CN104483898A - Method for searching Delta robot inscribed cylinder expected work space - Google Patents

Method for searching Delta robot inscribed cylinder expected work space Download PDF

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Publication number
CN104483898A
CN104483898A CN201410587370.XA CN201410587370A CN104483898A CN 104483898 A CN104483898 A CN 104483898A CN 201410587370 A CN201410587370 A CN 201410587370A CN 104483898 A CN104483898 A CN 104483898A
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China
Prior art keywords
work space
delta robot
radius
cylinder
inscribed
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CN201410587370.XA
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刘宏伟
梁艳阳
王效杰
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Southwest University of Science and Technology
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Southwest University of Science and Technology
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Priority to CN201410587370.XA priority Critical patent/CN104483898A/en
Publication of CN104483898A publication Critical patent/CN104483898A/en
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    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
    • G05B19/00—Programme-control systems
    • G05B19/02—Programme-control systems electric
    • G05B19/18—Numerical control [NC], i.e. automatically operating machines, in particular machine tools, e.g. in a manufacturing environment, so as to execute positioning, movement or co-ordinated operations by means of programme data in numerical form
    • G05B19/19—Numerical control [NC], i.e. automatically operating machines, in particular machine tools, e.g. in a manufacturing environment, so as to execute positioning, movement or co-ordinated operations by means of programme data in numerical form characterised by positioning or contouring control systems, e.g. to control position from one programmed point to another or to control movement along a programmed continuous path

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  • Engineering & Computer Science (AREA)
  • Human Computer Interaction (AREA)
  • Manufacturing & Machinery (AREA)
  • Physics & Mathematics (AREA)
  • General Physics & Mathematics (AREA)
  • Automation & Control Theory (AREA)
  • Numerical Control (AREA)

Abstract

A method for searching Delta robot inscribed cylinder expected work space is characterized by determining height range of an inscribed cylinder, determining maximum radius of the inscribed circle with the circle center position being given, determining radius and position of the maximum inscribed circle in the work space, determining the height of the inscribed cylinder with the radius being given in the work space, and determining the expected work space of the inscribed largest-size cylinder in the work space and the like, and thus the inscribed cylinder expected work space in the Delta robot work space can be found. The work space in regular shape helps to eliminate unfavorable influence of irregular protrusions at the edges of the actual work space on movement and control of a robot. The method can be used for searching the cylinder inscribed expected work space, and also can be used for searching other regular inscribed expected work spaces.

Description

A kind of method of searching for Delta robot inscribed circle cylinder expectation work space
Technical field
The present invention relates to and a kind ofly search in parallel robot the method connecing Rules space, a kind of particularly method of searching for Delta robot inscribed circle cylinder work space.
Background technology
Parallel robot is that a kind of moving platform is connected by least two independent operating chains with between fixed platform, and has the robot of two and above degree of freedom.Compared with serial manipulator, the plurality of advantages such as parallel robot has that precision is high, bearing capacity is large, rigidity is high, compact conformation, response are fast, but there is the relatively little shortcoming of work space simultaneously.The Delta robot with three translation freedoms is a kind of parallel robot being successfully applied to the industries such as medical treatment, food, medicine.But Delta robot working space is little, and there are many irregular projections on border, easily enters unusual state when robot runs near border.Therefore, design and controllers often " expectation " replace former work space with regular shape " inside connect and expect work space ", and this has important meaning to the motion control of robot and path planning.Determine that can hold rule in work space expects that the size of work space also can be used as the index of Delta robot mechanism design, and in order to be beneficial to robotization, application is necessary with the scalarization method of programming realization simultaneously.
Summary of the invention
In order to make Delta away from unusual pose thus ensure its trouble free service, and be more prone to carry out motion control and trajectory planning to it, the invention provides and a kind ofly search for inscribed circle cylinder in Delta work space and expect the method for work space.The method is easy to programming realization.In order to realize above function, the present invention adopts following methods:
First the geometric model of Delta robot is set up; Then obtain the relational expression between its work space and robot architecture's parameter according to geometric model, and expression formula be divided into bound to carry out parametrization the Representation Equation; Then determine in Delta robot working space, to hold the maximum height that work space expected by right cylinder; Subsequently, can hold based on greatest circle method by given central coordinate of circle determination work space, the inscribed circle of maximum radius in the space that finds a job, and obtain the method determining the cylindrical maximum height holding given radius in work space; Finally, the right cylinder obtaining determining to hold maximum volume in work space expects that the method for work space is keyed in summary of the invention herein and described paragraph.
Accompanying drawing explanation
Fig. 1 Delta robot architecture schemes;
Fig. 2 determines (0,0, z) can greatest circle be held in place's work space;
Fig. 3 search strategy;
The highest right cylinder of given radius can be held in Fig. 4 determination work space.
Embodiment
Originally by reference to the accompanying drawings, workflow of the present invention is as follows:
(1) geometric model of Delta robot and work space thereof is set up
Accompanying drawing 1 is Delta robot architecture model.Delta robot is formed primarily of fixed platform, moving platform, motor, master arm, slave arm.Three motors be fixed on fixed platform drive three master arms respectively, drive moving platform, thus realize the motion of end by three slave arms.The initial point of coordinate system is positioned at the tie point of motor and master arm f i ( i=1,2,3, lower with) center of equilateral triangle that forms, zaxle perpendicular to this triangle place plane, y-axis perpendicular to f 2 f 3place straight line also deviates from f 1, three coordinate axis meet right-handed coordinate system.The intersection point of slave arm and moving platform e i the leg-of-mutton center formed e 0( x 0, y 0, z 0) be the reference point of end effector position, therefore e 0's zcoordinate is always negative.True origin oarrive f i distance be f, end effector reference point e 0arrive e i distance be e, master arm length f i j i = r f , slave arm length is e i j i = r e .Article one, oE i j i f i e 0form a single side chain;
According to the geometric model set up, the boundary representation of single side chain work space of Delta robot can be obtained:
Be expressed as parametric form:
Coboundary: ,
If , ; Otherwise,
Lower boundary: ,
Because moving platform is driven jointly by three single side chains, the common factor of three single side chain spaces constitutes the work space of Delta robot.Further, parametric form is known thus, x 0< r e , therefore the radius of inscribed circle cylinder r< r e .
(2) determine in Delta robot working space, to hold the maximum height that work space expected by right cylinder
When cylindrical radius is 0, highly maximum, namely its work space with zthe intersection point of axle is cylindrical upper bottom surface.Therefore,
z min=-| r e + r f |cos( θ)， θ=-arcsin( L/| r e + r f |)；
If | r e - r f | <| l|, z max=0; Otherwise, z max=-| r e - r f | cos ( θ), θ=-arcsin ( l/ | r e - r f |);
Maximum height is: h= z max- z min.
(3) determine that in Delta robot working space, the center of circle is positioned at (0,0, z) inradius
Accompanying drawing 2 for determining that in Delta robot working space, the center of circle is positioned at (0,0, z) the method flow diagram of inradius.First determine hold cylindrical maximum height in its work space according to the structural parameters of Delta robot of input, and judge given central coordinate of circle whether within the scope of this.If not, then r=0, and terminate program; Otherwise carry out next step, the lower bound being radius with 0, r e for binary chop is carried out in the upper bound.When being obtained a radius by dichotomy, for determining that the circle of this radius is positioned at work space completely, random generation one is positioned at the point of this circle, judges whether to be positioned at work space by comparing with work space bound.If this point is not positioned at work space, then carry out binary chop using this radius as the new upper bound.Until produce N number of point thereupon and institute be a little all positioned at work space, just determine to be positioned at completely in this circle work space, and be that new lower bound carries out binary chop with this radius.When the upper bound is less than given threshold value with next difference, the lower bound average on now radius is as final result;
in order to reduce calculated amount, when determine this circulation in circle be positioned at work space completely time, next time circulation will no longer the point in this circle be checked, namely judge radius as [ r min, r max] annulus whether be positioned at work space completely.
(4) inscribed circle that in Delta robot working space, radius is maximum is determined
Accompanying drawing 3 is for determining the search strategy of the inscribed circle that radius is maximum in Delta robot working space.When right cylinder bottom surface radius is maximum, be highly 0, upper bottom surface overlaps.This radius is the upper bound that the search of cylinder radius provides scope.Because in above-mentioned altitude range, there is maximal value and unique in right cylinder bottom surface radius, and dull in maximal value both sides, therefore adopt the following search strategy shown in accompanying drawing 3:
Known R (z) [ a, b] between there is maximal value, and uniquely.[ a, b] in get 2 different points c, d, and hypothesis c< d, then compare its functional value:
If r( c) > r( d), then maximal value be positioned at [ a, c] in;
If r( c) < r( d), then maximal value be positioned at [ d, b] in;
then, carry out aforesaid operations between new district, until burst length is less than given threshold value, then think that interval midpoint is functional value maximum.
(5) maximum height of the inscribed circle cylinder of given radius in Delta robot working space is determined
Accompanying drawing 4 is for determining the method flow diagram of the maximum height of the inscribed circle cylinder of given radius in Delta robot working space.Input information is the structural parameters parameter of Delta robot, the bottom surface radius of given expectation right cylinder work space radius, and maximum inscribed circle radius in the Delta robot working space obtained by (4) r( r< radius) and central coordinate of circle (0,0, z).According to input determine to hold cylindrical altitude range [ z min, z max], then with dichotomy respectively [ z, z max] and [ z min, z] in search radius be radiusinscribed circle central coordinate of circle position z upwith z down.If do not found z up, then judge z maxwhether be 0.If so, then z up=0; Otherwise z up= r.
(6) the inscribed circle cylinder that in Delta robot working space, volume is maximum is determined
Because the cylinder volume that can hold maximum volume in work space only has a maximal value about the function of bottom surface radius; And in maximal value both sides, function is dull.Solid yardage method is identical really for this situation and right cylinder maximum sole radius, therefore adopts the searching method in (4).

Claims (4)

1. the maximum inscribed circle cylinder that can hold given radius in a Delta robot working space expects that work space searches plain method, the method expects the maximum height of work space by determining to hold in Delta robot working space right cylinder, the center of circle is positioned at (0,0 z) place's inradius, the method such as maximum inscribed circle radius and position obtain.
2. in a Delta robot working space can expect that work space searches plain method by the maximum inscribed circle cylinder of receiving volume, the method expects the maximum height of work space by determining to hold in Delta robot working space right cylinder, the center of circle is positioned at (0,0 z) place's inradius, maximum inscribed circle radius and position, given radius the method such as maximum inscribed circle cylinder obtain.
3. method according to claim 1 or 2, wherein determine that in Delta robot working space, the center of circle is positioned at (0,0, z) determination of inradius at place, mainly through producing point in garden at random and by whether being positioned at work space with up-and-down boundary multilevel iudge obtaining.
4. the method that is worth most of search function, this function in given area in existence anduniquess maximum (little) value, and be worth both sides dullness most, by determining two points in interval, and comparing the functional value of 2, thus reduce interval range.
CN201410587370.XA 2014-10-29 2014-10-29 Method for searching Delta robot inscribed cylinder expected work space Pending CN104483898A (en)

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Citations (7)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
JPS62165206A (en) * 1986-01-17 1987-07-21 Hitachi Metals Ltd Determining method for work position in robot visual device
JPH06143166A (en) * 1992-11-06 1994-05-24 Meidensha Corp Method for correcting displacement in position of articulated robot
JP2005346718A (en) * 2004-06-02 2005-12-15 Kuka Roboter Gmbh Method and device for improving positional accuracy of manipulator
JP2008221428A (en) * 2007-03-14 2008-09-25 Nidec Sankyo Corp Robot teaching system and method
CN101359224A (en) * 2007-07-31 2009-02-04 洛克威尔自动控制技术股份有限公司 Improved blending algorithm for trajectory planning
CN103192364A (en) * 2013-03-27 2013-07-10 北京工业大学 Improved Delta parallel mechanism robot
CN104062902A (en) * 2014-05-15 2014-09-24 江南大学 Delta robot time optimal trajectory planning method

Patent Citations (7)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
JPS62165206A (en) * 1986-01-17 1987-07-21 Hitachi Metals Ltd Determining method for work position in robot visual device
JPH06143166A (en) * 1992-11-06 1994-05-24 Meidensha Corp Method for correcting displacement in position of articulated robot
JP2005346718A (en) * 2004-06-02 2005-12-15 Kuka Roboter Gmbh Method and device for improving positional accuracy of manipulator
JP2008221428A (en) * 2007-03-14 2008-09-25 Nidec Sankyo Corp Robot teaching system and method
CN101359224A (en) * 2007-07-31 2009-02-04 洛克威尔自动控制技术股份有限公司 Improved blending algorithm for trajectory planning
CN103192364A (en) * 2013-03-27 2013-07-10 北京工业大学 Improved Delta parallel mechanism robot
CN104062902A (en) * 2014-05-15 2014-09-24 江南大学 Delta robot time optimal trajectory planning method

Non-Patent Citations (1)

* Cited by examiner, † Cited by third party
Title
王效杰等: "Delta机器人期望工作空间求解算法研究", 《机械设计与制造》 *

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Application publication date: 20150401