CN108196540A - A kind of method for improving artificial physics avoidance smooth trajectory degree using second order gradient information - Google Patents
A kind of method for improving artificial physics avoidance smooth trajectory degree using second order gradient information Download PDFInfo
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Abstract
The invention discloses a kind of methods for improving artificial physics avoidance smooth trajectory degree using second order gradient information, belong to robotic technology field.The present invention is rotated in the avoidance path of robot by First-order Gradient descent direction, so as to improve the method for robot obstacle-avoiding path smooth degree by the dynamic regulation of parameter towards second order Gauss direction.The moving direction of robot is adjusted using the second order gradient information of conservative force field, while the performance further to improve original algorithm is adjusted by the dynamic to parameter.Compared with original artificial physics method, robot obstacle-avoiding path that institute's extracting method of the present invention obtains is more smooth, by the speed of barrier zone faster.This method is to solve the guiding of robot mobile route and the effective technical way of obstacle avoidance under narrow space, can also be applied to the technical fields such as airborne aircraft routeing, automatic driving vehicle guiding.
Description
Technical field
The present invention proposes a kind of method for improving artificial physics avoidance smooth trajectory degree using second order gradient information, belongs to
Robotic technology field.
Background technology
Robot can encounter various obstacles or infeasible region during autonomous, thus need to have in real time
The ability of urgent avoidance.Artificial physics method is to solve for a kind of effective method of robot obstacle-avoiding problem, and it is multiple that it is not required to construction
Miscellaneous potential field function, the directly effect to robot construction physical vlan power, thus it is simpler, and with clearly physics
Meaning.
Consider that ground robot is free on two dimensional surface, dynamic characteristic is described by following differential equation group：
Position coordinates of the p=(x, y) for robot, v=(v in formulax,vy) be robot velocity vector, Acceleration Control
Input u=(ax,ay) represent that the control of robot inputs, play the role of controlling robot moving direction.
Robot has two class basic act of obstacle avoidance and target search towards in target moving process.Wherein, mesh
Mark search behavior is provided by robot by the attraction that target point applies, and is moved for guided robot towards designated position.
In artificial physics method, the attraction of robot is applied to using newton law of universal gravitation calculating target, it is as follows
In formula, | | probot-pgoal| | it is distance of the robot to target point,It represents and refers to from robot location
To the unit vector of target point, GgoalGravitational constant for target point.
The repulsive force that the obstacle avoidance behavior of robot is applied to robot by barrier provides, for guided robot tune
The whole direction of motion is to avoid barrier, the virtual repulsive force of the similary form calculus robot using newton law of universal gravitation,
It is as follows
In formula, | | probot-pobs| | for the distance of robot to barrier, useIt represents to be directed toward machine from barrier
The unit vector of people, RrepFor the sphere of action of repulsive force, when robot and barrier are close to a certain extent,
It can be by the repulsive interaction of barrier.
In addition, rate limit link is introduced to robot | | v | |≤vmax.Meanwhile robot is also by virtual frictional force
Effect, have
F=-fv (4)
To sum up, the control action that artificial physics method is acted in robot is made of three parts, i.e.,
U=Fatt+∑Frep+f (5)
But in existing artificial physics method, active force that robot is subject to along corresponding gravitational field negative ladder
Spend direction.This method has a drawback in that, when robot is close to barrier or when passing through gallery, robot can be
It is swung left and right under the guiding of active force, generates serious oscillation.This defect can cause robot make largely It is not necessary to
Maneuver dramatically increases time and the energy expenditure of tasks carrying.
For the present invention for artificial physics method in notable defect present on handling machine people's avoidance problem, design utilizes guarantor
The second order gradient information in the field of force is kept to adjust the moving direction of robot, while adjust further to change by the dynamic to parameter
It is apt to the performance of original algorithm.Compared with original artificial physics method, the robot obstacle-avoiding path that institute's extracting method of the present invention obtains is more
Add it is smooth, by the speed of barrier zone faster.This method is to solve the guiding of robot mobile route and obstacle under narrow space
The effective technical way evaded can also be applied to the technical fields such as airborne aircraft routeing, automatic driving vehicle guiding.
Invention content
The object of the present invention is to provide a kind of sides for improving artificial physics avoidance smooth trajectory degree using second order gradient information
Method.It is a kind of dynamic regulation by parameter, by the avoidance path of robot by First-order Gradient descent direction towards second order Gauss
Direction rotates, so as to improve the method for robot obstacle-avoiding path smooth degree.The method can eliminate original artificial physics method and exist
The defects of easily acutely being shaken close to barrier or when passing through gallery, and the unusual avoidance direction brought of Gaussian matrix can be overcome
Intangibility, so as to calculate best avoidance direction for robot.The method can also be applied to solve in airborne aircraft, the water surface
The avoidance problem of the intelligent bodies such as naval vessels.
The technical solution adopted by the present invention improves artificial physics avoidance smooth trajectory degree to be a kind of using second order gradient information
Method, this method using artificial physics power second order gradient information calculating robot avoidance direction, kept away with improving robot
Hinder path smooth degree, specific implementation process is as follows：
Determine the initial coordinate p of robotrobot(0)=(x0,y0) and coordinate of ground point pgoal=(xgoal,ygoal), machine
People's maximum movement speed vmax, target point gravitational constant Ggoal, obstacle repulsive force sphere of action Rrep, obstacle repulsion coefficient Gobs, it is empty
The position of quasi-frictional coefficient f and each barrier, (x0,y0) for initial coordinate, (xgoal,ygoal) it is coordinate of ground point.
Step 1：According to robot current location probotWith aiming spot pgoalThe distance between and relative bearing, meter
Calculate the virtual attraction F that robot is subject toattEffect, FattCalculating it is as follows,
Step 2：Gaussian matrix G (p, F of the calculating robot in target gravitational fieldatt), Gaussian matrix G (p, Fatt) meter
Calculation mode is as follows,
In formula, FattFor virtual attraction FattVector representation, Fatt,xAnd Fatt,yRespectively virtual attraction force vector Fatt
Component on x directions and y directions.
Step 3：According to G (p, Fatt) whether it is positive definite matrix, parameter ν is adjusted, and it is as follows to calculate inverse matrix
B(p,Fatt)=(G (p, Fatt)+ν·I)-1 (8)
I in formula is unit matrix.
Step 4：Calculating robot arrives the distance between peripheral obstacle, if the minimum of robot and i-th of barrier
Distance | | probot-pobs,i| | less than Rrep, pobs,iRepresent the position of i-th of barrier, then robot is by i-th barrier
Repulsive force, the F of i-th of barrierrep,iRepulsive force calculation is as follows
In formula,For robot to the distance of i-th of barrier, useIt represents from i-th of obstacle
Object is directed toward the unit vector of robot.
Step 5：Gaussian matrix G (p, F of the calculating robot in i-th of barrier repels the field of forcerep,i), calculation
It is as follows
In formula,WithRespectively virtual attraction force vector Frep,iComponent on x directions and y directions.
Step 6：According to G (p, Frep,i) whether it is positive definite matrix, parameter ν is adjusted, and it is as follows to calculate inverse matrix
B(p,Frep,i)=(G (p, Frep,i)+ν·I)-1 (11)
I in formula is unit matrix.
Step 7：The virtual frictional force effect f=-fv that calculating robot is subject to.
Step 8：The effect of each power of summary, the control input of calculating robot are as follows
Step 9：Robot controlled quentity controlled variable in formula (12) is updated in robot motion equation, updates the speed of robot
Degree and position.
Step 10：Judge whether robot reaches target point, if having reached, robot stop motion；If not reaching,
Back to step 1.
Parameter ν is required to obtain according to following S1-S4：
S1：If matrix G+ ν I are positive definite, then enable ν=ν/2, go to S3；Otherwise, the ν of ν=4 is enabled, goes to S2.
S2：If matrix G+ ν I are positive definite, then go to S4；Otherwise, back to S1.
S3：If matrix G+ ν I are positive definite, then back to S1；Otherwise, the ν of ν=2 is enabled, goes to S4.
S4：Parameter adjustment terminates, and obtains the value of parameter ν.
The present invention proposes a kind of method for improving artificial physics avoidance smooth trajectory degree using second order gradient information.The party
Method principle is simple, and control parameter is few, it is easy to accomplish, robot can be made with more smooth track avoiding obstacles.Especially
It is acutely shaken close to barrier or when passing through gallery, original artificial physics method can be improved being easy to cause robot
The defects of, so that robot can quickly reach target point, the time of consumption is less.The present invention can efficiently solve machine
The obstacle avoidance problem of device people, it can also be used to other pahtfinder hard planning problems.
Description of the drawings
For Fig. 1 in more space with obstacle, institute's extracting method of the present invention obtains the comparison diagram of robot motion track with original method.
For Fig. 2 when passing through gallery, institute's extracting method of the present invention obtains the comparison of robot motion track with original method
Figure.
The partial enlarged view of Fig. 3 Fig. 2.
Specific embodiment
Institute Tilly of the present invention is described below by specific example to be put down with second order gradient information improvement artificial physics avoidance track
The embodiment of the method for slippery, and verify the performance of institute's extracting method of the present invention.Software for calculation used in example is MATLAB
2009a, detailed implementation steps are following (length unit in step is m).
Determine robot initial coordinate probot(0)=(10,0) and coordinate of ground point pgoal=(100,100), robot is most
Big movement speed vmax=1m/s, target point gravitational constant Ggoal=1000, obstacle repulsive force sphere of action Rrep=2, obstacle row
Denounce coefficient Gobs=100, virtual friction coefficient f=0.2.Here two examples are set：Example one is in the pros of 120m × 120m
Some round obstacles are arranged in shape space at random, to represent complicated, unknown, random obstacle environment；Second example is two
The gallery that a rectangular obstacle is formed.
Step 1：According to robot current location probotWith aiming spot pgoalThe distance between and relative bearing, profit
It is acted on the virtual attraction that following formula calculating robot is subject to,
Step 2：The partial derivative of attraction is calculated using following formula, obtains Gaussian matrix of the robot in target gravitational field
In formulaWithRespectively virtual attraction force vector FattComponent on x directions and y directions.
Step 3：According to G (p, Fatt) whether it is positive definite matrix, the value of parameter ν is obtained to four according to supplement step 1, and
Calculate following inverse matrix
B(p,Fatt)=(G (p, Fatt)+ν·I)-1
Step 4：Calculating robot is the distance between to all barriers of surrounding, if robot and i-th of obstacle of surrounding
The minimum range of object | | probot-pobs,i| | less than Rrep, then using following formula calculating robot by the repulsive force of corresponding barrier
Step 5：Utilize Gaussian matrix of the following formula calculating robot in i-th of barrier repels the field of force
Step 6：According to G (p, Frep,i) whether it is positive definite matrix, the value of parameter ν is obtained to four using step 1 is supplemented, and
Calculate following inverse matrix
B(p,Frep,i)=(G (p, Frep,i)+ν·I)-1
Step 7：The virtual frictional force effect f=-fv that calculating robot is subject to.
Step 8：Each power in summary step, the control input in summary computer device people are as follows
Step 9：The total control amount of obtained robot is updated in robot motion equation, is obtained one under robot
The movement velocity at moment and position.
Step 10：Judge whether robot reaches target point, if having reached, robot stop motion；If not reaching,
Continue to control robot movement back to step 1.
Parameter ν is required to obtain according to following S1-S4：
S1：If matrix G+ ν I are positive definite, then enable ν=ν/2, go to S3；Otherwise, the ν of ν=4 is enabled, goes to S2.
S2：If matrix G+ ν I are positive definite, then go to S4；Otherwise, back to S1.
S3：If matrix G+ ν I are positive definite, then back to S1；Otherwise, the ν of ν=2 is enabled, goes to S4.
S4：Parameter adjustment terminates, and obtains the value of parameter ν.
Attached drawing 1 shows that original artificial physical method is moved with institute's extracting method of the present invention control robot under multiple obstacles
Track, " triangle " symbology starting point in figure, " five-pointed star " the symbology target point in upper right side.Both of which can
Complex barrier region is got around with guided robot and reaches target point.But when close to barrier, the movement locus of original method
Significantly there are many oscillations, can not show a candle to the smooth trajectory that institute's extracting method of the present invention obtains.
The robot that attached drawing 2 and 3 this section of attached drawing compared under two methods passes through movement locus during gallery.It is attached
Fig. 2 shows the track comparison diagram that original method is obtained with improved method.It can be clearly from partial enlarged view (attached drawing 3)
Going out, improved method proposed by the present invention can obtain smooth track so that robot can quickly pass through gallery, and
Then there is serious oscillation situation in the track that original artificial physical method obtains.
Table 1 is given under two examples, and robot reaches the target point required time using distinct methods.It can see
Go out, relative to original artificial physical method, institute's extracting method of the present invention can make robot reach target point faster.
Algorithms of different compares the time required to reaching target point under 1 each example of table
The method that the present invention carries second order gradient information improvement artificial physics avoidance smooth trajectory degree is kept away to solve robot
Barrier problem provides a kind of effective solution, while also provides one for the path planning problem of robot in complicated environment
The effective solution route of kind, can be widely applied to robot, Aeronautics and Astronautics, industrial production etc. and is related to path planning, obstacle avoidance
The field of problem.
Claims (2)
- A kind of 1. method for improving artificial physics avoidance smooth trajectory degree using second order gradient information, it is characterised in that：This method Using the avoidance direction of the second order gradient information calculating robot of artificial physics power, to improve robot obstacle-avoiding path smooth degree, Specific implementation process is as follows：Determine the initial coordinate p of robotrobot(0)=(x0,y0) and coordinate of ground point pgoal=(xgoal,ygoal), robot is most Big movement speed vmax, target point gravitational constant Ggoal, obstacle repulsive force sphere of action Rrep, obstacle repulsion coefficient Gobs, virtually rub Wipe the position of coefficient f and each barrier, (x0,y0) for initial coordinate, (xgoal,ygoal) it is coordinate of ground point；Step 1：According to robot current location probotWith aiming spot pgoalThe distance between and relative bearing, computer The virtual attraction F that device people is subject toattEffect, FattCalculating it is as follows,Step 2：Gaussian matrix G (p, F of the calculating robot in target gravitational fieldatt), Gaussian matrix G (p, Fatt) calculating side Formula is as follows,In formula, FattFor virtual attraction FattVector representation, Fatt,xAnd Fatt,yRespectively virtual attraction force vector FattIn x side To with the component on y directions；Step 3：According to G (p, Fatt) whether it is positive definite matrix, parameter ν is adjusted, and it is as follows to calculate inverse matrixB(p,Fatt)=(G (p, Fatt)+ν·I)-1 (8)I in formula is unit matrix；Step 4：Calculating robot arrives the distance between peripheral obstacle, if the minimum range of robot and i-th of barrier ||probot-pobs,i| | less than Rrep, pobs,iRepresent the position of i-th of barrier, then robot is repelled by i-th of barrier Power, the F of i-th of barrierrep,iRepulsive force calculation is as followsIn formula, | | probot-pobs,i| | for the distance of robot to i-th of barrier, useIt represents from i-th of barrier It is directed toward the unit vector of robot；Step 5：Gaussian matrix G (p, F of the calculating robot in i-th of barrier repels the field of forcerep,i), calculation is as followsIn formula, Frep,i,xAnd Frep,i,yRespectively virtual attraction force vector Frep,iComponent on x directions and y directions；Step 6：According to G (p, Frep,i) whether it is positive definite matrix, parameter ν is adjusted, and it is as follows to calculate inverse matrixB(p,Frep,i)=(G (p, Frep,i)+ν·I)-1 (11)I in formula is unit matrix；Step 7：The virtual frictional force effect f=-fv that calculating robot is subject to；Step 8：The effect of each power of summary, the control input of calculating robot are as followsU=B (p, Fatt)·Fatt+∑B(p,Frep,i)·Frep,i+f (12)Step 9：Robot controlled quentity controlled variable in formula (12) is updated in robot motion equation, update robot speed and Position；Step 10：Judge whether robot reaches target point, if having reached, robot stop motion；If not reaching, return To step 1.
- 2. a kind of side for improving artificial physics avoidance smooth trajectory degree using second order gradient information according to claim 1 Method, it is characterised in that：Parameter ν is required to obtain according to following S1-S4：S1：If matrix G+ ν I are positive definite, then enable ν=ν/2, go to S3；Otherwise, the ν of ν=4 is enabled, goes to S2；S2：If matrix G+ ν I are positive definite, then go to S4；Otherwise, back to S1；S3：If matrix G+ ν I are positive definite, then back to S1；Otherwise, the ν of ν=2 is enabled, goes to S4；S4：Parameter adjustment terminates, and obtains the value of parameter ν.
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| CN110186459A (en) * | 2019-05-27 | 2019-08-30 | 深圳市海柔创新科技有限公司 | Air navigation aid, mobile vehicle and navigation system |
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