CN114734441A - Method for optimizing motion capability of mechanical arm in failure fault space of joint part - Google Patents

Method for optimizing motion capability of mechanical arm in failure fault space of joint part Download PDF

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CN114734441A
CN114734441A CN202210414943.3A CN202210414943A CN114734441A CN 114734441 A CN114734441 A CN 114734441A CN 202210414943 A CN202210414943 A CN 202210414943A CN 114734441 A CN114734441 A CN 114734441A
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mechanical arm
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CN114734441B (en
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陈钢
王含笑
徐文倩
符颖卓
李东方
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Beijing University of Posts and Telecommunications
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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
    • 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
    • B25J9/1602—Programme controls characterised by the control system, structure, architecture
    • B25J9/1605—Simulation of manipulator lay-out, design, modelling of manipulator
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02T—CLIMATE CHANGE MITIGATION TECHNOLOGIES RELATED TO TRANSPORTATION
    • Y02T90/00—Enabling technologies or technologies with a potential or indirect contribution to GHG emissions mitigation

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Abstract

The embodiment of the invention provides a method for optimizing the motion capability of a space manipulator with a failure fault of a joint part, which comprises the following steps: establishing a kinematics and dynamics model of a joint part failure space manipulator floating on a base according to joint part failure fault characteristics, further obtaining a kinematics and dynamics coupling relation of the failure manipulator, further establishing a system state space equation taking terminal track tracking and base self-disturbance suppression as control targets based on the kinematics and dynamics model of the joint part failure fault space manipulator, further designing a fault-tolerant controller capable of overcoming the influence of system uncertainty parameters based on a sliding mode control method under the condition that the joint speed/moment part fails respectively, realizing the terminal track tracking of the manipulator and the base attitude self-disturbance suppression, then introducing random variables into joint speed part failure and joint moment part failure fault-tolerant control rates respectively based on space manipulator redundancy characteristics, establishing a manipulator motion capability optimization model, and combining the manipulator motion capability optimization model with a fault-tolerant control system under the base disturbance condition, meanwhile, the tail end track tracking, the base posture self-disturbance suppression and the motion capability optimization of the joint part failure fault space manipulator are realized.

Description

Method for optimizing motion capability of mechanical arm in failure fault space of joint part
[ technical field ] A method for producing a semiconductor device
The invention relates to a method for optimizing the motion capability of a mechanical arm in a joint part failure fault space, and belongs to the technical field of fault-tolerant control of mechanical arms.
[ background of the invention ]
With the development of national economy and national defense industrial technology in China, the demand of on-orbit service tasks is increasing day by day. The space manipulator has the characteristics of strong load capacity, wide working range, flexible operation and the like, and is often used for assisting or replacing astronauts to execute on-orbit operation tasks. Considering that the space environment has the characteristics of microgravity, large temperature difference, strong radiation and the like, the space manipulator is easy to have joint faults when working in the environment for a long time. Once the joint breaks down, the joint cannot be repaired in the outer space in time, and the space manipulator cannot complete the expected task in time. Therefore, in order to ensure that the space manipulator can still continue to complete the task after the joint of the space manipulator fails, research needs to be carried out on the fault-tolerant control of the space manipulator with the joint failure.
The joint fault types of the space manipulator mainly comprise a joint locking fault, a joint part failure fault and a joint free swing fault. The joint locking fault and the joint free swing fault respectively correspond to two extreme conditions of complete loss of joint movement capacity and complete loss of torque output capacity, and the joint is considered to be in fault if the joint movement or the torque output capacity is perturbed in a broad sense and cannot reach an expected value, namely the joint is in fault of partial failure. Joint part failure faults are usually caused by internal factors (such as lubrication failure, clearance increase and the like) or external factors (such as heavy work, bad environment and the like), and usually cause a certain degree of degradation of the motion capability of the mechanical arm, such as reduction of motion flexibility, reduction of dynamic load capability and the like, and even possibly cause failure of operation tasks. Therefore, a general fault model is established for the joint part failure fault, and the research on the joint part failure fault space manipulator fault-tolerant control method with the optimal motion capability is developed, so that the method has important significance for further improving the in-orbit service reliability of the space manipulator.
The joint part failure fault space mechanical arm fault-tolerant control is a universal operation means which plans and controls the motion of a fault mechanical arm by considering the actual task requirement on the basis of the motion capability of the known fault space mechanical arm and ensures that an operation task is smoothly completed. Most of researches on the existing joint fault space manipulator fault-tolerant control method are developed aiming at joint locking faults, and related researches on joint part failure fault manipulators are few. In addition, the existing joint part failure fault space manipulator fault-tolerant control method does not consider the failure condition of a joint speed output part, and cannot be applied to a speed control mode, and a fault model is not comprehensive; the existing fault-tolerant control method for the space manipulator with the failure fault of the joint part only realizes the tracking of the tail end track of the manipulator, does not consider the self-disturbance of the base posture caused by the kinematic coupling relationship between the floating base and the space manipulator, and the base posture disturbance poses great threats to the operation stability and the safety of the space manipulator and the spacecraft; the existing joint part failure fault-tolerant control method for the space manipulator ignores the requirement of an actual on-orbit operation task on the motion capability of the space manipulator, the joint part failure fault causes the reduction of the motion flexibility, the load operation capability and the like of the space manipulator, the requirement of a subsequent task can not be met, and further the task failure is caused.
[ summary of the invention ]
In view of this, the invention provides a fault-tolerant control method for a joint part failure fault space manipulator with optimal motion capability, so as to realize stable tracking of a tail end track, self-disturbance suppression of a base and optimization of motion capability of the joint part failure fault space manipulator.
The embodiment of the invention provides a method for optimizing the motion capability of a mechanical arm in a joint part failure space, which comprises the following steps:
establishing a kinematics and dynamics model of the joint part failure space mechanical arm floating on the base according to the failure fault characteristics of the joint part, and further obtaining a kinematics and dynamics coupling relation of the failure mechanical arm;
according to the kinematics and dynamics model of the joint part failure fault space manipulator, a system state space equation taking tail end trajectory tracking and base self-disturbance suppression as control targets is constructed, and then a fault-tolerant controller capable of overcoming the influence of uncertain parameters of the system is designed based on a sliding mode control method under the condition that the joint speed/moment part fails respectively, so that the tail end trajectory tracking and the base attitude self-disturbance suppression of the manipulator are realized;
according to the mechanical arm fault-tolerant controller under the base disturbance condition, random variables are respectively introduced into the fault-tolerant control laws of joint speed part failure and joint moment part failure based on the redundancy characteristic of the space mechanical arm, a mechanical arm motion capability optimization model is established and combined with the fault-tolerant controller under the base disturbance condition, and meanwhile tail end trajectory tracking, base attitude self-disturbance suppression and motion capability optimization of the space mechanical arm under the joint part failure fault condition are achieved.
In the method, the establishing of the kinematics and dynamics model of the joint part failure space manipulator floating on the base according to the joint part failure fault characteristics to further obtain the kinematics and dynamics coupling relation of the failure manipulator comprises the following steps:
(1) and (3) establishing a fault general model which can be used for describing the joint motion output part failure and the joint torque output part failure at the same time by considering fault characteristics:
Uk(t)＝Ukc(t)+α(t)(ρk(t)-1)Ukc(t)+α(t)Ue(t)
wherein, Uk(t) actual output of faulty joint k at time t, Ukc(t) is the desired output of the failed joint k at time t,
Figure BDA0003598719260000031
as a step function, TeTime of occurrence of k-joint failure, TfFor task execution time, pk(t) outputting an effective factor, rho, for the multiplicative fault joint at time tk(t)∈[0,1]；
When the motion output by the joint k perturbs, the output speed can be expressed as:
Figure BDA0003598719260000032
when the torque output by the joint k perturbs, the output torque can be expressed as:
τk(t)＝τkc(t)+α(t)(ρk(t)-1)τkc(t)+α(t)τe(t)
(2) and (3) establishing a joint part failure fault space manipulator kinematics model by combining a joint fault general model:
Figure BDA0003598719260000041
wherein the content of the first and second substances,
Figure BDA0003598719260000042
respectively the tail end speed of the mechanical arm, the linear speed of the base, the angular speed of the base and the angular speed of the joint,
Figure BDA0003598719260000043
n is the degree of freedom of the mechanical arm;
Figure BDA0003598719260000044
jacobian matrix for base velocity to tip velocity mapping, E ∈ R3×3As unit vector, p0e＝pe-r0For base-to-tip position vectors, the corner mark "x" represents the inverse symmetric matrix of the vector; j. the design is a squareh,JfJacobian matrices, J, mapping healthy joint velocity and faulty joint velocity to terminal velocity, respectivelyh＝[J1,…,Jk-1,Jk+1,…,Jn]，Jf＝Jk；
Figure BDA0003598719260000045
For healthy joint angular velocity and faulty joint angular velocity,
Figure BDA0003598719260000046
Figure BDA0003598719260000047
and (3) establishing a dynamic model of the joint part failure fault space manipulator by combining a joint fault general model:
Figure BDA0003598719260000048
wherein, MbIs a basis mass matrix, MbmhAnd MmbhMass matrix for the coupling of the robot arm, base and healthy joint, MbmfAnd MmbfMass matrix, M, for the coupling of the robot arm, pedestal and failed jointmhh＝[Mmh1,…,Mmhk-1,Mmhk+1,…,Mmhn]，Mmhf＝Mmhk，Mmfh＝[Mmf1,…,Mmfk-1,Mmfk+1,…,Mmfn]，Mmff＝Mmfk，MmhAnd MmfQuality matrix for mechanical arm coupling with healthy and faulty joints, cbIs the centrifugal and Copeng force vectors of the susceptor, cmhAnd cmfThe centrifugal and Copenforces vectors, τ, of healthy and failed joints, respectivelymhAnd τmfRespectively outputting matrixes for healthy joints and fault joints,
Figure BDA0003598719260000049
is the acceleration of the base and is,
Figure BDA00035987192600000410
and
Figure BDA00035987192600000411
the angular acceleration of the healthy joint and the fault joint respectively;
(3) based on the conservation of linear momentum and angular momentum of the mechanical arm in the floating space of the base, the mapping relation between the speed of the healthy joint and the fault joint and the speed of the base is obtained as follows:
Figure BDA0003598719260000051
wherein v isbAnd wbIs the speed and angular velocity of the base,
Figure BDA0003598719260000052
and
Figure BDA0003598719260000053
angular velocities of healthy and faulty joints, HbmMomentum matrices for coupling the base and the mechanical arm respectively;
obtaining a mapping relation between a healthy joint, a fault joint speed and a mechanical arm tail end speed based on the above formula and a joint part failure fault space mechanical arm kinematics model:
Figure BDA0003598719260000054
wherein, JetA Jacobian matrix that maps joint velocity to tip velocity;
when the output torque part of the fault joint of the space manipulator fails, the expected output speed of the fault joint is not deviated from the actual output speed, so that the speed mapping relations among the healthy joint, the fault joint, the base and the tail end are shown in the formula;
when the output speed of the fault joint of the space manipulator is partially failed, based on the failure fault speed failure model of the joint part and the kinematic coupling relation of the space manipulator, obtaining the mapping relation between the expected output speed of the joint and the speed of the base and the mapping relation between the expected output speed of the joint and the speed of the tail end respectively as follows:
Figure BDA0003598719260000055
Figure BDA0003598719260000056
wherein HbIs a matrix of the momentum of the base,
Figure BDA0003598719260000057
the output speed of the tail end of the mechanical arm,
Figure BDA0003598719260000058
desired output speed for faulty joints, HbmcMomentum matrix for the mapping of joint desired velocity to base velocity, HmfMomentum matrix for failed joints, JetJacobian matrix, J, for the mapping of joint velocity to tip velocityevJacobian matrix, J, mapping healthy joint velocity and faulty joint control input velocity to terminal velocityefA Jacobian matrix for mapping the speed of the fault joint to the speed of the tail end of the mechanical arm;
based on a dynamic model of the joint part failure fault space manipulator, acquiring mapping relations between angular accelerations of healthy joints and fault joints and moments of the joints, between accelerations of a base and the healthy joints and between the accelerations of the fault joints and the moments of the joints, wherein the mapping relations between the terminal accelerations and the moments of the joints are respectively as follows:
Figure BDA0003598719260000061
Figure BDA0003598719260000062
Figure BDA0003598719260000063
wherein M isτhfAs a coupling matrix between healthy joints, faulty joint moments and their accelerations, cτhfIn the case of a non-linear term,
Figure BDA0003598719260000064
in order to accelerate the base, the acceleration of the base,
Figure BDA0003598719260000065
Figure BDA0003598719260000066
Mτea＝[Jeh Jef]Mτhf -1，
Figure BDA0003598719260000067
Jeha Jacobian matrix for mapping the healthy joint speed to the tail end speed of the mechanical arm;
if the output speed part of the failed joint of the space manipulator fails, the angular speed and the angular acceleration of the healthy joint and the failed joint under the known task can be obtained based on the analysis of the kinematic coupling relation of the failed space manipulator of the joint part, and the moment of each joint is obtained based on the formula;
if the output torque part of the fault joint of the space manipulator fails, the actual output torque of the fault joint is deviated from the expected output torque (control input torque); the mapping relation between the base and the terminal acceleration and the expected output torque of the healthy joint and the fault joint is as follows:
Figure BDA0003598719260000068
Figure BDA0003598719260000069
wherein M isτbIs a coupling matrix between joint moment and base acceleration, taumfcDesired output moment matrix, tau, for a faulty jointeFor outputting a torque matrix, M, at the end of the armτbi＝Mτbai,i≠n，Mτbn＝ρkMτban，cτb＝Mτbanτe+cτbaIs a non-linear term, MτeIs a coupling matrix between joint torque and terminal acceleration of the mechanical arm, Mτei＝Mτeai,i≠n，Mτen＝ρkMτean，cτe＝Mτeanτe+cτeaIs a non-linear term;
in the method, a system state space equation taking tail end trajectory tracking and base self-disturbance suppression as control targets is constructed according to a kinematics and dynamics model of a joint part failure fault space manipulator, and then a fault-tolerant controller capable of overcoming the influence of uncertain parameters of the system is designed based on a sliding mode control method under the condition that a joint speed/moment part fails respectively, so that tail end trajectory tracking and base attitude self-disturbance suppression of the manipulator are realized, and the method comprises the following steps:
(1) order to
Figure BDA0003598719260000071
And the terminal velocity and the base angular velocity are used as output to obtain a state space equation of the joint velocity partial failure fault space mechanical arm system:
Figure BDA0003598719260000072
wherein, PeTo the end position of the arm, θbThe posture of the base is taken as the posture of the base,
Figure BDA0003598719260000073
in order to determine the speed of the tail end of the mechanical arm,
Figure BDA0003598719260000074
is the speed of the base, and is,
Figure BDA0003598719260000075
and
Figure BDA0003598719260000076
respectively the expected motion states of the tail end position of the mechanical arm and the base posture,
Figure BDA0003598719260000077
Jev_upis a Jacobian matrix JevFirst three rows of (1), Hbmc_downFor coupling matrix HbmcThe last three rows;
Figure BDA0003598719260000078
θe_upis a matrix
Figure BDA0003598719260000079
First three rows of (a) (-), (theta)b_downIs a matrix
Figure BDA00035987192600000710
The last three rows of (C), JevAs a degenerate Jacobian matrix, HbMomentum matrix of the base HmfIs a momentum matrix of the failed joint,
Figure BDA00035987192600000711
in order to be the terminal angular velocity,
Figure BDA00035987192600000712
and
Figure BDA00035987192600000713
respectively setting the healthy joint angular velocity and the fault joint expected angular velocity;
order to
Figure BDA00035987192600000714
And the terminal linear acceleration and the base angular acceleration are used as output to obtain a state space equation of the joint velocity part failure fault space mechanical arm system:
Figure BDA0003598719260000081
wherein the content of the first and second substances,
Figure BDA0003598719260000082
and
Figure BDA0003598719260000083
respectively the acceleration of the base and the tail end of the mechanical arm,
Figure BDA0003598719260000084
Mτe_upis MτeFirst three rows of (M)τe＝[Mτe1，…，Mτen]Is a coupling matrix between joint torque and terminal acceleration of the mechanical arm, Mτb_downIs MτbLast three rows Mτb＝[Mτb1，…，Mτbn]For coupling between joint moment and base accelerationThe matrix is a matrix of a plurality of matrices,
Figure BDA0003598719260000085
cτe_upis a matrix cτeThe first three rows of (c)τb_downIs a matrix cτbThe last three rows of (c)τeAnd cτbFor non-linear terms, τmhOutput matrix for healthy joints, [ tau ]mfcAn output matrix is expected for the failed joint;
(2) under the condition that the joint speed part fails, a fault-tolerant controller capable of overcoming the influence of uncertain parameters of a system is obtained based on a sliding mode control method and comprises the following steps:
Figure BDA0003598719260000086
wherein the content of the first and second substances,
Figure BDA0003598719260000087
and
Figure BDA0003598719260000088
ki＞0，s＝[s1,…,s6]Tfor the end position P of the armeAnd base attitude θbThe surface of the sliding mould is in a manifold shape,
Figure BDA0003598719260000089
0<α<1，sgn(si) Is a sign function;
(3) under the condition that a joint moment part fails, designing a fault-tolerant controller capable of overcoming the influence of uncertain parameters of a system based on a sliding mode control method:
Figure BDA0003598719260000091
in the method, according to a mechanical arm fault-tolerant controller under the base disturbance condition, random variables are respectively introduced into joint speed part failure and joint torque part failure fault-tolerant control rates based on the redundancy characteristics of the spatial mechanical arm, a mechanical arm motion capability optimization model is established and combined with a fault-tolerant control system under the base disturbance condition, and meanwhile tail end trajectory tracking, base attitude self-disturbance suppression and motion capability optimization of the spatial mechanical arm under the joint part failure fault condition are realized, and the method comprises the following steps:
based on the redundancy characteristic of the space manipulator, random variables are respectively introduced into a joint speed part failure fault-tolerant control law and a joint torque part failure fault-tolerant control law:
Figure BDA0003598719260000092
Figure BDA0003598719260000093
wherein the content of the first and second substances,
Figure BDA0003598719260000094
and
Figure BDA0003598719260000095
healthy joint angular velocity and desired angular velocity of a faulty joint respectively,
Figure BDA0003598719260000096
Jev_upis a Jacobian matrix JevThe first three rows of (1), JevIn order to degenerate the jacobian matrix,
Figure BDA0003598719260000097
and
Figure BDA0003598719260000098
respectively the expected motion states of the tail end position of the mechanical arm and the base posture,
Figure BDA0003598719260000099
and
Figure BDA00035987192600000910
respectively the acceleration of the base and the tail end of the mechanical arm,
Figure BDA00035987192600000911
θe_upis a matrix
Figure BDA00035987192600000912
The first three rows of the first row of the first,
Figure BDA00035987192600000913
to the terminal angular velocity, JefJacobian matrix, θ, mapping fault joint velocity to robot tip velocityb_downIs a matrix
Figure BDA00035987192600000914
The last three rows of the first row of the second row,
Figure BDA00035987192600000915
and
Figure BDA00035987192600000916
ki＞0，s＝[s1,…,s6]Tis a terminal position PeAnd base attitude θbThe surface of the sliding mould is in a manifold shape,
Figure BDA0003598719260000101
0<α<1，sgn(si) As a function of the sign, τmhFor healthy joints the output matrix, τmfcAn output matrix is expected for the failed joint,
Figure BDA0003598719260000102
Mτe_upis MτeFirst three rows of (M)τe＝[Mτe1，…，Mτen]Is a coupling matrix between joint torque and terminal acceleration of the mechanical arm, Mτb_downIs MτbLast three rows, MτbIs a coupling matrix between joint moments and base accelerations,
Figure BDA0003598719260000103
cτe_upis a matrix cτeThe first three rows of (c)τb_downIs a matrix cτbLast three rows of (c)τeAnd cτbIn the case of a non-linear term,
Figure BDA0003598719260000104
Figure BDA0003598719260000105
the zero space term is a zero space term of the joint part failure fault space mechanical arm, corresponds to the self-motion of each joint, and does not contribute to the linear velocity of the tail end of the mechanical arm and the angular velocity of the base;
Figure BDA0003598719260000106
a null space item of a joint moment part failure fault space mechanical arm control system,
Figure BDA0003598719260000107
the vector is a random vector and can be used as a motion capability optimization item;
constructing a joint part failure fault space manipulator motion capability optimization model based on an optimization objective function and constraint conditions:
find
Figure BDA0003598719260000108
max Sd,or Wd,orKd,or Mt
s.t.
Figure BDA0003598719260000109
wherein the motion dexterity (including the minimum singular value S)dDegree of operability
Figure BDA00035987192600001010
Condition number Kd) And dynamic load capacity optimization objective function
Figure BDA00035987192600001011
The optimization objective function is:
Figure BDA00035987192600001012
Figure BDA00035987192600001013
Figure BDA0003598719260000111
max
Figure BDA0003598719260000112
s.t
Figure BDA0003598719260000113
i＝1,…,n
the constraint conditions are as follows: constraint solving based on joint angle, angular velocity and angular acceleration
Figure BDA0003598719260000115
The selection range of (1):
Figure BDA0003598719260000114
the motion capability optimization model is introduced into the fault-tolerant controller under the base disturbance condition, the motion capability optimization model is constructed at each moment in the operation process of the mechanical arm, random vectors corresponding to the optimal motion capability are obtained through solving based on a particle swarm algorithm, then the control law of the mechanical arm under the condition of optimal motion capability is obtained, and the motion capability optimization control of the mechanical arm in the joint part failure fault space is realized.
The technical scheme of the embodiment of the invention has the following beneficial effects:
(1) according to the failure fault characteristics of the joint part, the kinematics and dynamics model of the joint part failure space mechanical arm floating on the base is established, and further the kinematics and dynamics coupling relation of the failure mechanical arm is obtained;
(2) according to the method, a system state space equation taking base track tracking and base self-disturbance suppression as control targets is constructed according to a kinematics and dynamics model of a joint part failure fault space manipulator, and then a fault-tolerant controller capable of overcoming the influence of uncertain parameters of the system is designed based on a sliding mode control method under the condition that a joint speed/moment part fails, so that the tail end track tracking and base attitude self-disturbance suppression of the manipulator are realized;
(3) according to the fault-tolerant controller of the mechanical arm under the condition of base disturbance, random variables are respectively introduced into the fault-tolerant control rates of joint speed partial failure and joint moment partial failure based on the redundancy characteristic of the space mechanical arm, a mechanical arm motion capability optimization model is established, and meanwhile tail end track tracking, base attitude self-disturbance suppression and motion capability optimization of the space mechanical arm with joint partial failure are achieved.
[ description of the drawings ]
In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings needed to be used in the embodiments will be briefly described below, and it is obvious that the drawings in the following description are only some embodiments of the present invention, and it is obvious for those skilled in the art to obtain other drawings without creativity and labor.
FIG. 1 is a schematic flow chart diagram of a method for optimizing the shutdown of a space manipulator with a joint locking fault provided by an embodiment of the invention;
FIG. 2 is a schematic diagram of changes of indexes corresponding to a failure space manipulator of a joint speed part under the condition of disturbance of a base in the embodiment of the invention;
FIG. 3 is a schematic diagram showing changes of indexes corresponding to a space manipulator with failure of a joint moment part under the condition of disturbance of a base in the embodiment of the invention;
FIG. 4 is a schematic diagram of changes of indexes corresponding to a failure space mechanical arm with a joint speed part having optimal motion capability in the embodiment of the invention;
FIG. 5 is a schematic diagram of changes of indexes corresponding to a failure space mechanical arm with optimal motion capability in the embodiment of the invention, wherein the failure space mechanical arm has a failure moment part;
[ EXAMPLES ]
For better understanding of the technical solutions of the present invention, the following detailed descriptions of the embodiments of the present invention are provided with reference to the accompanying drawings.
It should be understood that the described embodiments are only some embodiments of the invention, and not all embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
The embodiment of the invention provides a fault-tolerant control method for a joint part failure fault space manipulator with optimal motion capability, and please refer to fig. 1, which is a schematic flow chart of the fault-tolerant control method for the joint part failure fault space manipulator with optimal motion capability provided by the embodiment of the invention, as shown in fig. 1.
According to the fault-tolerant control method for the joint part failure fault space manipulator with the optimal motion capability, which is provided by the embodiment of the invention, the method is simulated by taking the seven-degree-of-freedom space manipulator as a research object.
1. Assuming that the joint 1 has a speed partial failure fault, the initial joint angle of the mechanical arm is thetaini＝[-30°,-120°,100°,-20°,140°,160°,0°]The target position at the tail end of the mechanical arm is Pdes＝[5.8m,7.5m,1.8m]The initial pose of the base is xb＝[0m,0m,0m,0°,0°,0°]. Assuming that the joint 1 has a speed partial failure fault, the initial joint angle of the mechanical arm is thetaini＝[-30°,-120°,100°,-20°,140°,160°,0°]The target position at the tail end of the mechanical arm is Pdes＝[5.8m,7.5m,1.8m]Base initial pose is xb＝[0m,0m,0m,0°,0°,0°]. During task execution, the tail end of the mechanical arm moves to a desired position P along a straight linedesAnd the posture of the base is kept unchanged. Multiplicative fault effective factor rho of fault joint10.9, additive fault factor θe-2, the arm uncertainty parameter is in the form of a sine function,
Figure BDA0003598719260000131
selection ci＝0.5,i＝1,…,6，ki＝0.1,i＝1,…,6，αi0.9, 1, …, 6. A trapezoidal velocity interpolation method is adopted to plan the linear velocity of the tail end of the mechanical arm, the angular velocity of the base is limited to be 0, the expected motion track of the mechanical arm is obtained, and based on the joint velocity partial failure fault-tolerant control method, the actual motion track and the base posture of the tail end of the mechanical arm, the change of the function value of the sliding mode surface and the angles of all joints can be obtained as shown in figure 2. Under the uncertainty of model parameters, in the simulation execution process, the actual operation track of the mechanical arm is basically overlapped with the expected track, and the maximum position error of the tail end is 0.0253 m. The attitude deflection of the base is approximately 0, and the maximum deflection of the base in the X direction is-3.599 multiplied by 10-5°The maximum deflection of the base in the Y direction is-6.185X 10-5°The maximum deflection of the base in the Z direction is 2.823X 10-4°. Fig. 2(c) shows the deviation between the end position of the robot arm and the base angle and the expected value, which is the same as the model uncertainty parameter, and has a sinusoidal function trend and converges to about 0. Therefore, under the common influence of the joint speed part failure fault and the model uncertainty parameter, the fault-tolerant controller designed by the invention can effectively track the expected track of the tail end of the mechanical arm and inhibit the base attitude disturbance.
2. Assuming that the joint 1 has a speed partial failure fault, the initial joint angle of the mechanical arm is thetaini＝[-30°,-120°,100°,-20°,140°,160°,0°]The target position at the tail end of the mechanical arm is Pdes＝[5.2m,7.2m,2.0m]Base initial pose is xb＝[0m,0m,0m,0°,0°,0°]. In the task execution process, the tail end of the mechanical arm moves to the expected position P along a straight linedesAnd the posture of the base is kept unchanged. Multiplicative fault efficiency factor rho of fault joint10.9, additive fault factor θeThe arm uncertainty parameter takes the form of a sine function, Δ M ═ 2τeb＝0.01sin(πt)MτebAnd Δ cτeb＝0.011sin(πt)cτeb. Selection ci＝0.7,i＝1,…,6，ki＝0.4,i＝1,…,6，αi0.9, 1, …, 6. Planning tail end linear speed of mechanical arm by adopting trapezoidal speed interpolation methodAnd limiting the angular speed of the base to be 0 to obtain an expected motion track of the mechanical arm, solving the expected output torque of each joint of the mechanical arm based on the joint speed partial failure fault-tolerant control method provided by the invention, and bringing the expected output torque into a joint torque partial failure fault space mechanical arm model to obtain the actual motion track and the base posture of the mechanical arm tail end, the change of the sliding mode surface function value and the joint angle as shown in figure 3. Under the effect of uncertainty of model parameters, in the simulation execution process, the actual operation track of the mechanical arm is basically overlapped with the expected track, and the maximum position error of the tail end is 0.028 m. The attitude deflection of the base is approximately 0, and the maximum deflection of the base in the X direction is 2.538 multiplied by 10-5°The maximum deflection of the base in the Y direction is-1.223 x 10-5°The maximum deflection of the susceptor in the Z direction is-2.84X 10-8°. The sliding mode surface function of the mechanical arm is approximate to the variation trend of the uncertain parameters, is in a sine function form, and gradually approaches to the position near 0. Therefore, under the common influence of the joint moment part failure fault and the model uncertainty parameter, the fault-tolerant controller designed by the invention can effectively track the expected track of the tail end of the mechanical arm and inhibit the base attitude disturbance.
3. Assuming that the joint 1 is in failure and the multiplicative failure joint outputs an effective factor rho equal to 0.9, an additive failure unknown function term Ue0.1. The initial configuration of the mechanical arm is thetaini＝[-30°,-120°,100°,-20°,140°,160°,0°]The desired position is Pdes＝[6.5m,8m,2.6m]The motion flexibility of the mechanical arm is represented by the minimum singular value of degradation, and based on the joint speed partial failure fault space mechanical arm fault-tolerant control method considering the motion capability optimization, the tail end trajectory tracking, the base posture disturbance suppression and the minimum singular value of degradation optimization of the mechanical arm are realized. The tail end track tracking result and attitude disturbance suppression result of the failed space manipulator with the joint speed part as well as the optimization results of the angles and the minimum degradation singular values of all joints are shown in fig. 4. As can be seen from fig. 4(a), the actual trajectory of the end of the mechanical arm substantially coincides with the desired trajectory, and the end of the mechanical arm can move according to the desired trajectory. As can be seen from FIG. 4(b), the maximum value of the X-direction attitude disturbance of the base is-3.627X 10-5°The maximum value of the attitude disturbance in the Y direction is-6.228 multiplied by 10-5°The maximum value of the posture disturbance in the Z direction is 2.837 multiplied by 10-4°The base perturbation is substantially 0. In fig. 4(d), the minimum singular value of degradation of the mechanical arm after the motion capability optimization is greater than that before the optimization, which indicates that the optimization control method for the mechanical arm in the joint speed partial failure fault space based on the invention can realize the motion capability optimization of the mechanical arm on the basis that the tail end of the mechanical arm moves along the expected track and the posture of the base is undisturbed.
4. Assume the initial configuration of the mechanical arm is thetaini＝[-30°,-120°,100°,-20°,140°,160°,0°]The desired position is Pdes＝[6.5m,8.0m,2.7m]The output torque limit of the healthy joint is-1000,1000]Nm. By taking the dynamic load capacity as an optimization target, the fault-tolerant control method of the mechanical arm in the joint speed partial failure fault space, which is provided by the invention and takes the optimization of the motion capacity into consideration, realizes the tracking of the tail end track of the mechanical arm, the suppression of the base attitude disturbance and the optimization of the dynamic load capacity. The tail end track tracking result and the attitude disturbance suppression result of the joint moment partial failure fault space manipulator are respectively shown in fig. 5(a)5(b), and the dynamic load capacity optimization result is shown in fig. 5 (d). As can be seen from fig. 5(a), the actual trajectory of the end of the mechanical arm substantially coincides with the desired trajectory, and the end of the mechanical arm can move according to the desired trajectory. As can be seen from FIG. 5(b), the maximum value of the X-direction attitude disturbance of the base is 4.858X 10-6°The maximum value of the attitude disturbance in the Y direction is-3.605 multiplied by 10-6°The maximum value of the posture disturbance in the Z direction is-1.703 multiplied by 10-8°The base perturbation is substantially 0. FIG. 5(d) is a comparison graph of the dynamic load capacity of the failed robot arm before optimization and after optimization, and it can be seen from the graph that the dynamic load capacity of the robot arm before optimization is 176kg, the dynamic load capacity after optimization is 296kg, and the lifting rate of the dynamic load capacity of the robot arm is
Figure BDA0003598719260000151
Therefore, the optimization control method for the joint moment partial failure fault space manipulator can realize the optimization of the motion capability of the manipulator on the basis that the tail end of the manipulator moves along an expected track and the posture of the base is undisturbed.
The above description is only for the purpose of illustrating the preferred embodiments of the present invention and is not to be construed as limiting the invention, and any modifications, equivalents, improvements and the like made within the spirit and principle of the present invention should be included in the scope of the present invention.
Those skilled in the art will appreciate that those matters not described in detail in the present specification are well known in the art.

Claims (4)

1. A method for optimizing the motion capability of a mechanical arm in a joint part failure fault space is characterized by comprising the following steps:
(1) establishing a kinematics and dynamics model of the joint part failure space mechanical arm floating on the base according to the failure fault characteristics of the joint part, and further obtaining a kinematics and dynamics coupling relation of the failure mechanical arm;
(2) according to the kinematics and dynamics model of the joint part failure fault space manipulator, a system state space equation taking terminal trajectory tracking and base self-disturbance suppression as control targets is constructed, and then a fault-tolerant controller capable of overcoming the influence of uncertain parameters of the system is designed based on a sliding mode control method under the condition that the joint speed/moment part fails respectively, so that the terminal trajectory tracking and the base attitude self-disturbance suppression of the manipulator are realized;
(3) according to the mechanical arm fault-tolerant controller under the base disturbance condition, random variables are respectively introduced into the fault-tolerant control laws of joint speed part failure and joint moment part failure based on the redundancy characteristic of the space mechanical arm, a mechanical arm motion capability optimization model is established and combined with the fault-tolerant controller under the base disturbance condition, and meanwhile tail end trajectory tracking, base attitude self-disturbance suppression and motion capability optimization of the space mechanical arm under the joint part failure fault condition are achieved.
2. The method of claim 1, wherein the establishing a kinematics and dynamics model of the floating joint failure space manipulator of the base according to the failure characteristics of the joint, thereby obtaining a kinematics and dynamics coupling relationship of the failed manipulator comprises:
(1) and (3) establishing a fault general model which can be used for describing the joint motion output part failure and the joint torque output part failure at the same time by considering fault characteristics:
Uk(t)＝Ukc(t)+α(t)(ρk(t)-1)Ukc(t)+α(t)Ue(t)
wherein, Uk(t) actual output of faulty joint k at time t, Ukc(t) is the expected output of the failed joint k at time t,
Figure FDA0003598719250000011
as a step function, TeTime of occurrence of k-joint failure, TfFor task execution time, pk(t) outputting an effective factor, rho, for the multiplicative fault joint at time tk(t)∈[0,1]；
When the motion output by the joint k perturbs, the output speed can be expressed as:
Figure FDA0003598719250000021
when the torque output by the joint k perturbs, the output torque can be expressed as:
τk(t)＝τkc(t)+α(t)(ρk(t)-1)τkc(t)+α(t)τe(t)
(2) and (3) establishing a joint part failure fault space manipulator kinematics model by combining a joint fault general model:
Figure FDA0003598719250000022
wherein, the first and the second end of the pipe are connected with each other,
Figure FDA0003598719250000023
vb,wb,
Figure FDA0003598719250000024
the tail end speed, the linear speed, the angular speed and the joint angular speed of the mechanical armThe degree of the water is measured by the following method,
Figure FDA0003598719250000025
n is the degree of freedom of the mechanical arm;
Figure FDA0003598719250000026
jacobian matrix for base velocity to tip velocity mapping, E ∈ R3×3As unit vector, p0e＝pe-r0For base-to-tip position vectors, the corner mark "x" represents the vector's anti-symmetric matrix; j. the design is a squareh,JfJacobian matrices, J, mapping healthy joint velocity and faulty joint velocity to terminal velocity, respectivelyh＝[J1,…,Jk-1,Jk+1,…,Jn]，Jf＝Jk；
Figure FDA00035987192500000211
For healthy joint angular velocity and faulty joint angular velocity,
Figure FDA0003598719250000028
Figure FDA0003598719250000029
and (3) establishing a dynamic model of the joint part failure fault space manipulator by combining a joint fault general model:
Figure FDA00035987192500000210
wherein M isbIs a base mass matrix, MbmhAnd MmbhMass matrix for the coupling of the robot arm, base and healthy joint, MbmfAnd MmbfMass matrix, M, for the coupling of the robot arm, pedestal and failed jointmhh＝[Mmh1,...,Mmhk-1,Mmhk+1,…,Mmhn]，Mmhf＝Mmhk，Mmfh＝[Mmf1,...,Mmfk-1,Mmfk+1,…,Mmfn]，Mmff＝Mmfk，MmhAnd MmfQuality matrix for mechanical arm coupling with healthy and faulty joints, cbIs the centrifugal and Copeng force vectors of the susceptor, cmhAnd cmfThe centrifugal and Copenforces vectors, τ, of healthy and failed joints, respectivelymhAnd τmfRespectively outputting matrixes for healthy joints and fault joints,
Figure FDA0003598719250000031
is the acceleration of the base and is,
Figure FDA0003598719250000032
and
Figure FDA0003598719250000033
the angular acceleration of the healthy joint and the fault joint respectively;
(3) based on the conservation of linear momentum and angular momentum of the mechanical arm in the floating space of the base, the mapping relation between the speed of the healthy joint and the fault joint and the speed of the base is obtained as follows:
Figure FDA0003598719250000034
wherein v isbAnd wbIs the speed and angular velocity of the base,
Figure FDA0003598719250000035
and
Figure FDA0003598719250000036
angular velocities of healthy and faulty joints, HbmMomentum matrices for coupling the base and the mechanical arm respectively;
obtaining a mapping relation between a healthy joint, a fault joint speed and a mechanical arm tail end speed based on the above formula and a joint part failure fault space mechanical arm kinematics model:
Figure FDA0003598719250000037
wherein, JetA Jacobian matrix that maps joint velocity to tip velocity;
when the output torque part of the fault joint of the space manipulator fails, the expected output speed of the fault joint is not deviated from the actual output speed, so that the speed mapping relations among the healthy joint, the fault joint, the base and the tail end are shown as the formula;
when the output speed of the fault joint of the space manipulator is partially failed, based on the failure fault speed failure model of the joint part and the kinematic coupling relation of the space manipulator, obtaining the mapping relation between the expected output speed of the joint and the speed of the base and the mapping relation between the expected output speed of the joint and the speed of the tail end respectively as follows:
Figure FDA0003598719250000038
Figure FDA0003598719250000039
wherein HbIs a matrix of the momentum of the base,
Figure FDA00035987192500000310
the output speed of the tail end of the mechanical arm,
Figure FDA00035987192500000311
desired output speed for a faulty joint, HbmcMomentum matrix for mapping of joint desired velocity to base velocity, HmfMomentum matrix for failed joints, JetJacobian matrix, J, for the mapping of joint velocity to tip velocityevJacobian matrix, J, mapping healthy joint velocity and faulty joint control input velocity to terminal velocityefA Jacobian matrix for mapping the speed of the fault joint to the speed of the tail end of the mechanical arm;
based on a dynamic model of the joint part failure fault space manipulator, acquiring mapping relations between angular accelerations of healthy joints and fault joints and moments of the joints, mapping relations between the accelerations of the base and the moments of the healthy joints and the fault joints, and mapping relations between the accelerations of the tail end and the moments of the joints are respectively as follows:
Figure FDA0003598719250000041
Figure FDA0003598719250000042
Figure FDA0003598719250000043
wherein M isτhfIs a coupling matrix between healthy joints, faulty joint moments and their accelerations, cτhfIn the case of a non-linear term,
Figure FDA0003598719250000044
in order to accelerate the base, the acceleration of the base,
Figure FDA0003598719250000045
Figure FDA0003598719250000046
Mτea＝[Jeh Jef]Mτhf -1，
Figure FDA0003598719250000047
Jeha Jacobian matrix for mapping the healthy joint speed to the tail end speed of the mechanical arm;
if the output speed part of the failed joint of the space manipulator fails, the angular speed and the angular acceleration of the healthy joint and the failed joint under the known task can be obtained based on the analysis of the kinematic coupling relation of the failed space manipulator of the joint part, and the moment of each joint is obtained based on the formula;
if the output torque part of the fault joint of the space manipulator fails, the actual output torque of the fault joint is deviated from the expected output torque (control input torque); the mapping relation between the base and the terminal acceleration and the expected output torque of the healthy joint and the fault joint is as follows:
Figure FDA0003598719250000051
Figure FDA0003598719250000052
wherein M isτbIs a coupling matrix between joint moment and base acceleration, taumfcDesired output moment matrix, tau, for a faulty jointeFor outputting a torque matrix, M, at the end of the armτbi＝Mτbai,i≠n，Mτbn＝ρkMτban，cτb＝Mτbanτe+cτbaIs a non-linear term, MτeIs a coupling matrix between joint torque and terminal acceleration of the mechanical arm, Mτei＝Mτeai,i≠n，Mτen＝ρkMτean，cτe＝Mτeanτe+cτeaIs a non-linear term.
3. In the method, a system state space equation taking terminal trajectory tracking and base self-disturbance suppression as control targets is constructed according to a kinematics and dynamics model of the joint part failure fault space manipulator, and then a fault-tolerant controller capable of overcoming the influence of uncertain parameters of the system is designed based on a sliding mode control method under the condition that the joint speed/moment part fails respectively, so that the terminal trajectory tracking and the base attitude self-disturbance suppression of the manipulator are realized, and the method comprises the following steps:
(1) order to
Figure FDA0003598719250000053
And the terminal velocity and the base angular velocity are used as output to obtain a state space equation of the joint velocity partial failure fault space mechanical arm system:
Figure FDA0003598719250000054
wherein, PeThe end position of the arm, thetabThe posture of the base is taken as the posture of the base,
Figure FDA0003598719250000055
in order to determine the speed of the tail end of the mechanical arm,
Figure FDA0003598719250000056
is the speed of the base, and is,
Figure FDA0003598719250000057
and
Figure FDA0003598719250000058
respectively the expected motion states of the tail end position of the mechanical arm and the posture of the base,
Figure FDA0003598719250000059
Jev_upis Jacobi matrix JevFirst three rows of (1), Hbmc_downFor coupling matrix HbmcThe last three rows;
Figure FDA00035987192500000510
θe_upis a matrix
Figure FDA00035987192500000511
First three rows of (a) (-), (theta)b_downIs a matrix
Figure FDA00035987192500000512
Last three rows, JevIs a degenerate Jacobian matrix, HbMomentum matrix of the base HmfIs a momentum matrix of the failed joint,
Figure FDA0003598719250000061
in order to be the terminal angular velocity,
Figure FDA0003598719250000062
and
Figure FDA0003598719250000063
respectively setting healthy joint angular velocity and fault joint expected angular velocity;
order to
Figure FDA0003598719250000064
And the terminal linear acceleration and the base angular acceleration are used as output to obtain a state space equation of the joint velocity part failure fault space mechanical arm system:
Figure FDA0003598719250000065
wherein the content of the first and second substances,
Figure FDA00035987192500000614
and
Figure FDA00035987192500000613
the acceleration of the base and the tail end of the mechanical arm respectively,
Figure FDA0003598719250000068
Mτe_upis MτeFirst three rows of (M)τe＝[Mτe1，…，Mτen]Is a coupling matrix between joint torque and terminal acceleration of the mechanical arm, Mτb_downIs MτbLast three rows Mτb＝[Mτb1，…，Mτbn]Is a coupling matrix between joint moments and base accelerations,
Figure FDA0003598719250000069
cτe_upis a matrix cτeThe first three rows of (c)τb_downIs a matrix cτbLast three rows of (c)τeAnd cτbFor non-linear terms, τmhFor healthy joints the output matrix, τmfcAn output matrix is expected for the failed joint;
(2) under the condition that the joint speed part fails, a fault-tolerant controller capable of overcoming the influence of uncertain parameters of a system is obtained based on a sliding mode control method and comprises the following steps:
Figure FDA00035987192500000610
wherein the content of the first and second substances,
Figure FDA00035987192500000611
and
Figure FDA00035987192500000612
ki＞0，s＝[s1,…,s6]Tfor the end position P of the armeAnd base attitude θbThe surface of the sliding mould is in a manifold shape,
Figure FDA0003598719250000071
sgn(si) Is a sign function;
(3) under the condition that a joint moment part fails, designing a fault-tolerant controller capable of overcoming the influence of uncertain parameters of a system based on a sliding mode control method:
Figure FDA0003598719250000072
4. the method according to claim 1, wherein according to the fault-tolerant controller of the mechanical arm under the base disturbance condition, random variables are respectively introduced into fault-tolerant control laws of joint speed partial failure and joint moment partial failure based on the redundancy characteristic of the spatial mechanical arm, a mechanical arm motion capability optimization model is established, and is combined with the fault-tolerant controller under the base disturbance condition, and meanwhile, the tail end trajectory tracking, base attitude self-disturbance suppression and motion capability optimization of the spatial mechanical arm under the joint partial failure condition are realized, and the method comprises the following steps:
based on the redundancy characteristic of the space manipulator, random variables are respectively introduced into a joint speed part failure fault-tolerant control law and a joint torque part failure fault-tolerant control law:
Figure FDA0003598719250000073
Figure FDA0003598719250000074
wherein the content of the first and second substances,
Figure FDA0003598719250000075
and
Figure FDA0003598719250000076
healthy joint angular velocity and desired angular velocity of a faulty joint respectively,
Figure FDA0003598719250000077
Jev_upis a Jacobian matrix JevThe first three rows of (1), JevIn order to degenerate the jacobian matrix,
Figure FDA0003598719250000078
and
Figure FDA0003598719250000079
respectively the expected motion states of the tail end position of the mechanical arm and the base posture,
Figure FDA00035987192500000710
and
Figure FDA00035987192500000711
respectively the acceleration of the base and the tail end of the mechanical arm,
Figure FDA00035987192500000712
θe_upis a matrix
Figure FDA00035987192500000713
The first three rows of the first row of the first,
Figure FDA00035987192500000714
to the terminal angular velocity, JefJacobian matrix, θ, mapping fault joint velocity to robot tip velocityb_downIs a matrix
Figure FDA0003598719250000081
The last three rows of the first row of the second row,
Figure FDA0003598719250000082
and
Figure FDA0003598719250000083
s＝[s1,…,s6]Tis a terminal position PeAnd base attitude θbThe surface of the sliding mould is in a manifold shape,
Figure FDA0003598719250000084
sgn(si) As a function of the sign, τmhFor healthy joints the output matrix, τmfcAn output matrix is expected for the failed joint,
Figure FDA0003598719250000085
Mτe_upis MτeFirst three rows of (M)τe＝[Mτe1，…，Mτen]Is a coupling matrix, M, between joint torque and the acceleration of the tail end of the mechanical armτb_downIs MτbLast three rows, MτbIs a coupling matrix between joint moments and base accelerations,
Figure FDA0003598719250000086
cτe_upis a matrix cτeThe first three rows of (c)τb_downIs a matrix cτbLast three rows of (c)τeAnd cτbIn the case of a non-linear term,
Figure FDA0003598719250000087
the zero space term is a zero space term of the joint part failure fault space mechanical arm, corresponds to the self-motion of each joint, and does not contribute to the linear velocity of the tail end of the mechanical arm and the angular velocity of the base;
Figure FDA0003598719250000088
a null space item of a joint moment part failure fault space mechanical arm control system,
Figure FDA0003598719250000089
the vector is a random vector and can be used as a motion capability optimization item;
constructing a joint part failure fault space manipulator motion capability optimization model based on an optimization objective function and constraint conditions:
Figure FDA00035987192500000810
max Sd,or Wd,orKd,or Mt
Figure FDA00035987192500000811
wherein the motion dexterity (including the minimum singular value S)dDegree of operability
Figure FDA00035987192500000812
Condition number Kd) And dynamic load capacity optimization objective function
Figure FDA0003598719250000091
The optimization objective function is:
Figure FDA0003598719250000092
Figure FDA0003598719250000093
Figure FDA0003598719250000094
Figure FDA0003598719250000095
Figure FDA0003598719250000096
the constraint conditions are as follows: constraint solving based on joint angle, angular velocity and angular acceleration
Figure FDA0003598719250000098
The selection range of (1):
Figure FDA0003598719250000097
the motion capability optimization model is introduced into the fault-tolerant controller under the base disturbance condition, the motion capability optimization model is constructed at each moment in the operation process of the mechanical arm, random vectors corresponding to the optimal motion capability are obtained through solving based on a particle swarm algorithm, then the control law of the mechanical arm under the condition of optimal motion capability is obtained, and the motion capability optimization control of the mechanical arm in the joint part failure fault space is realized.
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