CN105082156B - Space trajectory smoothing method based on speed optimum control - Google Patents
Space trajectory smoothing method based on speed optimum control Download PDFInfo
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Abstract
The invention proposes a space trajectory smoothing method based on speed optimum control. The method comprises the steps of: obtaining a starting point, a middle point and an ending point of a space trajectory, a preset turning area radius and preset parameters in the mechanical arm operation of a robot; judging if the preset turning area radius r exceeds one half of the length of a first simple trajectory; selecting a turning mode of the robot as equal-length turning or equal-time turning, and calculating coordinates of M, S and E points formed by intersecting first and second simple trajectories; and building a local coordinate system according to the calculated coordinates of the S, M and E points, and calculating a trajectory equation of a turning area of the space trajectory under the local coordinate system, wherein the trajectory equation is a secondary curve of a smooth turning area. The method can guarantee the speed direction continuity, can conveniently position the space positions of terminal actuators of the mechanical arms at any time, and is convenient to control.
Description
Technical field
The present invention relates to technical field of robot control, more particularly to a kind of space tracking based on speed optimum control is put down
Sliding method.
Background technology
Space tracking smooth be spatial kinetics a branch.Space tracking can be by a series of simple track splicings
Into.Simple track is divided into two kinds of straight line and circular arc, and its beginning and end is referred to as node.The node that operation task need to be carried out is referred to as stopping
Stop, the node without operation task is referred to as transition point.In motor process, by speed be zero to reach formulate speed, by formulating
Speed reduction, to zero, is all very time-consuming.In order to improve mass motion speed, lift work efficiency and set it is necessary to the side of thinking
Method removes unnecessary acceleration and deceleration process from, and high-speed cruising is kept as far as possible.The presence of transition point is often to get around barrier.
Along the traveling process of track, without the need for accurately arriving at transition point, therefore the smooth concept of turning area is proposed, i.e., residing for transition point
Track joint, takes smooth curved transition, fair speed is kept by new smooth track, so as to lift turning speed.
Existing smooth trajectory scheme mainly has two categories below.
(1) based on speed planning curve, according to principle when waiting (according to former speed planning, in turning starting point to turning
Between time for putting it is equal with the time of intermediate point to terminal) carry out the smooth planning of track.Calculated by speed planning curve and turned
Each spot speed on path, carries out the space vector superposition of displacement.
(2) based on speed planning curve, according to principle of equidistance, (i.e. according to former speed planning, turning starting point is in the middle of turning
The distance of point is equal with the distance of intermediate point to terminal) carry out the smooth planning of track.Turning road is calculated by speed planning curve
Each spot speed on footpath, carries out the space vector superposition of displacement.
The defect of existing above two scheme is：It is excessively multiple without explicit track expression formula, or track expression formula
It is miscellaneous, it is not simple curve, it is difficult to complete the precise control to mechanical arm trajectory planning, also it is unfavorable for calculating obstacle avoidance space.
Meanwhile, performing according to such scheme, the track in Euclidean space for obtaining not is simple smooth curve, and its track is not
Intuitively, it is unfavorable for the direct observation to operation result of operator and evaluates.
The content of the invention
The purpose of the present invention is intended at least solve one of described technological deficiency.
For this purpose, it is an object of the invention to propose a kind of space tracking smoothing method based on speed optimum control, can be with
Ensure the seriality of velocity attitude, the end effector of positioning mechanical arm locus at any time can be facilitated, be easy to control
System.
To achieve these goals, embodiments of the invention provide a kind of space tracking based on speed optimum control and smooth
Method, comprises the steps：
Step S1, obtains starting point Ps, midpoint Pm, terminal Pe, the default turning of the space tracking of robot arm operation
Area radius r and parameter preset flag_dist, wherein, between starting point Ps and midpoint Pm constitute the first simple track, it is described in
The second simple track is constituted between point Pm and terminal Pe；
Step S2, by the default turning area radius r and the described first simple track and the length of the second simple track
Degree is compared, if the default turning area radius r is not above the half of the length of the described first simple track, and does not have
More than the half of the length of the second described simple track, then execution step S3；
Step S3, the turning mode for choosing the robot is that equal length is turned or waits the time to turn, and is calculated first
Coordinate, the first and second simple track of the transition point M formed with the second simple intersection of locus respectively with default circular phase
The coordinate of the S and E points of friendship；
Step S4, according to the coordinate for being calculated S, M and E point local coordinate system is set up, and calculates the space tracking in institute
The equation of locus of the turning area under local coordinate system is stated, wherein, the equation of locus is the conic section of smooth turning area.
Further, in step S2, judge whether the default turning area radius r exceedes described first using following formula
The half of the length of the half and the second simple track of the length of simple track,
Wherein,It is the vector that midpoint Pm is pointed to by starting point Ps,It is the vector that terminal Pe is pointed to by midpoint Pm.
Further, in step S3, when the turning mode chosen is turned for equal length, S, M and E point coordinates is calculated
Comprise the steps：
Being turned according to equal length needs to meetUsing vectorial stacking method, folded respectively by the coordinate of midpoint M
PlusLength is the vector of r in both direction, you can obtain starting point coordinate S, the terminal point coordinate E of turning area, wherein, in
Point M is point Pm, calculates point S and E point coordinates is as follows：
Further, in step S3, when the turning mode chosen is to wait time to turn, comprise the steps：
Being turned according to the time of grade needs to meet t1=t2, wherein, t1For SM section turning times, t2For ME section turning times,
T=min (t1, t2),
Speed planning is substituted into, S, E point is calculated away from M points apart from dists、dists,
Further, in step S4, the turning area for calculating the space tracking under the local coordinate system
Equation of locus, comprise the steps：
Step S41, calculating coordinate change parameter θ and A, comprise the steps：
Wherein, 0 the angle of rotation transformation is carried out for coordinate axess, A is spin matrix, xSMIt is to calculate according in step S3
Distance of the S points and M points for going out on the x-axis direction of coordinate system, xMEIt is to be existed according to the M points and E points calculated in step S3
Distance on the x-axis direction of coordinate system, ySMIt is in the y-axis direction of coordinate system according to the S points and M points calculated in step S3
On distance, yMEIt is the distance according to the M points and E points calculated in step S3 on the y-axis direction of coordinate system；
Step S42, derives vectorial coordinateWithComprise the steps：
Wherein,ForExpression under the local coordinate system,ForTable under the local coordinate system
Show,
Step 43, the equation of locus y for calculating the turning area of the space tracking under the local coordinate system is：
Y=ax2,
Wherein,A is the parameter of the corresponding conic section of the equation of locus, O=S-As, r are default radius of turn, p, q are parabola parameter, and O is the zero of the local coordinate system
Expression under global coordinate system, As is the translating sections in coordinate transformation process, s (xs, ys), m (xm, ym),Respectively
For the starting point of turning area, intermediate point, terminal point coordinate.
Space tracking smoothing method based on speed optimum control according to embodiments of the present invention, can be by robotic
The conic section Jing coordinate transforms of arm running space track generate smooth turning area expression formula, so as to ensure the continuous of velocity attitude
Property, by seamlessly transitting two straight paths, with reference to S type speed plannings, the smooth turning scheme of acceleration, speed, displacement is obtained,
Track simple, intuitive, can facilitate the end effector of positioning mechanical arm locus at any time, be easy to control.While by
In track be simple conic section, therefore can simple and Convenient Calculation go out obstacle avoidance space.Additionally, the present invention be adapted to equidistantly with
Deng when two kinds of turning demands, user can easily compare and choose more excellent scheme according to practical situation.
The additional aspect of the present invention and advantage will be set forth in part in the description, and partly will become from the following description
Obtain substantially, or recognized by the practice of the present invention.
Description of the drawings
The above-mentioned and/or additional aspect and advantage of the present invention will become from the description with reference to accompanying drawings below to embodiment
It is substantially and easy to understand, wherein：
Fig. 1 is the flow process of the space tracking smoothing method based on speed optimum control according to one embodiment of the invention
Figure；
Fig. 2 is the schematic diagram of the first and second simple tracks according to the embodiment of the present invention；
The flow process of Fig. 3 space tracking smoothing methods based on speed optimum control in accordance with another embodiment of the present invention
Figure.
Specific embodiment
Embodiments of the invention are described below in detail, the example of embodiment is shown in the drawings, wherein identical from start to finish
Or similar label represents same or similar element or the element with same or like function.Retouch below with reference to accompanying drawing
The embodiment stated is exemplary, it is intended to for explaining the present invention, and be not considered as limiting the invention.
The present invention carries a kind of space tracking smoothing method based on speed optimum control, using the smooth spy of conic section
Property, according to the radius of turn of two straight line path starting points, terminal and folded turning area, generate conic section, two straight line in smoothing junction
Path, generates smooth turning area expression formula, so as to ensure the seriality of velocity attitude by conic section Jing coordinate transforms.
As shown in figure 1, the space tracking smoothing method based on speed optimum control of the embodiment of the present invention, including following step
Suddenly：
Step S1, obtains starting point Ps, midpoint Pm, terminal Pe, the default turning of the space tracking of robot arm operation
Area radius r and parameter preset flag_dist.Wherein, the first simple track, midpoint Pm and end are constituted between starting point Ps and midpoint Pm
The second simple track is constituted between point Pe.Parameter preset flag_dist is to take the parameter equidistantly turned or turn when waiting, its value
For 1 when for equidistant turning, turn when otherwise to wait.
Fig. 2 is the schematic diagram of the first and second simple tracks according to the embodiment of the present invention.
Definition first to turning area is illustrated：At the transition point M that two simple intersection of locus are formed, with transition point
For origin, circle is done as radius with a certain particular value R, intersect two simple tracks in S, 2 points of E, by line segment SM, ME, circular arc ES is surrounded
Region be turning area.With reference to Fig. 2, the starting point of the first simple track is Ps, and terminal is transition point M；Second simple track
Starting point is M, and terminal is Pe.First and second simple tracks are straight path.
Before starting to plan turning area track, simple track need to be intersected by two and determine the plane that current path is located, and
Two dimensional surface and three-dimensional Coordinate Conversion equation are set up, it is then determined that coordinate of each key point in two dimensional surface.Follow-up step
Suddenly carry out on this plane.
Step S2, default turning area radius r is compared with the length of the first simple track and the second simple track, such as
The default turning area radius r of fruit is not above the half of the length of the first simple track, and the second simple track being not above
The half of length, then execution step S3.
In this step, using following formula judge default turning area radius r whether more than the first simple track length one
Partly with the half of the length of the second simple track,
Wherein,The vector that midpoint Pm is pointed to by starting point Ps, i.e., the first simple track in former track,Be by
Midpoint Pm points to the vector of terminal Pe, i.e., the second simple track in former track.
Step S3, the turning mode for choosing robot is that equal length is turned or waits the time to turn, and is calculated first and the
Coordinate, the first and second simple tracks of the transition point M that two simple intersection of locus are formed respectively with the S and E of default circular intersection
The coordinate of point.
Specifically, equidistantly planned according to starting point Ps, midpoint Pm, terminal Pe, default turning area radius r or advised when waiting
Draw.Wherein, equidistant planning can directly be tried to achieve by radius of turn r.For planning when waiting, turned by S type speed plannings
Point calculates turning final position to the time of transition point with this, thus obtains turning area starting and terminal point coordinate.That is, the present invention can
With based on S types speed planning and while support etc. when with equidistant two kinds planning turning area algorithms.
Planning when separately below to equidistantly planning and waiting is illustrated.
When the turning mode chosen is turned for equal length, calculate S, M and E point coordinates and comprise the steps：
Equal length mode is turned and requires that turning area starting point is long to turning area terminal to turning area intermediate point, turning area intermediate point
Degree is equal, i.e.,Being turned according to equal length needs to meetUsing vectorial stacking method, by midpoint M
The coordinate of (midpoint M is point Pm) is superimposed respectivelyLength is the vector of r in both direction, you can obtain turning area
The coordinate of starting point S, the coordinate of terminal E.
When the turning mode chosen is to wait time to turn, comprise the steps：
Require that turning area starting point is used to turning area intermediate point, turning area intermediate point to turning area terminal Deng time turning mode
When equal, i.e. t1=t2, wherein, t1For SM section turning times, t2For ME section turning times,
T=min (t1, t2), (4)
Speed planning is substituted into, S, E point is calculated away from M points apart from dists、dists,
According to the calculated point coordinates of S, M, E tri- of step S3, local coordinate system is set up, by coordinate transform by the problem
It is transferred under local coordinate system and solves so that the equation of locus of turning area of the track tried to achieve under local coordinate system is simple
Conic section.Meet the solution procedure of the turning area curvilinear equation of smoothness condition for calculating below.
Step S4, according to the coordinate for being calculated S, M and E point local coordinate system is set up, and is calculated space tracking and is sat in local
The equation of locus of the turning area under mark system, i.e. turning area equation of locus.Wherein, equation of locus is the secondary song of smooth turning area
Line.
In algorithm flow, the statement to quadratic curve equation is set up under local coordinate system, is passed through with global coordinate system
Linear transformation is mapped.
Step S41, calculating coordinate change parameter θ and A, comprise the steps：
Wherein, θ carries out the angle of rotation transformation for coordinate axess, and A is spin matrix, xSMIt is to calculate according in step S3
Distance of the S points and M points for going out on the x-axis direction of coordinate system, xMEIt is to be existed according to the M points and E points calculated in step S3
Distance on the x-axis direction of coordinate system, ySMIt is in the y-axis direction of coordinate system according to the S points and M points calculated in step S3
On distance, yMEIt is the distance according to the M points and E points calculated in step S3 on the y-axis direction of coordinate system；
Step S42, derives vectorial coordinateWithComprise the steps：
Wherein,ForExpression under local coordinate system,ForExpression under local coordinate system, coordinate becomes
Changing can decouple to translate and rotating two parts.For the conversion of vector, the translating sections of coordinate transform are eliminated, only surplus
Lower rotating part, therefore the expression under two coordinates can directly connect by transformation matrix A.
Step S43, the equation of locus y for calculating turning area of the space tracking under local coordinate system is：
Y=ax2,
Wherein,A is the parameter of the corresponding conic section of equation of locus, O=S-As, r are default radius of turn, and p, q are parabola parameter, and O is the zero of local coordinate system in the overall situation
Expression under coordinate system, As is the translating sections in coordinate transformation process, s (xs, ys), m (xn, ym), c (xe, ye) respectively turn
The starting point in curved area, intermediate point, terminal point coordinate.
The flow process of Fig. 3 space tracking smoothing methods based on speed optimum control in accordance with another embodiment of the present invention
Figure.
Step S301, is input into Ps, Pm, r, flag_dist.
Step S302, judges radius of turn, less than the half of arbitrary simple track.
Specifically, judge that turning area radius r is not above the half of the length of the first simple track, and for being not above
The half of the length of two simple tracks,
Step S303, is turned tactful using equal length.
Equal length mode is turned and requires that turning area starting point is long to turning area terminal to turning area intermediate point, turning area intermediate point
Degree is equal, i.e.,
The times such as step S304, employing turn tactful.
Require that turning area starting point is used to turning area intermediate point, turning area intermediate point to turning area terminal Deng time turning mode
When equal, i.e. t1=t2.
It should be noted that step S303 and step S304 can select an execution.
Step S305, obtains the point coordinates of S, M, E tri-.
Step S306, solves transformation matrix of coordinates.
Wherein,
Step S307, solves the local coordinate of SM, ME vector.
Wherein,
Step S308, by formula parabola parameter, each point coordinates, local coordinate system origin relative coordinates are derived.
Step S309, output trajectory parameter and coordinate conversion parameter.
Y=ax2,
Wherein,A is the parameter of the corresponding conic section of equation of locus, O=S-As, r are default radius of turn, and p, q are parabola parameter, and O is the zero of local coordinate system in the overall situation
Expression under coordinate system, As is the translating sections in coordinate transformation process, s (xa, ya), m (xn, ym), e (xe, ye) respectively turn
The starting point in curved area, intermediate point, terminal point coordinate.
Space tracking smoothing method based on speed optimum control according to embodiments of the present invention, can be by robotic
The conic section Jing coordinate transforms of arm running space track generate smooth turning area expression formula, so as to ensure the continuous of velocity attitude
Property, by seamlessly transitting two straight paths, with reference to S type speed plannings, the smooth turning scheme of acceleration, speed, displacement is obtained,
Track simple, intuitive, can facilitate the end effector of positioning mechanical arm locus at any time, be easy to control.While by
In track be simple conic section, therefore can simple and Convenient Calculation go out obstacle avoidance space.Additionally, the present invention be adapted to equidistantly with
Deng when two kinds of turning demands, user can easily compare and choose more excellent scheme according to practical situation.
In the description of this specification, reference term " one embodiment ", " some embodiments ", " example ", " specifically show
The description of example " or " some examples " etc. means to combine specific features, structure, material or spy that the embodiment or example are described
Point is contained at least one embodiment of the present invention or example.In this manual, to the schematic representation of above-mentioned term not
Necessarily refer to identical embodiment or example.And, the specific features of description, structure, material or feature can be any
One or more embodiments or example in combine in an appropriate manner.
Although embodiments of the invention have been shown and described above, it is to be understood that above-described embodiment is example
Property, it is impossible to limitation of the present invention is interpreted as, one of ordinary skill in the art is in the principle and objective without departing from the present invention
In the case of above-described embodiment can be changed within the scope of the invention, change, replace and modification.The scope of the present invention
Limited by claims and its equivalent.
Claims (5)
1. a kind of space tracking smoothing method based on speed optimum control, it is characterised in that comprise the steps：
Step S1, obtains starting point Ps, midpoint Pm, terminal Pe, the default turning area half of the space tracking of robot arm operation
Footpath r and parameter preset flag_dist, wherein, the first simple track, the midpoint Pm are constituted between starting point Ps and midpoint Pm
The second simple track is constituted and terminal Pe between；
Step S2, the default turning area radius r is entered with the length of the described first simple track and the second simple track
Row compares, if the default turning area radius r is not above the half of the length of the described first simple track, and is not above
The half of the length of the second described simple track, then execution step S3；
Step S3, the turning mode for choosing the robot is that equal length is turned or waits the time to turn, and is calculated first and the
Coordinate, the first and second simple track of the transition point M that two simple intersection of locus are formed respectively with the S of default circular intersection
With the coordinate of E points；
Step S4, according to the coordinate for being calculated S, M and E point local coordinate system is set up, and calculates the space tracking in the office
The equation of locus of the turning area under portion's coordinate system, wherein, the equation of locus is the conic section of smooth turning area.
2. the space tracking smoothing method of speed optimum control is based on as claimed in claim 1, it is characterised in that in the step
In rapid S2, using following formula judge the default turning area radius r whether exceed the half of the length of the described first simple track with
The half of the length of the second simple track,
Wherein,It is the vector that midpoint Pm is pointed to by starting point Ps,It is the vector that terminal Pe is pointed to by midpoint Pm.
3. the space tracking smoothing method of speed optimum control is based on as claimed in claim 2, it is characterised in that in the step
In rapid S3, when the turning mode chosen is turned for equal length, calculate S, M and E point coordinates and comprise the steps：
Being turned according to equal length needs to meetUsing vectorial stacking method, it is superimposed respectively by the coordinate of midpoint MLength is the vector of r in both direction, you can obtain starting point coordinate S, the terminal point coordinate E of turning area, wherein, midpoint M
As point Pm, calculates point S and E point coordinates is as follows：
4. the space tracking smoothing method of speed optimum control is based on as claimed in claim 2, it is characterised in that in the step
In rapid S3, when the turning mode chosen is to wait time to turn, comprise the steps：
Being turned according to the time of grade needs to meet t1=t2, wherein, t1For SM section turning times, t2For ME section turning times,
T=min (t1, t2),
Speed planning is substituted into, S, E point is calculated away from M points apart from distS、distE,
5. the space tracking smoothing method of speed optimum control is based on as claimed in claim 1, it is characterised in that in the step
In rapid S4, the equation of locus of the turning area under the local coordinate system that calculates the space tracking comprises the steps：
Step S41, calculating coordinate change parameter θ and A, comprise the steps：
Wherein, θ carries out the angle of rotation transformation for coordinate axess, and A is spin matrix, xSMAccording to calculating in step S3
The distance of S points and M points on the x-axis direction of coordinate system, xMEIt is in coordinate according to the M points and E points calculated in step S3
Distance on the x-axis direction of system, ySMBe according to the S points and M points calculated in step S3 on the y-axis direction of coordinate system
Distance, yMEIt is the distance according to the M points and E points calculated in step S3 on the y-axis direction of coordinate system；
Step S42, derives vectorial coordinateWithComprise the steps：
Wherein,ForExpression under the local coordinate system,ForExpression under the local coordinate system,
Step 43, the equation of locus y for calculating the turning area of the space tracking under the local coordinate system is：
Y=ax2,
Wherein,A is the parameter of the corresponding conic section of the equation of locus, O=S-As, r are default radius of turn, and p, q are parabola parameter, and O is that the zero of the local coordinate system exists
Expression under global coordinate system, As is the translating sections in coordinate transformation process, s (xs, ys), m (xm, ym), e (xe, ye) respectively
For the starting point of turning area, intermediate point, terminal point coordinate.
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| CN102374866A (en) * | 2011-08-25 | 2012-03-14 | 光庭导航数据（武汉）有限公司 | Destructive road shape fusion method based on traveling direction |
| CN103914629A (en) * | 2014-04-23 | 2014-07-09 | 东南大学 | Method for real-time simulation of unstable target motion trail based on B spline fitting |
| CN104191428A (en) * | 2014-08-27 | 2014-12-10 | 深圳科瑞技术股份有限公司 | Movement path planning method and system based on SCARA |
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