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CN106695802A - Improved RRT<*> obstacle avoidance motion planning method based on multi-degree-of-freedom mechanical arm - Google Patents

Improved RRT<*> obstacle avoidance motion planning method based on multi-degree-of-freedom mechanical arm Download PDF

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Publication number
CN106695802A
CN106695802A CN201710163211.0A CN201710163211A CN106695802A CN 106695802 A CN106695802 A CN 106695802A CN 201710163211 A CN201710163211 A CN 201710163211A CN 106695802 A CN106695802 A CN 106695802A
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path
node
rand
search
point
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龚道雄
李赟程
邵杰
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Beijing University of Technology
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Beijing University of Technology
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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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  • Engineering & Computer Science (AREA)
  • Robotics (AREA)
  • Mechanical Engineering (AREA)
  • Management, Administration, Business Operations System, And Electronic Commerce (AREA)

Abstract

The invention discloses an improved RRT<*> obstacle avoidance motion planning method based on a multi-degree-of-freedom mechanical arm, and belongs to the field of mechanical arm motion planning. A six-degree-of-freedom mechanical arm model with seven connecting rods and six rotary joints is built; parameters in a to-be-searched space are determined; if the distance is shorter than the distance of a path with lowest cost, the distances between a near node in a set to an initial point and the distance between the node to a random point are temporarily determined as the minimum path; a newly generated sigma is subjected to collision detection, and the node and the path are added if the newly generated path does not collide an obstacle interval; the steps are repeated until the optimal path is found; and the generated path is added into a path planning device. Compared with the prior art, the method has the following advantages that the random search characteristic is changed in a mode of adding normal distribution, the algorithm convergence rate can be increased through the heuristic search, the RRT<*> algorithm has the evolutionary optimization path, and a large number of calculations is not needed; and after Gaussian distribution of an inspiration point near a target point is added, the convergence rate is increased, and the search time is shortened.

Description

The avoidance motion planning method of the improvement type RRT* based on multi-degree-of-freemechanical mechanical arm
Technical field
The present invention relates to motion planning method in mechanical arm avoidance link, specifically a kind of quick random search of improvement type Method be applied to global space, belong to manipulator motion planning field
Background technology
The motion planning problem of robot proposes that the motion planning of early stage is to be related to road early in the sixties in last century Footpath plans that robot is seen as a bit, and motion planning is just seen as being found in configuration space one from initial pose point to mesh The continuous path of mark appearance point, path planning by a process for search, modeling and searching method according to world environments Difference is largely divided into the planning of free space geometrical construction, intelligent method planning and the planing method based on stochastical sampling.But it is early The path planning of phase can not be adapted to the high-freedom degree and Obstacles complex environment of Current mechanical arm, the planning side of early stage Method can only increase substantial amounts of calculating, reduce the efficiency of search.
The avoidance object of planning of mechanical arm is one optimal path for meeting all kinds of indexs of planning department, for this problem, The C space laws that have used, A* search methods, artificial examination hall method, genetic algorithm all have some limitations, the calculating of C space laws Time is more long than the response time of mechanical arm, limits its application in avoidance, and ant group algorithm is substantially parallel algorithm, it Being started simultaneously in problem space multiple spot carries out multi-thread independent solution search, but it is more long to change the algorithm search time, is easily absorbed in stagnation and asks Topic.
The problem of many inefficiencies that searching algorithm is present till now is considered, the present invention is directed to propose a kind of improved The motion planning method of the multi-degree-of-freemechanical mechanical arm avoidance of RRT* (rapidly exploring random tree) algorithm, it is right The cost time is long when solving search, and iterations is more, it is easy to be limited to local infinitesimal, and the low problem of convergency factor makes mechanical arm Being capable of fast and effeciently avoiding obstacles.This probabilistic programming is even more effective particularly with the planning problem in higher dimensional space.
The content of the invention
To achieve these goals, the technical solution adopted by the present invention is the improvement type RRT* based on multi-degree-of-freemechanical mechanical arm Avoidance motion planning method, the implementation process of the method is as follows：
Step one：Build the sixdegree-of-freedom simulation model of seven-link assembly and six rotary joints, sets target point of arrival pose Value, inverse solution seeks its joint angles, it is determined that whether inverse solution has solution, if solution, is set as dbjective state xgoal, dbjective state xgoal Comprising position and attitude information；If inverse solution is without solution, object pose point in resampling area of space, until choosing reachable mesh Untill mark state；
Step 2：Determine space intrinsic parameter initialization to be searched, initiation parameter is：Initial bit-type xinit, target position Type xgoal, extension step-length λ, current iterations n；
Step 3：Stochastical sampling chooses x in bit-type spacerand, choose xrandNeighbouring neighbor node region, according to node Region formulaObtain xnearSet Xnear, wherein d is space Dimension, γ is the constant of selection, and V is the set for having constituted search tree node, and x ' is a certain node in region of search.
Step 4：In order to select xmin,σminAs tentative father node and father path, traversal set Xnear, define optimal Path minCost, by xmin,σminNull values are assigned, from random point xrandTo child node x in setnearGenerate respective path σ；
Step 5：Judge Cost (xnear)+Cost(σ)<Whether minCost sets up, if less than the least cost path away from From, then by this gather in neighbouring node to be fixed tentatively to the distance of random point to initial point and the node be minimal path, correspondingly, xnearJust fixed tentatively with σ is respective xmin,σmin, if greater than the least cost path, then other neighbouring nodes are traveled through, until finding Untill minimal path；
Step 6：Collision detection is done to newly-generated σ, if newly-generated path is not impinging upon barrier interval, By node xrandIt is added in tree with path σ；
Step 7：It is node and side and X by existing treenearGather remaining xnear, xrandIt is added to Rewire functions to enter Capable path of welding again, redundant path is rejected；
Step 8：Travel through remaining xnear, from newly-generated node xrandCall Steer (xrand,xnear) step function life Into path σ；
Step 9：Judge Cost (xrand)+Cost(σ)<Cost(xnear) whether set up, if initial point is to random point road Footpath is less than original initial point to corresponding node path nearby plus the distance in newly-generated path, then carry out collision inspection to its σ Survey, if being not impinging upon barrier, define the xnearAs father node, all of father node and remaining x are removednearSide E ←E\{xparent,xnear, E represents the set on constituted side, and the side of random point and father node is re-added into E in tree ←E∪{xrand,xnear}；
Step 10：The next random point of resampling, the rule according to normal distribution changes the characteristic of stochastical samplingμ represents average value, and σ is standard deviation.Average is set to xgoal, by changing standard deviation Value changes the stochastic behaviour of search, sets the parameter value of standard deviation sigma；
Step 11：Judge the size and symmetrical degree of search space, the sample area of normal distribution is changed again Planning, uses-φ(xlower) it is that sampling can Up to maximum region, by probability density function change to adapt to different actual environments, f ' (x | μ, σ) it is revised sample area Probability density；
Step 12：Repeat step three arrives step 11, until optimum route search is arrived；
The track of generation is added in trajectory planning device, the present invention has advantages below compared with prior art, passes through The mode for adding normal distribution changes the characteristic of random search, this to improve convergence of algorithm with heuristic search Rate, RRT* algorithms have the path of gradual optimization, without by substantial amounts of calculating；Add the Gauss for inspiring point near impact point After distribution, rate of convergence is improve, saved search time.
Brief description of the drawings
Fig. 1 is the sixdegree-of-freedom simulation built
Fig. 2 is invention flow chart
Fig. 3 is that RRT* searches for schematic diagram
Fig. 4 is searching route figures of the RRT* under three-dimensional environment
Fig. 5 object poses point adds Gaussian distribution density functional arrangement
Fig. 6 is to add the improvement type RRT* optimum search path profiles after Gaussian Profile
Fig. 7 is the simulation paths figure that sixdegree-of-freedom simulation adds improvement type RRT* motion plannings under ROS simulated environment
Specific embodiment
With reference to explanation the drawings and specific embodiments the present invention is further described, embodiments of the invention be according to Implement under the premise of technical scheme.Detailed implementation method and specific operating process is given, but it is of the invention Protection domain is not limited to following instance scope.
The mechanical arm of the rotary joint of seven-link assembly six is initially set up, selection two refers to clamper as end effector, such as Fig. 1 mono- Sample (x0, y0, z0), as z-axis, end is gone out according to DH parameter value calculations as basis coordinates system, remaining joint around the axle for rotating Position auto―controlWherein A1 to A6 is each joint spin matrix, is led to Cross each joint angles that Analysis of Inverse Kinematics is solved under dbjective state
Flow chart according to Fig. 2 completes the search in algorithm path, specially
In the three-dimensional space of 100*100*100, initial bit-type xinitIt is set as (5,5,5), is not considering mechanical arm Attitude, in the case of only considering locus, target bit-type xgoal(95,95,95), extension step-length λ is set to 1.5, current iteration time Number is 0 time, and stochastical sampling chooses x in search spacerand, according to formula Obtain xnearSet Xnear, whereindIt is set as 3, γ selections 0.618, the section on search tree is checked whether in the set Point, if not further expanding iterations increases region of search until set XnearComprising neighbouring node；Selected xmin,σminMake It is the father node and father path fixed tentatively, traversal set Xnear, optimal path minCost is defined, by xmin,σminNull values are assigned, from Random point xrandTo child node x in setnearGenerate respective path σ；
Judge Cost (xnear)+Cost(σ)<Whether minCost sets up, and if less than the least cost path distance, then will It is minimal path that neighbouring node in the set is fixed tentatively to initial point and the node to the distance of random point, correspondingly, xnearAnd σ It is respective x just to fix tentativelymin,σmin, if greater than the least cost path, then other neighbouring nodes are traveled through, until finding minimal path Untill footpath；Collision detection is done to newly-generated σ, if newly-generated path is not impinging upon barrier interval, by node xrandIt is added in tree with path σ；By existing tree (node and side) and XnearGather remaining xnear, xrandIt is added to Rewire functions carry out path of welding again, and redundant path is rejected；Travel through remaining xnear, from newly-generated node xrandAdjust With Steer (xrand,xnear) step function generation path σ, judge Cost (xrand)+Cost(σ)<Cost(xnear) whether set up, If initial point is less than original initial point to corresponding node path nearby to random point path plus the distance in newly-generated path, Collision detection so is carried out to its σ, if being not impinging upon barrier, the x is definednearAs father node, dispel all of Father node and remaining xnearSide E ← E { xparent,xnear, and by the side of random point and father node be re-added to tree in E ← E ∪{xrand,xnear, such as Fig. 3 schematic diagrames show, expand the mode of node and the existing node of welding and side are that RRT* is different from again A kind of searching method of original RRT, the next random point of resampling, the rule according to normal distribution changes the spy of stochastical sampling PropertyAverage is set to xgoal(95,95,95), are changed by changing the value of standard deviation and searched The stochastic behaviour of rope, sets standard deviation sigma=1；The size and symmetrical degree of search space are judged, by the sample region of normal distribution Planning is changed in domain again, as shown in figure 5, usingBy probability Density function change is repeated such as the step of explanatory diagram, until finding a suitable search road with adapting to different actual environments Untill footpath.
Fig. 4 is the searching route figure of RRT*, contains 8 spherical barriers, starting point be (5,5,5) terminal be (95, 95,95) only consider the position of end, the searching route figure of search strategy as described above is not considered in the case of attitude, its Middle iterations is 792 times, and the time of path planning is 17.89s, and black line is the final path for searching.
Fig. 6 is sampled come the Gaussian Profile after the amendment for debugging suitable actual conditions by changing the value of σ, by by μ Value is set to impact point, changes σ values to change the distribution situation of random point, and Fig. 6 show σ values and is respectively 20, in the case of 50,80 RRT* path profiles, by this change, the time of search successively decreases, search for sampling iterations successively decrease, it can be seen that the side of changing The improvement of method can improve convergence.A series of joint angle set are obtained finally by the anti-solution of impact point, obtains final Each joint position of mechanical arm.Finally manifest sixdegree-of-freedom simulation application using moveit and rviz in ros simulated environment to change The crawl lab diagram of the RRT* algorithms for entering.

Claims (2)

1. the avoidance motion planning method of the improvement type RRT* of multi-degree-of-freemechanical mechanical arm is based on, it is characterised in that：The reality of the method Existing process is as follows：
Step one：The sixdegree-of-freedom simulation model of seven-link assembly and six rotary joints is built, sets target point of arrival pose value is inverse Solution seeks its joint angles, it is determined that whether inverse solution has solution, if solution, is set as dbjective state xgoal, dbjective state xgoalComprising position Put and attitude information；If inverse solution is without solution, object pose point in resampling area of space, until choosing reachable dbjective state Untill；
Step 2：Determine space intrinsic parameter initialization to be searched, initiation parameter is：Initial bit-type xinit, target bit-type xgoal, extension step-length λ, current iterations n；
Step 3：Stochastical sampling chooses x in bit-type spacerand, choose xrandNeighbouring neighbor node region, according to node region FormulaObtain xnearSet Xnear, wherein d is Spatial Dimension, γ is the constant of selection, and V is the set for having constituted search tree node, and x ' is a certain node in region of search；
Step 4：In order to select xmin,σminAs tentative father node and father path, traversal set Xnear, define optimal path MinCost, by xmin,σminNull values are assigned, from random point xrandTo child node x in setnearGenerate respective path σ；
Step 5：Judge Cost (xnear)+Cost(σ)<Whether minCost sets up, if less than the least cost path distance, then By this gather in neighbouring node to be fixed tentatively to the distance of random point to initial point and the node be minimal path, correspondingly, xnear Just fixed tentatively with σ is respective xmin,σmin, if greater than the least cost path, then other neighbouring nodes are traveled through, until finding minimum Untill path；
Step 6：Collision detection is done to newly-generated σ, if newly-generated path is not impinging upon barrier interval, will section Point xrandIt is added in tree with path σ；
Step 7：It is node and side and X by existing treenearGather remaining xnear, xrandBeing added to Rewire functions carries out weight New path of welding, redundant path is rejected；
Step 8：Travel through remaining xnear, from newly-generated node xrandCall Steer (xrand,xnear) step function generation road Footpath σ；
Step 9：Judge Cost (xrand)+Cost(σ)<Cost(xnear) whether set up, if initial point adds to random point path The distance in upper newly-generated path is less than original initial point to corresponding node path nearby, then carry out collision detection to its σ, such as Fruit is not impinging upon barrier, then define the xnearAs father node, all of father node and remaining x are removednearSide E ← E {xparent,xnear, E represents the set on constituted side, and the side of random point and father node is re-added into E ← E ∪ in tree {xrand,xnear}；
Step 10：The next random point of resampling, the rule according to normal distribution changes the characteristic of stochastical samplingμ represents average value, and σ is standard deviation；Average is set to xgoal, by changing standard deviation Value change the stochastic behaviour of search, the parameter value of standard deviation sigma is set；
Step 11：Judge the size and symmetrical degree of search space, the sample area of normal distribution changed into planning again, Using-φ(xlower) it is reachable maximum sampling Region, by probability density function change to adapt to different actual environments, f ' (x | μ, σ) it is that revised sample area probability is close Degree；
Step 12：Repeat step three arrives step 11, until optimum route search is arrived.
2. the avoidance motion planning method of the improvement type RRT* based on multi-degree-of-freemechanical mechanical arm according to claim 1, its It is characterised by：
The mechanical arm of the rotary joint of seven-link assembly six is initially set up, selection two refers to clamper as end effector, (x0, y0, z0) Used as basis coordinates system, remaining joint, as z-axis, the position auto―control of end is gone out according to DH parameter value calculations around the axle for rotatingWherein A1 to A6 is each joint spin matrix, by inverse motion Learn each joint angles under analysis and solution dbjective state；The search in algorithm path is completed, specially：100*100*100's In three-dimensional space, initial bit-type xinitIt is set as (5,5,5), is not considering mechanical arm attitude, only considers locus In the case of, target bit-type xgoal(95,95,95), extension step-length λ is set to 1.5, and current iteration number of times is 0 time, in search space Stochastical sampling chooses xrand, according to formulaObtain xnearCollection Close Xnear, wherein d is set as 3,γSelection 0.618, checks whether the node on search tree, if do not entered in the set One step extension iterations increases region of search until set XnearComprising neighbouring node；Selected xmin,σminSaved as tentative father Point and father path, traversal set Xnear, optimal path minCost is defined, by xmin,σminNull values are assigned, from random point xrandTo collection Child node x in closingnearGenerate respective path σ；
Judge Cost (xnear)+Cost(σ)<Whether minCost sets up, if less than the least cost path distance, then by the set Neighbouring node to be fixed tentatively to the distance of random point to initial point and the node be minimal path, correspondingly, xnearJust fixed tentatively with σ and be Respective xmin,σmin, if greater than the least cost path, then travel through other neighbouring nodes, until finding minimal path untill；It is right Newly-generated σ does collision detection, if newly-generated path is not impinging upon barrier interval, by node xrandAdd with path σ It is added in tree；By existing tree (node and side) and XnearGather remaining xnear, xrandBeing added to Rewire functions is carried out again Path of welding, redundant path is rejected；Travel through remaining xnear, from newly-generated node xrandCall Steer (xrand,xnear) Step function generates path σ, judges Cost (xrand)+Cost(σ)<Cost(xnear) whether set up, if initial point is to random point Path is less than original initial point to corresponding node path nearby plus the distance in newly-generated path, then its σ is collided Detection, if being not impinging upon barrier, defines the xnearAs father node, all of father node and remaining x are dispellednear's Side E ← E { xparent,xnear, and by the side of random point and father node be re-added to tree in E ← E ∪ { xrand,xnear, expand The existing node of the mode of node and again welding and side are a kind of searching methods that RRT* is different from original RRT, under resampling One random point, the rule according to normal distribution changes the characteristic of stochastical samplingAverage is set It is set to xgoal(95,95,95), by the stochastic behaviour for changing the value of standard deviation to change search, set standard deviation sigma=1；Judge The size of search space and symmetrical degree, planning is changed by the sample area of normal distribution again, is usedProbability density function is changed to adapt to different actual rings Border, repeat as explanatory diagram the step of, until finding a suitable searching route untill.
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Application publication date: 20170524