CN107263466A - Pedestal unperturbed control method of the robot for space based on quadratic programming problem - Google Patents
Pedestal unperturbed control method of the robot for space based on quadratic programming problem Download PDFInfo
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- CN107263466A CN107263466A CN201710330726.5A CN201710330726A CN107263466A CN 107263466 A CN107263466 A CN 107263466A CN 201710330726 A CN201710330726 A CN 201710330726A CN 107263466 A CN107263466 A CN 107263466A
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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
- B25J9/1628—Programme controls characterised by the control loop
- B25J9/1633—Programme controls characterised by the control loop compliant, force, torque control, e.g. combined with position control
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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
- B25J9/1612—Programme controls characterised by the hand, wrist, grip control
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Abstract
The invention discloses a kind of pedestal unperturbed control method of robot for space based on quadratic programming problem, including the kinetic model under robot for space operating space is derived；Establish the governing equation of pedestal unperturbed task and end effector tracing task；By solving quadratic programming problem, the joint moment of pedestal, end effector mission requirements and Filters with Magnitude Constraints is met；The validity of method proposed by the present invention finally by case verification.The present invention is by deriving the kinetic model under robot for space operating space, it is not necessary to solve Inverse Kinematics Problem, directly obtains and meets mission requirements and can be applied directly to the joint moment of system.
Description
Technical field
The present invention relates to a kind of robot for space pedestal unperturbed control method, more particularly to robot for space is based on secondary rule
The pedestal unperturbed control method for the problem of drawing.
Background technology
Robot for space possesses the ability for performing the fine space tasks such as in-orbit spacecraft maintenance, space junk cleaning, because
And begun one's study from 1990s mid-term, each spacefaring nation and the concern of researcher are constantly caused so far.With ground machine
Tool arm is different, because Dynamics Coupling is acted on, space manipulator meeting in motion process
Reaction force and torque are produced to the pedestal spacecraft freely floated, and cause the change of pedestal pose.Reduce this
Plant the pedestal spacecraft of microgravity environment and holding disturbance of the manipulator motion to pedestal keeps to(for) Space Robot System
Communicate over the ground significant.Part work trial pedestal control system, such as propeller and counteraction flyback, to mend
The disturbance that manipulator motion is produced to pedestal is repaid, however, propeller fuel is a kind of precious for system performs orbit maneuver
Expensive resource, the torque that counteraction flyback is produced is limited, it is necessary to limits mechanical arm and is moved with the speed of very little.Another part works
The motion using mechanical arm is then attempted, including the pose of pedestal is adjusted by the motion of mechanical arm or is expected that by constructing redundancy
Mechanical arm makes not producing the disturbance to pedestal during mechanical arm execution task.
Include disturbance figure/enhancing disturbance figure (Disturbance map/ using the typical method of manipulator motion
Enhanced disturbance map, DM/EDM) method and reaction kernel (Reaction null space, RNS) side
Method.Wherein, disturbance figure/enhancing disturbance drawing method shows manipulator motion to pedestal disturbance minimum and maximum under joint space
Direction, so that the motion of mechanical arm is instructed, the property of the reaction Zero Space Method and Its utilization space robot system conservation of angular momentum,
Pedestal speed is solution conservation of angular momentum equation under conditions of zero, so as to find the joint motions speed for being zero to pedestal disturbance.
Solution to redundant mechanical arm track is described as optimization problem by other methods, including solution local optimum problem obtains machinery
The pedestal unperturbed track of arm, wherein, the track in each joint is by the technologies such as Rayleigh-Ritz and polynomial function by parameter
Change；Or require pedestal unperturbed etc. to be included in object function by Lagrange multiplier, so that by solving nonlinear equation
Obtain mechanical arm pedestal unperturbed track；And the minimum variance problem containing linear equality constraints is solved, so as to obtain simultaneously full
The manipulator motion track of sufficient pedestal unperturbed and end effector tracer request.However, above-mentioned all methods can be attributed to greatly
Redundancy decomposition strategy of the robot for space based on inverse kinematics, obtained result is the angular speed or angular acceleration in joint, is
Result is applied to Space Robot System, in addition it is also necessary to which extra kinematics control method calculates moment method.The present invention
Propose a kind of pedestal unperturbed control method of robot for space based on quadratic programming problem, it is not necessary to inverse kinematics, obtain
Result be to meet pedestal unperturbed, end effector tracking desired trajectory etc. mission requirements and the phase in joint can be applied directly to
Hope joint moment.
The content of the invention
Manipulator motion may cause the problem of pedestal spacecraft pose is disturbed during for robot for space execution task,
The present invention proposes a kind of pedestal unperturbed control method of the robot for space based on quadratic programming problem, is different from conventional method needs
The solution for solving Inverse Kinematics Problem and obtaining is can not act directly on joint angular speed, the angular acceleration of system, the present invention
By deriving the kinetic model under robot for space operating space, it is not necessary to solve Inverse Kinematics Problem, satisfaction is directly obtained
Mission requirements and the joint moment that system can be applied directly to.
The technical proposal of the invention is realized in this way：
The present invention proposes a kind of control method of robot for space pedestal unperturbed, including has derived robot for space operation
Kinetic model under space；Establish the governing equation of pedestal unperturbed task and end effector tracing task；By solving
Quadratic programming problem, is met the joint moment of pedestal, end effector mission requirements and Filters with Magnitude Constraints；Finally by
The case verification validity of method proposed by the present invention.The implementation of the invention mainly includes three below step：
Step 1: setting up robot for space operating space kinetic model.
Space Robot System is made up of the mechanical arm of pedestal spacecraft and the n frees degree, be typically chosen the line of pedestal/
The rotary speed in angular speed and joint is as generalized variable, based on lagrange equation of the second kind, the dynamics of robot for space
Model can be expressed as follows：
Wherein,For line/angular speed of pedestal,It is the vector of each joint rotating speed composition, Hb,HmFor pedestal and
Mechanical arm inertia matrix, HbmFor the coupling torque matrix c between end effector and mechanical armb,cmTo be non-with velocity correlation
Linear term, fb,feThe external force and moment of face being subject to for pedestal and end effector, τ are the opplied moment at joint of mechanical arm.
In the present invention, it is considered to the pedestal that the Space Robot System freely floated is not fixed, from the point of view of modeling,
The end effector of mechanical arm can also be considered as " pedestal " of system, and pedestal spacecraft can then be considered as " end " of system,
Modeled so as to carry out system from end effector to pedestal.Because in existing modeling method, representing end effector
Body coordinate system is built upon greatly the end of last connecting rod, and the present invention is moved the body coordinate system of pedestal by its barycenter
To pedestal one end so that Space Robot System turns into a symmetrical system, so as to be modeled down from end effector to pedestal
Obtained kinetic model will have identical structure with the kinetic model obtained under the modeling of pedestal end-effector.So
And, generalized variable in kinetic model is by the line/angular speed for being changed into end effector and the rotary speed in each joint：
Wherein,For line/angular speed of end effector, symbol '~' represent equation from end effector to
Pedestal modeling is obtained.Because the motion state variable of end effector is occurred directly in kinetics equation (2), thus, for
The control task of end effector, designing corresponding control law using equation (2) will be more simpler than using equation (1).
It is pointed out that because kinetics equation is obtained by the kinetic energy of system is substituted into Lagrange's equation, and this hair
It is bright that the establishment of coordinate system of pedestal is needed to use into pedestal barycenter at one end of pedestal, the kinetic energy for calculating pedestal in step one
Linear velocity：
v′b=vb+ωb×a0 (15)
Rather than directly use vb, a0It is position vector of the base body coordinate origin to pedestal barycenter, symbol ' × ' table
Show multiplication cross computing.Meanwhile, with the nonlinear terms c of velocity correlation in kinetics equationbPass through Recursive Newton-Euler method numerical computations
Obtain, wherein including the inertia force for calculating pedestal.At this time, it may be necessary to use the linear acceleration of pedestal barycenter：
Rather than directly use ab.When modeled from end effector to pedestal, above-mentioned change is equally applicable to pair
The calculating of end effector kinetic energy and inertia force.
Pedestal is considered in the present invention not by controling power/torque, while end effector is not in contact with outside, so that dynamic
F in mechanical equation (1) and (2)b,fe=0.Equation (1) can be reduced to：
Eliminate joint velocity from above-mentioned equation, equation can be reduced to only with pedestal variableIt is relevant,
Wherein,
Similarly, by causing f in equation (2)b,fe=0 and joint velocity is eliminated, robot for space is in operation
The kinetics equation in space can be expressed as：
Wherein,
Step 2: setting up the governing equation of pedestal and end effector task.
The desired trajectory of given pedestalIt is readily obtained by equation (6), on pedestal desired trajectoryClosed with its correspondence
Section input τ governing equation meets following relation：
In order to ensure that the motion of mechanical arm is not disturbed to pedestal, the desired track of pedestal isAbove-mentioned controlling party
Journey can be further simplified as：
Similarly, task is expected on end effectorJoint input corresponding with itsGoverning equation be：
In addition, in being modeled by pedestal end-effector, joint JiConnect connecting rod Bi-1And Bi.If joint JiLocate motor
To connecting rod BiThe torque of effect is τi, it is clear that equally can be to connecting rod Bi-1Opplied moment-τi.Because from end effector to base
During seat modeling, joint Ji, connecting rod BiAnd Bi-1It is changed into joint J respectivelyn-i+1, connecting rod Bn-iAnd Bn-i+1, while created symbolRepresent each
The torque in joint,Represent joint Jn-i+1To connecting rod Bn-i+1The torque of application, thus, there is following relation：
Meanwhile, joint variable θi,WithAlso there is the relation that above formula is represented.
Thus, governing equation (10) can be expressed as the equation on τ：
As long as so that matrixI-th row turn into matrix(n-i+1) row.
Step 3: being described as the optimal input that quadratic programming problem solves joint.
To be met the joint input of pedestal unperturbed and end effector tracking desired trajectory mission requirements, step 2 point
Equation (9) and the governing equation shown in (12) have not been obtained.Below, under quadratic programming problem framework, obtained governing equation
It is described as linear equality constraints, and further considers the amplitude range τ of joint momentmin≤τ≤τmax, describe it as linear
Inequality constraints.For the object function in quadratic programming problem, consume to save system capacity and obtain smooth joint
Track, uses following object function：
F (τ)=λττTIτ (25)
Wherein, λτFor adjustment factor, I ∈ Rn×nFor unit matrix.
Thus, meeting the expectation joint moment of pedestal unperturbed, end effector tracing task and Filters with Magnitude Constraints can lead to
Cross and solve following quadratic programming problem and obtain：
The beneficial effects of the invention are as follows：Propose a kind of pedestal unperturbed control of robot for space based on quadratic programming problem
Method.Wherein, by deriving and setting up kinetic model of the robot for space under task space, it is not necessary to solve inverse kinematics
Problem, the Linear Control equation on joint moment can be described as by realizing the tracing task of end effector.By further
It is described as quadratic programming problem, by governing equation, joint moment Filters with Magnitude Constraints and system capacity consumption and generation can be saved
The mission requirements of smooth articular track is respectively depicted as linear equality constraints, linear inequality constraint and the target of planning problem
Function.By solving obtained quadratic programming problem, pedestal unperturbed, end effector tracing task and width can be met
It is worth the expectation joint moment of constraint.
Brief description of the drawings
Fig. 1 Space Robot System schematic diagrames
Fig. 2 end effectors position desired trajectory and actual path
Fig. 3 end effector position tracking errors
Pedestal attitude error caused by Fig. 4 manipulator motions
Each joint moment tracks of Fig. 5
Embodiment
The implementation of the invention mainly includes three below step：
Step 1: setting up robot for space operating space kinetic model.
Space Robot System is made up of the mechanical arm of pedestal spacecraft and the n frees degree, be typically chosen the line of pedestal/
The rotary speed in angular speed and joint is as generalized variable, based on lagrange equation of the second kind, the dynamics of robot for space
Model can be expressed as follows：
Wherein,For line/angular speed of pedestal,It is the vector of each joint rotating speed composition, Hb,HmFor pedestal and
Mechanical arm inertia matrix, HbmFor the coupling torque matrix c between end effector and mechanical armb,cmTo be non-with velocity correlation
Linear term, fb,feThe external force and moment of face being subject to for pedestal and end effector, τ are the opplied moment at joint of mechanical arm.
In the present invention, it is considered to the pedestal that the Space Robot System freely floated is not fixed, from the point of view of modeling,
The end effector of mechanical arm can also be considered as " pedestal " of system, and pedestal spacecraft can then be considered as " end " of system,
Modeled so as to carry out system from end effector to pedestal.Because in existing modeling method, representing end effector
Body coordinate system is built upon greatly the end of last connecting rod, and the present invention is moved the body coordinate system of pedestal by its barycenter
To pedestal one end so that Space Robot System turns into a symmetrical system, so as to be modeled down from end effector to pedestal
Obtained kinetic model will have identical structure with the kinetic model obtained under the modeling of pedestal end-effector.So
And, generalized variable in kinetic model is by the line/angular speed for being changed into end effector and the rotary speed in each joint：
Wherein,For line/angular speed of end effector, symbol '~' represent equation from end effector to
Pedestal modeling is obtained.Because the motion state variable of end effector is occurred directly in kinetics equation (2), thus, for
The control task of end effector, designing corresponding control law using equation (2) will be more simpler than using equation (1).
It is pointed out that because kinetics equation is obtained by the kinetic energy of system is substituted into Lagrange's equation, and this hair
It is bright that the establishment of coordinate system of pedestal is needed to use into pedestal barycenter at one end of pedestal, the kinetic energy for calculating pedestal in step one
Linear velocity：
v′b=vb+ωb×a0 (29)
Rather than directly use vb, a0It is position vector of the base body coordinate origin to pedestal barycenter, symbol ' × ' table
Show multiplication cross computing.Meanwhile, with the nonlinear terms c of velocity correlation in kinetics equationbPass through Recursive Newton-Euler method numerical computations
Obtain, wherein including the inertia force for calculating pedestal.At this time, it may be necessary to use the linear acceleration of pedestal barycenter：
Rather than directly use ab.When modeled from end effector to pedestal, above-mentioned change is equally applicable to pair
The calculating of end effector kinetic energy and inertia force.
Pedestal is considered in the present invention not by controling power/torque, while end effector is not in contact with outside, so that dynamic
F in mechanical equation (1) and (2)b,fe=0.Equation (1) can be reduced to：
Eliminate joint velocity from above-mentioned equation, equation can be reduced to only with pedestal variableIt is relevant,
Wherein,
Similarly, by causing f in equation (2)b,fe=0 and joint velocity is eliminated, robot for space is in operation
The kinetics equation in space can be expressed as：
Wherein,
Step 2: setting up the governing equation of pedestal and end effector task.
The desired trajectory of given pedestalIt is readily obtained by equation (6), on pedestal desired trajectoryClosed with its correspondence
Section input τ governing equation meets following relation：
In order to ensure that the motion of mechanical arm is not disturbed to pedestal, the desired track of pedestal isAbove-mentioned controlling party
Journey can be further simplified as：
Similarly, task is expected on end effectorJoint input corresponding with itsGoverning equation be：
In addition, in being modeled by pedestal end-effector, joint JiConnect connecting rod Bi-1And Bi.If joint JiLocate motor
To connecting rod BiThe torque of effect is τi, it is clear that equally can be to connecting rod Bi-1Opplied moment-τi.Because from end effector to base
During seat modeling, joint Ji, connecting rod BiAnd Bi-1It is changed into joint J respectivelyn-i+1, connecting rod Bn-iAnd Bn-i+1, while created symbolRepresent each
The torque in joint,Represent joint Jn-i+1To connecting rod Bn-i+1The torque of application, thus, there is following relation：
Meanwhile, joint variable θi,WithAlso there is the relation that above formula is represented.
Thus, governing equation (10) can be expressed as the equation on τ：
As long as so that matrixI-th row turn into matrix(n-i+1) row.
Step 3: being described as the optimal input that quadratic programming problem solves joint.
To be met the joint input of pedestal unperturbed and end effector tracking desired trajectory mission requirements, step 2 point
Equation (9) and the governing equation shown in (12) have not been obtained.Below, under quadratic programming problem framework, obtained governing equation
It is described as linear equality constraints, and further considers the amplitude range τ of joint momentmin≤τ≤τmax, describe it as linear
Inequality constraints.For the object function in quadratic programming problem, consume to save system capacity and obtain smooth joint
Track, uses following object function：
F (τ)=λττTIτ (39)
Wherein, λτFor adjustment factor, I ∈ Rn×nFor unit matrix.
Thus, meeting the expectation joint moment of pedestal unperturbed, end effector tracing task and Filters with Magnitude Constraints can lead to
Cross and solve following quadratic programming problem and obtain：
Kinematics/kinetic parameter of the degree-of-freedom manipulator robot for space of 1 band of table 7
Table 1 is the kinematics of Space Robot System and kinetic parameter used in example, and Fig. 1 is robot for space system
System schematic diagram, Fig. 2 is the desired trajectory and actual path of end effector position, and Fig. 3, Fig. 4 are respectively the position of end effector
Put the pedestal attitude disturbance of tracking error and pedestal spacecraft, Fig. 5 joint moments that each joint applies during being task.
The present invention verifies the robot for space pedestal unperturbed proposed by taking the robot for space of the degree-of-freedom manipulator of band 7 as an example
Control method, kinematics/kinetic parameter of system is as shown in table 1.
End effector is set to track the location track of following " lemniscate " shape,
And require manipulator motion to pedestal posture unperturbed, i.e. pedestal Attitude Tracking reference locus
Mechanical arm initial configuration is] control r ad device parameters be set to λτ=10-3, τmax=0.2N
m,τmin=-0.2Nm.
Fig. 2 is the desired trajectory and actual path that robot arm end effector is moved, and can be intuitive to see, end is performed
Device can track desired trajectory well；Fig. 3 furthermore present the position tracking error of end effector, and tracking accuracy reaches
10-4；Fig. 4 illustrates interference of the manipulator motion to pedestal posture in the form of Eulerian angles (" 3-2-1 " order), can see
Go out, the angle maximum of pedestal attitude misalignment is no more than 0.1 °, it is believed that realize manipulator motion and pedestal posture is not produced
Interference；Fig. 5 gives the variation track of each joint moment, and each joint moment is all not above the amplitude range set.By this
Example illustrates robot for space control method proposed by the present invention to realize by the motion of mechanical arm and completes end well
Actuator tracing task is held, each joint moment meets the amplitude requirement proposed, and does not produce disturbance to pedestal.
Claims (1)
1. pedestal unperturbed control method of the robot for space based on quadratic programming problem, including derived robot for space operation sky
Between under kinetic model；Establish the governing equation of pedestal unperturbed task and end effector tracing task；By solving two
Secondary planning problem, is met the joint moment of pedestal, end effector mission requirements and Filters with Magnitude Constraints；Its feature exists
In, including three below step：
Step 1: setting up robot for space operating space kinetic model
Space Robot System is made up of the mechanical arm of pedestal spacecraft and the n frees degree, is typically chosen line/angle speed of pedestal
The rotary speed in degree and joint is as generalized variable, based on lagrange equation of the second kind, the kinetic model of robot for space
It can be expressed as follows：
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Wherein,For line/angular speed of pedestal,It is the vector of each joint rotating speed composition, Hb,HmFor pedestal and machinery
Arm inertia matrix, HbmFor the coupling torque matrix c between end effector and mechanical armb,cmTo be non-linear with velocity correlation
, fb,feThe external force and moment of face being subject to for pedestal and end effector, τ are the opplied moment at joint of mechanical arm, it is considered to from
The pedestal do not fixed by the Space Robot System floated, the end effector of mechanical arm can also be considered as " the base of system
Seat ", and pedestal spacecraft can then be considered as " end " of system, so that the system of progress is modeled from end effector to pedestal, obtain
The kinetic model arrived will have identical structure with equation (1), however, the generalized variable in kinetic model will be changed into end
Line/angular speed of actuator and the rotary speed in each joint：
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Wherein,For line/angular speed of end effector, symbol '~' represents equation from end effector to pedestal
Modeling is obtained, because the motion state variable of end effector is occurred directly in kinetics equation (2), thus, for end
The control task of actuator, designing corresponding control law using equation (2) will be more simpler than using equation (1)；
Pedestal is considered not by controling power/torque, while end effector is not in contact with outside, so that kinetics equation (1)
(2) f inb,fe=0, equation (1) is reduced to：
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Eliminate joint velocity from above-mentioned equation, equation simplification for only with pedestal variableIt is relevant,
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Wherein,
Similarly, by causing f in equation (2)b,fe=0 and joint velocity is eliminated, robot for space is in operating space
Kinetics equation can be expressed as：
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Wherein,
Step 2: setting up the governing equation of pedestal and end effector task
The desired trajectory of given pedestalIt is readily obtained by equation (4), on pedestal desired trajectoryIt is defeated with its corresponding joint
The governing equation for entering τ meets following relation：
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1
In order to ensure that the motion of mechanical arm is not disturbed to pedestal, the desired track of pedestal isAbove-mentioned governing equation can
To be further simplified as：
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Similarly, task is expected on end effectorCorresponding with its joint input τ governing equation is：
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In addition, in being modeled by pedestal end-effector, joint JiConnect connecting rod Bi-1And BiIf, joint JiLocate motor to even
Bar BiThe torque of effect is τi, it is clear that equally can be to connecting rod Bi-1Opplied moment-τi, because being built from end effector to pedestal
During mould, joint Ji, connecting rod BiAnd Bi-1It is changed into joint J respectivelyn-i+1, connecting rod Bn-iAnd Bn-i+1, while created symbolRepresent each joint
Torque,Represent joint Jn-i+1To connecting rod Bn-i+1The torque of application, thus, there is following relation：
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Meanwhile, joint variable θi,WithAlso there is the relation that above formula is represented；
Thus, governing equation (8) can be expressed as the equation on τ：
As long as so that matrixI-th row turn into matrix(n-i+1) row；
Step 3: being described as the optimal input that quadratic programming problem solves joint
To be met the joint input of pedestal unperturbed and end effector tracking desired trajectory mission requirements, step 2 is obtained respectively
Equation (7) and the governing equation shown in (10) have been arrived, below, under quadratic programming problem framework, obtained governing equation is retouched
State as linear equality constraints, and further consider the amplitude range τ of joint momentmin≤τ≤τmax, describe it as linear
Formula is constrained, for the object function in quadratic programming problem, is consumed to save system capacity and is obtained smooth joint trajectories,
Use following object function：
F (τ)=λττTIτ (11)
Wherein, λτFor adjustment factor, I ∈ Rn×nFor unit matrix；
Thus, the expectation joint moment for meeting pedestal unperturbed, end effector tracing task and Filters with Magnitude Constraints can be by asking
Following quadratic programming problem is solved to obtain：
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| CN109571484A (en) * | 2019-01-10 | 2019-04-05 | 北京邮电大学 | A kind of submissive assembly control method of space manipulator for self assembly task |
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| CN108132601B (en) * | 2017-12-06 | 2020-04-28 | 西北工业大学 | Method for suppressing spacecraft base attitude interference by using mechanical arm |
| CN108445778A (en) * | 2018-02-06 | 2018-08-24 | 南京航空航天大学 | A kind of dynamic modeling method non-fully constraining assembly for space non-cooperative target |
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| CN109794939A (en) * | 2019-02-19 | 2019-05-24 | 宁波凯德科技服务有限公司 | A kind of parallel Shu Fangfa of welding robot motion planning |
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| CN111558941B (en) * | 2020-07-14 | 2020-09-29 | 深圳市优必选科技股份有限公司 | Floating base dynamics feedforward control method and device and multi-legged robot |
| CN111558941A (en) * | 2020-07-14 | 2020-08-21 | 深圳市优必选科技股份有限公司 | Floating base dynamics feedforward control method and device and multi-legged robot |
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