CN109015657A - A kind of final state network optimized approach towards redundant mechanical arm repeating motion planning - Google Patents
A kind of final state network optimized approach towards redundant mechanical arm repeating motion planning Download PDFInfo
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- CN109015657A CN109015657A CN201811042159.4A CN201811042159A CN109015657A CN 109015657 A CN109015657 A CN 109015657A CN 201811042159 A CN201811042159 A CN 201811042159A CN 109015657 A CN109015657 A CN 109015657A
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- mechanical arm
- final state
- joint
- end effector
- redundant mechanical
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Classifications
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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
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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
A kind of final state network optimized approach towards redundant mechanical arm repeating motion planning, comprising the following steps: 1) determine redundant mechanical arm end effector expectation target track r*(t) the joint angles θ to back with expectation*(0)；2) design final state attracts optimizing index, forms mechanical arm repeating motion programme, wherein the initial joint angle when actual motion of redundant mechanical arm can be arbitrarily designated, and end effector is not required to be on desired trajectory；Initial joint angles θ (0) when given redundant mechanical arm actual motion is movement starting point, the repeating motion programme for attracting optimization characteristics with final state of formation with θ (0)；3) the final state network model of finite value activation primitive is constructed, with final state Solution To The Network time-varying matrix equation；4) obtained result will be solved and be used to control each joint motor, driving mechanical arm executes task.The present invention provides that a kind of precision is high, redundant mechanical arm of finite time convergence control repeats movement technique.
Description
Technical field
Repeating motion planning and control technology the present invention relates to redundant mechanical arm, and in particular, to a kind of final state attraction
Optimality criterion, the inverse movement of redundant mechanical arm under each movable joint angle initial position offset desired trajectory situation of mechanical arm
Learn method for solving.
Background technique
Mechanical arm is always the research hotspot in robot field.Mechanical arm refers to the active mechanical device in an end,
Its end task includes carrying, welding, paint and assemble etc., is widely used to industrial manufacture, therapeutic treatment, entertainment garment at present
In the fields such as business, fire-fighting, military affairs and space probation.According to freedom degree (Degrees-of-Freedom, DOF) number, it is mechanical
Arm can be divided into redundant mechanical arm and non redundant manipulator.Redundant mechanical arm refers to possessed DOF more than the given end of completion
The mechanical arm of the DOF of required by task.Accordingly, non redundant manipulator, which refers to when executing given end task, does not have extra DOF
Mechanical arm.Obviously, compared with non redundant manipulator, redundant mechanical arm because of it has extra DOF more flexible and more advantage,
This be also its in practical engineering applications it is increasingly prominent go out importance the reason of one of.
Redundant mechanical arm underlying issue present in real time kinematics control is redundancy parsing problem, also referred to as
Inverse kinematics.Position and posture by known end effector solve the value of its corresponding each joint angle of redundant mechanical arm.
Scheme is parsed by using specific redundancy, redundant mechanical arm is while completing given end task, additionally it is possible to one
Barrier and the joint physical limit of itself in environment are hidden in free movement in a biggish joint subspace.Classical does
Method is the redundancy parsing scheme based on pseudoinverse.Consider the mechanical arm with n freedom degree of the operation in m-dimensional space, end
Relationship (i.e. positive kinematics problem) between track and joint displacements
R (t)=f (θ (t))
Wherein, r (t) indicates displacement of the robot arm end effector in working space under cartesian coordinate system, θ (t) table
Show joint displacements.Differential motion relationship between end cartesian space and joint space is
Wherein,It is the time-derivative of r,It is joint velocity vector,It is the Jacobian matrix of mechanical arm.
For redundant mechanical arm, conventional method is to solve for Moore-Penrose generalized inverse (pseudoinverse), can obtain joint variable speed
The least square solution of degree is
Here, J+=JT(JJT)-1It is the pseudoinverse of Jacobian matrix J.
When repeating motion is done in Descartes operating space, the end effector motion profile of closure may not have end effector
There is the joint angle track for generating and being closed, leads to joint angle bias phenomenon.Deviation brought by this non-duplicate motion problems may
Mechanical arm can be caused unexpected situation occur in repeating operation.In most cases, it will use the method for autokinesis
Carry out improvement processing to replace usually used pseudoinverse control methods because pseudoinverse control methods can not obtain can complete it is original heavy
The repeatability moved again.But use the regulated efficiency from method often not high.
Summary of the invention
In order to overcome the relatively slow without finite time convergence, convergence rate of existing final state network optimized approach, convergence
The lower deficiency of precision, the present invention in, with finite time convergence can recurrent neural network by with solve time-varying problem.Phase
Than in the recurrent neural network with asymptotic convergence dynamic characteristic, final state, which restrains dynamic characteristic, has finite time convergence, no
Convergence rate can be only improved, and reaches higher convergence precision.In order to keep each joint angle of redundant mechanical arm inclined in initial position
When moving desired locations, the repeating motion of redundant mechanical arm is realized, the present invention provides a kind of higher precision, finite time convergence control, is easy to
That realizes attracts the redundant mechanical arm method for planning track of optimizing index based on final state, with the final state with finite value activation primitive
Network is as solver, when initial position deviates situation, after each joint angle of redundant mechanical arm is by desired trajectory movement, finally
Still initial desired locations be may return to.
In order to solve the above-mentioned technical problem the present invention provides the following technical solution:
A kind of final state network optimized approach towards redundant mechanical arm repeating motion planning, comprising the following steps:
1) redundant mechanical arm end effector expectation target track r is determined*(t) the joint angles θ to back with expectation*(0)；
2) design final state attracts optimizing index, forms mechanical arm repeating motion programme, and wherein redundant mechanical arm is practical
Initial joint angle when movement can be arbitrarily designated, and end effector is not required to be on desired trajectory；Given redundant mechanical arm
Initial joint angles θ (0) when actual motion, is movement starting point with θ (0), and the repeating motion programme of formation is described as
Have the quadratic programming that final state attracts optimizing index:
Wherein,θ、It respectively indicates
The joint angles and joint angular speed of redundant mechanical arm, θ*(0) be each joint angle expectation initial value, ρ > 0, βθ0,0 < δ of >
< 1 is a design parameter, for forming the dynamic property of joint displacements；θ(t)-θ*(0) each joint angle and initial expectation are indicated
Joint angle offset deviation, r*Indicate the desired motion profile of robot arm end effector,Indicate the desired speed of end effector
Spend vector；Due to mechanical arm initial position may not on desired track, by reduce end effector expected path with
Error (r between actual motion track position*- f (θ)), change the direction of motion of end effector, βrThe locative parameter of > 0
Gain, for adjusting the rate that end effector moves to expected path；J (θ) is redundant mechanical arm Jacobian matrix, and f (θ) is
Redundant mechanical arm actual motion track；
3) the final state network model of finite value activation primitive is constructed, dynamic characteristic is described by following equations
Wherein, joint angle offset deviation E (t)=θ (t)-θ (0), system finite time convergence control expressed by this dynamical equation
In zero, 0 < δ < 1, ρ > 0, βE> 0, the convergence time T needed are as follows:
When target function reaches minimum value, each joint angle of redundant mechanical arm can back to desired target trajectory
On；
For solution procedure 2) in quadratic programming, establish Lagrangian:
In formula, λ (t) is Lagrange multiplier vector, λTIt is the transposition of λ (t) vector；By Lagrangian to each
Variable derivation, and enabling it is zero, can obtain following time-varying matrix equations
WY=v (3)
Wherein,
I is unit matrix
Remember that E=WY-v obtains system with finite value final state Solution To The Network time-varying matrix equation (3) described in formula (2)
It is as follows to solve equation
4) obtained result will be solved in step 3) execute task for controlling each joint motor, driving mechanical arm.
Beneficial effects of the present invention are mainly manifested in: the present invention provides a kind of final state attraction optimizing index, makes redundant mechanical
Arm does not have to the position for considering initial each joint angle, and each joint angle still may return to desired first behind the track by giving
Repeating motion planning tasks are realized in beginning position.The program for existing motion planning scheme there is finite time to receive
The characteristics of holding back, the final state provided attract optimizing index that can be conducive to improve the precision calculated.
Dynamic network compared to traditional repeating motion programme and asymptotic convergence restrains effect, and there is final state to attract
The repeating motion programme of convergence property have finite time convergence control characteristic, corresponding to final state Solution To The Network method not only
The convergence rate of dynamic network is accelerated, and improves the convergence precision of network.The solution of this network by activation letter
Number is finite value activation primitive, this provides calculating instrument to solve relevant time-varying problem, and is easier in practical application
In realization.
Detailed description of the invention
Fig. 1 is the flow chart provided by the invention for repeating programme.
Fig. 2 is the redundant mechanical arm ER6B-C60 that programme is repeated using the present invention, wherein (a) is solid mechanical arm
ER6B-C60 front view is (b) solid mechanical arm ER6B-C60 side view
Fig. 3 is the motion profile of redundant mechanical arm ER6B-C60 end effector.
Fig. 4 is error locus when being solved with final state network and recurrent neural network.
Fig. 5 is the y with x when final state Solution To The Network, the error locus in z-axis.
Fig. 6 is with the motion profile of each joint angle of redundant mechanical arm ER6B-C60 when final state Solution To The Network.
Specific embodiment
The invention will be further described below in conjunction with the accompanying drawings.
Referring to Fig.1~Fig. 6, a kind of final state network optimized approach towards redundant mechanical arm repeating motion planning, by following 4
A step composition: 1), determine redundant mechanical arm end effector expectation target track and expectation back each joint angles 2), establish
With final state attract optimizing index redundant mechanical arm repeating motion quadratic programming scheme 3), with finite value final state Solution To The Network two
Secondary planning problem obtains each joint angle track.4) obtained result driving motor, will be solved to run, mechanical arm is made to complete track
Task.Detailed process is as follows:
1) determines desired trajectory
Setting redundant mechanical arm ER6B-C60 it is expected the joint angles to back.It is a length of that destination path is set as a leaf
The eight leaf rose tracks of 0.04m determine the rose desired trajectory equation r of eight leaves*。
Wherein α=1, β=4,Mechanical arm tail end completes eight leaves
The trajectory time T=2.25 π s of rose, area are S=2* α2*π≈0.01m2.Eight leaf rose faces are parallel with Z axis plane, setting
Redundant mechanical arm ER6B-C60 it is expected the joint angles to back
θ*(0)=[0 ,-π/4,0, pi/2 ,-π/4,0]T
Since the initial position of each joint angle of redundant mechanical arm ER6B-C60 may not be on desired motion profile, by machine
Six joint angles initial values of tool arm are set as θ (0)=[0 ,-π/4,0, pi/2 ,-π/4+2,0]T, wherein the 5th joint angle deviates
Desired locations 2rad.
2) the quadratic programming scheme of redundant mechanical arm repeating motion is established
For the repeating motion planning for realizing redundant mechanical arm finite time convergence control, redundant mechanical arm repeating motion track is advised
It draws and is described as following quadratic programming problem, the optimizing index that final state attracts is
Wherein,θ、It respectively indicates
The joint angles and joint angular speed of redundant mechanical arm, θ*(0) be each joint angle expectation initial value, βθ0,1 > δ of > 0, ρ >
> 0 is design parameter, for forming the dynamic property of joint displacements.θ(t)-θ*(0) indicate that each joint angle and initial expectation close
Save angular displacement deviation, r*Indicate the desired motion profile of robot arm end effector,Indicate the desired speed of end effector
Vector.Since the initial position of mechanical arm may not be on desired track, by reducing end effector expected path and reality
Error (r between the motion profile position of border*- f (θ)), change the direction of motion of end effector, βrThe locative parameter of > 0 increases
Benefit, for adjusting the rate that end effector moves to expected path；J (θ) is redundant mechanical arm Jacobian matrix, and f (θ) is superfluous
Remaining mechanical arm actual motion track.
3) is with the above-mentioned quadratic programming problem of finite value final state Solution To The Network
By to each variable derivation of Lagrangian, and enabling it is zero, can obtain following time-varying matrix equation
WY=v
I is unit matrix
The bending moment battle array error in equation that clocks E=WY-v.Neural network mould is constructed according to finite value final state network dynamic equation (2)
Type
4) obtained result will be solved in step 3) execute task for controlling each joint motor, driving mechanical arm.
The redundant mechanical arm ER6B-C60 for repeating programme for realizing the present invention is as shown in Figure 2.The mechanical arm is by 1
Pedestal, 7 connecting rods are constituted, and are made up of joint a1, joint a2, joint a3, joint a4, joint a5, joint a6.The redundancy machine
Tool arm such as figure length of connecting rod is respectively L1=0.563m, L2=0.9m, L3=0.16m, L4=1.0135m, L5=0.195m, L6=
0.22m, L7=0m.
The motion profile of the end effector of mechanical arm in space is as shown in Figure 3.Eight leaf rose rail of target is provided in figure
Mark and robot arm end effector motion profile.As can be seen that the initial position of end effector is not on desired track.With
The increase of time, actual path and desired trajectory coincide.When solving repeating motion programme with Recursive Networks, end is held
The speed that backs of row device is slower than the solving speed of final state network.Repeating motion planning side is solved in order to further compare heterogeneous networks
Angle when case backs effect, and Fig. 4 gives the error convergence effect picture obtained using different networks.
Definition calculates error JE(t)=| | W (t) y (t)-v (t) | |2.Fig. 4 provides secondary with finite value final state Solution To The Network
The error convergence track of planning problem.It can be seen from the figure that when with finite value final state Solution To The Network, when time t was close to 1 second
When, error convergence precision reaches 4*10-3。
Error such as Fig. 5 institute of the end effector of redundant mechanical arm in execution track task, on tri- directions XYZ
Show.It can be seen from the figure that the error precision on three directions reaches 10 as t=5s-6。
For redundant mechanical arm when completing track task, the motion profile of each joint angle is as shown in Figure 6.It can understand in figure
The motion process of two joint angles is seen on ground, has been eventually returned to the initial desired locations of movement.
Claims (1)
1. a kind of final state network optimized approach towards redundant mechanical arm repeating motion planning, which is characterized in that the method packet
Include following steps:
1) redundant mechanical arm end effector expectation target track r is determined*(t) the joint angles θ to back with expectation*(0)；
2) design final state attracts optimizing index, forms mechanical arm repeating motion programme, wherein redundant mechanical arm actual motion
When initial joint angle be arbitrarily designated, do not require end effector to be on desired trajectory；Given redundant mechanical arm actual motion
When initial joint angles θ (0), with θ (0) be movement starting point, the repeating motion programme of formation be described as have final state inhale
Draw the quadratic programming of optimizing index:
Wherein,θ、Respectively indicate redundancy
The joint angles and joint angular speed of mechanical arm, θ*(0) be each joint angle expectation initial value, ρ > 0, βθ0,0 < δ < 1 of >
It is a design parameter, for forming the dynamic property of joint displacements；θ(t)-θ*(0) indicate that each joint angle and initial expectation close
Save angular displacement deviation, r*Indicate the desired motion profile of robot arm end effector,Indicate the desired speed of end effector to
Amount；Since the initial position of mechanical arm may not be on desired track, by reducing end effector expected path and reality
Error (r between motion profile position*- f (θ)), change the direction of motion of end effector, βrThe locative parameter of > 0 increases
Benefit, for adjusting the rate that end effector moves to expected path；J (θ) is redundant mechanical arm Jacobian matrix, and f (θ) is superfluous
Remaining mechanical arm actual motion track；
3) the final state network model of finite value activation primitive is constructed, dynamic characteristic is described by following equations
Wherein, joint angle offset deviation E (t)=θ (t)-θ (0), system finite time convergence control expressed by this dynamical equation in
Zero, 0 < δ < 1, ρ > 0, βE> 0, the convergence time T needed are as follows:
When target function reaches minimum value, each joint angle of redundant mechanical arm backs onto desired target trajectory；To ask
The quadratic programming in step 2) is solved, Lagrangian is established:
In formula, λ (t) is Lagrange multiplier vector, λTIt is the transposition of λ (t) vector；By Lagrangian to each variable
Derivation, and enabling it is zero, obtains following time-varying matrix equations
WY=v (3)
Wherein,
I is unit matrix
Remember that E=WY-v obtains the solution of system with finite value final state Solution To The Network time-varying matrix equation (3) described in formula (2)
Equation is as follows
4) obtained result will be solved in step 3) execute task for controlling each joint motor, driving mechanical arm.
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| CN110695994A (en) * | 2019-10-08 | 2020-01-17 | 浙江科技学院 | Finite time planning method for cooperative repetitive motion of double-arm manipulator |
| CN111687844A (en) * | 2020-06-19 | 2020-09-22 | 浙江大学 | Method for completing unrepeatable covering task by using mechanical arm to lift up for minimum times |
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