CN106625671B - A kind of robot for space arrests the optimal trajectory planning method of Tum bling Target - Google Patents

A kind of robot for space arrests the optimal trajectory planning method of Tum bling Target Download PDF

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Publication number
CN106625671B
CN106625671B CN201611229840.0A CN201611229840A CN106625671B CN 106625671 B CN106625671 B CN 106625671B CN 201611229840 A CN201611229840 A CN 201611229840A CN 106625671 B CN106625671 B CN 106625671B
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space
robot
effector
target
arresting
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CN201611229840.0A
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CN106625671A (en
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罗建军
宗立军
王明明
袁建平
朱战霞
王保丰
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西北工业大学
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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
    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
    • G05B2219/00—Program-control systems
    • G05B2219/30—Nc systems
    • G05B2219/40—Robotics, robotics mapping to robotics vision
    • G05B2219/40511—Trajectory optimization, coarse for arm, medium for wrist, fine for finger

Abstract

The invention discloses a kind of optimal trajectory planning method that robot for space arrests Tum bling Target, the equation of motion including establishing robot for space and Tum bling Target；It proposes the derivation algorithm of robot for space working space and optimal arrest opportunity and fix really then；Obtained robot arm end effector it is optimal arrest track；Finally with the validity of case verification method proposed by the present invention.The best opportunity of arresting proposed by the present invention determines that criterion can guarantee to arrest generation in the unrelated working space in the path of robot for space, so that dynamic singularity problem will not be encountered.The optimal of the robot arm end effector obtained using the theory of optimal control arrests track, then arresting on end effector and target a little reaches same position with identical speed when can guarantee to arrest, so that the impact force generated when arresting is minimum.

Description

A kind of robot for space arrests the optimal trajectory planning method of Tum bling Target
[technical field]
The invention belongs to robot for space and automatic control technology field, it is related to a kind of robot for space and arrests Tum bling Target Optimal trajectory planning method.
[background technique]
Robot for space technology has been achieved for huge progress, and each spacefaring nation all successively implements in-orbit experimental verification Robot for space technology.However, the object of robot for space service is all with attitude control energy in the in-orbit experiment completed The cooperative target of power, and ground monitoring shows that most of inert satellite all has tumbling motion, so that robot for space is to such Target, which carries out in-orbit service task, becomes highly difficult, the robot for space serviced for non-cooperation, particularly Tum bling Target Technology need further to develop.
The method for planning track of existing robot for space can be roughly divided into two types: 1) completing track under joint space Planning.Nonlinear programming problem is solved by parameterizing joint trajectories, and using intelligent optimization algorithm, to directly obtain the phase The joint of mechanical arm motion profile of prestige.When the shortcomings that such methods, is to solve for nonlinear programming problem and may need largely to calculate Between.Meanwhile the requirement that a relative velocity is arrested on robot arm end effector and target is difficult in the space constantly arresting Under be indicated.2) trajectory planning is completed under task space.Such methods obtain mechanical arm using the theory of optimal control first The optimal motion track of end effector obtains corresponding joint of mechanical arm movement rail by solving inverse kinematics equation later Mark.However, robot for space is due to having a dynamic singularity, during solving inverse kinematics equation, end effector is very Small speed may correspond to excessive joint angular speed.A large amount of technique study robot for space Inverse Kinematics Problem it is unusual Robust derivation algorithm avoids generating excessive joint angular speed, but all unusual robust derivation algorithms all may cause machinery Arm end effector deviates desired trajectory.If the moment is being arrested in deviation generation, it would be possible to cause to generate excessive impact force.
[summary of the invention]
The present invention arrests the trajectory planning problem of Tum bling Target for robot for space, provides a kind of robot for space and arrests The optimal trajectory planning method of Tum bling Target guarantees that dynamic singularity problem will not be encountered arresting moment robot for space, and It realizes and constantly minimizes impact force arresting.
In order to achieve the above objectives, the present invention is achieved by the following scheme:
A kind of robot for space arrests the optimal trajectory planning method of Tum bling Target, comprising the following steps:
1) equation of motion of robot for space and Tum bling Target is established；
2) it calculates robot for space working space and determination is most preferably arrested opportunity；
3) it generates the optimal of robot arm end effector and arrests track.
A further improvement of the present invention lies in that:
The specific method is as follows for step 1):
Space Robot System is made of the mechanical arm of base satellite and n freedom degree, kinematics and kinetics equation table It is shown as:
Wherein, ve, ωeThe respectively linear velocity and angular speed of end effector,For base satellite line/ Angular speed,It is joint angular velocity vector；
To save fuel or reducing the influence moved to end effector, robot for space is in and freely floats work shape State, i.e. fb,fe=0；At this point, the kinetic model of robot for space simplifies are as follows:
Wherein, Hθ=Hm-Hbm THb -1HbmReferred to as " the broad sense inertial tensor of free-floating space robot ", For the nonlinear terms of free-floating space robot；Free-floating space robot system meets principle of conservation of momentum:
Assuming that the linear momentum P of initial time system, angular momentum L are zero, then formula (4) are substituted into formula (1), obtain free floating The kinematics model that robot for space simplifies:
Wherein, JgThe referred to as broad sense Jacobian matrix of free-floating space robot；
For Tum bling Target, the equation of motion of Tum bling Target is established；Based on euler dynamical equations, it is assumed that target is in space Not by any external force, then its attitude dynamic equations indicates are as follows:
Use the posture changing matrix of quaternion representation rigid body:
Wherein,For the unit quaternion for indicating posture, first three parameter represents Euler's shaft Direction, the 4th parameter represent the size of Euler's corner, and the component of angular speed is full under quaternary number each element and body coordinate system Attitude kinematics equations shown in sufficient formula (8):
It is denoted as assuming that only uniquely arresting the position vector a little arrested a little under body coordinate system on Tum bling TargetThen Under inertial coodinate system, the position vector arrested a little can be indicated are as follows:
Wherein, inv is indicated to matrix inversion.
The specific method is as follows for step 2):
2) it calculates robot for space working space and determination is most preferably arrested opportunity；
Formula (5) gives the kinematical equation of free-floating space robot, under base satellite body coordinate system, freely Shown in the kinematical equation of floating space robot such as formula (10):
Wherein, subscript " o " indicates the expression under base body coordinate system, meets,
Wherein, T0For base satellite attitude matrix, always meet reversal condition, then matrix JgSingularity be solely dependent upon matrixoJgIt is whether unusual；Because of matrixoJgWith joint of mechanical arm rotational angle theta, each Rigid Mass miWith inertia IiIt is related, while only joint Rotational angle theta is variation, so its unusual arm type can be determined by way of traversing robot for space joint space；
After obtaining the unusual arm type set of robot for space, using virtual machine arm concept, space machine is calculated The unrelated working space in the path of people and path related work space；
It is proposed that following three criterion determine robot for space most preferably arresting opportunity to noncooperative target, it is ensured that energy when arresting Enough so that the impact force between end effector and target is minimum:
Criterion 1: it when arresting, along direction is arrested, arrests and a little should be the nearest point of metric space robot system in target；
Criterion 2: arresting to arrest constantly should a little appear in the unrelated working space in robot for space path；
Criterion 3: when the first two criterion meets, arrest occur as early as possible.
Determining the unusual arm type of robot for space, the specific method is as follows:
2-1) all joint angles are initialized to minimum value θint=θmin；
2-2) calculate Jacobian matrixoJgIf det (oJg(θ)) < ε, then θ is saved as into unusual arm type；
2-3) since k=n, θ is checked whetherk+dθk< θmax, if so, going to step 4；If not, taking k=k-1, follow Ring step 3 terminates until k=1；Wherein, ' n ' is joint sum, and d θ is the angle step-length of very little；
2-4) take θI=k+1 ..., n=θi,max, θk=θk+ d θ, goes to step 2-2)；Wherein, subscript i represents i-th of joint.
The specific method is as follows for step 3):
To reduce the impact force arrested between moment end effector and target, it is expected that arresting moment end effector and arresting Relative velocity between point is decreased to zero；Assuming that the motion profile of end effector is by control forceIt generates, wherein reIt indicates The position of end effector；Define end effector state beObtain following system equation:
Assuming that the optimal control input u of robot for space makes following performance index function minimum:
Wherein, c (u) generates excessive acceleration for confinement end actuator:
Meet following end conswtraint simultaneously:
Using the theory of optimal control, the optimal control input of robot arm end effector is obtained are as follows:
u*=α (t-t0)+β (14)
Correspondingly, what end effector was optimal arrests motion profile are as follows:
Wherein,
Compared with prior art, the invention has the following advantages:
The optimal trajectory planning method of robot for space of the present invention, the fortune including establishing robot for space and Tum bling Target Dynamic equation；It proposes the derivation algorithm of robot for space working space and optimal arrest opportunity and fix really then；Machinery is obtained Arm end effector it is optimal arrest track；Finally with the validity of case verification method proposed by the present invention.The present invention mentions The best opportunity of arresting out determines that criterion can guarantee to arrest generation in the unrelated working space in the path of robot for space, thus not Dynamic singularity problem can be encountered.The optimal of the robot arm end effector obtained using the theory of optimal control arrests track, then Arresting on end effector and target a little reaches same position with identical speed when can guarantee to arrest, so that arresting When the impact force that generates it is minimum.
[Detailed description of the invention]
Fig. 1 is Space Robot System schematic diagram of the present invention；
Fig. 2 is robot for space working space schematic diagram of the present invention；
Fig. 3 is robot arm end effector of the present invention and arrests a motion profile；
Fig. 4 is end effector of the present invention and arrests a relative position and relative speed relationship schematic diagram.
[specific embodiment]
The invention will be described in further detail with reference to the accompanying drawing:
Robot for space of the present invention arrests the optimal trajectory planning method of Tum bling Target, comprising the following steps:
Step 1: establishing the equation of motion of robot for space and Tum bling Target.
As shown in Figure 1, Space Robot System is made of the mechanical arm of base satellite and n freedom degree, kinematics and dynamic Mechanical equation can indicate are as follows:
Wherein, ve, ωeThe respectively linear velocity and angular speed of end effector,For base satellite line/ Angular speed,It is joint angular velocity vector, the physical significance of other symbols is as shown in table 1.
1 Space Robot System physical parameter of table
To save fuel or reducing the influence moved to end effector, robot for space is often in and freely floats work State, i.e. fb,fe=0.At this point, the kinetic model of robot for space can simplify are as follows:
Wherein, Hθ=Hm-Hbm THb -1HbmReferred to as " the broad sense inertial tensor of free-floating space robot ", For the nonlinear terms of free-floating space robot.Free-floating space robot system meets principle of conservation of momentum,
Assuming that the linear momentum P of initial time system, angular momentum L are zero, then formula (4) are substituted into formula (1), available freedom The kinematics model that floating space robot simplifies:
Wherein, JgThe referred to as broad sense Jacobian matrix of free-floating space robot.
For Tum bling Target, considers that target has the situation of rotation around three principal axis of inertia, establish the movement of Tum bling Target Equation.Based on euler dynamical equations, it is assumed that target is not in space by any external force, then its attitude dynamic equations can indicate Are as follows:
Using the posture changing matrix of quaternion representation rigid body,
Wherein,For the unit quaternion for indicating posture, first three parameter represents Euler's shaft Direction, the 4th parameter represent the size of Euler's corner, and the component of angular speed is full under quaternary number each element and body coordinate system Attitude kinematics equations shown in sufficient formula (8):
It is denoted as assuming that only uniquely arresting the position vector a little arrested a little under body coordinate system on Tum bling TargetThen Under inertial coodinate system, the position vector arrested a little can be indicated are as follows:
Wherein, inv is indicated to matrix inversion.
It is most preferably arrested opportunity Step 2: calculating robot for space working space and determining.
Formula (5) gives the kinematical equation of free-floating space robot, under base satellite body coordinate system, freely Shown in the kinematical equation of floating space robot such as formula (10):
Wherein, subscript " o " indicates the expression under base body coordinate system, meets,
Wherein, T0For base satellite attitude matrix, always meet reversal condition, then matrix JgSingularity be solely dependent upon matrixoJgIt is whether unusual.Because of matrixoJgWith joint of mechanical arm rotational angle theta, each Rigid Mass miWith inertia IiIt is related, while only joint Rotational angle theta is variation, and the present invention proposes that algorithm 1 determines the unusual arm type of robot for space.
After obtaining the unusual arm type set of robot for space, using virtual machine arm concept, space can be calculated The unrelated working space in the path of robot and path related work space.Because robot arm end effector is in the unrelated work in path When spatial movement, it is ensured that robot for space will not encounter dynamic singularity problem, and the present invention proposes that following three criterion is true Determine robot for space most preferably arresting opportunity to noncooperative target, it is ensured that enable between end effector and target when arresting Impact force is minimum:
Criterion 1: it when arresting, along direction is arrested, arrests and a little should be the nearest point of metric space robot system in target；
Criterion 2: arresting to arrest constantly should a little appear in the unrelated working space in robot for space path；
Criterion 3: when the first two criterion meets, arrest occur as early as possible.
Step 3: generating the optimal of robot arm end effector arrests track.
In step 2, opportunity available robot arm end effector is most preferably arrested by determination and arrests an intersection Position and moment, provide that latter end actuator is optimal to arrest track in this step.
To reduce the impact force arrested between moment end effector and target, it is expected that arresting moment end effector and arresting Relative velocity between point is decreased to zero.Assuming that the motion profile of end effector is by control forceIt generates, wherein reIt indicates The position of end effector.Define end effector state beAvailable following system equation:
Assuming that the optimal control input u of robot for space makes following performance index function minimum:
Wherein, c (u) generates excessive acceleration for confinement end actuator:
Meet following end conswtraint simultaneously:
Using the theory of optimal control, the optimal control input of available robot arm end effector are as follows:
u*=α (t-t0)+β (14)
Correspondingly, the optimal motion profile of end effector are as follows:
Wherein,
Terminal juncture tfIt determines in step 2 and has been obtained when most preferably arresting opportunity, thus this step gives mechanical arm end End actuator it is optimal arrest track.
Kinematics/kinetic parameter of the table 2 with 3DOF mechanical arm robot for space
The unusual arm type of robot for space determines algorithm
Subscript i represents i-th of joint, and ' n ' is joint sum, and d θ is the angle step-length of very little, and such as 0.5 °
Step 1: all joint angles are initialized to minimum value θint=θmin；
Step 2: Jacobian matrix is calculatedoJgIf det (oJg(θ)) < ε, then θ is saved as into unusual arm type；
Step 3: since k=n, θ is checked whetherk+dθk< θmax, if so, going to step 4；If not, k=k-1 is taken, Step 3 is recycled until k=1, terminates；
Step 4: θ is takenI=k+1 ..., n=θi,max, θk=θk+ d θ, goes to step 2.
Table 1 is the physical significance of each parameter in the Space Robot System equation of motion, and table 2 is space machine used in example The kinematics and kinetic parameter of device people's system, Fig. 1 are Space Robot System schematic diagram, and Fig. 2 is robot for space in example The analysis of working space is as a result, Fig. 3, Fig. 4 are respectively the mechanical arm tail end that method for planning track proposed according to the present invention obtains Actuator and arrest motion profile a little and the relation schematic diagram of the two relative position and relative velocity.
Embodiment:
Tum bling Target is arrested as example using band three-freedom mechanical arm robot for space, illustrates robot for space in the present invention The optimal validity for arresting method for planning track.Kinematics/kinetic parameter of robot for space is as shown in table 2, it is assumed that rolling The rotary inertia of target are as follows:
Under body coordinate system, the position vector arrested a little isIt carves at the beginning, the rotation speed of target Spend component respectively [- 4-2-4] deg/sec in three axial directions of body coordinate system.
Using calculating process described in step 2, the working space for obtaining robot for space is distributed as shown in Fig. 2, simultaneously Obtaining the optimal opportunity of arresting corresponds to moment t=127s.At this point, arrest point out present position [0.3538,0.4949 ,- 0.0702] at m, speed is [0.0395, -0.0271,0.0084] m/s.
Determine that the best of robot arm end effector arrests track using the method proposed in step 3, such as Fig. 3 and Fig. 4 institute Show, it can be seen that can guarantee robot arm end effector and arrest a little to carve when arresting using method proposed by the present invention Present same position, and relative velocity is zero, so that impact force when guaranteeing to arrest between end effector and target is minimum.
The above content is merely illustrative of the invention's technical idea, and this does not limit the scope of protection of the present invention, all to press According to technical idea proposed by the present invention, any changes made on the basis of the technical scheme each falls within claims of the present invention Protection scope within.

Claims (2)

1. a kind of optimal trajectory planning method that robot for space arrests Tum bling Target, which comprises the following steps:
1) equation of motion of robot for space and Tum bling Target is established；
The specific method is as follows for step 1):
Space Robot System is made of the mechanical arm of base satellite and n freedom degree, and kinematics and kinetics equation indicate are as follows:
Wherein, ve, ωeThe respectively linear velocity and angular speed of end effector,For line/angle speed of base satellite Degree,It is each joint angular speed, Jb, JmThe respectively Jacobian matrix of pedestal and arm, Hb, HmThe respectively inertia of pedestal and arm Battle array, HbmFor the coupling torque matrix of pedestal and arm, cb, cmRespectively pedestal and arm nonlinear terms relevant to speed, fb, fePoint The external force and moment of face of pedestal and end effector Wei not be acted on, τ is each joint moment；
To save fuel or reducing the influence moved to end effector, robot for space is in and freely floats working condition, i.e., fb,fe=0；At this point, the kinetic model of robot for space simplifies are as follows:
Wherein, Hθ=Hm-Hbm THb -1HbmReferred to as " the broad sense inertial tensor of free-floating space robot ", For the nonlinear terms of free-floating space robot；Free-floating space robot system meets principle of conservation of momentum:
Wherein, P and L is respectively the linear momentum and angular momentum of system, r0For the relative position of pedestal mass center and System Nature in the heart to Amount；
Assuming that the linear momentum P of initial time system, angular momentum L are zero, then formula (4) are substituted into formula (1), obtain free floating space The kinematics model that robot simplifies:
Wherein, JgThe referred to as broad sense Jacobian matrix of free-floating space robot；
For Tum bling Target, the equation of motion of Tum bling Target is established；Based on euler dynamical equations, it is assumed that target space not by Any external force, then its attitude dynamic equations indicates are as follows:
Wherein, Ix,Iy,IzFor pedestal rotary inertia component, ωx,ωy,ωzFor pedestal angular velocity component,For base corner Component of acceleration；
Use the posture changing matrix of quaternion representation rigid body:
Wherein,For the unit quaternion for indicating posture, first three parameter represents the side of Euler's shaft To the 4th parameter represents the size of Euler's corner, and the component of angular speed meets formula under quaternary number each element and body coordinate system (8) attitude kinematics equations shown in:
It is denoted as assuming that only uniquely arresting the position vector a little arrested a little under body coordinate system on Tum bling TargetThen used Under property coordinate system, the position vector arrested a little can be indicated are as follows:
Wherein, inv is indicated to matrix inversion；
2) it calculates robot for space working space and determination is most preferably arrested opportunity；
The specific method is as follows for step 2):
Formula (5) gives the kinematical equation of free-floating space robot, under base satellite body coordinate system, freely floats Shown in the kinematical equation of robot for space such as formula (10):
Wherein, subscript " o " indicates the expression under base body coordinate system, meets,
Wherein, T0For base satellite attitude matrix, always meet reversal condition, then matrix JgSingularity be solely dependent upon matrixoJgIt is It is no unusual；Because of matrixoJgWith joint of mechanical arm rotational angle theta, each Rigid Mass miWith inertia IiIt is related, while only joint rotation angle θ It is variation, so its unusual arm type can be determined by way of traversing robot for space joint space；
Determining the unusual arm type of robot for space, the specific method is as follows:
2-1) all joint angles are initialized to minimum value θint=θmin；
2-2) calculate Jacobian matrixoJgIf det (oJg(θ)) < ε, then θ is saved as into unusual arm type；Wherein, det indicates square The determinant of battle array, ε are the normal number of very little；
2-3) since k=n, θ is checked whetherk+dθk< θmax, if so, going to step 4；If not, take k=k-1, circulation the 3 steps terminate until k=1；Wherein, ' n ' is joint sum, and d θ is the angle step-length of very little；
2-4) take θI=k+1 ..., n=θi,max, θk=θk+ d θ, goes to step 2-2)；Wherein, subscript i represents i-th of joint；
After obtaining the unusual arm type set of robot for space, using virtual machine arm concept, robot for space is calculated The unrelated working space in path and path related work space；
It is proposed that following three criterion determine robot for space most preferably arresting opportunity to noncooperative target, it is ensured that can make when arresting The impact force obtained between end effector and target is minimum:
Criterion 1: it when arresting, along direction is arrested, arrests and a little should be the nearest point of metric space robot system in target；
Criterion 2: arresting to arrest constantly should a little appear in the unrelated working space in robot for space path；
Criterion 3: when the first two criterion meets, arrest occur as early as possible；
3) it generates the optimal of robot arm end effector and arrests track.
2. the optimal trajectory planning method that robot for space according to claim 1 arrests Tum bling Target, which is characterized in that The specific method is as follows for step 3):
To reduce the impact force arrested between moment end effector and target, it is expected that arresting moment end effector and arresting point Between relative velocity be decreased to zero；Assuming that the motion profile of end effector is by control forceIt generates, wherein reIndicate end The position of actuator；Define end effector state beObtain following system equation:
Assuming that the optimal control input u of robot for space makes following performance index function minimum:
Wherein, c (u) generates excessive acceleration for confinement end actuator:
Meet following end conswtraint simultaneously:
Using the theory of optimal control, the optimal control input of robot arm end effector is obtained are as follows:
u*=α (t-t0)+β (14)
Correspondingly, what end effector was optimal arrests motion profile are as follows:
Wherein,
CN201611229840.0A 2016-12-27 2016-12-27 A kind of robot for space arrests the optimal trajectory planning method of Tum bling Target CN106625671B (en)

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CN107263466B (en) * 2017-05-11 2020-07-17 西北工业大学 Base undisturbed control method of space robot based on quadratic programming problem
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CN107529630A (en) * 2017-06-23 2018-01-02 西北工业大学 A kind of method that robot for space establishes kinetic model
CN107529498B (en) * 2017-06-23 2020-02-18 西北工业大学 Method for capturing non-cooperative target by space robot
CN107490965B (en) * 2017-08-21 2020-02-07 西北工业大学 Multi-constraint trajectory planning method for space free floating mechanical arm
CN107520844B (en) * 2017-09-21 2019-09-24 西北工业大学 Space manipulator arrests the polyhedron crash dynamics analysis method of noncooperative target
CN108445778B (en) * 2018-02-06 2020-12-25 南京航空航天大学 Dynamics modeling method for space non-cooperative target non-complete constraint assembly
CN108469737A (en) * 2018-04-28 2018-08-31 北京空间飞行器总体设计部 A kind of dynamic control method and system of space non-cooperative target navigation capture
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CN108942943B (en) * 2018-08-16 2020-03-17 居鹤华 Positive kinematics calculation method of multi-axis robot based on axis invariants
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