CN105573315B - Geometric smoothing method for Cartesian space trajectory of industrial robot - Google Patents
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Abstract
The invention provides a geometrical smoothing method for a Cartesian space trajectory of an industrial robot, which comprises the following steps: parameterizing geometric curves corresponding to a front track and a rear track in a turning area; calculating the parameter values of the geometrical curves of the front track and the rear track at the joint point of the turning area; judging whether the turning radius exceeds a preset limit condition according to the parameter values of the geometrical curves of the front track and the rear track at the joint point of the turning area, and if so, cutting off the geometrical curves; generating a turning area space curve by utilizing a Bezier curve generation principle; calculating the endpoint speed and acceleration of the geometric curve; and generating a turning area track by adopting a one-dimensional speed planning algorithm and speed planning boundary conditions. The method and the device perform geometric superposition smoothing on the front track and the rear track of the industrial robot in the turning area so as to ensure the curvature continuity of the geometric curve corresponding to the tracks, and perform speed planning on the smoothed geometric curve to achieve the purpose of controlling the speed of the turning area.
Description
Technical Field
The invention relates to the technical field of industrial robots, in particular to a geometrical smoothing method for a Cartesian space trajectory of an industrial robot.
Background
The movement of an industrial robot in its working space is combined from trajectories generated by a plurality of movement commands entered by a user. The track (such as a straight line and an arc) generated by each motion instruction is smooth, the speed at the endpoint of the track is zero, which is equivalent to the fact that the robot needs to stop first when moving from one track to the next track, namely, when turning, otherwise, the robot can cause severe jitter. If the user does not make a request for the position of the turning point of the two tracks, the user can smoothly transit from one track to the other track without passing through the turning point.
The existing cartesian space trajectory smoothing methods mainly have the following two types,
(1) vector transfer superposition method
And describing the front track and the rear track by using a vector function, and superposing vectors of the two tracks in a track turning area by using a vector transfer principle so as to achieve the effect of smooth transition. The method is simple and direct, and the track superposed in the turning area is the sum of the speeds of the two tracks. However, the superposed tracks are related to the speed, and if the speeds of the front track and the rear track are changed, the track of the turning area is also changed, and the speed change of the track of the turning area cannot be controlled.
(2) Special curve joining method
And connecting the front track and the rear track by using a special curve in the robot track turning area, such as connecting two straight tracks by using a parabola. The method is independent of the speeds of the front track and the rear track, and facilitates speed control in a turning area. However, the special curve often has abrupt changes of curvature at the joint with the front and rear tracks, and further acceleration abrupt changes are caused.
Disclosure of Invention
The object of the present invention is to solve at least one of the technical drawbacks mentioned.
Therefore, the invention aims to provide a geometrical smoothing method for Cartesian space tracks of an industrial robot, which is used for geometrically superposing and smoothing front and rear tracks of the industrial robot in a turning area so as to ensure that the curvature of a geometrical curve corresponding to the tracks is continuous, and planning the speed of the smoothed geometrical curve to achieve the purpose of controlling the speed of the turning area.
In order to achieve the above object, an embodiment of the present invention provides a geometric smoothing method for cartesian space trajectory of an industrial robot, comprising the steps of:
step S1, acquiring the corresponding geometric curves of the front track and the rear track of the industrial robot in the turning area, and parameterizing the geometric curves corresponding to the two tracks, wherein the method comprises the following steps: parameterizing the length of a spatial straight line and the length of a spatial arc in the geometric curve;
step S2, calculating the parameter values of the geometrical curves of the front track and the rear track at the joint point of the turning area according to the preset turning radius Rz;
step S3, judging whether the parameter value of the geometrical curve of the front track and the back track at the joint point of the turning area and the turning radius Rz exceed the preset limit condition, if so, cutting off the geometrical curve;
step S4, generating a turning area space curve by using a Bezier curve generation principle;
step S5, calculating the endpoint speed and the acceleration of the geometric curve according to the turning area space curve and the geometric curve parameter value judged by exceeding the preset limit condition in the step S3, and generating a speed planning boundary condition;
and step S6, generating a turning area track by adopting a one-dimensional rate planning algorithm and the rate planning boundary condition, wherein the turning area track accords with a one-dimensional rate constraint condition to realize the smooth motion of the industrial robot in the turning area.
Further, in the step S1, the parameterized form of the spatial straight line length of the geometric curve is:
wherein s is the length of the space straight line,
and
respectively are the end point coordinates of the space straight line;
the parameterization form of the arc length of the spatial arc of the geometric curve is as follows:
wherein,
parameterizing an arc under a circle center coordinate system of the arcAnd R is a rotation matrix from a center coordinate system to a world coordinate system, and c is a coordinate of the origin of the center coordinate system under the world coordinate system.
Further, in the step S2, for the spatial straight line, the geometric curve parameter value entering the turning zone is: l1z＝L1-RZ(ii) a The value of the geometric curve parameter leaving the turning zone is l2z＝RZ(ii) a Wherein L is1Is the length of the spatial line.
Further, in the step S2,
for the spatial arc, the geometric curve parameter value entering the turning area is as follows:
the values of the geometric curve parameters leaving the turning zone are,
wherein R isCIs the radius of said spatial arc, L1The arc length of the spatial arc.
Further, the preset limiting conditions are as follows:
for a spatial straight line:
wherein Length is the Length of the spatial straight line;
for a spatial arc:
wherein Rc is the radius of the spatial circular arc, and theta is the central angle of the spatial circular arc.
Further, in step S4, the generating a curve of the turning area space using the bezier curve generation principle is:
wherein p(s) is a control function.
Further, the end point speed of the geometric curve is as follows:
the acceleration of the geometric curve is:
further, in the step S6, the one-dimensional rate constraint condition is:
when t is 0, the starting point:
s(0)＝0；
when t is tf, the end point:
s(tf)＝1；
according to the geometric smoothing method for the Cartesian space track of the industrial robot, disclosed by the embodiment of the invention, based on the Bezier curve generation principle, the front track and the rear track of the industrial robot in the turning area are overlapped and smoothed geometrically, so that the curvature continuity of the geometric curves corresponding to the tracks is ensured, and the speed of the smoothed geometric curves is planned to achieve the purpose of controlling the speed of the turning area. The track generated by the invention is irrelevant to the speeds of the front track and the rear track, so that the use precision is ensured, the industrial robot can be in smooth transition during turning, the robot can move smoothly in a turning area, and the efficiency is improved.
Additional aspects and advantages of the invention will be set forth in part in the description which follows and, in part, will be obvious from the description, or may be learned by practice of the invention.
Drawings
The above and/or additional aspects and advantages of the present invention will become apparent and readily appreciated from the following description of the embodiments, taken in conjunction with the accompanying drawings of which:
fig. 1 is a flow chart of a method for geometrical smoothing of cartesian space trajectories for an industrial robot according to one embodiment of the invention;
fig. 2 is a flow chart of a method for geometrical smoothing of cartesian space trajectories for an industrial robot according to another embodiment of the invention;
FIG. 3 is a schematic diagram of a turn zone trajectory generated in accordance with an embodiment of the present invention.
Detailed Description
Reference will now be made in detail to embodiments of the present invention, examples of which are illustrated in the accompanying drawings, wherein like or similar reference numerals refer to the same or similar elements or elements having the same or similar function throughout. The embodiments described below with reference to the drawings are illustrative and intended to be illustrative of the invention and are not to be construed as limiting the invention.
As shown in fig. 1, a method for geometrically smoothing cartesian space trajectory of an industrial robot according to an embodiment of the present invention includes the following steps:
step S1, acquiring the corresponding geometric curves of the front track and the rear track of the industrial robot in the turning area, and parameterizing the geometric curves corresponding to the two tracks, wherein the method comprises the following steps: parameterizing the length of a spatial straight line and the length of a spatial arc in the geometric curve.
In step S1, the spatial straight length parameterization of the geometric curve is:
wherein s is the length of the space straight line,
and
respectively are the end point coordinates of the space straight line;
in order to make the curvature of the geometric curve of the turning zone continuous and feed-forward control, the first derivative and the second derivative of the formula (1) are further calculated:
first derivative of the spatial straight-line parametric form:
second derivative of the spatial straight-line parametric form:
then, the parameterization form of the arc length of the spatial arc of the geometric curve is as follows:
wherein,
the method is characterized in that the method is in a circular arc parameterization form under a circle center coordinate system where a circular arc is located, R is a rotation matrix from the circle center coordinate system to a world coordinate system, and c is a coordinate of an origin of the circle center coordinate system under the world coordinate system.
The first and second derivatives of equation (4) are further calculated: (ii) a
And step S2, calculating the parameter values of the geometrical curves of the front track and the rear track at the connecting point of the turning area according to the preset turning radius Rz.
And calculating the parameter values of the front and rear geometric curves at the joint point of the turning area according to the turning radius value Rz set by the user. Let the turning radius be Rz, when1＝l1zWhen the first curve enters the turning area; when l is2＝l2zWhile the second curve exits the turn zone.
Specifically, for a spatial straight line, the values of the geometric curve parameters entering the turn zone are: l1z＝L1-Rz；
The value of the geometric curve parameter leaving the turning zone is l2z＝RzWherein L is1Is the length of the spatial line.
For a spatial arc, the values of the geometric curve parameters entering the turning zone are as follows:
the values of the geometric curve parameters leaving the turning zone are,
wherein Rc is the radius of the spatial circular arc, L1The arc length of the spatial arc.
And step S3, judging whether the preset limit condition is exceeded or not according to the parameter values of the geometrical curves of the front track and the rear track at the joint point of the turning area and the turning radius Rz, and if so, cutting off the geometrical curves.
For a curve, if the two ends of the curve are provided with turning areas, the two turning areas cannot be overlapped, so that the judgment of the turning radius by preset limiting conditions needs to be set, and the curve is cut off if the preset limiting conditions exceed the limits.
In one embodiment of the present invention, the preset limiting conditions are:
for a spatial straight line:
wherein Length is the Length of a spatial straight line;
for a spatial arc:
where Rc is the radius of the spatial arc and θ is the central angle of the spatial arc.
In step S4, a turning area space curve is generated using the bezier curve generation principle.
The Bezier curve generation principle is
S in this equation is changed to a control function p(s) to achieve a continuation of the curvature of the junction in the turn region.
Calculating the first and second derivatives of the curve of equation (8), wherein,
the first derivative is that of the first order,
the second derivative is that of the first derivative,
and step S5, calculating the endpoint speed and the acceleration of the geometric curve according to the turning zone space curve and the geometric curve parameter values judged by exceeding the preset limiting conditions in the step S3, and generating a speed planning boundary condition.
It is desirable to satisfy the requirement that the velocity and acceleration at the splice point of the turn zone trajectory be continuous, i.e.,
when s is 0, i.e. when entering the junction,
when s is 1, i.e. when leaving the junction point,
the end point velocity of the geometric curve is calculated as:
the acceleration of the geometric curve is calculated as:
the speed and the acceleration of the track of the turning area at any moment can be calculated and output by the method.
And step S6, generating a turning area track by adopting a one-dimensional rate planning algorithm and a rate planning boundary condition, wherein the turning area track accords with a one-dimensional rate constraint condition so as to realize the smooth motion of the industrial robot in the turning area.
And calling a one-dimensional speed planning algorithm to generate the turning area track. The constraints of the one-dimensional rate planning are,
when t is 0, the starting point:
s(0)＝0；
when t is tf, the end point:
s(tf)＝1；
according to the constraint conditions, the effects that the end points of the turning area are smooth and continuous and the speed in the turning area is controllable can be achieved, so that the robot moves smoothly in the turning area.
Fig. 2 is a flow chart of a method for geometrical smoothing of cartesian space trajectories for an industrial robot according to another embodiment of the invention.
In step S201, two space curves before and after the input.
Step S202, parameterizing the spatial straight line length.
And step S203, parameterizing the arc length of the spatial arc.
And step S204, calculating the parameter values of the front curve and the rear curve at the turning area transferring point.
For a spatial straight line, the values of the geometric curve parameters entering the turning zone are: l1z＝L1-RZ；
The value of the geometric curve parameter leaving the turning zone is l2z＝RZWherein L is1Is the length of the spatial line.
For a spatial arc, the values of the geometric curve parameters entering the turning zone are as follows:
the values of the geometric curve parameters leaving the turning zone are,
wherein Rc is the radius of the spatial circular arc, L1The arc length of the spatial arc.
In step S205, truncation is performed if the limit is exceeded.
In step S206, a turning area space curve is generated.
In step S207, the endpoint velocity and acceleration are calculated.
Step S208, calling a general one-dimensional rate planning algorithm and rate planning boundary conditions,
in step S209, a turning area locus is generated.
Fig. 3 is a schematic illustration of a generated cartesian space trajectory of a turning zone of an industrial robot according to an embodiment of the invention.
Step S210, an arbitrary time position, speed, and acceleration are output.
According to the geometric smoothing method for the Cartesian space track of the industrial robot, disclosed by the embodiment of the invention, based on the Bezier curve generation principle, the front track and the rear track of the industrial robot in the turning area are overlapped and smoothed geometrically, so that the curvature continuity of the geometric curves corresponding to the tracks is ensured, and the speed of the smoothed geometric curves is planned to achieve the purpose of controlling the speed of the turning area. The track generated by the invention is irrelevant to the speeds of the front track and the rear track, so that the use precision is ensured, the industrial robot can be in smooth transition during turning, the robot can move smoothly in a turning area, and the efficiency is improved.
In the description herein, references to the description of the term "one embodiment," "some embodiments," "an example," "a specific example," or "some examples," etc., mean that a particular feature, structure, material, or characteristic described in connection with the embodiment or example is included in at least one embodiment or example of the invention. In this specification, the schematic representations of the terms used above do not necessarily refer to the same embodiment or example. Furthermore, the particular features, structures, materials, or characteristics described may be combined in any suitable manner in any one or more embodiments or examples.
Although embodiments of the present invention have been shown and described above, it is understood that the above embodiments are exemplary and should not be construed as limiting the present invention, and that variations, modifications, substitutions and alterations can be made in the above embodiments by those of ordinary skill in the art without departing from the principle and spirit of the present invention. The scope of the invention is defined by the appended claims and their full range of equivalents.
Claims (8)
1. A method for geometrical smoothing of cartesian spatial trajectories for an industrial robot, characterized by the steps of:
step S1, acquiring the corresponding geometric curves of the front track and the rear track of the industrial robot in the turning area, and parameterizing the geometric curves corresponding to the two tracks, wherein the method comprises the following steps: parameterizing the length of a spatial straight line and the length of a spatial arc in the geometric curve;
step S2, calculating the parameter values of the geometrical curves of the front track and the rear track at the joint point of the turning area according to the preset turning radius Rz;
step S3, judging whether the parameter value of the geometrical curve of the front track and the back track at the joint point of the turning area and the turning radius Rz exceed the preset limit condition, if so, cutting off the geometrical curve;
step S4, generating a turning area space curve by using a Bezier curve generation principle;
step S5, calculating the endpoint speed and the acceleration of the geometric curve according to the turning area space curve and the geometric curve parameter value judged by exceeding the preset limit condition in the step S3, and generating a speed planning boundary condition;
and step S6, generating a turning area track by adopting a one-dimensional rate planning algorithm and the rate planning boundary condition, wherein the turning area track accords with a one-dimensional rate constraint condition to realize the smooth motion of the industrial robot in the turning area.
2. The geometric smoothing method for cartesian spatial trajectories of an industrial robot according to claim 1, wherein in step S1, if the trajectory of an industrial robot is a spatial straight line, its trajectory parameterization is in the form of:
wherein s is the length of the track,
and
respectively the end point coordinates of the trajectory lines;
if the trajectory of the industrial robot is a circular arc of space, its trajectory parameterization is: :
wherein,
the method is characterized in that the method is in a circular arc parameterization form under a circle center coordinate system where a circular arc is located, s is the track length of the robot, R is a rotation matrix from the circle center coordinate system to a world coordinate system, c is a coordinate of an origin of the circle center coordinate system under the world coordinate system, and R is the radius of the space circular arc.
3. The geometric smoothing method for cartesian space trajectory of an industrial robot according to claim 1, characterized in that in said step S2,
for a spatial straight line, the values of the geometric curve parameters entering the turning zone are: l1z＝L1-RZ；
The value of the geometric curve parameter leaving the turning zone is l2z＝RZ；
Wherein L is1Is the length of the spatial line.
4. The geometric smoothing method for cartesian space trajectory of an industrial robot according to claim 1, characterized in that in said step S2,
for the spatial arc, the geometric curve parameter value entering the turning area is as follows:
the values of the geometric curve parameters leaving the turning zone are,
wherein R isCIs the radius of said spatial arc, L1The arc length of the spatial arc.
5. A method for geometrical smoothing of cartesian spatial trajectories for an industrial robot according to claim 1, characterized in that the preset constraints are:
for a spatial straight line:
wherein Length is the Length of the spatial straight line;
for a spatial arc:
wherein,rc is the radius of the spatial circular arc, and theta is the central angle of the spatial circular arc.
6. The geometric smoothing method for cartesian space trajectory of an industrial robot according to claim 1, wherein in the step S4, the generating the turning zone space curve using the bezier curve generation principle is:
wherein p(s) is a control function, s is a spatial trajectory length,
and
the spatial curve expressions for the entering turning zone and the leaving turning zone are respectively.
7. A method of geometrical smoothing of a cartesian space trajectory for an industrial robot according to claim 6, characterized in that the end point velocities of the geometrical curves are:
the acceleration of the geometric curve is:
wherein r is1For the expression of the geometrical curve entering the turn zone, r2Is a geometric curve expression of the leaving turning zone; s is the spatial trajectory length; p(s) is a control function.
8. The geometric smoothing method for cartesian space trajectory of an industrial robot according to claim 7, wherein in said step S6, said one-dimensional velocity constraint is:
when t is 0, the starting point:
s(0)＝0；
t＝tfand (3) time, end point:
s(tf)＝1；
where s (0) is the spatial trajectory length when t is 0, s (t)f) Is t ═ tfThe spatial trajectory length of time.
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