CN108297105B - Optimal trajectory planning method for task-level time of mechanical arm - Google Patents
Optimal trajectory planning method for task-level time of mechanical arm Download PDFInfo
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- CN108297105B CN108297105B CN201810042868.6A CN201810042868A CN108297105B CN 108297105 B CN108297105 B CN 108297105B CN 201810042868 A CN201810042868 A CN 201810042868A CN 108297105 B CN108297105 B CN 108297105B
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- B—PERFORMING OPERATIONS; TRANSPORTING
- B25—HAND TOOLS; PORTABLE POWER-DRIVEN TOOLS; MANIPULATORS
- B25J—MANIPULATORS; CHAMBERS PROVIDED WITH MANIPULATION DEVICES
- B25J11/00—Manipulators not otherwise provided for
- B25J11/005—Manipulators for mechanical processing tasks
- B25J11/0065—Polishing or grinding
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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 relates to a method for planning task-level time optimal trajectory of a mechanical arm, which is characterized by firstly planning a processing path trajectory between any two points; then rearranging the processing path track to obtain a task-level time optimal processing path track; and then, converting the task-level time optimal machining path track into a machining path track which can be executed by the grinding mechanical arm through the initial point repositioning. The optimization algorithm for rearranging the track path points adopts a simulated annealing algorithm. The scheme can not only meet the requirement of meeting the task-level collision avoidance track in polishing processing, but also meet the requirement of optimal processing total time, can be used for high-speed automatic production, and has remarkable economic benefit.
Description
Technical Field
The invention relates to a method for planning a task-level time optimal trajectory of a mechanical arm, in particular to a method for planning a motion trajectory of a mechanical arm with a plurality of discrete non-connected grinding areas.
Background
An important function of the intelligent manufacturing system is to automatically plan the task-level time optimal collision avoidance trajectory of the mechanical arm, which is directly related to the processing efficiency and the intelligent degree of the manufacturing system. After detecting the distribution of the stripe projections of a plurality of discrete non-contiguous grinding areas by means of a three-dimensional vision measuring system, the position of a certain number of machining path points can be determined on each grinding area in combination with the size of the grinding tool. The grinding of the surface of the workpiece can be completed as long as the grinding tool on the mechanical arm traverses the machining path points.
When a plurality of discrete non-contiguous abrasive regions on the workpiece surface require robotic arm abrading, a series of tool path points may be extracted from the abrasive regions, typically in conjunction with an abrading process, with the abrading tool beginning at the beginning of one abrasive region and ending at the end of the abrading process and then proceeding to another abrasive region until all abrasive regions are finished. In order to achieve the total time required for the entire grinding task, it is necessary to plan the total trajectory of the grinding robot for the entire grinding process.
Simulated annealing algorithm (SA) is derived from statistical physics and is an iterative combinatorial optimization algorithm introduced based on the similarity existing between the solid annealing process and the combinatorial optimization problem. SA is an extension of the local search algorithm that differs from local search in that the optimal state in the neighborhood is selected with some probability. Theoretically, it has been proved that it is a global optimal solution and approaches the optimal solution with a probability of 1, so the simulated annealing algorithm can be used to optimize the arrangement of the grinding tracks to obtain the task-level time optimal collision avoidance track planning.
Disclosure of Invention
The invention aims to plan a processing track with optimal task-level time of a polishing mechanical arm aiming at an area to be polished when an initial position of the polishing mechanical arm is given.
The invention provides a method for planning a task-level time optimal trajectory of a mechanical arm, which is characterized by comprising the following steps of:
step 1, planning a processing path track between any two points;
step 2, rearranging the track path points to obtain a task-level time optimal processing path;
and 3, converting the global optimal solution into a processing path which can be executed by the grinding mechanical arm by repositioning the starting point.
Further, step 1 comprises the following substeps:
step 11, obtaining point cloud data to be polished through a three-dimensional visual detection system;
step 12, initializing a collision-prevention path planner;
step 13, planning a collision avoidance path by adopting a BiTRRT collision avoidance path planning algorithm;
step 14, performing collision detection and mechanical arm track planning on the planned path;
step 15, repeating the step 13 and the step 14 within a set time, and storing all successfully planned paths;
and step 16, preferably selecting a collision avoidance track with optimal time.
Further, step 14 collision detection employs the FCL algorithm.
Further, step 14, the trajectory planning of the mechanical arm uses TRAC-IK to calculate an inverse kinematics solution of the redundant robot.
Further, step 14 inserts dense points on the planned collision avoidance path before computing the inverse kinematics solution for the redundant robot.
Furthermore, the optimization algorithm for rearranging the track path points in the step 2 adopts a simulated annealing algorithm, and comprises the following sub-steps:
step 21, initializing cooling schedule parameters, giving a variation range of each parameter, randomly selecting an initial path m0 in the range, and calculating a corresponding objective function E (m 0);
step 22, making a disturbance on the track point sequence to generate a new arrangement sequence, and calculating a corresponding objective function E (m) to obtain Δ E ═ E (m) -E (m 0);
step 23, executing an acceptance determination process; if Δ E <0, then the new model m is accepted; if Δ E ≦ 0, the new model m is accepted with probability P ═ exp (- Δ E/T), T being the current temperature. When the model is accepted, set m0 ═ m.
Step 24, repeatedly executing steps 22 and 23L times at the temperature T;
step 25, the temperature T is slowly lowered.
And 26, repeating the steps 24 and 25 until convergence is finished.
Further, the objective function E in step 21 is the objective function with the minimum total time.
Further, T decreases geometrically in step 25.
Further, the end condition in step 26 is T < 0.001.
Further, step 3 comprises the following substeps:
step 31, searching a point closest to the initial position of the mechanical arm in the optimal arrangement track path;
and step 32, taking the point closest to the initial position of the mechanical arm as a first position, and rearranging the path points in sequence.
Drawings
Figure 1 is a schematic view of a plurality of discrete non-contiguous abrasive regions processing paths.
FIG. 2 is a flow chart of time-optimal sub-trajectory planning.
FIG. 3 is a flow chart of a simulated annealing algorithm.
Detailed Description
Examples
In order to make the technical solution of the present invention clearer, the technical solution of the present invention will be described in further detail below with reference to the accompanying drawings.
Fig. 1 shows a plurality of discrete non-contiguous abrasive areas a1, a2 … … An and randomly generated machining paths distributed over the surface of a workpiece. From the enlarged detail view in the lower left corner of fig. 1, m machining path points, i.e., v, contained inside the nth region An to be ground can be seenn1,vn2,…,vnm. The processing task of the polishing robot arm refers to a process in which the end effector (polishing tool) starts from the start position P0, traverses the polishing start points, the polishing intermediate points and the polishing end points on all the polishing areas, and finally returns to the end position P0. It can be seen from fig. 1 that the workpiece surface is irregularly distributed with a plurality of grinding areas, which are surrounded by oval lines.
According to the scheme, the three-dimensional visual detection system on the automatic polishing system is used for obtaining the striped protrusions to be polished, and the three-dimensional coordinates of the points in the polishing areas are obtained by combining the size of the striped protrusions, the parameters of the polishing tool and the parameters of the polishing process. Setting a starting point P of a planning taskstartAnd a termination point PendAnd (3) starting the path planning by the sub-track planner with the optimal starting time. The specific flow chart is shown in fig. 2.
201, initializing a sub-planner, setting the planning time to be 8 seconds, and adopting a BiTRRT collision avoidance path planning algorithm;
202 represents the execution of path planning, if successful, 203, otherwise, re-planning;
and 203, collision detection and robot arm trajectory planning.
Dense points are inserted into the planned collision avoidance path, and the inverse kinematics solution of the redundant robot is calculated by adopting TRAC-IK, so that the success rate of track planning is improved, the calculation time of the inverse solution is reduced to a certain extent, and more collision avoidance tracks can be obtained within the same time. This example uses the inverse jacobian method to run two inverse kinematics algorithms, namely KDL and SQP, simultaneously. By default, the inverse kinematics solution computation search ends immediately when either of these algorithms gets an answer.
The collision detection uses the FCL algorithm. To calculate the static barrier cost, euclidean distance variation (EDT) and geometric collision detection are used. This embodiment divides the workspace into a three-dimensional grid of voxels and pre-computes the distance of each voxel from the nearest static obstacle boundary. Further, the shape of the robot is approximated by using a set of overlapping spheres.
And 204, storing the current collision avoidance track data, adding one to a counter of successful planning times, checking whether the consumed time exceeds a 201 set value, if so, finishing the operation of the planning device, storing the track Q into a container, and if not, repeating 201-204.
205 denotes selecting a time-optimal collision avoidance sub-track.
The returned tracks in the container are acceptable solutions, and for the same planning task, a plurality of different collision avoidance tracks can be obtained. In order to evaluate the performance of the planned collision avoidance trajectories and select a collision avoidance trajectory with the optimal time, the present embodiment uses an evaluation function of the collision avoidance trajectory. The collision avoidance trajectory Q is defined hereiHas an evaluation function of
And is
Where i ∈ [1, M ], M denotes the number of collision avoidance trajectories obtained in a given time period.
The optimum collision avoidance trajectory is then the evaluation value F of the trajectoryoptimalTake the minimum value fminThe trajectory of time, namely:
through the steps, the time optimal collision avoidance sub-track is obtained, and the time optimal collision avoidance sub-track corresponds to the track points in the n polishing areas in the graph 1. The sum of the processing time of all the grinding areas is fixed, the optimization of the collision avoidance trajectory is not needed, but different total processing time can be obtained by traversing the grinding areas according to different sequences, and the direction of the black arrow in fig. 1 is the moving path of the grinding tool from one grinding area to another grinding area. Next, a simulated annealing algorithm (SA) is used to optimize the task-level total time-minimized path.
Assuming a given sanding area v1,v2,…,vr. Grinding tool initial positions P0 and n-1 are located at the machining path points v at both ends of the grinding area11,v1m,v21,v2n,…,vr1,vroThese points are denoted as pi1,π2,…,πn. From P0, the grinding tool enters the grinding area from the initial point of the grinding area in sequence, finishes grinding, then exits from the end point to enter the next grinding area, and returns to P0 after finishing all grinding tasks.
Thus, one solution to the planned task-level collision avoidance trajectory can be expressed as a circular arrangement of sub-trajectories between any two points
π＝(π1,π2,…,πn)
Can also be expressed as
π1→π2→…→πn→π1
Is determined by the one or more of the paths of,
πi(1. ltoreq. i.ltoreq.n) is the point that passes through the ith in the path. Obviously, satisfy
πi≠πjThe solution is a feasible solution when i ≠ j.
The set of all feasible solutions constitutes a solution space S of
S ═ permutation of all cycles of n points }
The total duration of the collision avoidance trajectory during the non-machining process is
Thus, the objective function of the task-level time optimal trajectory planning problem can be obtained as
The optimization of the grinding mechanical arm to a group of collision-avoiding tracks is converted into the minimization of the objective function (3) by optimizing the grinding mechanical arm to the problem that each point passes through only once and the total time is shortest, and the optimization process can be realized by a simulated annealing algorithm.
FIG. 3 is a flow chart of a simulated annealing algorithm, described in detail below:
301 denotes model initialization, giving the variation range of each parameter of the model, randomly selecting an initial model m0 within the range, and calculating the corresponding objective function E (m 0);
302, making a perturbation on the track point sequence, generating a new arrangement sequence, and calculating a corresponding objective function E (m) to obtain Δ E ═ E (m) — E (m 0);
and 303 denotes an acceptance determination process. If Δ E <0, then the new model m is accepted. If Δ E ≦ 0, the new model m is accepted with probability P ═ exp (- Δ E/T), T being the current temperature. When the model is accepted, setting m0 ═ m;
304 represents that the perturbation and acceptance determination process is repeated for L times at the temperature T, namely, the steps are repeatedly executed for 302 and 303L times;
305 denotes a slow decrease in temperature T, where T decreases geometrically, T ═ T × q, q ═ 0.92.
306 represent repetitions 304,305 until T <0.001 converges.
After the steps are completed, the grinding tool can be obtained to traverse all grinding points v from any point11,v12,v13,…,vn1,vn2,…,vnmThis ensures that machining according to such a trajectory takes the least time. But processing pathThe arrangement of radial points cannot be used directly by a grinding robot arm. In actual production, the default position P0 of the arm grinding tool is usually fixed, so P0 is required as the starting and ending positions of the machining path. Therefore, it is necessary to search out the nearest position Mu corresponding to P0 in the original arrangement from these points and place it at the first position of the new arrangement N, and move the other points in sequence to obtain the final processing path that the robot arm can execute.
The scheme can meet the requirement of meeting the task-level collision avoidance track in polishing processing, meets the optimal total time of processing the track, can be used for high-speed automatic production, and has remarkable economic benefit.
It should be understood that the above-mentioned embodiments are only for illustrating the technical concept and features of the present invention, and the purpose of the present invention is to enable those skilled in the art to understand the technical scheme of the present invention and implement the technical scheme accordingly, and the protection scope of the present invention is not limited thereby. Especially, in the process of rearranging and optimizing the planned track, the simulated annealing algorithm should not be taken as a limitation, and other algorithms capable of realizing the optimizing function, such as a genetic algorithm, should be regarded as the protection scope of the invention. Without departing from the principles of the invention, several improvements and optimizations may be made, which should also be considered as the scope of protection of the invention.
Claims (7)
1. A method for planning a task-level time optimal trajectory of a mechanical arm is characterized by comprising the following steps:
step 1, planning a processing path track between any two points;
the step 1 comprises the following substeps:
step 11, obtaining point cloud data to be polished through a three-dimensional visual detection system;
step 12, initializing a collision-prevention path planner;
step 13, planning a collision avoidance path by adopting a BiTRRT collision avoidance path planning algorithm;
step 14, performing collision detection and mechanical arm track planning on the planned path;
step 15, repeating the step 13 and the step 14 within a set time, and storing all successfully planned paths;
step 16, selecting a collision avoidance track with optimal time;
step 2, rearranging the processing path tracks to obtain task-level time optimal processing path tracks;
the optimization algorithm for rearranging the track path points in the step 2 adopts a simulated annealing algorithm, and comprises the following substeps:
step 21, initializing cooling schedule parameters, giving a variation range of each parameter, randomly selecting an initial path m0 in the range, and calculating a corresponding objective function E (m 0);
step 22, making a disturbance on the track point sequence to generate a new arrangement sequence, and calculating a corresponding objective function E (m) to obtain Δ E ═ E (m) -E (m 0);
step 23, executing an acceptance determination process; if Δ E <0, then the new model m is accepted; if delta E is less than or equal to 0, the new model m is received according to the probability P ═ exp (-delta E/T), and T is the current temperature;
when the model is accepted, setting m0 ═ m;
step 24, repeatedly executing steps 22 and 23L times at the temperature T;
step 25, slowly reducing the temperature T;
step 26, repeating steps 24 and 25 until convergence is finished;
step 3, repositioning the starting point, and converting the task-level time optimal machining path track into a machining path track which can be executed by the polishing mechanical arm;
the step 3 comprises the following substeps:
step 31, searching a point closest to the initial position of the mechanical arm in the optimal arrangement track path;
and step 32, taking the point closest to the initial position of the mechanical arm as a first position, and rearranging the path points in sequence.
2. The method for planning a task-level time-optimal trajectory of a robotic arm of claim 1, wherein the sub-step 14 collision detection employs an FCL algorithm.
3. The method for task-level time-optimal trajectory planning for a robotic arm of claim 1, wherein said substep 14 comprises calculating an inverse kinematics solution for the redundant robot using TRAC-IK.
4. A robot arm task-level time-optimal trajectory planning method according to claim 3, characterized in that the sub-step 14 inserts dense points on the planned collision avoidance path before calculating the inverse kinematics solution of the redundant robot.
5. The method for planning a task-level time-optimal trajectory of a mechanical arm according to claim 1, wherein the objective function E in the step 21 is an objective function with a minimum total time.
6. The method for planning the task-level time-optimal trajectory of the mechanical arm according to claim 1, wherein T is reduced geometrically in the step 25.
7. The method for planning a task-level time-optimal trajectory of a mechanical arm according to claim 1, wherein the condition for ending in step 26 is T < 0.001.
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| CN110196590B (en) * | 2019-04-23 | 2021-12-14 | 华南理工大学 | Time optimal trajectory planning method for robot path tracking |
| CN111216124B (en) * | 2019-12-02 | 2020-11-06 | 广东技术师范大学 | Robot vision guiding method and device based on integration of global vision and local vision |
| WO2021253391A1 (en) | 2020-06-19 | 2021-12-23 | 浙江大学 | Method of using robotic arm to complete non-repeatable covering task with the minimum number of lifts |
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