CN109227549A - A kind of smooth avoidance motion planning method of robot based on tangent line recursion - Google Patents
A kind of smooth avoidance motion planning method of robot based on tangent line recursion Download PDFInfo
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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 embodiment of the invention discloses a kind of smooth avoidance motion planning methods of robot based on tangent line recursion, suitable for surpassing redundant robot, the following steps are included: establishing ball-type barrier in task space first, recursion tangent line is done to barrier and intersects at safe distance circle, obtains the collisionless path point of avoiding barrier.Then, the position-based routing that super redundant robot is acquired with crestal line modal method obtains joint space pose corresponding with without path point is touched.Finally, carrying out seven B-spline interpolation to pose, the smooth avoidance motion path of robot is obtained.Robot motion's path smooth that the present invention solves, and robot respectively drives joint velocity, acceleration and jerk continuously without mutation in motion process.With the increase of robot redundancy, the small advantage of this method calculation amount is become apparent.
Description
Technical field
The present invention relates to a kind of robot path planning method more particularly to a kind of robot based on tangent line recursion are smooth
Avoidance motion planning method.
Background technique
Super redundant robot can effectively make up that traditional robot freedom degree is few, obstacle avoidance ability is insufficient, flexibility is poor etc. and lack
Point, is one of research hotspot of recent domestic, and application range has been no longer limited to traditional industrial production line.Robot
In the changing environments such as interspace aviation, undersea detection, disease examination, pipe-line maintenance, the anti-dangerous disaster relief using more and more extensive.With
The extensive use of robot, the environment of variation requirement also is proposed to the obstacle avoidance ability of robot.With the increase of redundancy,
Super redundant robot's structure is more complicated, and the calculation amount of kinematics solution constantly increases, and solves also difficulty further, and movement is steady
Also it is difficult to ensure.In order to reduce the vibration and impact of robot operational process, extends the service life of robot, cope with and constantly become
The smooth avoidance Motion trajectory of the environment of change, super redundant robot is necessary.
The avoidance motion planning of robot refers to the collisionless path of the planning robot in the complex environment for having barrier.
Common collision-free motion planing method has: free-space Method, cell decomposition, path map method, Artificial Potential Field Method and base
In the planing method probability map of sampling and Quick Extended random tree etc..The obstacle-avoiding route planning method of super redundant robot
Common Artificial Potential Field Method and the law of planning based on sampling.Path rule would generally be carried out under conditions of meeting constraint in practice
Draw, recycle that various optimization method search times are most short, the smallest planing method of driving moment, or it is comprehensive it is optimal for index into
Row optimization.For above method mostly in task space planning path, the trajectory calculation for obtaining motion smoothing is more complex.
Summary of the invention
It is smoothly kept away the technical problem to be solved by the embodiment of the invention is that providing a kind of robot based on tangent line recursion
Hinder motion planning method so that super redundant robot's avoidance calculation amount is small, smooth trajectory and respectively drive joint velocity, acceleration and
Jerk is continuously without mutation.
In order to solve the above-mentioned technical problem, the embodiment of the invention provides a kind of robots based on tangent line recursion smoothly to keep away
Hinder motion planning method, comprising the following steps:
S1: task space establishes ball-type barrier, determines collision-free trajectory according to starting point, target point and obstacle information
In critical path point；
S2: a series of corresponding joint space poses of the critical path point are acquired against solution using mode crestal line method；
S3: interpolation is carried out to each joint space state of robot, obtains smooth avoidance motion path.
Further, the method for determination of the critical path point is the mode of tangent line recursion.
Further, the inverse solution of the mode crestal line method is carried out by following formula:
Wherein, [0,1] s ∈, L indicate that curve arc long, κ (δ) indicate tangent vector of the curve at point δ.
Further, the tangent vector κ (s) indicates are as follows:
κ (s)=[cos α (s) sin β (s), sin α (s) sin β (s), cos β (s)]T
Wherein, α (s) indicates κ (s) in xkOkykThe projection of plane and the angle of positive direction of the y-axis, β (s) indicate κ (s) with
xkOkykThe angle of plane, function alpha (s) and β (s) expression formula are as follows:
Wherein, aiIt is mode collaborative parameters, fiIt (s) is mode subfunction, n1It is of mode function relevant to α (s)
Number, n2It is the total number of mode function；gi(s) be crestal line deflection auxiliary control function, biαAnd biβIt is then deflection auxiliary
Control parameter.
Further, the mode function is at least 3, deflection of the crestal line in arbitrary point are as follows:
Position and direction angle of the crestal line at s are as follows:
V (s)=[p (s)T α(s) β(s)]T, c=[a1 a2 a3 a4 b2α b2β]T, c indicate position of the crestal line s at
The control parameter in direction；
C thinks that following methods acquire:
vDFor the crestal line for giving terminal position and deflection, wherein λ is control
The constringent constant of iteration function,JcPseudo inverse matrix
It further, further include according to the control parameter c, construction meets desired space crestal line equation, utilizes two
Match point of the moving platform center of each parallel institution of point-score searching robot on crestal line.
Further, step S3 is specifically included:
K-th of parallel institution module moving platform of super redundant robot is obtained using the method for B-spline function inverse interpolation
Function expression of the motion profile S about (0≤t≤1) time t:
Sk,i(t)=F0(t)Vk,i-1+F1(t)Vk,i+F2(t)Vk,i+1+F3(t)Vk,i+2
+F4(t)Vk,i+3+F5(t)Vk,i+4+F6(t)Vk,i+5+F7(t)Vk,i+6
Wherein, Sk,i=[Sk,i,x Sk,i,y Sk,i,z], F (t) is the basic function of seven B-spline functions, Vk,i+j=[Vk,i+j,x
Vk,i+j,y Vk,i+j,z] (j=-1,0 ..., 6；I=1,2 ..., m-1) be the Duan Qici B-spline curves control point.
The implementation of the embodiments of the present invention has the following beneficial effects: having, calculation amount is small, avoidance smooth trajectory is without impact and each
The advantages that driving joint velocity, acceleration and jerk continuously without mutation, is more suited to super redundant robot.
Detailed description of the invention
Fig. 1 is obstacle avoidance algorithm flow chart；
Fig. 2 is recursion tangent line schematic diagram；
Fig. 3 is the avoidance motion planning figure of super redundancy bionic proboscis robot；
Fig. 4 is that super redundancy bionic proboscis robot respectively drives joint position curve；
Fig. 5 is that super redundancy bionic proboscis robot respectively drives joint velocity curve；
Fig. 6 is that super redundancy bionic proboscis robot respectively drives joint velocity curve；
Fig. 7 is that super redundancy bionic proboscis robot respectively drives joint jerk diagram.
Specific embodiment
To make the object, technical solutions and advantages of the present invention clearer, the present invention is made into one below in conjunction with attached drawing
Step ground detailed description.
A kind of smooth avoidance motion planning method of robot based on tangent line recursion of the embodiment of the present invention, thought be
It is obtained with method of geometry without path point is hit under conditions of safe distance is certain, calculation amount is relatively small, then is obtained with crestal line modal method
Pass through seven B-spline interpolation after to inverse solution and obtain smooth avoidance motion path, respectively joint velocity, acceleration and jerk is driven to connect
Continue without mutation, kinetic characteristic is good, theoretically realizes no impact.
To make the objectives, technical solutions, and advantages of the present invention more comprehensible, below with reference to case and attached drawing to this hair
It is bright to be described in further detail.
There are six cell cubes for robot in present case, it is by 6 3U with three rotation one-movement-freedom-degreesPS-PS
The super redundant robot that parallel module is connected in series, barrier are ball known to radius.The task of present case is robot from
Initial point P0Avoiding obstacles OrMove to target point Pf, robot is located at starting point P0With target point PfWhen speed, acceleration and jump
Degree is 0.The specific implementation steps are as follows:
1, ball-type barrier is established in task space, according to starting point P0, target point PfAnd obstacle information OrDeng determination
Whether avoidance, acquired when needing avoidance without hitting a series of critical path point P in track0, P1..., Pn+1, Pm, PfDeng avoidance
Algorithm flow chart is as shown in Fig. 1.
When needing avoidance, critical path point is solved by the way of tangent line recursion.It crosses whole story location point and is round OrTangent line,
The center of circle and two point of contacts are connected, circle O is handed overr+lIn point P1、Pm, successively cross P0、P1... find out a series of round OrTangent line and circle Or+lFriendship
Point P2, P3..., Pn+2, untilFinally take P0, P1..., Pn+1, Pm, PfFor without the path point touched on path, such as attached drawing
Shown in 2.
2, the position-based routing that super redundant robot is acquired with crestal line modal method obtains joint corresponding with without path point is touched
Spatial pose.
Thought of the crestal line modal method based on Differential Geometry, with the arbitrary point on the method for parametrization expression curve, and with joining
Number metaplasias at space crestal line the whole geometry configuration of super redundant robot described.The integral expression of space arbitrary curve
Are as follows:
Wherein, [0,1] s ∈, L indicate that curve arc long, κ (δ) indicate tangent vector of the curve at point δ.Curve tangent vector κ
(s) it can indicate are as follows:
κ (s)=[cos α (s) sin β (s), sin α (s) sin β (s), cos β (s)]T
Wherein, α (s) indicates κ (s) in xkOkykThe projection of plane and the angle of positive direction of the y-axis, β (s) indicate κ (s) with
xkOkykThe angle of plane.Using the linear combination of mode function come representative function α (s) and β (s):
Wherein, aiIt is mode collaborative parameters, fiIt (s) is mode subfunction, n1It is of mode function relevant to α (s)
Number, n2It is the total number of mode function；gi(s) be crestal line deflection auxiliary control function, biαAnd biβIt is then deflection auxiliary
Control parameter.Since the terminal position of space crestal line has three-dimensional constraining, at least need the mode letter of 3 linear independences
It counts to limit the overall shape of crestal line.According to the mode function of selection, deflection of the crestal line in arbitrary point are as follows:
After parameterized treatment, the inverse kinematics of crestal line, which is converted into, solves ai、biαAnd biβThe problem of.Ridge is indicated with v (s)
Position and direction angle of the line at s, the control parameter of position and direction of the crestal line at s is indicated with c, then v (s)=[p (s)T α
(s) β(s)]T, c=[a1 a2 a3 a4 b2α b2β]T.For giving the crestal line v of terminal position and deflectionD, Model control
Parameter c can be acquired by following iterative equation:
Wherein, λ is the control constringent constant of iteration function,JcPseudo inverse matrix
After iteration goes out mode control parameter, construction meets desired space crestal line equation, utilizes dichotomy searching robot
Each parallel institution match point of the moving platform center on crestal line.For i-th branch of k-th of parallel institution
Chain need to meet constraint condition:
lb,ki≤qki≤lr,ki+lb,ki, (i=0,1,2,3；K=1,2 ... n)
Wherein, lb,kiAnd lr,kiRespectively indicate the length of branch chain bush and push rod.With vector Lc=[q10 q20 … qn0]T
Indicate that intermediary movements branch chain bar is long, then
Wherein, H=[h1 h2 … hn]T, hk(k=1,2 ... n, hk∈ [0,1]) it is that control intermediary movements branch chain bar is grown
Parameter.The pose of parallel institution after using fitting carries out position-based routing operation and obtains the length of other each branches, and discontented
When sufficient constraint condition, it can be re-searched for by adjusting parameter H.Since pedestal parallel institution module is to be vertically mounted on fixation
On frame, the match point of moving platform position can not be fallen on crestal line.If p0=[0 0 0]T, then p1=[0 0 l1]T.K-th
Posture changing matrix of the parallel institution moving platform coordinate system relative to basis coordinates systemEulerian angles φ can be usediWithIt indicates:
If the unit vector w of the middle pole vector of k-th of parallel institutionk=[wkx wky wkz]T, by wkAnd spin matrixThird column it is equal, i.e.,
To sum up, module and carriage transformation matrix of the moving platform relative to silent flatform in k-th of parallel institutionIt can be described as:
The center of each parallel institution moving platform under each pose, i.e., a series of joint spaces are acquired according to transformation matrix
Pose.
3, seven B-spline interpolation are carried out to a series of joint space poses, obtains the smooth avoidance motion path of robot.
K-th of parallel institution module moving platform of super redundant robot is obtained using the method for B-spline function inverse interpolation
Function expression of the motion profile S about (0≤t≤1) time t.
Assuming that the function expression of super k-th of parallel institution moving platform motion profile of redundant robot are as follows:
Sk,i(t)=F0(t)Vk,i-1+F1(t)Vk,i+F2(t)Vk,i+1+F3(t)Vk,i+2
+F4(t)Vk,i+3+F5(t)Vk,i+4+F6(t)Vk,i+5+F7(t)Vk,i+6
Wherein, Sk,i=[Sk,i,x Sk,i,y Sk,i,z], F (t) is the basic function of seven B-spline functions, Vk,i+j=[Vk,i+j,x
Vk,i+j,y Vk,i+j,z] (j=-1,0 ..., 6；I=1,2 ..., m-1) be the Duan Qici B-spline curves control point.
Since joint motions have continuity, adjacent two sections of B-spline curves are equal in junction, i.e.,
Sk,i(1)=Sk,i+1(0)
By the derivative continuity of robot moving platform motion profile it is found that the B-spline letter of junction seven times two sections of tracks
It is continuous that number need to meet simultaneously one to six order derivative, it may be assumed that
According to the property ∑ F of B-spline basic functioni(t)=1 it, obtains:
F0(t)+F1(t)+F2(t)+F3(t)+F4(t)+F5(t)+F6(t)+F7(t)=1
Assuming that B-spline basic function Fi(t) form are as follows:
Fi(t)=Ait7+Bit6+Cit5+Dit4+Eit3+Git2+Hit+Qi
The basic function of seven B-spline functions can be acquired according to above-mentioned constraint, then robot k-th of parallel institution moving platform
Motion profile are as follows:
The speed, acceleration and jerk of each movement branched chain can be obtained to the derivation of time t.
Assuming that the motion profile of each parallel institution moving platform of robot is made of seven B-spline curves of m-1 section, k-th simultaneously
The center of online structure moving platform is Pk,i(i=1,2,3 ..., m), can be obtained by track continuity:
Being equal to zero with the speed, acceleration of starting point and ending point, jerk is constraint condition, i.e.,It arranges
MV=P
Wherein, vector matrix V is a series of control points of seven B-spline curves,
V=[Vk,0 Vk,1 … Vk,m+5]T, vector matrix P is to consider boundary constraint, touches super redundancy machine at path point in nothing
The center of k-th of parallel institution moving platform of device people,
M is coefficient matrix,
Solving the system of linear equations can determine unique solution Vk,0, Vk,1..., Vk,m+4, Vk,m+5, required seven B-splines can be obtained
Curvilinear function expression formula finally obtains the smooth avoidance motion profile of robot indicated by m-1 seven B-spline functions segmentations.
Avoidance motion planning figure such as attached drawing 3, each joint position, speed, acceleration, jerk diagram such as attached drawing 4-7.
Above disclosed is only a preferred embodiment of the present invention, cannot limit the power of the present invention with this certainly
Sharp range, therefore equivalent changes made in accordance with the claims of the present invention, are still within the scope of the present invention.
Claims (7)
1. a kind of smooth avoidance motion planning method of robot based on tangent line recursion, which comprises the following steps:
S1: task space establishes ball-type barrier, is determined in collision-free trajectory according to starting point, target point and obstacle information
Critical path point；
S2: a series of corresponding joint space poses of the critical path point are acquired against solution using mode crestal line method；
S3: interpolation is carried out to each joint space state of robot, obtains smooth avoidance motion path.
2. the smooth avoidance motion planning method of the robot according to claim 1 based on tangent line recursion, which is characterized in that
The method of determination of the critical path point is the mode of tangent line recursion.
3. the smooth avoidance motion planning method of the robot according to claim 2 based on tangent line recursion, which is characterized in that
The mode crestal line method crestal line is carried out by following formula:
Wherein, [0,1] s ∈, L indicate that curve arc long, κ (δ) indicate tangent vector of the curve at point δ.
4. the smooth avoidance motion planning method of the robot according to claim 3 based on tangent line recursion, which is characterized in that
The tangent vector κ (s) indicates are as follows:
κ (s)=[cos α (s) sin β (s), sin α (s) sin β (s), cos β (s)]T
Wherein, α (s) indicates κ (s) in xkOkykThe projection of plane and the angle of positive direction of the y-axis, β (s) indicate κ (s) and xkOkykIt is flat
The angle in face, function alpha (s) and β (s) expression formula are as follows:
Wherein, aiIt is mode collaborative parameters, fiIt (s) is mode subfunction, n1It is the number of mode function relevant to α (s), n2It is
The total number of mode function；gi(s) be crestal line deflection auxiliary control function, biαAnd biβIt is then deflection auxiliary control ginseng
Number.
5. the smooth avoidance motion planning method of the robot according to claim 4 based on tangent line recursion, which is characterized in that
The mode function is at least 3, deflection of the crestal line in arbitrary point are as follows:
Position and direction angle of the crestal line at s are as follows:
V (s)=[p (s)T α(s) β(s)]T, c=[a1 a2 a3 a4 b2α b2β]T, position and direction of the c expression crestal line at s
Control parameter；
C thinks that following methods acquire:
vDFor the crestal line for giving terminal position and deflection, wherein λ is control iteration
The constant of function convergence,JcPseudo inverse matrix
6. the smooth avoidance motion planning method of the robot according to claim 5 based on tangent line recursion, which is characterized in that
It further include according to the control parameter c, construction meets desired space crestal line equation, utilizes each of dichotomy searching robot
Match point of the moving platform center of a parallel institution on crestal line.
7. the smooth avoidance motion planning method of the robot according to claim 1-6 based on tangent line recursion,
It is characterized in that, step S3 is specifically included:
The movement of k-th of parallel institution module moving platform of super redundant robot is obtained using the method for B-spline function inverse interpolation
Function expression of the track S about (0≤t≤1) time t:
Sk,i(t)=F0(t)Vk,i-1+F1(t)Vk,i+F2(t)Vk,i+1+F3(t)Vk,i+2+F4(t)Vk,i+3+F5(t)Vk,i+4+F6(t)
Vk,i+5+F7(t)Vk,i+6
Wherein, Sk,i=[Sk,i,x Sk,i,y Sk,i,z], F (t) is the basic function of seven B-spline functions, Vk,i+j=[Vk,i+j,x
Vk,i+j,y Vk,i+j,z] (j=-1,0 ..., 6；I=1,2 ..., m-1) be the Duan Qici B-spline curves control point.
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| CN109773791A (en) * | 2019-01-31 | 2019-05-21 | 北京华航唯实机器人科技股份有限公司 | Path generating method and device |
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| CN109986554A (en) * | 2019-01-21 | 2019-07-09 | 中国船舶重工集团公司第七一六研究所 | A kind of geometry method for optimally controlling of industrial robot path planning |
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| CN112276953A (en) * | 2020-10-27 | 2021-01-29 | 清华大学深圳国际研究生院 | Arm type collaborative planning method of continuous super-redundant mechanical arm, terminal equipment and storage medium |
| CN113352319A (en) * | 2021-05-08 | 2021-09-07 | 上海工程技术大学 | Redundant mechanical arm obstacle avoidance trajectory planning method based on improved fast expansion random tree |
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| WO2021012125A1 (en) * | 2019-07-19 | 2021-01-28 | Huawei Technologies Co., Ltd. | Global path planning using piecewise sigmoid curves |
| CN112157678B (en) * | 2020-09-24 | 2021-10-22 | 河北工业大学 | Plane redundant mechanical arm collision position detection method based on dichotomy |
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| CN112276953B (en) * | 2020-10-27 | 2021-12-28 | 清华大学深圳国际研究生院 | Arm type collaborative planning method of continuous super-redundant mechanical arm, terminal equipment and storage medium |
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| CN113352319A (en) * | 2021-05-08 | 2021-09-07 | 上海工程技术大学 | Redundant mechanical arm obstacle avoidance trajectory planning method based on improved fast expansion random tree |
| CN113459086A (en) * | 2021-05-28 | 2021-10-01 | 北京精密机电控制设备研究所 | Super-redundant mechanical arm path planning method |
| CN113459086B (en) * | 2021-05-28 | 2022-07-29 | 北京精密机电控制设备研究所 | Super-redundancy mechanical arm path planning method |
| CN115179282A (en) * | 2022-07-07 | 2022-10-14 | 珠海格力电器股份有限公司 | Robot motion track determination method and device and robot |
| CN117464693A (en) * | 2023-12-27 | 2024-01-30 | 成都电科星拓科技有限公司 | Three-dimensional mechanical arm particle swarm path planning method based on cubic spline interpolation |
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