CN104325462A - Method for constructing motion space for robot under inherent constraints - Google Patents
Method for constructing motion space for robot under inherent constraints Download PDFInfo
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- CN104325462A CN104325462A CN201410521891.5A CN201410521891A CN104325462A CN 104325462 A CN104325462 A CN 104325462A CN 201410521891 A CN201410521891 A CN 201410521891A CN 104325462 A CN104325462 A CN 104325462A
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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
- B25J9/1602—Programme controls characterised by the control system, structure, architecture
- B25J9/1605—Simulation of manipulator lay-out, design, modelling of manipulator
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Abstract
The invention relates to a method for constructing a motion space for a robot under inherent constraints. The method is characterized in that the method includes: (Step S1) with supporting legs as an origin of coordinates, floating body kinematics is introduced into a body base coordinate system to create a joint chain and kinematic model based on the joints of the whole body; (Step S2) on the basis of the joint chain and kinematic model, a joint angle range constraint and a stability constraint are introduced, and the Monte Carlo method is utilized to sample and solve a working space for the end actuators of the robot, so that a three-dimensional point cloud grid formed by the working space is obtained; (Step S3) on the basis of the three-dimensional point cloud grid, plane cutting is carried out, and by means of extreme value analysis, the extreme value state and position and posture diagram of the robot in each direction are obtained. In comparison with the prior art, with the solution of the working space of the robot under the complex motion of the whole body as a goal, the method obtains the boundary range of the working space of end tracks under a complex condition meeting inherent constraints on the basis of the numerical algorithm.
Description
Technical field
The present invention relates to robot controlling field, under especially relating to a kind of inherent constraint, build the method in robot motion space.
Background technology
The usual task of anthropomorphic robot in routine use goes to capture object for utilizing arm and hand, and one of them relevant problem is the scope that can encounter of robot or space.In these tasks, whether the operator of robot can encounter target object is the problem that must answer.As the judgement flow process in Fig. 1, if object at hand can in coverage area, robot can directly perform crawl behavior to finish the work, and otherwise, robot needs, by mobile or walking, to make the arm of robot can arrive space and comprise target object.
The cartesian space that robot working space can reach under the constraints for end effector is exactly any on the robot end's component set of point that can reach.The size of robot working space represents the scope of activities of robot, and it is the important kinematics indexes weighing robot ability to work.Robot is contributed to for the analysis of the working space of each end effector and calculating more efficiently planning is carried out to task.If robot is to the task prerequisite of the crawl of object and release, be exactly that object is in the Work Space Range of robot.
The positioning precision that general robot captures is not high, often need resetting, the principal element affecting its positioning precision be exactly existing method mainly based on traditional kinematics, and health pedestal is designated as constant static, thus the robot motion space calculated build not precisely, not comprehensive.
Summary of the invention
Object of the present invention is exactly build the method in robot motion space under providing a kind of inherent constraint to overcome defect that above-mentioned prior art exists, to solve robot working space under complicated all-around exercises for target, based on numerical algorithm, ask for the bounds of the complicated case lower end track working space meeting inherent constraint.
Object of the present invention can be achieved through the following technical solutions:
Build the method in robot motion space under inherent constraint, the method comprises the following steps:
Step S1: take feet as the origin of coordinates, introduces floating motion to health basis coordinates system of robot, sets up an articulated chain based on general joint and kinematics model;
Step S2: based on articulated chain and kinematics model, introduces joint angle range constraint, stable constraint, utilizes Monte Carlo method sample and solves the working space of end effector of robot, obtaining the three-dimensional point cloud grid of working space formation;
Step S3: on the basis of three-dimensional point cloud grid, carries out planar interception, and by extreme value analysis, obtains robot extreme value state in all directions and pose figure.
Described step S2 is specially:
Step 201: retrain at the joint angle of movable joint, within the scope of stable constraint, adopt Monte Carlo method to carry out linear random sampling and obtain joint states value, one group of parameter that each stochastical sampling obtains is as a sample point;
Step 202: based on articulated chain and kinematics model, carries out positive kinematics calculating to sample point, obtains robot barycenter and end effector pose point, is the three-dimensional point cloud that pose point is drawn on basis, obtains end effector working space with basis coordinates;
Step 203: three-dimensional point cloud obtains three-dimensional point cloud grid after grid matrix assignment.
Described grid matrix assignment is specially: represent with the most contiguous mesh point pose point each in three-dimensional point cloud, normalize in same mesh point by close pose point, each mesh point occupy the center of respective mesh space.
Described planar interception is specially: carry out planar interception according to key position or demand position to three-dimensional point cloud grid, numerical value satisfies condition at grade: | z-z
0|≤ε, z are numerical value in plane, z
0for binding occurrence, ε is setting value.
Compared with prior art, the present invention has the following advantages:
1) compared with the conventional method, the present invention fully uses the redundancy of anthropomorphic robot, by to the coordinate system of robot based on feet, introducing floating motion, representative Monte Carlo method in numerical method is adopted to carry out solving of working space Point Set, and introduce various inherent constraint, the Work Space Range under the complicated case meeting these constraints is discussed, and the ultimate attainment situation under single pin support situation;
2) the present invention is directed to the three-dimensional point cloud grid solved, carry out planar interception, the three-dimensional point cloud solving value composition due to overall sample point is not easy to carry out observing accurate shape and structure, therefore first can carry out planar interception to key position or demand position, then analysis and the discussion of working range are carried out to the cross section obtaining key position;
3) the present invention is directed to the three-dimensional point cloud solved and carry out grid matrix assignment, the redundancy in joint is solved by normalization, gridding, and the larger mesh point of difference can be distinguished, because two extremely close pose points may be correspond to by multiple parameter space, across comparison similarly different when, Euclidean distance reality between a large amount of pose point is very little, for the ease of carrying out the contrast of similar pose point normalizing and spatial dimension, needs the process be normalized pose point.
Accompanying drawing explanation
Working space decision flow chart when Fig. 1 is robot crawl object;
Fig. 2 is the inventive method flow chart;
Fig. 3 is robot buoyancy aid coordinate system in the present invention;
Fig. 4 is joint of robot chain schematic diagram in the present invention;
Fig. 5 is working space calculation flow chart in the present invention;
Fig. 6 is the position coordinates figure of three-dimensional point cloud in robot space in the present invention.
Detailed description of the invention
Below in conjunction with the drawings and specific embodiments, the present invention is described in detail.The present embodiment is implemented premised on technical solution of the present invention, give detailed embodiment and concrete operating process, but protection scope of the present invention is not limited to following embodiment.
The combination of the value in each joint correspond to the state space of a robot.The locus of end effector is the nonlinear function about joint, and one group of parameter under joint space correspond to a unique locus and separates.Only have when this group parameter of joint space meets the constraint of introducing, the pose point coordinates of corresponding end effector is just meaningful, only when satisfied constraint, this parameter just can by the parameters combination under a large amount of sampling joint space, each combination correspond to a locus point, the three-dimensional point cloud atlas meeting the locus point composition under constraints in a large number can describe out range size and the boundary surface of work, necessity of the present invention that Here it is clearly in the graphic.
The working space of robot i.e. end orbit, as the three-dimensional space position point set of hand under various joint space configuration.Some basic inherent constraints of the motion demand fulfillment of anthropomorphic robot, comprise joint angle constraint, stable constraint.The present invention will solve, discuss and contrast two kinds of situations: be that reachable tree under the workspace calculation in simple arm joint space and floating motion/all-around exercises solves respectively.
Embodiment one:
As shown in Figure 2, for working space grid in Fig. 1, the simple working space in arm joint space that uses is solved and description, and Monte Carlo method solves the detailed process of working space, namely build the method in robot motion space under inherent constraint, the method comprises the following steps:
Step S1: take feet as the origin of coordinates, introduces floating motion as X to health basis coordinates system of robot
e=f (θ
f, θ
e), set up an articulated chain based on general joint and kinematics model, the end effector of robot not only with end to the joint of barycenter about being also subject to the impact of barycenter to the joint of feet, as shown in Figure 3,4.
Step S2: based on articulated chain and kinematics model, introduce joint angle constraint, stable constraint utilize Monte Carlo method to sample and solve the working space of end effector of robot, obtain the three-dimensional point cloud grid that working space is formed, as shown in Figure 5, concrete steps are:
Step 201: the robot arm joint space of this example contains 5 joints, retrain at the joint angle of movable joint, adopt within the scope of stable constraint Monte Carlo method to carry out Nsample sublinear stochastical sampling to obtain joint states value, one group of parameter that each stochastical sampling obtains is as a sample point, wherein, joint angle constraint representation is: θ
min≤ θ≤θ
max, θ is joint value, θ
max, θ
minbe respectively the minimum and maximum value in this joint of θ, stable constraint is as constraint during sampling, and the sampling number chosen is Nsample=10000 time.
Step 202: based on articulated chain and kinematics model, carries out positive kinematics calculating to sample point, obtains robot barycenter, according to formula
which is only feet to judge left and right pin, wherein,
for the position of left foot end in z-axis,
for the position of right crus of diaphragm end in z-axis, then the relation in conjunction with barycenter and supporting zone judges that whether this sampling is effective, if, continue to calculate end effector pose point, if not, continue stochastical sampling in shutdown space, it is finally the three-dimensional point cloud of basis drafting pose point with basis coordinates, obtain end effector working space, as shown in Figure 6, for robot uses merely the working space in arm joint space.
Positive kinematics is basic method and the principle of robot, and according to the state of joint angle, solve the pose of target connecting rod under preferred coordinates system, therefore it is usually used in the center of gravity calculation of robot, the state description of robot.
Step 203: three-dimensional point cloud obtains three-dimensional point cloud grid after grid matrix assignment.Grid matrix assignment is specially: represent with the most contiguous mesh point pose point each in three-dimensional point cloud, normalize in same mesh point by close pose point, each mesh point occupy the center of respective mesh space.
As shown in Figure 6, the three-dimensional point cloud atlas that the pose point solved by great amount of samples point is formed can be found out under different parameter samples, due to the redundancy in joint, in fact may correspond to two extremely close pose points by multiple parameter space; Same in order to carry out the across comparison different when, the Euclidean distance reality between a large amount of pose point is very little.For the ease of carrying out the contrast of similar pose point normalizing and spatial dimension, need process pose point being carried out to normalizing.The present invention is by setting up three-dimensional grid to be normalized, and by carrying out gridding process to three dimensions, be divided into intensive a large amount of mesh points to represent three dimensions, each mesh point occupy the center of respective mesh space.Like this for each pose point, the mesh point of arest neighbors can be found to represent, close pose point all can be normalized in same mesh point like this, treat into same pose point, the larger mesh point of difference can be distinguished like this.
Step S3: on the basis of three-dimensional point cloud grid, carries out planar interception, and by extreme value analysis, obtains robot extreme value state in all directions and pose figure.Planar interception is specially: carry out planar interception according to key position (as robot arm horizontal plane) or demand position (as the position that researcher is concerned about) to three-dimensional point cloud grid, numerical value satisfies condition at grade: | z-z
0|≤ε, z are numerical value in plane, z
0for binding occurrence, ε is setting value.
Extreme value scope and the boundary surface of working space directly can be found out from the three-dimensional point cloud atlas of sampling, but because overall sample point solves the three-dimensional point cloud of composition, be not easy to carry out observing accurate shape and structure, so can by carrying out planar interception to key position or demand position, analysis and the discussion of working range be carried out in the cross section obtaining key position.Such as, need to know height and working space during initial position same level position, namely meet constraints z=z
0.But due to gather sample point be random, the z value calculated can not all just in the plane.Increase a relaxation condition, namely think and satisfy condition | z-z
0|≤ε thinks in the plane, with this understanding, be met the truncated of constraints and.
Embodiment two:
Robot working space under complicated all-around exercises is solved.Adopt representative Monte Carlo method in numerical method to carry out solving of working space Point Set, and by introducing such as the range of articulation constraint in each joint of robot under all-around exercises etc. of various inherent constraint equally, the scope of the working space under the complicated case met under these constraints is discussed.Implementation step is with embodiment one, and solving object is the robot Work Space Range of each joint under inherent constraint.
Claims (4)
1. build the method in robot motion space under inherent constraint, it is characterized in that, the method comprises the following steps:
Step S1: take feet as the origin of coordinates, introduces floating motion to health basis coordinates system of robot, sets up an articulated chain based on general joint and kinematics model;
Step S2: based on articulated chain and kinematics model, introduces joint angle range constraint, stable constraint, utilizes Monte Carlo method sample and solves the working space of end effector of robot, obtaining the three-dimensional point cloud grid of working space formation;
Step S3: on the basis of three-dimensional point cloud grid, carries out planar interception, and by extreme value analysis, obtains robot extreme value state in all directions and pose figure.
2. build the method in robot motion space under a kind of inherent constraint according to claim 1, it is characterized in that, described step S2 is specially:
Step 201: retrain at the joint angle of movable joint, within the scope of stable constraint, adopt Monte Carlo method to carry out linear random sampling and obtain joint states value, one group of parameter that each stochastical sampling obtains is as a sample point;
Step 202: based on articulated chain and kinematics model, carries out positive kinematics calculating to sample point, obtains robot barycenter and end effector pose point, is the three-dimensional point cloud that pose point is drawn on basis, obtains end effector working space with basis coordinates;
Step 203: three-dimensional point cloud obtains three-dimensional point cloud grid after grid matrix assignment.
3. under a kind of inherent constraint according to claim 2, build the method in robot motion space, it is characterized in that, described grid matrix assignment is specially: represent with the most contiguous mesh point pose point each in three-dimensional point cloud, normalize in same mesh point by close pose point, each mesh point occupy the center of respective mesh space.
4. under a kind of inherent constraint according to claim 1, build the method in robot motion space, it is characterized in that, described planar interception is specially: carry out planar interception according to key position or demand position to three-dimensional point cloud grid, numerical value satisfies condition at grade: | z-z
0|≤ε, z are numerical value in plane, z
0for binding occurrence, ε is setting value.
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Cited By (10)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN107336231A (en) * | 2017-05-26 | 2017-11-10 | 山东科技大学 | Six Degree-of-Freedom Parallel Platform structure parameter optimizing method |
| CN110264577A (en) * | 2019-06-26 | 2019-09-20 | 中国人民解放军火箭军工程大学 | A kind of collision real-time detection method based on temporal and spatial correlations tracking strategy |
| CN110494261A (en) * | 2017-04-07 | 2019-11-22 | X开发有限责任公司 | For establishing and keeping the method and system of prebuild relationship |
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| CN112192567A (en) * | 2020-09-29 | 2021-01-08 | 珠海格力智能装备有限公司 | Method and device for acquiring working range of robot |
| CN112847338A (en) * | 2020-12-25 | 2021-05-28 | 环球车享汽车租赁有限公司 | Method, computing device, and storage medium for determining vehicle energy replenishment location |
| CN113500602A (en) * | 2021-07-23 | 2021-10-15 | 鲁东大学 | Distributed sampling control for multi-link manipulator system |
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Citations (6)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US20080011904A1 (en) * | 2005-05-06 | 2008-01-17 | United States Of America As Represented By The Administrator Of The Nasa | Method and Associated Apparatus for Capturing, Servicing, and De-Orbiting Earth Satellites Using Robotics |
| JP2011255500A (en) * | 2011-08-01 | 2011-12-22 | National Institute Of Advanced Industrial Science & Technology | Control device for legged mobile robot |
| CN103019096A (en) * | 2012-11-23 | 2013-04-03 | 北京理工大学 | Humanoid robot inverse dynamics controller based on acceleration optimization |
| CN103092196A (en) * | 2011-10-28 | 2013-05-08 | 同济大学 | Two-foot robot track generating and modulating method based on certified program generator (CPG) mechanism |
| CN103192397A (en) * | 2012-01-09 | 2013-07-10 | 沈阳新松机器人自动化股份有限公司 | Off-line visual programming method and system for robot |
| CN103714242A (en) * | 2013-12-06 | 2014-04-09 | 中国石油大学(华东) | Singularity-avoiding input parameter value space method for avoiding kinematic singularity in parallel mechanisms |
-
2014
- 2014-09-30 CN CN201410521891.5A patent/CN104325462B/en active Active
Patent Citations (6)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US20080011904A1 (en) * | 2005-05-06 | 2008-01-17 | United States Of America As Represented By The Administrator Of The Nasa | Method and Associated Apparatus for Capturing, Servicing, and De-Orbiting Earth Satellites Using Robotics |
| JP2011255500A (en) * | 2011-08-01 | 2011-12-22 | National Institute Of Advanced Industrial Science & Technology | Control device for legged mobile robot |
| CN103092196A (en) * | 2011-10-28 | 2013-05-08 | 同济大学 | Two-foot robot track generating and modulating method based on certified program generator (CPG) mechanism |
| CN103192397A (en) * | 2012-01-09 | 2013-07-10 | 沈阳新松机器人自动化股份有限公司 | Off-line visual programming method and system for robot |
| CN103019096A (en) * | 2012-11-23 | 2013-04-03 | 北京理工大学 | Humanoid robot inverse dynamics controller based on acceleration optimization |
| CN103714242A (en) * | 2013-12-06 | 2014-04-09 | 中国石油大学(华东) | Singularity-avoiding input parameter value space method for avoiding kinematic singularity in parallel mechanisms |
Non-Patent Citations (2)
| Title |
|---|
| 蔡志强等: ""基于CPG的双足机器人NAO的行走控制"", 《华中科技大学学报（自然科学版）》 * |
| 陈毅鸿等: ""基于动量控制的人型机器人实时稳定全身运动规划"", 《控制理论与应用》 * |
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| US11226621B2 (en) * | 2018-02-14 | 2022-01-18 | Teradyne, Inc. | Method for optimization of robotic transportation systems |
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| CN110992372A (en) * | 2019-11-21 | 2020-04-10 | 浙江大华技术股份有限公司 | Article grabbing method and device, storage medium and electronic device |
| CN110992372B (en) * | 2019-11-21 | 2023-08-29 | 浙江大华技术股份有限公司 | Article grabbing method and device, storage medium and electronic device |
| CN111045333A (en) * | 2019-12-31 | 2020-04-21 | 山东交通学院 | Determination method for control reachable set of overdrive system under each pair of linear constraint control components |
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