CN116027791A - Robot formation control method based on formation integrity evaluation index - Google Patents
Robot formation control method based on formation integrity evaluation index Download PDFInfo
- Publication number
- CN116027791A CN116027791A CN202310127288.8A CN202310127288A CN116027791A CN 116027791 A CN116027791 A CN 116027791A CN 202310127288 A CN202310127288 A CN 202310127288A CN 116027791 A CN116027791 A CN 116027791A
- Authority
- CN
- China
- Prior art keywords
- formation
- robot
- error
- average center
- evaluation index
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Pending
Links
Images
Classifications
-
- Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
- Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
- Y02P—CLIMATE CHANGE MITIGATION TECHNOLOGIES IN THE PRODUCTION OR PROCESSING OF GOODS
- Y02P90/00—Enabling technologies with a potential contribution to greenhouse gas [GHG] emissions mitigation
- Y02P90/02—Total factory control, e.g. smart factories, flexible manufacturing systems [FMS] or integrated manufacturing systems [IMS]
Abstract
The invention provides a robot formation control method based on formation integrity evaluation indexes, and relates to the field of robot formation motion control. According to the method, the formation integrity evaluation index is calculated according to the weight of each error in an actual formation application scene by calculating the formation average center distance error of the actual formation and the ideal formation of the robot, the error of the average center distance sum of the robot and the robot angle error. Under the premise of keeping the position constraint of the virtual structure method, fusing the speed constraint, preferentially using the speed constraint with small operand as a formation motion control method, and calculating the formation integrity evaluation index of the robot in real time, when the formation motion error reaches a threshold value, switching the formation control method to the position constraint, eliminating the motion error, avoiding the position constraint adopted in the whole motion process, reducing the robot path planning times on the premise of ensuring the stability of formation, reducing the operand in the formation motion process, and more meeting the application requirements in the practical environment.
Description
Technical Field
The invention relates to the technical field of robot formation control, in particular to a robot formation control method based on formation integrity evaluation indexes.
Background
The formation control of the robot mainly adopts a pilot following method, a behavior-based method and a virtual structure method to ensure that formation integrity is kept in the movement process of the formation. The robot system formed by adopting the virtual structure method has a definite formation structure, is more convenient for controlling the formation of the robot to execute specific tasks, and can better analyze the movement behavior of the formation in the task planning stage. The multi-robot is regarded as a rigid integral virtual structure method, the robots do the same action, and the robot macroscopically represents that the integral robot moves, and the rigidity, namely the relative position, of the integral robot is kept unchanged. The virtual structure method may be regarded as a pilot following method in which the robot follows a corresponding virtual pilot. Due to the characteristics of the virtual structure method, the formation rigid structure is required to be maintained all the time in the operation process, and the calculation amount is large.
The robots formed by adopting the virtual structure method adopt position constraint in the whole process, each robot runs a complete target navigation algorithm to carry out path planning, thereby ensuring the stability of formation, and a large amount of position constraint information is needed, and as the number of robots in the formation increases, the constraint information which needs to be considered by the robots correspondingly increases, so that the operation amount increases, the real-time requirement is difficult to meet, and a certain limitation exists in practical application.
Disclosure of Invention
Aiming at the defects of the prior art, the invention provides a robot formation control method based on formation integrity evaluation indexes, which comprehensively evaluates formation integrity of a robot formation from factors such as formation average error, formation robot to average center distance and error and angle error, and switches speed constraint and position constraint according to the evaluation indexes, so that the integral operation amount is reduced on the premise of ensuring stable formation structure.
In order to solve the technical problems, the invention adopts the following technical scheme:
a robot formation control method based on formation integrity evaluation indexes comprises the following steps:
step 1: calculating an actual average center coordinate according to the position coordinates of the robots in the actual formation, and simultaneously calculating an average center coordinate under the ideal formation; calculating Euclidean distance between the two average center coordinates according to the two average center coordinates to obtain average center error;
step 2: respectively calculating Euclidean distances from actual coordinates to actual average center coordinates of all robots in formation, and summing; simultaneously calculating Euclidean distances from ideal coordinates to ideal average center coordinates of all robots in an ideal formation, and summing; the two distance sums are subjected to difference to obtain a distance sum error;
step 3: respectively calculating the difference between the actual yaw axis angle and the ideal yaw axis angle of each robot, and finally summing the difference values to obtain an angle error;
step 4: summing the average center error, the distance and the error and the angle error according to different weights to obtain a formation integrity evaluation index;
step 5: and judging that the machine adopts position constraint or speed constraint to carry out robot formation control according to the formation integrity evaluation index calculated in real time and a preset threshold value, so as to realize the formation control method based on the formation integrity evaluation index.
Further, the average center error E in the step 1 c Defined as the Euclidean distance between two average centers, i.e., the average center error;
in the map coordinate system, only the position coordinates of the robots are considered, each robot forms an n-polygon, and the vertex coordinates are (x i ,y i ) I=1, 2 … n, the average center C of the n-sided polygon having coordinates (x c ,y c ) Wherein
The actual position and the ideal position of the robot in the formation respectively form two polygons, and the average centers of the two polygons are respectively C and C'; average center error E c As shown in formula (1):
wherein, (x' i ,y′ i ) Vertex coordinates of the n-sided polygon are the ideal formation shape.
Further, the Euclidean distance from each robot coordinate to the average center coordinate in the step 2 and L are shown in a formula (2);
the average center distance and error of the formation robot to the average center are E L As shown in formula (3), wherein L and L 'are the sum of distances from the respective robot coordinates to the average center coordinates C and C' in the actual formation and the ideal formation, respectively;
E L ＝|L-L′| (3)。
further, in the step 3, the yaw angle is used to describe the direction of the head of the robot, and the actual yaw angle of the robot
∈[-π,π]And ideal yaw angle->
E of the difference e of (2) i As shown in formula (4);
angle error
As shown in formula (5);
further, the formation integrity evaluation index P in the step 4 is shown in formula (6), wherein P is a non-negative number, and the smaller P is, the closer the actual formation is to the ideal formation;
wherein, given weight q= [ Q ] 1 ,q 2 ,q 3 ] T ；q 1 ,q 2 ,q 3 Are all nonnegative numbers and respectively correspond to the average center error E C Error E of average center distance sum L Error of angle
Is a sensitive degree of (a).
Further, q 1 ,q 2 ,q 3 Scaling the specific values of (a) in equal proportion; q 1 ,q 2 ,q 3 The proportional relation of the data is determined by the running environment and the task requirements executed by formation, and the specific numerical value of the data is a corresponding numerical range set for facilitating later data processing.
Further, for the task environment, E C 、E L 、
Is determined, then q 1 ≤P/E C_max ，q 2 ≤P/E L_max ，/>
Q is 1 ,q 2 ,q 3 The proportional relation of->
Further, in the step 5, the speed constraint is preferentially used as the constraint condition of the formation during the movement process after the formation of the formation, and in this open loop control system, the formation cannot maintain a stable structure for a long time due to the existence of the accumulated error of the robot; and (3) introducing formation integrity evaluation indexes to quantify the loosening degree of formation of the robots, setting a proper threshold according to the running environment of the robots and the requirements of formation tasks, switching to a position constraint condition at proper time, and enabling each robot to move to a corresponding position in an ideal formation through path planning, so that accumulated errors can be eliminated, and switching to a speed constraint condition again.
Further, according to the speed constraint condition, in the formation travelling process, one robot is used as a lead to conduct path planning, a robot complete target point navigation algorithm is realized, the travelling of the robot formation is maintained by adopting speed constraint for other robots in the formation, the actual position of the robot subjected to speed constraint is only related to the initial pose and the subsequent speed control instruction of the robot, and is irrelevant to the positions of other robots in the formation, no global map feedback exists, and at the moment, the formation is kept to be in open-loop control; therefore, under the ideal condition of not considering the movement error of the robot, the robot can still ensure the stability of the formation of the robot only through the speed constraint after the formation of the formation.
Further, the robots in the formation are regarded as followers in the piloting following method under the position constraint condition, and each robot has a corresponding virtual navigator; the motion of the virtual navigator can be separated from the influence of the hardware of the robot and the actual friction factor, and all the virtual navigator can realize the motion under an ideal state, so that the formation formed by the virtual navigator is absolutely stable; the actual robot is used as a follower only needs to set the motion target pose of the robot as the real-time pose of the virtual navigator, path planning is carried out, a global map is used as pose information feedback, the formation is kept to be closed-loop control under the position constraint condition, the formation of the formation can be ensured to be complete all the time through the uninterrupted path planning of each robot, and therefore, the robot formation is a rigid whole for the outside, the internal structure of the robot formation is stable, and the robot formation is realized.
The beneficial effects of adopting above-mentioned technical scheme to produce lie in: according to the robot formation control method based on the formation integrity evaluation index, speed constraints are fused on the premise of keeping virtual structure method position constraints, and two constraint conditions are switched automatically through the formation integrity evaluation index. Finally, the number of path planning times of the robot can be reduced on the premise of ensuring the stability of formation, the operand in the formation movement process can be reduced, the functional tasks of the robot can be additionally increased, and the requirements in the actual environment are met.
Drawings
Fig. 1 is a flowchart of a robot formation control method based on a formation integrity evaluation index according to an embodiment of the present invention;
fig. 2 is a schematic diagram of an average center provided in an embodiment of the present invention.
Detailed Description
The following describes in further detail the embodiments of the present invention with reference to the drawings and examples. The following examples are illustrative of the invention and are not intended to limit the scope of the invention.
As shown in fig. 1, the method of this embodiment is as follows.
Step 1: as shown in fig. 2, the average center error is calculated, the dotted line is the ideal formation shape of the robot, the corresponding average center is C', the solid line is the actual formation shape of the robot, and the corresponding average center is C.
In the map coordinate system, only the position coordinates of the robots are considered, each robot can form an n-polygon, and the vertex coordinates are (x i ,y i ) I=1, 2 … n. The average center C of this n-sided polygon has coordinates (x c ,y c ) Wherein
Average center error E c Defined as the Euclidean distance between two average centers as shown in equation (1)
Wherein, (x' i ,y′ i ) The vertex coordinates of the n-sided polygon, the dashed pentagon of fig. 2, are the ideal formation shape.
Step 2: and (3) calculating the error of the distance sum from the formation robots to the average center, and calculating the distance sum L from each robot to the average center according to the average center obtained in the step (1), as shown in a formula (2).
The error of the sum of the average center distances of the formation robots is E L As shown in equation (3), where L and L 'are the sum of the distances of each robot from the average center C and C' in the actual formation and the ideal formation, respectively.
E L ＝|L-L′| (3)
Step 3: calculating an angle error, wherein in the process of any movement of the robot in the two-dimensional map, a yaw angle is used for describing the head direction of the robot, and the actual yaw angle of the robot
And ideal yaw angle->
E of the difference e of (2) i As shown in equation (4).
For the formation integrity evaluation index, more emphasis is placed on the analysis of the actual deviation of the robot, and the direction of the robot angle error has no influence on the evaluation index. Thus angle error
As shown in equation (5).
Step 4: and calculating formation integrity evaluation indexes according to the average center error, the distance and error, the angle error and the corresponding weight.
In the formation movement process of the robot, the actual influence weights of the position deviation and the angle deviation on the formation integrity are different, and the position deviation and the angle deviation have different sensitivities for different application scenes. Introducing a weight q= [ Q ] 1 ,q 2 ,q 3 ] T Wherein q is 1 ,q 2 ,q 3 Are all nonnegative numbers and respectively correspond to the average center error E C Error E of average center distance sum L Error of angle
Is a sensitive degree of (a).
The formation integrity evaluation index P is shown in formula (6), where P is a non-negative number, the smaller P, the closer the actual formation is to the ideal formation.
q 1 ,q 2 ,q 3 The proportional relationship between the three parameters affects the importance of the formation integrity index, thus q 1 ,q 2 ,q 3 The specific values of (c) may be scaled equally. q 1 ,q 2 ,q 3 The proportional relation of the data is determined by the running environment and the task requirements executed by formation, and the specific numerical value of the data can set a corresponding value range for facilitating later data processing.
For task environments, E C ,E L ,
Is determined, then q 1 ≤P/E C_max ，q 2 ≤P/E L_max ，q 3 ≤P//>
It can be deduced that the proportional relationship is +.>
Step 5: and judging that the machine adopts position constraint or speed constraint to carry out robot formation control according to the formation integrity evaluation index calculated in real time and a preset threshold value, so as to realize the formation control method based on the formation integrity evaluation index.
In the formation operation process adopting speed constraint, the movement speeds of all robots in the formation are kept consistent, and the relative speed between the robots in the formation is 0 under the condition of not considering errors, so that the robots can be considered to keep stable formation.
In the formation advancing process, one robot is used as a lead to conduct path planning, a robot complete target point navigation algorithm is achieved, other robots in the formation adopt speed constraint to maintain the advancing of the robot formation, the actual position of the robot constrained by the speed is only related to the initial pose and the subsequent speed control instruction of the robot, and is irrelevant to the positions of other robots in the formation, global map feedback is not needed, and at the moment, the formation is kept in open loop control. Therefore, under the ideal condition of not considering the movement error of the robot, the robot can still ensure the stability of the formation of the robot only through the speed constraint after the formation of the formation.
However, each robot in the actual robot formation may have different movement routes due to individual differences, and the actual movement conditions under the same movement command control are different from the ideal conditions due to the influence of the actual movement environment, so that accumulated errors may be generated. Finally, under the influence of accumulated errors, only robots which completely run a target point navigation algorithm in the formation can accurately reach an ideal target point, and other robots which are constrained by speed in the formation have position deviations in the movement process, so that the formation of the robot formation is loose and cannot reach the ideal target point, the formation structure of the formation is finally broken, and the formation stability cannot be maintained by the speed constraint alone.
And each robot in the formation maintains the stability of the formation by maintaining the stability of the relative position relationship inside the formation by adopting position constraint. Robots in a team can be considered as followers in a pilot following method, each robot having a corresponding virtual pilot. The motion of the virtual pilot can be separated from the influence of the hardware of the robot, the actual friction force and other factors, and all the virtual pilot can realize the motion under an ideal state, so that the formation formed by the virtual pilot is absolutely stable. The actual robot is used as a follower only needs to set the motion target pose of the robot as the real-time pose of the virtual navigator, path planning is carried out, a global map is used as pose information feedback, the formation is kept to be closed-loop control under the position constraint condition, the formation of the formation can be ensured to be complete all the time through the uninterrupted path planning of each robot, and therefore, the robot formation is a rigid whole for the outside, the internal structure of the robot formation is stable, and the robot formation is realized.
In the formation control method based on the integrity evaluation index, speed constraint is preferentially used as constraint condition of the formation in the movement process after the formation of the formation, and in the open loop control system, the formation cannot maintain a stable structure for a long time due to the existence of accumulated errors of robots. And (3) introducing formation integrity evaluation indexes to quantify the loosening degree of formation of the robots, setting a proper threshold according to the running environment of the robots and the requirements of formation tasks, switching to a position constraint condition at proper time, and enabling each robot to move to a corresponding position in an ideal formation through path planning, so that accumulated errors can be eliminated, and switching to a speed constraint condition again.
Finally, it should be noted that: the above embodiments are only for illustrating the technical solution of the present invention, and not for limiting the same; although the invention has been described in detail with reference to the foregoing embodiments, it will be understood by those of ordinary skill in the art that: the technical scheme described in the foregoing embodiments can be modified or some or all of the technical features thereof can be replaced by equivalents; such modifications and substitutions do not depart from the spirit of the corresponding technical solutions, which are defined by the scope of the appended claims.
Claims (10)
1. A robot formation control method based on formation integrity evaluation index is characterized in that: the method comprises the following steps:
step 1: calculating an actual average center coordinate according to the position coordinates of the robots in the actual formation, and simultaneously calculating an average center coordinate under the ideal formation; calculating Euclidean distance between the two average center coordinates according to the two average center coordinates to obtain average center error;
step 2: respectively calculating Euclidean distances from actual coordinates to actual average center coordinates of all robots in formation, and summing; simultaneously calculating Euclidean distances from ideal coordinates to ideal average center coordinates of all robots in an ideal formation, and summing; the two distance sums are subjected to difference to obtain a distance sum error;
step 3: respectively calculating the difference between the actual yaw axis angle and the ideal yaw axis angle of each robot, and finally summing the difference values to obtain an angle error;
step 4: summing the average center error, the distance and the error and the angle error according to different weights to obtain a formation integrity evaluation index;
step 5: and judging that the machine adopts position constraint or speed constraint to carry out robot formation control according to the formation integrity evaluation index calculated in real time and a preset threshold value, so as to realize the formation control method based on the formation integrity evaluation index.
2. The robot formation control method based on the formation integrity evaluation index according to claim 1, wherein: the average center error E in the step 1 c Defined as the Euclidean distance between two average centers, i.e., the average center error;
in the map coordinate system, only the position coordinates of the robots are considered, each robot forms an n-polygon, and the vertex coordinates are (x i ,y i ) I=1, 2 … n, the average center C of the n-sided polygon having coordinates (x c ,y c ) Wherein
The actual position and the ideal position of the robot in the formation respectively form two polygons, and the average centers of the two polygons are respectively C and C'; average center error E c As shown in formula (1):
wherein, (x' i ,y′ i ) Vertex coordinates of the n-sided polygon are the ideal formation shape.
3. The robot formation control method based on the formation integrity evaluation index according to claim 2, characterized in that: the Euclidean distance sum L from each robot coordinate to the average center coordinate in the step 2 is shown in a formula (2);
the average center distance and error of the formation robot to the average center are E L As shown in formula (3), wherein L and L 'are the sum of distances from the respective robot coordinates to the average center coordinates C and C' in the actual formation and the ideal formation, respectively;
E L ＝|L-L′| (3)。
4. a robot formation control method based on a formation integrity evaluation index according to claim 3, characterized in that: in the step 3, the yaw angle is used for describing the head direction of the robot, and the actual yaw angle of the robot
And ideal yaw angle->
E of the difference e of (2) i As shown in formula (4);
angle error
As shown in formula (5);
5. the robot formation control method based on the formation integrity evaluation index according to claim 4, wherein: the formation integrity evaluation index P in the step 4 is shown in a formula (6), wherein P is a non-negative number, and the smaller P is, the closer the actual formation is to the ideal formation;
wherein, given weight q= [ Q ] 1 ,q 2 ,q 3 ] T ；q 1 ,q 2 ,q 3 Are all nonnegative numbers and respectively correspond to the average center error E C Error E of average center distance sum L Error of angle
Is a sensitive degree of (a).
6. The robot formation control method based on the formation integrity evaluation index according to claim 5, wherein: q 1 ,q 2 ,q 3 Scaling the specific values of (a) in equal proportion; q 1 ,q 2 ,q 3 Is proportional to the operating environmentThe task requirements of formation execution are determined, and specific values thereof set corresponding value ranges for facilitating later data processing.
7. The robot formation control method based on the formation integrity evaluation index according to claim 6, wherein: e (E) C 、E L 、
Is determined, then q 1 ≤P/E C_max ，q 2 ≤P/E L_max ，/>
Q is 1 ,q 2 ,q 3 The proportional relation of->
8. The robot formation control method based on the formation integrity evaluation index according to claim 1, wherein: in the step 5, the speed constraint is preferentially used as the constraint condition of the formation in the movement process after the formation, and in the open loop control system, the formation cannot keep a stable structure for a long time due to the existence of the accumulated errors of the robot; and (3) introducing formation integrity evaluation indexes to quantify the loosening degree of formation of the robots, setting a proper threshold according to the running environment of the robots and the requirements of formation tasks, switching to a position constraint condition at proper time, and enabling each robot to move to a corresponding position in an ideal formation through path planning, so that accumulated errors can be eliminated, and switching to a speed constraint condition again.
9. The robot formation control method based on the formation integrity evaluation index according to claim 8, wherein: in the speed constraint condition, one robot is used as a lead to conduct path planning in the formation advancing process, a robot complete target point navigation algorithm is realized, other robots in the formation adopt speed constraint to maintain the advancing of the robot formation, the actual position of the robot constrained by the speed is only related to the initial pose and the subsequent speed control instruction of the robot, and is irrelevant to the positions of other robots in the formation, no global map feedback exists, and at the moment, the formation is kept in open loop control; therefore, under the ideal condition of not considering the movement error of the robot, the robot can still ensure the stability of the formation of the robot only through the speed constraint after the formation of the formation.
10. The robot formation control method based on the formation integrity evaluation index according to claim 8, wherein: the position constraint condition is that robots in formation are regarded as followers in a pilot following method, and each robot has a corresponding virtual pilot; the motion of the virtual navigator can be separated from the influence of the hardware of the robot and the actual friction factor, and all the virtual navigator can realize the motion under an ideal state, so that the formation formed by the virtual navigator is absolutely stable; the actual robot is used as a follower only needs to set the motion target pose of the robot as the real-time pose of the virtual navigator, path planning is carried out, a global map is used as pose information feedback, the formation is kept to be closed-loop control under the position constraint condition, the formation of the formation can be ensured to be complete all the time through the uninterrupted path planning of each robot, and therefore, the robot formation is a rigid whole for the outside, the internal structure of the robot formation is stable, and the robot formation is realized.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN202310127288.8A CN116027791A (en) | 2023-02-17 | 2023-02-17 | Robot formation control method based on formation integrity evaluation index |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN202310127288.8A CN116027791A (en) | 2023-02-17 | 2023-02-17 | Robot formation control method based on formation integrity evaluation index |
Publications (1)
| Publication Number | Publication Date |
|---|---|
| CN116027791A true CN116027791A (en) | 2023-04-28 |
Family
ID=86076041
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CN202310127288.8A Pending CN116027791A (en) | 2023-02-17 | 2023-02-17 | Robot formation control method based on formation integrity evaluation index |
Country Status (1)
| Country | Link |
|---|---|
| CN (1) | CN116027791A (en) |
-
2023
- 2023-02-17 CN CN202310127288.8A patent/CN116027791A/en active Pending
Similar Documents
| Publication | Publication Date | Title |
|---|---|---|
| CN110502032B (en) | Unmanned aerial vehicle cluster formation flying method based on behavior control | |
| CN110039542B (en) | Visual servo tracking control method with speed and direction control function and robot system | |
| Liang et al. | Leader-following formation tracking control of mobile robots without direct position measurements | |
| CN108594815B (en) | Staged wheeled robot moving path planning method | |
| Meier et al. | Towards robust online inverse dynamics learning | |
| CN107807069B (en) | Self-adaptive tracking control method and system for sea surface oil spill | |
| Ji et al. | Elastic tracker: A spatio-temporal trajectory planner for flexible aerial tracking | |
| CN113031621B (en) | Bridge crane safety obstacle avoidance path planning method and system | |
| CN113126644A (en) | Unmanned aerial vehicle three-dimensional track tracking method based on adaptive line-of-sight method | |
| CN111309002A (en) | Wheel type mobile robot obstacle avoidance method and system based on vector | |
| CN113093804B (en) | Unmanned ship formation control method and control system based on inversion sliding mode control | |
| CN112650217B (en) | Robot trajectory tracking strategy dynamic optimization method based on evaluation function | |
| Feng et al. | Image-based trajectory tracking through unknown environments without absolute positioning | |
| CN116027791A (en) | Robot formation control method based on formation integrity evaluation index | |
| Kim et al. | Single 2D lidar based follow-me of mobile robot on hilly terrains | |
| Wang et al. | Fuzzy-PI double-layer stability control of an online vision-based tracking system | |
| CN114378830B (en) | Robot wrist joint singular avoidance method and system | |
| CN112925323B (en) | Rule-based mobile robot speed adjusting method and system | |
| Özdemir et al. | Gap based elastic trees as a novel approach for fast and reliable obstacle avoidance for UGVs | |
| CN116117786A (en) | Method and system for planning track of mechanical arm under high visual visibility | |
| Fu et al. | Adaptive safety motion control for underactuated hovercraft using improved integral barrier lyapunov function | |
| CN113885514B (en) | AGV path tracking method and system based on fuzzy control and geometric tracking | |
| CN114967697A (en) | AGV path tracking method and system based on MPC control | |
| Gams et al. | Optimizing parameters of trajectory representation for movement generalization: robotic throwing | |
| CN108073162B (en) | Control method for realizing smooth motion of robot by inserting motion segment |
Legal Events
| Date | Code | Title | Description |
|---|---|---|---|
| PB01 | Publication | ||
| PB01 | Publication | ||
| SE01 | Entry into force of request for substantive examination | ||
| SE01 | Entry into force of request for substantive examination |