many studies and patents have been made heretofore about path planning algorithms, but most focus on one aspect of the above-described problem.
Disclosure of Invention
The invention aims to provide a planning method for a path of a mechanical arm, which aims to overcome the defects in the prior art, comprehensively consider the length, the arrival speed and more targets for avoiding singular points of the path of the mechanical arm, and find out the optimal path of the mechanical arm.
The invention provides a planning method of a mechanical arm path, which comprises the following steps:
(1) Constructing a cost function L(s) of a mechanical arm path to be planned:
wherein s is any path of the mechanical arm, l(s) is the total length of the path s, q i is the displacement of the ith degree of freedom of the mechanical arm at any point in the path s, n is the total number of degrees of freedom, And/>The square of the velocity and acceleration of the displacement of the ith degree of freedom,/>, respectivelyThe coordinate of the displacement singular point of the ith degree of freedom of the mechanical arm; the four terms in the formula respectively represent the total length, the maximum speed and the maximum acceleration of the tail end movement of the mechanical arm and the inverse number of the distance between the mechanical arm and the non-working area of the mechanical arm, and k 1、k2、k3 and k 4 are weighted average parameters of the four terms in the formula; k 1、k2、k3 and k 4 are set manually in advance;
(2) Taking an initial position of a mechanical arm to be planned as a starting point of a planned path, taking a target position of the mechanical arm as an end point of the planned path, randomly selecting a plurality of intermediate points between the starting point and the end point, and obtaining a smooth curve s by using a cubic spline interpolation method, wherein the curve s is taken as the initial planned path;
(3) According to the cost function of the step (1), optimizing the initial planning path s of the step (2) by adopting an interior point method to obtain a path s * which enables the cost function to be locally optimal:
s*＝argmin L(s)
(4) Judging any point on the local optimal path s *, if any point falls in the area which is in contact with the known object, canceling the local optimal path s *, returning to the step (2), if any point falls in the area which is in contact with the known object, reserving the local optimal path s *, and performing the step (5);
(5) Setting the circulation times, repeating the steps (2) - (4) to obtain a plurality of local optimal paths s *, and selecting a path with the smallest Pricing value function from the plurality of local optimal paths s * as a final mechanical arm planning path.
The planning method for the path of the mechanical arm enables the mechanical arm to move in a relatively optimal mode. The main process is to construct a cost function of the path, randomly generate the path, optimize the path by using a nonlinear optimization method and solve extremum, and select the optimal path in each group to input the mechanical arm. The path planning method provided by the invention has the advantages that the movement of the mechanical arm of the robot has short movement distance, long distance from an unworkable area, small maximum speed and acceleration and the like, the path planning of the mechanical arm is reasonable and reliable, and the efficiency and the safety of the robot for completing tasks are improved.
Drawings
Fig. 1 is a flow chart of a planning method for a path of a mechanical arm according to the present invention.
Detailed Description
The flow chart of the planning method of the mechanical arm path provided by the invention is shown in figure 1, and the method comprises the following steps:
(1) Constructing a cost function L(s) of a mechanical arm path to be planned:
wherein s is any path of the mechanical arm, l(s) is the total length of the path s, q i is the displacement of the ith degree of freedom of the mechanical arm at any point in the path s, n is the total number of degrees of freedom, And/>The square of the velocity and acceleration of the displacement of the ith degree of freedom,/>, respectivelyCoordinates of a displacement singular point (i.e., an inoperable position of the mechanical arm) of the ith degree of freedom of the mechanical arm; the four terms in the formula respectively represent the total length, the maximum speed and the maximum acceleration of the tail end movement of the mechanical arm and the inverse number of the distance between the mechanical arm and the non-working area of the mechanical arm, and k 1、k2、k3 and k 4 are weighted average parameters of the four terms in the formula; k 1、k2、k3 and k 4 are set in advance by a person in accordance with the planning accuracy and the like, and k 1＝1、k2＝ 3、k3 =3 and k 4 =0.003 in one embodiment of the present invention.
(2) Taking an initial position of a mechanical arm to be planned as a starting point of a planned path, taking a target position of the mechanical arm as an end point of the planned path, randomly selecting a plurality of intermediate points between the starting point and the end point, and obtaining a smooth curve s by using a cubic spline interpolation method, wherein the curve s is taken as the initial planned path;
(3) According to the cost function of the step (1), optimizing the initial planning path s of the step (2) by adopting an interior point method to obtain a path s * which enables the cost function to be locally optimal:
s*＝argmin L(s)
The meaning of the local optimal path s * in the step corresponding to the four cost functions in the step (1) is that the total distance of the movement of the tail end of the mechanical arm is small, the maximum speed is small, the maximum acceleration is small and the distance from the non-working area is far.
(4) Judging any point on the local optimal path s *, if any point falls in the area which is in contact with the known object, canceling the local optimal path s *, returning to the step (2), if any point falls in the area which is in contact with the known object, reserving the local optimal path s *, and performing the step (5);
(5) Setting the circulation times, repeating the steps (2) - (4) to obtain a plurality of local optimal paths s *, and selecting a path with the smallest Pricing value function from the plurality of local optimal paths s * as a final mechanical arm planning path.
In this specification, the invention has been described with reference to specific embodiments thereof. It will be apparent that various modifications and variations can be made without departing from the spirit and scope of the invention. The specification and drawings are, accordingly, to be regarded in an illustrative rather than a restrictive sense.
Claims (1)
1. The planning method of the mechanical arm path is characterized by comprising the following steps:
(1) Constructing a cost function L(s) of a mechanical arm path to be planned:
wherein s is any path of the mechanical arm, l(s) is the total length of the path s, q i is the displacement of the ith degree of freedom of the mechanical arm at any point in the path s, n is the total number of degrees of freedom, And/>The square of the velocity and acceleration of the displacement of the ith degree of freedom,/>, respectivelyThe coordinate of the displacement singular point of the ith degree of freedom of the mechanical arm; the four terms in the formula respectively represent the total length, the maximum speed and the maximum acceleration of the tail end movement of the mechanical arm and the inverse number of the distance between the mechanical arm and the non-working area of the mechanical arm, and k 1、k2、k3 and k 4 are weighted average parameters of the four terms in the formula; k 1、k2、k3 and k 4 are set manually in advance;
(2) Taking an initial position of a mechanical arm to be planned as a starting point of a planned path, taking a target position of the mechanical arm as an end point of the planned path, randomly selecting a plurality of intermediate points between the starting point and the end point, and obtaining a smooth curve s by using a cubic spline interpolation method, wherein the curve s is taken as the initial planned path;
(3) According to the cost function of the step (1), optimizing the initial planning path s of the step (2) by adopting an interior point method to obtain a path s * which enables the cost function to be locally optimal:
s*＝argmin L(s)
The meaning of the local optimal path s * in the step corresponding to the four cost functions in the step (1) is that the total distance of the movement of the tail end of the mechanical arm is small, the maximum speed is small, the maximum acceleration is small and the distance from the non-working area is far;
(4) Judging any point on the local optimal path s *, if any point falls in the area which is in contact with the known object, canceling the local optimal path s *, returning to the step (2), and if any point does not fall in the area which is in contact with the known object, reserving the local optimal path s *, and performing the step (5);
(5) Setting the circulation times, repeating the steps (2) - (4) to obtain a plurality of local optimal paths s *, and selecting a path with the smallest Pricing value function from the plurality of local optimal paths s * as a final mechanical arm planning path.
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Citations (6)
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| US8972057B1 (en) * | 2013-01-09 | 2015-03-03 | The Boeing Company | Systems and methods for generating a robotic path plan in a confined configuration space |
| CN108621157A (en) * | 2018-04-27 | 2018-10-09 | 上海师范大学 | Mechanical arm energetic optimum trajectory planning control method and device based on model constraint |
| CN109571466A (en) * | 2018-11-22 | 2019-04-05 | 浙江大学 | A kind of seven freedom redundant mechanical arm dynamic obstacle avoidance paths planning method based on quick random search tree |
| CN109877838A (en) * | 2019-03-25 | 2019-06-14 | 重庆邮电大学 | Time optimal mechanical arm method for planning track based on cuckoo searching algorithm |
| CN111251297A (en) * | 2020-02-20 | 2020-06-09 | 西北工业大学 | Double-arm space robot coordinated path planning method based on random sampling |
| CN112809665A (en) * | 2020-12-16 | 2021-05-18 | 安徽工业大学 | Mechanical arm motion planning method based on improved RRT algorithm |
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| Publication number | Priority date | Publication date | Assignee | Title |
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| CN109202904B (en) * | 2018-09-30 | 2020-10-20 | 湘潭大学 | Method and system for determining motion path of mechanical arm |
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Patent Citations (6)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US8972057B1 (en) * | 2013-01-09 | 2015-03-03 | The Boeing Company | Systems and methods for generating a robotic path plan in a confined configuration space |
| CN108621157A (en) * | 2018-04-27 | 2018-10-09 | 上海师范大学 | Mechanical arm energetic optimum trajectory planning control method and device based on model constraint |
| CN109571466A (en) * | 2018-11-22 | 2019-04-05 | 浙江大学 | A kind of seven freedom redundant mechanical arm dynamic obstacle avoidance paths planning method based on quick random search tree |
| CN109877838A (en) * | 2019-03-25 | 2019-06-14 | 重庆邮电大学 | Time optimal mechanical arm method for planning track based on cuckoo searching algorithm |
| CN111251297A (en) * | 2020-02-20 | 2020-06-09 | 西北工业大学 | Double-arm space robot coordinated path planning method based on random sampling |
| CN112809665A (en) * | 2020-12-16 | 2021-05-18 | 安徽工业大学 | Mechanical arm motion planning method based on improved RRT algorithm |
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