CN105904458B - A kind of incomplete remote operating about beam control method based on complex operations task - Google Patents
A kind of incomplete remote operating about beam control method based on complex operations task Download PDFInfo
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- CN105904458B CN105904458B CN201610323695.6A CN201610323695A CN105904458B CN 105904458 B CN105904458 B CN 105904458B CN 201610323695 A CN201610323695 A CN 201610323695A CN 105904458 B CN105904458 B CN 105904458B
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- B—PERFORMING OPERATIONS; TRANSPORTING
- B25—HAND TOOLS; PORTABLE POWER-DRIVEN TOOLS; MANIPULATORS
- B25J—MANIPULATORS; CHAMBERS PROVIDED WITH MANIPULATION DEVICES
- B25J9/00—Programme-controlled manipulators
- B25J9/16—Programme controls
- B25J9/1656—Programme controls characterised by programming, planning systems for manipulators
- B25J9/1664—Programme controls characterised by programming, planning systems for manipulators characterised by motion, path, trajectory planning
Abstract
The invention discloses a kind of incomplete remote operating about beam control method based on complex operations task, by calculating constraint matrix CVF, complex operations Task-decomposing, final design constraint controller；The present invention compared with general Mechanical arm control method, has two big beneficial effects of task aspect and control method for complicated spatial manipulation task.First, the manipulation tasks to be completed in space of mechanical arm include close target, path trace and hide obstacle etc., the present invention chooses suitable motion spinor set come structure constraint matrix according to the difference of operation task, the ability compared with previous methods with more adaptation complex task；Secondly, nonholonomic constraint control method can make operation more flexible, and operator can only be moved with control machinery arm in translation or direction of rotation, without providing extra constraint, so as to mitigate operator's pressure.
Description
【Technical field】
The invention belongs to Space teleoperation technical field, is related to a kind of incomplete remote operating based on complex operations task about
Beam control method.
【Background technology】
Have been proven that virtual clamp in terms of task execution time and overall precision all in many robot fields
It is improved, but fixture is also the auxiliary of non-sensitive-type, such as during Space teleoperation, it is necessary to by virtual clamp to machinery
The position of arm end and posture are controlled simultaneously, are often lost to terminal angle in the case where ensureing that position control is optimal
Accurate control.In order to realize good operating effect in Space teleoperation, it is necessary to suitable auxiliary to mechanical arm tail end addition
Help, it is flexibly carried out position and attitude harmony according to task environment and operation task.
In unstructured moving grids, the motion of robot by geometry and Dynamic Constraints, translation and rotary freedom by
To limitation.In Space teleoperation task process, mechanical arm tail end is general only just to be completed to grasp under the restraint condition of translation direction
Make task, but be directed to some complicated spatial manipulation tasks, the only constraint limitation in translation direction is difficult to ensure that the height of operation
Effect property and security, therefore require also to add booster action in mechanical arm tail end direction of rotation, allow the operator to dynamic basis
Actual operating condition changes the virtual clamp auxiliaring effect of translation and direction of rotation, so as to preferably complete remote operating task.
【The content of the invention】
The shortcomings that it is an object of the invention to overcome above-mentioned prior art, there is provided a kind of based on the non-complete of complex operations task
Whole remote operating about beam control method.
To reach above-mentioned purpose, the present invention is achieved using following technical scheme：
A kind of incomplete remote operating about beam control method based on complex operations task, comprises the following steps：
1) constraint matrix C is calculatedVF；
Define constraint matrix CVFRestriction ability corresponding to expression, and CVFIt is 6 × 6 positive semidefinite symmetrical matrixes, and by steric forces
It is mapped to CVFMatrix element；The motion of operator control machinery arm end towards optimal direction and non-optimal direction constitutes sky
Between geometrical constraint, and spinor set S is all provided by the unit spinor representation in se (3)：
ThenResolve into m rank-1 positive semidefinite matrix sum：
Wherein, direct proportion coefficient ciRepresent each constraint matrix CiRestriction ability size, strong constraint makes operator's control
Mechanical arm tail end moves along optimal direction, and weak constraint makes to deviate along non-optimal direction；
Operator's controling powerSize determine the position that mechanical arm tail end occurs in rotation and translation direction
Move change δ Xb=(δ φb,δqb), have
Wherein,Expression acts on operator's controling power of mechanical arm tail end, δ XbRepresent the small of rotation and translation direction
Displacement；It is non-singular matrix that holonomic constriants under virtual clamp auxiliary, which are equal to constraint matrix C, and nonholonomic constraint then corresponds to constraint
Matrix C is non-non-singular matrix；
2) complex operations Task-decomposing；
Complex operations task in remote operating can resolve into the combination of multiple tasks；For several different tasks, choosing
Take optimal motion spinor set；
3) controller design is constrained；
If the spatial movement speed of mechanical arm is Vb=(ωb,vb), wherein ωb、vbMechanical arm in inertial space is represented respectively
Angular velocity of rotation and tangential velocity；Controller design is as follows：
Wherein, constraint matrix CVF(g,gd) represent to be defined as F to the restriction ability of mechanical arm, operator's controling powerb=(mb,
fb), Proportional coefficient Kc=diag (crI3×3,cpI3×3) control operation person's effect of contraction power size.
2. the incomplete remote operating about beam control method according to claim 1 based on complex operations task, it is special
Sign is, in the step 2), the specific method for choosing optimal motion spinor set is as follows：
2-1) target approaches
If reference locus of the mechanical arm in configuration space is gd, its present bit shape is g, then distance reference track error
It is expressed as
The logarithmic table of corresponding motion spinor collection conjunction error reaches, and has
Corresponding constraint matrix CVF=cS is made up of motion spinor set, and c size determines the power of effect of contraction power；
2-2) track following
If the reference locus of manipulator motion is gr(λ, t), the axis of manipulator motion areR is fortune
Any point in shaft line, λ be translation direction precession parameter, | | s | |=1, then corresponding tangential velocity be
Note tangential velocity is unit spinor set S1, S2For the logarithmic form of error:
Then constraint matrix is
CVF=c1S1+c2S2 (7)
Wherein, direct proportion coefficient c1Size determine the movement velocity size that mechanical arm is constrained by virtual clamp, and c1More
Movement velocity corresponding to big can reduce, c2Size determine the ability of mechanical arm track reference track；
2-3) plane motion
Assuming that the movement velocity vector of mechanical arm tail end is v1And v2, then span { v1,v2Refer to v1, v2For base generation
Plane, operator's control machinery arm move in the two dimensional surface, definition motion spinor ξ=(ω, v), when along v1Transport in direction
When dynamic, ω=s=0 is taken, then v1The motion spinor collection in direction is combined into S1=(0, v1), similarly v2The motion spinor collection in direction is combined into S2
=(0, v2), then mechanical arm spinor collection of s motions vertically under effect of contraction is combined into S3=(s, r × s), r are any one on s
Point；
So as to which constraint matrix is defined as
CVF=c1S1+c2S2+c3S3 (8)
Wherein, c1Size determine mechanical arm along v1The ability of direction motion, c2Size determine mechanical arm along v2Transport in direction
Dynamic ability, c3Size determine that mechanical arm is constraining the ability of axial s motion, including the constraint work around axial rotation
With.
Compared with prior art, the invention has the advantages that：
The present invention compared with general Mechanical arm control method, has task layer for complicated spatial manipulation task
Face and two big beneficial effects of control method.First, the manipulation tasks to be completed in space of mechanical arm include that target is close, road
Footpath tracks and hidden obstacle etc., and the present invention chooses suitable motion spinor set come structure constraint square according to the different of operation task
Battle array, compared with previous methods with more the ability for adapting to complex task；Secondly, nonholonomic constraint control method can make operation cleverer
Living, operator can only be moved with control machinery arm in translation or direction of rotation, without providing extra constraint, so as to mitigate operation
Person's pressure.
【Brief description of the drawings】
Fig. 1 constrains power principle figure.
Fig. 2 plane restrictions move schematic diagram.
Fig. 3 spheres and its section schematic diagram.
Fig. 4 spheres section operation chart.
【Embodiment】
The present invention is described in further detail below in conjunction with the accompanying drawings：
Referring to Fig. 1-4, the incomplete remote operating about beam control method based on complex operations task, it is characterised in that including
Following steps：
Step 1：Calculate constraint matrix CVF。
Operator's control machinery arm completes complex task in space environment, it is desirable to has to mechanical arm tail end controling power
Effect of contraction is imitated, a kind of such effect of contraction forms virtual clamp, defines constraint matrix CVFRestriction ability corresponding to expression, and
CVFIt is 6 × 6 positive semidefinite symmetrical matrixes, and steric forces is mapped to CVFMatrix element.Operator's control machinery arm end
Motion towards optimal direction and non-optimal direction constitutes space geometry constraint, and can be by the unit spinor in se (3)
Represent, provide spinor set S：ThenM rank-1 positive semidefinite can be resolved into
Matrix sum：
Wherein, direct proportion coefficient ciRepresent each constraint matrix CiRestriction ability size, strong constraint makes operator's control
Mechanical arm tail end moves along optimal direction, and weak constraint makes to deviate along non-optimal direction.Such motion priority area
Dividing reduces the operating pressure of operator, i.e. operator only needs control machinery arm in virtual clamp effect of contraction range of motion.
Operator's controling powerSize determine the position that mechanical arm tail end occurs in rotation and translation direction
Move change δ Xb=(δ φb,δqb), have
Wherein,Expression acts on operator's controling power of mechanical arm tail end, δ XbRepresent the small of rotation and translation direction
Displacement.It is non-singular matrix that holonomic constriants under virtual clamp auxiliary, which are equal to constraint matrix C, and nonholonomic constraint then corresponds to constraint
Matrix C is non-non-singular matrix.
Step 2：Complex operations Task-decomposing.
Based on above-mentioned theory knowledge, the complex operations task in remote operating can resolve into multiple simple task (such as targets
Close, path trace, hide obstacle etc.) combination.For several different simple tasks, optimal motion spinor collection is chosen
Close：
(1) target approaches
If reference locus of the mechanical arm in configuration space is gd, its present bit shape is g, then distance reference track error
It is expressed as
The logarithmic table of corresponding motion spinor collection conjunction error reaches, and has
Corresponding constraint matrix CVF=cS is made up of motion spinor set, and c size determines the power of effect of contraction power,
The servo-actuated completion operation task of effect of contraction power that operator need to only provide according to virtual clamp, it is not necessary to which extra control is provided
Power processed.
(2) track following
If the reference locus of manipulator motion is gr (λ, t), the axis of manipulator motion isR is fortune
Any point in shaft line, λ be translation direction precession parameter, | | s | |=1, then corresponding tangential velocity be
Note tangential velocity is unit spinor set S1, S2In being saved with 4.3.1, the logarithmic form of error is defined as
Then constraint matrix is
CVF=c1S1+c2S2 (7)
Wherein, direct proportion coefficient c1Size determine the movement velocity size that mechanical arm is constrained by virtual clamp, and c1More
Movement velocity corresponding to big can reduce, c2Size determine the ability of mechanical arm track reference track.
(3) plane motion
Assuming that the movement velocity vector of mechanical arm tail end is v1And v2, then span { v1,v2Refer to v1, v2For base generation
Plane, operator's control machinery arm move in the two dimensional surface, as shown in Fig. 2 definition motion spinor ξ=(ω, v), works as edge
V1When direction is moved, ω=s=0 is taken, then v1The motion spinor collection in direction is combined into S1=(0, v1), similarly v2The motion rotation in direction
Quantity set is combined into S2=(0, v2), then mechanical arm spinor collection of s motions vertically under effect of contraction is combined into S3=(s, r × s), r is
The upper any point of s.
So as to which constraint matrix may be defined as
CVF=c1S1+c2S2+c3S3 (8)
Wherein, c1Size determine mechanical arm along v1The ability of direction motion, c2Size determine mechanical arm along v2Transport in direction
Dynamic ability, c3Size determine that mechanical arm is constraining the ability of axial s motion, including the constraint work around axial rotation
With.
Step 3：Constrain controller design.
, it is necessary to which mechanical arm is held at stabilization in rotation and translation direction when operator's control machinery arm completes Given task
Threshold speed in, based on this, if the spatial movement speed of mechanical arm is Vb=(ωb,vb), wherein ωb、vbInertia is represented respectively
The angular velocity of rotation and tangential velocity of mechanical arm in space.Controller design is as follows：
Wherein, constraint matrix CVF(g,gd) represent to be defined as F to the restriction ability of mechanical arm, operator's controling powerb=(mb,
fb), Proportional coefficient Kc=diag (crI3×3,cpI3×3) control operation person's effect of contraction power size, because strong constraint makes mechanical arm
It is very fast along optimal direction movement velocity, to prevent excessive velocities from causing the generation of the fortuitous events such as collision, choose suitable cr、
cpThe size for applying operator's restraining force is controlled, and prevents mechanical arm from causing the failure of task because out of hand.
The principle of the present invention：
In classical analysis mechanics, constraint can be divided into holonomic constriants and nonholonomic constraint.Mechanical arm is being grasped in Space teleoperation
Can author's control is lower to realize given motion, relevant with the integrality for constraining controling power and simplified operation task etc..Non- complete
Under whole restraint condition, i.e., partially restrained limitation is carried out to mechanical arm, the operation free degree for being embodied in reference locus is less than machine
The dimension of tool arm configuration space, control machinery arm end moves to B points, Given task sequence T from A points such as on Two-dimensional Surfacesr
([mx,my,mz],pr), wherein (mx,my,mz) refer to any point coordinates on task sequence, prRepresent about beam power, such as Fig. 1
It is shown, whether given motion can be realized for restrained object, its method of discrimination is typically to investigate constraint force screwWith to
Determine velocity screwThe i.e. instantaneous about beam power (referred to as about beam power) of product whether be zero, the motion if being zero if about beam power
The motion allowed for constraint.
In order to verify operative constraint to mechanical arm effect of the designed controller in change operation environment, design dynamic
Track following experiment is as follows：
(1) in testing, operator controls end effector instrument to be moved along reference locus, and designs the behaviour where control end
It is dynamic change as environment.In dynamic trajectory tracking test, the dynamic of experimental situation (dynamic change sphere) is set first
Change frequency is ω (0~45rad/s), if the parallel that reference locus is r=50mm on sphere justifies (radius of sphericity r0=
100mm), as shown in figure 3,
(2) when being moved by starting point towards target point, motion spinor set is made up of mechanical arm tail end two parts, and note is cut
It is unit spinor set S to speed1, S2It is defined as the logarithmic form of errorThen constraint matrix is
CVF=c1S1+c2S2
Wherein, c is made1=0.6, c2=0.8, direct proportion coefficient c1Size determine that mechanical arm is constrained down by virtual clamp
Movement velocity size, c2Size determine the ability of mechanical arm track reference track.
(3) in Two-dimensional Surfaces, about beam power p is mader=0 mode of operation is that control machinery arm end is axially transported along a certain
Dynamic (such as z-axis), and surround motion no effect of constraint value of all rotations of z-axis to z directions, then mechanical arm tail end can be along z-axis
Do continuous motion.
The radius of sphericity of change is set as r=r0+ Δ r sin ω t, wherein Δ r=20mm.Proportional coefficient Kc=diag
(crI3×3,cpI3×3) control operation person's effect of contraction power size, during experiment, choose cr=0.1rad/s, cp=100mm/
S, operator control end effector instrument from original position g0Towards reference locus gdMotion, is illustrated in figure 4 spherical diameter direction
Cutting plane operation chart：
Test result indicates that in changing environment, operator chooses corresponding motion spinor collection according to different operating task
Structure constraint matrix is closed, is moved so as to constrain end effector instrument well along specified direction.
The technological thought of above content only to illustrate the invention, it is impossible to protection scope of the present invention is limited with this, it is every to press
According to technological thought proposed by the present invention, any change done on the basis of technical scheme, claims of the present invention is each fallen within
Protection domain within.
Claims (2)
1. a kind of incomplete remote operating about beam control method based on complex operations task, it is characterised in that comprise the following steps：
1) constraint matrix C is calculatedVF；
Define constraint matrix CVFRestriction ability corresponding to expression, and CVFIt is 6 × 6 positive semidefinite symmetrical matrixes, and by steric forces
It is mapped to CVFMatrix element；The motion of operator control machinery arm end towards optimal direction and non-optimal direction constitutes sky
Between geometrical constraint, and spinor set is all provided by the unit spinor representation in se (3)
ThenResolve into m rank-1 positive semidefinite matrix sum：
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Wherein, direct proportion coefficient ciRepresent each constraint matrix CiRestriction ability size, strong constraint makes operator's control machinery
Arm end is moved along optimal direction, and weak constraint makes to deviate along non-optimal direction；
Operator's controling powerSize determine that the displacement that mechanical arm tail end occurs in rotation and translation direction becomes
Change δ Xb=(δ φb,δqb), have
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Wherein,Expression acts on operator's controling power of mechanical arm tail end, δ XbRepresent the small position in rotation and translation direction
Move；It is non-singular matrix that holonomic constriants under virtual clamp auxiliary, which are equal to constraint matrix C, and nonholonomic constraint then corresponds to constraint square
Battle array C is non-non-singular matrix；
2) complex operations Task-decomposing；
Complex operations task in remote operating can resolve into the combination of multiple tasks；For several different tasks, choose most
Excellent motion spinor set；
3) controller design is constrained；
If the spatial movement speed of mechanical arm is Vb=(ωb,vb), wherein ωb、vbThe rotation of mechanical arm in inertial space is represented respectively
Tarnsition velocity and tangential velocity；Controller design is as follows：
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Wherein, constraint matrix CVF(g,gd) represent to be defined as the restriction ability of mechanical arm, operator's controling power
Proportional coefficient Kc=diag (crI3×3,cpI3×3) control operation person's effect of contraction power size.
2. the incomplete remote operating about beam control method according to claim 1 based on complex operations task, its feature exist
In in the step 2), the specific method for choosing optimal motion spinor set is as follows：
2-1) target approaches
If reference locus of the mechanical arm in configuration space is gd, its present bit shape is g, then the error of distance reference track represents
For
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The logarithmic table of corresponding motion spinor collection conjunction error reaches, and has
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Corresponding constraint matrix CVF=cS is made up of motion spinor set, and c size determines the power of effect of contraction power；
2-2) track following
If the reference locus of manipulator motion is gr(λ, t), the axis of manipulator motion areR is kinematic axis
Any point on line, λ be translation direction precession parameter, | | s | |=1, then corresponding tangential velocity be
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CVF=c1S1+c2S2 (7)
Wherein, direct proportion coefficient c1Size determine the movement velocity size that mechanical arm is constrained by virtual clamp, and c1It is more big right
The movement velocity answered can reduce, c2Size determine the ability of mechanical arm track reference track；
2-3) plane motion
Assuming that the movement velocity vector of mechanical arm tail end is v1And v2, then span { v1,v2Refer to v1, v2For the flat of base generation
Face, operator's control machinery arm move in the two dimensional surface, definition motion spinor ξ=(ω, v), when along v1Move in direction
When, ω=s=0 is taken, then v1The motion spinor collection in direction is combined into S1=(0, v1), similarly v2The motion spinor collection in direction is combined into S2=
(0,v2), then mechanical arm spinor collection of s motions vertically under effect of contraction is combined into S3=(s, r × s), r are any point on s；
So as to which constraint matrix is defined as
CVF=c1S1+c2S2+c3S3 (8)
Wherein, c1Size determine mechanical arm along v1The ability of direction motion, c2Size determine mechanical arm along v2Direction motion
Ability, c3Size determine that mechanical arm is constraining the ability of axial s motion, including the effect of contraction around axial rotation.
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Citations (6)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN102122172A (en) * | 2010-12-31 | 2011-07-13 | 中国科学院计算技术研究所 | Image pickup system and control method thereof for machine motion control |
| CN103144111A (en) * | 2013-02-26 | 2013-06-12 | 中山大学 | QP unified and coordinated motion describing and programming method for movable manipulator |
| CN104407611A (en) * | 2014-09-30 | 2015-03-11 | 同济大学 | Humanoid robot stable waling control method |
| CN104965517A (en) * | 2015-07-07 | 2015-10-07 | 张耀伦 | Robot cartesian space trajectory planning method |
| CN105183009A (en) * | 2015-10-15 | 2015-12-23 | 哈尔滨工程大学 | Trajectory control method for redundant mechanical arm |
| CN105234930A (en) * | 2015-10-15 | 2016-01-13 | 哈尔滨工程大学 | Control method of motion of redundant mechanical arm based on configuration plane |
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| Publication number | Priority date | Publication date | Assignee | Title |
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| CN102122172A (en) * | 2010-12-31 | 2011-07-13 | 中国科学院计算技术研究所 | Image pickup system and control method thereof for machine motion control |
| CN103144111A (en) * | 2013-02-26 | 2013-06-12 | 中山大学 | QP unified and coordinated motion describing and programming method for movable manipulator |
| CN104407611A (en) * | 2014-09-30 | 2015-03-11 | 同济大学 | Humanoid robot stable waling control method |
| CN104965517A (en) * | 2015-07-07 | 2015-10-07 | 张耀伦 | Robot cartesian space trajectory planning method |
| CN105183009A (en) * | 2015-10-15 | 2015-12-23 | 哈尔滨工程大学 | Trajectory control method for redundant mechanical arm |
| CN105234930A (en) * | 2015-10-15 | 2016-01-13 | 哈尔滨工程大学 | Control method of motion of redundant mechanical arm based on configuration plane |
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