CN111687834A - Reverse priority impedance control system and method for redundant mechanical arm of mobile manipulator - Google Patents

Reverse priority impedance control system and method for redundant mechanical arm of mobile manipulator Download PDF

Info

Publication number
CN111687834A
CN111687834A CN202010369760.5A CN202010369760A CN111687834A CN 111687834 A CN111687834 A CN 111687834A CN 202010369760 A CN202010369760 A CN 202010369760A CN 111687834 A CN111687834 A CN 111687834A
Authority
CN
China
Prior art keywords
control
manipulator
task
priority
inverse
Prior art date
Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
Granted
Application number
CN202010369760.5A
Other languages
Chinese (zh)
Other versions
CN111687834B (en
Inventor
刘海燕
苏宇
李敏斯
林春兰
吴雪颖
Current Assignee (The listed assignees may be inaccurate. Google has not performed a legal analysis and makes no representation or warranty as to the accuracy of the list.)
Guangxi University of Science and Technology
Original Assignee
Guangxi University of Science and Technology
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Application filed by Guangxi University of Science and Technology filed Critical Guangxi University of Science and Technology
Priority to CN202010369760.5A priority Critical patent/CN111687834B/en
Publication of CN111687834A publication Critical patent/CN111687834A/en
Application granted granted Critical
Publication of CN111687834B publication Critical patent/CN111687834B/en
Active legal-status Critical Current
Anticipated expiration legal-status Critical

Links

Images

Classifications

    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B25—HAND TOOLS; PORTABLE POWER-DRIVEN TOOLS; MANIPULATORS
    • B25J—MANIPULATORS; CHAMBERS PROVIDED WITH MANIPULATION DEVICES
    • B25J9/00—Programme-controlled manipulators
    • B25J9/16—Programme controls
    • B25J9/1628—Programme controls characterised by the control loop
    • B25J9/1633—Programme controls characterised by the control loop compliant, force, torque control, e.g. combined with position control
    • 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
    • B25J9/1679—Programme controls characterised by the tasks executed
    • 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
    • Y02P—CLIMATE CHANGE MITIGATION TECHNOLOGIES IN THE PRODUCTION OR PROCESSING OF GOODS
    • Y02P90/00—Enabling technologies with a potential contribution to greenhouse gas [GHG] emissions mitigation
    • Y02P90/02—Total factory control, e.g. smart factories, flexible manufacturing systems [FMS] or integrated manufacturing systems [IMS]

Landscapes

  • Engineering & Computer Science (AREA)
  • Robotics (AREA)
  • Mechanical Engineering (AREA)
  • Manipulator (AREA)

Abstract

The invention discloses a system and a method for controlling inverse priority impedance of a redundant manipulator of a mobile manipulator. The manipulator is convenient to move and comprises a movable moving platform, the manipulator and a control console for controlling the manipulator, wherein the movable moving platform is arranged on the manipulator; the manipulator comprises a mechanical arm, a mounting seat, a vertical column, an output gripper and a vertical cylinder; the mechanical arm comprises a vertical lifting moving platform, an arm section I, an arm section II, an arm section III and an arm section IV; a vertical rail is arranged on the left surface of the vertical column, and the vertical lifting mobile platform is vertically and slidably arranged on the vertical rail up and down; the lower end of the vertical column is fixedly connected to the upper surface of the mounting seat, the cylinder seat of the vertical cylinder is fixedly connected to the upper surface of the mounting seat positioned on the left side of the vertical track, and the upper end of the telescopic rod of the vertical cylinder is fixedly connected to the lower surface of the vertical lifting moving table; the mounting seat is fixed on the mobile platform.

Description

Reverse priority impedance control system and method for redundant mechanical arm of mobile manipulator
Technical Field
The invention relates to the technical field of reverse priority impedance control of manipulator redundant manipulators, in particular to a reverse priority impedance control system and a reverse priority impedance control method for a mobile manipulator redundant manipulator.
Background
The control method adopted by the industrial robot at present is that each joint on the manipulator is taken as an independent servo mechanism, namely each axis corresponds to a server, and each server is controlled by a bus and is uniformly controlled and coordinated by a controller;
the mechanical arm with six degrees of freedom is the mechanical arm with the minimum degree of freedom for finishing space positioning, and the mechanical arms with more than six degrees of freedom are collectively called as redundant mechanical arms;
the existing impedance control method for the mechanical arm of the manipulator cannot realize the expected impedance control task under different hierarchical structures, so that a method which can enable the redundant mechanical arm of the manipulator to realize the expected impedance control task under different hierarchical structures is very necessary to design.
Disclosure of Invention
The invention aims to overcome the defect that the existing impedance control method of the mechanical arm can not realize the expected impedance control task under different hierarchical structures, and provides a method which can control the balance of a mechanical arm and is convenient for the mechanical arm to move; and the other is a moving manipulator redundant mechanical arm inverse priority impedance control system and a control method which can enable the redundant mechanical arm of the mechanical arm to realize the expected impedance control task under different hierarchical structures.
The technical problem is solved by the following technical scheme:
the reverse priority impedance control system of the redundant mechanical arm of the mobile manipulator comprises the manipulator and a console for controlling the manipulator; the device also comprises a movable moving platform; the manipulator comprises a mechanical arm, a mounting seat, a vertical column, an output gripper and a vertical cylinder; the mounting seat is fixed on the mobile platform;
the mechanical arm comprises a vertical lifting moving platform, an arm section I, an arm section II, an arm section III and an arm section IV;
a vertical rail is arranged on the left surface of the vertical column, and the vertical lifting mobile platform is vertically and slidably arranged on the vertical rail up and down; the lower end of the vertical column is fixedly connected to the upper surface of the mounting seat, the cylinder seat of the vertical cylinder is fixedly connected to the upper surface of the mounting seat positioned on the left side of the vertical track, the telescopic rod of the vertical cylinder is vertically arranged upwards, and the upper end of the telescopic rod of the vertical cylinder is fixedly connected to the lower surface of the vertical lifting mobile platform; the vertical lifting mobile platform can move up and down along a vertical track under the driving of a telescopic rod of a vertical cylinder to form a first degree of freedom;
the arm section I comprises an A1 section pipe and an A2 section pipe which is telescopically connected in a left pipe orifice of the A1 section pipe, a first cylinder with a telescopic rod horizontally arranged towards the left is fixedly arranged at the right end in the A1 section pipe, and the telescopic rod of the first cylinder is fixedly connected at the right end of the A2 section pipe;
the arm section II comprises a section B1 pipe and a section B2 pipe which is telescopically connected in a left pipe orifice of the section B1 pipe, a second cylinder with a telescopic rod horizontally arranged towards the left is fixedly arranged at the right end in the section B1 pipe, and the telescopic rod of the second cylinder is fixedly connected at the right end of the section B2 pipe;
the left end of the vertical lifting moving platform is provided with a first horizontal rotating shaft driven by a first speed reducing motor, and the right end of the A1 section pipe is fixedly connected to the first horizontal rotating shaft, so that the first arm section can horizontally rotate to form a second degree of freedom; a first electromagnetic brake capable of controlling the first horizontal rotating shaft to rotate is further arranged on the first horizontal rotating shaft;
the left end of the section A2 pipe is provided with a second horizontal rotating shaft driven by a second speed reducing motor, and the right end of the section B1 pipe is fixedly connected to the second horizontal rotating shaft, so that the arm section II can horizontally rotate to form a third degree of freedom; a second electromagnetic brake capable of controlling the second horizontal rotating shaft to rotate is further arranged on the second horizontal rotating shaft;
the left end of the section B2 pipe is provided with a third horizontal rotating shaft driven by a third speed reducing motor, and the right end of the arm section III is fixedly connected to the third horizontal rotating shaft, so that the arm section III can horizontally rotate to form a fourth degree of freedom; a third electromagnetic brake capable of controlling the third horizontal rotating shaft to rotate is further arranged on the third horizontal rotating shaft;
the left end of the arm section III is provided with a first transverse vertical rotating shaft which is driven by a fourth speed reducing motor and can rotate on the left vertical surface and the right vertical surface, and the right end of the arm section IV is fixedly connected to the first transverse vertical rotating shaft, so that the arm section IV can vertically rotate on the left vertical surface and the right vertical surface to form a fifth degree of freedom; a fourth electromagnetic brake capable of controlling the first transverse vertical rotating shaft to rotate is further arranged on the first transverse vertical rotating shaft;
the left end of the arm section four is provided with a first longitudinal vertical rotating shaft which is driven by a fifth speed reducing motor and can rotate on the front vertical surface and the rear vertical surface, and the right end of the output gripper is fixedly connected to the first longitudinal vertical rotating shaft, so that the right end of the output gripper can vertically rotate on the front vertical surface and the rear vertical surface to form a sixth degree of freedom; a fifth electromagnetic brake capable of controlling the first longitudinal vertical rotating shaft to rotate is further arranged on the first longitudinal vertical rotating shaft;
the section A2 of the pipe can be driven by the telescopic rod of the first cylinder to move in a telescopic manner from side to side in the section A1 of the pipe to form a seventh degree of freedom;
the B2 section of pipe can be driven by the telescopic rod of the second cylinder to move in the B1 section of pipe in a left-right telescopic manner to form an eighth degree of freedom;
the left end of a first horizontal pipe is horizontally and fixedly connected to the right surface of the vertical column, a balance adjusting block is arranged in the first horizontal pipe in a sliding mode from left to right, a balance adjusting cylinder with a telescopic rod facing right horizontally is fixedly connected to the left end of the first horizontal pipe, and the right end of the telescopic rod of the balance adjusting cylinder is fixedly connected to the balance adjusting block;
the control end of No. one electromagnetic brake, the control end of No. two electromagnetic brakes, the control end of No. three electromagnetic brakes, the control end of No. four electromagnetic brakes, the control end of No. five electromagnetic brakes, the control end of a gear motor, the control end of No. two gear motor, the control end of No. three gear motor, the control end of No. four gear motor, the control end of No. five gear motor, the control end of a cylinder, the control end of No. two cylinders, the control end of balance adjustment cylinder and the control end of vertical cylinder are respectively control connection on the control cabinet.
The balance adjusting cylinder controls the balance of the vertical column by moving the balance adjusting block left and right, and then the balance of the manipulator is controlled. The manipulator is convenient to move. Because some mechanical arms of the invention have eight degrees of freedom, the invention has good flexibility and high reliability and is easy to complete control tasks.
A reverse priority impedance control method for a redundant mechanical arm of a mobile manipulator comprises the following steps:
step 1, establishing a kinematic model of the redundant mechanical arm, and giving a gradient direction strategy of a zero space vector of the redundant mechanical arm;
step 2, establishing a task priority solving strategy for obtaining a singularity elimination algorithm through a singular robust solution;
step 3, establishing a singular robust solution inverse kinematics analysis model;
step 4, establishing a reverse priority control strategy of the multi-task redundant mechanical arm;
step 5, simplifying a reverse control equation of the redundant mechanical arm with the main task and the secondary task;
step 6, establishing a reverse priority control strategy of the manipulator;
step 7, solving the relation between the external force and the joint acceleration in the reverse priority impedance control of the manipulator by adopting the joint speed, thereby obtaining the reverse priority impedance control guarantee of the manipulator;
and 8, expanding the reverse priority calculation of the position control space to the reverse priority calculation of the force control space, thereby obtaining the overall framework of the speed-level reverse priority impedance control of the manipulator.
The motion of the redundant mechanical arm in the joint space is derived according to the reverse order; then, the Cartesian impedance control is combined with the inverse priority impedance control, the inverse hierarchical impedance control problem is solved, and the Cartesian impedance control behavior is divided into high-priority impedance control and low-priority impedance control. The high-priority impedance control task does not interfere with the low-priority impedance control task, and the motion in the joint space is influenced in the reverse order and needs to work in a corresponding projection operator; and finally, a high-priority impedance control task is realized, and deformation caused by singularity possibly occurring in the low-priority impedance control task is avoided. Thus, the proposed inverse-priority impedance control method enables the redundant robotic arm to achieve the desired impedance control task at the appropriate hierarchical structure.
Preferably, a kinematic model of the redundant manipulator is established, and a gradient direction strategy implementation process of a zero space vector of the redundant manipulator is given as follows:
defining the pose and speed of the end effector in Cartesian spaceRespectively x,
Figure BDA0002475972440000031
The angular position and angular velocity of the joint space are q,
Figure BDA0002475972440000032
J is a Jacobian matrix of the n-degree-of-freedom robot, where x ∈ Rn，
Figure BDA0002475972440000033
Figure BDA0002475972440000034
J∈Rm-n(ii) a The positive kinematic equation for a redundant degree of freedom robotic arm can be described by:
Figure BDA0002475972440000035
equation (1) is also referred to as a robot arm kinematics velocity model;
considering the solution of the least squares method, the optimal problem can be listed as:
Figure BDA0002475972440000036
the solution of formula (1) can be optimized by finding the best
Figure BDA0002475972440000037
To solve the problem;
Figure BDA0002475972440000038
thus, the pseudo-inverse solution of equation (1) can be expressed as:
Figure BDA0002475972440000039
in the formula J+Pseudo-inverse of the Jacobian matrix
I-identity matrix
Figure BDA00024759724400000310
-arbitrary null space vector
Figure BDA00024759724400000311
Minimum norm solution, defining hand movements
Figure BDA00024759724400000312
Homogeneous solution, no action at the end
Equation (4) represents the position and attitude control of the end effector; adding any residual error into the formula (4) to obtain a general expression containing a null space; the multi-task optimization can be realized on a zero vector by using the equation;
however, the above equation ignores the ill-conditioned state of the jacobian matrix; the regularization equation may be modified by adding additional regularization values,
Figure BDA0002475972440000041
where λ ≧ 0 is the weighting matrix,
Figure BDA0002475972440000042
is a weighting coefficient, and satisfies
Figure BDA0002475972440000043
The solution to the above equation can be expressed as:
Figure BDA0002475972440000044
equation (7) is also referred to as a redundant manipulator kinematics model;
the joint limit function of the joint limit gradient direction of the position-dependent scalar index of the null-space vector of the redundant manipulator is as follows:
Figure BDA0002475972440000045
preferably, a task priority solving strategy for obtaining the singularity elimination algorithm through a singular robust solution is established as follows:
in the solution of the redundant mechanical arm of the Jacobian matrix, an optimization task is realized in a null space of a main task; the reverse task kinematics is established on the basis of the forward task kinematics:
Figure BDA0002475972440000046
wherein
Figure BDA0002475972440000047
And
Figure BDA0002475972440000048
representation task1 and task2
The inverse kinematics equation of the redundant manipulator is obtained from expression (5) as follows:
Figure BDA0002475972440000049
task1 as the main Task and Task2 as the auxiliary Task; that is to say that the position of the first electrode,
Figure BDA00024759724400000410
is that
Figure BDA00024759724400000411
Is implemented in the null space of (1); the final inverse kinematics expression for the redundant manipulator is as follows:
Figure BDA00024759724400000412
wherein
Figure BDA00024759724400000413
Figure BDA00024759724400000414
Is a projection matrix which gives the applicable range of the secondary task to the primary task;
Figure BDA00024759724400000415
and
Figure BDA00024759724400000416
is the desired commanded speed;
Figure BDA00024759724400000417
is the main task of the method, and the method comprises the following steps of,
Figure BDA00024759724400000418
is a secondary task;
if two related tasks are interdependent, then the corresponding Jacobian matrix is singular; if the task jacobian matrix is singular, the corresponding task is not satisfied; in this case, the jacobian correlation matrix will be singularities, defined as algorithmic singularities;
that is, if
Figure BDA00024759724400000419
Where ρ (·) is the rank of the matrix;
it is clear that the singularity of the algorithm is caused by task conflicts between the secondary tasks and the primary task; in addition, task priority based redundant robotic arm inverse kinematics aims to provide better control over the effectiveness of the primary tasks;
therefore, the position control direction is used as a main task, so that the position ensures the accuracy of the control direction task; then, establishing a task priority solving strategy equation for obtaining a singularity elimination algorithm through singular robust solution:
Figure BDA0002475972440000051
preferably, the singular robust solution inverse kinematics analysis model is established as follows:
the motion singularity can occur based on the Jacobian pseudo-inverse solution, which is caused by the secondary matrix; for the motion singularity problem, a DLS (damped least squares) solution should also be given;
the cost function for the DLS solution can be modified to:
Figure BDA0002475972440000052
thus, the singular robust pseudo-inverse solution of the above equation can be expressed as:
Figure BDA0002475972440000053
equation (15) is a singular robust solution inverse kinematics analysis model, where λ is η2I, the DLS solution is equivalent to an additional regularization solution, and the scalar value η balances the task precision and singularity;
for the calculation of the pseudo-inverse solution of the Jacobian matrix, the singular value SVD decomposition form of the Jacobian matrix can be given
J＝U∑VT(16)
Wherein U ∈ Rm×m，V∈Rn×n，∑∈Rm×nU is a column vector UiA unitary matrix of V is formed by column vectors ViThe constituent unary matrix, ∑, is a block matrix of m × n diagonal matrices containing the singular values σ of JiMore than or equal to 0 contains n-m zero column vectors in descending order;
Figure BDA0002475972440000054
wherein r is less than or equal to m is the rank of the matrix J;
for motion singularity, with reference to the singular value decomposition SVD required to compute the pseudo-inverse solution, the large resulting joint velocity is due to the smallest singular value rapidly approaching 0, as follows:
Figure BDA0002475972440000055
factor lambda0Will affect the singularity, λ0The higher the value is, the larger the damping is, and the closer the joint velocity is to the singular point; in addition, the strategy for defining the variable damping factor is also different; we can get
Figure BDA0002475972440000056
From the above equation, we can see that the parameter > 0 monitors the smallest singular value.
Preferably, establishing a reverse priority control strategy of the multitask redundant mechanical arm as follows;
introducing an inverse-priority projection matrix
Figure BDA0002475972440000061
The matrix comprises a null space of corresponding elements of the lowest priority l-k-1 task independent of the kth task, so derived
Figure BDA0002475972440000062
Figure BDA0002475972440000063
Wherein Ji|jIs a jacobian matrix associated with all components of the i-th task that are linearly independent of the j-th task;
therefore, the priority derivation formula is as follows:
Figure BDA0002475972440000064
in the above derivation, k ═ l, l-1, …, 1; initial value
Figure BDA0002475972440000065
To give a general form of computation of the linear independent Jacobian matrix J, the inverse augmented Jacobian matrix is defined as:
Figure BDA0002475972440000066
have therein
Figure BDA0002475972440000067
Wherein
Figure BDA0002475972440000068
To represent
Figure BDA0002475972440000069
A row of (2);
therefore, the method is not to be taken,
Figure BDA00024759724400000610
the pseudo-inverse solution of (a) can be expressed as:
Figure BDA00024759724400000611
and
Figure BDA00024759724400000612
wherein, TkRepresentation matrix
Figure BDA00024759724400000613
Expansion of (2);
the final inverse priority projection can be written as:
Figure BDA00024759724400000614
thus, we can derive the expression of the pseudo-inverse solution:
Figure BDA00024759724400000615
the reverse priority control strategy equation of the multi-task redundant mechanical arm is established as follows:
Figure BDA00024759724400000616
preferably, the inverse control equations for a redundant robotic arm having a primary task and a secondary task are simplified as follows:
for a six-degree-of-freedom or seven-degree-of-freedom redundant manipulator, there are not enough six-degree-of-freedom DOF to complete multiple levels of tasks; it is necessary to carry out a dual task priority control; that is, the motion control of the manipulator is a primary task and a secondary task;
the equations for the inverse control of a redundant robotic arm having primary and secondary tasks are as follows
Figure BDA0002475972440000071
The above formula is very different from the previous expression (11), but the algorithmic framework is similar; in the above-mentioned equations, the process of the present invention,
Figure BDA0002475972440000072
is a secondary task that is to be performed,
Figure BDA0002475972440000073
is the main task; the main task is realized in a designated null space of the main task; the core point of reverse priority being a projection matrix
Figure BDA0002475972440000074
Calculating (1);
Figure BDA0002475972440000075
is expressed as formula (30):
Figure BDA0002475972440000076
using similar guides as in previous equations (22) - (28), a simplified inverse control equation for a redundant robotic arm having a primary task and a secondary task can be obtained:
Figure BDA0002475972440000077
preferably, the reverse priority control strategy for the manipulator is established as follows:
the dynamics of the manipulator in force control space can be written as:
Figure BDA0002475972440000078
where X is the position in Cartesian space, M (X) is an inertial matrix,
Figure BDA0002475972440000079
non-linear force, F input control force, FeIs the contact force;
furthermore, the input joint moments are obtained on the basis of a conversion of the Jacobian matrix
τ＝JT(q)F (33)
The desired equation of motion of the manipulator in force control space may be defined as follows:
Figure BDA00024759724400000710
wherein M isdAnd BdIs an inertia and damping matrix; fdIs a command force, FeIs the contact force;
thus, the relationship between the environment and the manipulator response can be written as
Figure BDA00024759724400000711
The combination of the above two equations is as follows
Figure BDA00024759724400000712
From the above equationIt is seen that if M ise、BeAnd KeKnown, then MdAnd BdWill affect the system response;
force control enables the manipulator to interact with the environment or human; in addition, in some cases, it is not necessary to implement omnidirectional force control and guarantee omnidirectional force control, that is, sometimes we only want to guarantee the force tracking control accuracy in a certain direction;
it is therefore necessary to perform a hierarchical force control of the manipulator; that is, it is necessary to provide a new hierarchical force control framework; from the above equation we can derive the desired hierarchical force control relationship as follows
Figure BDA0002475972440000081
Figure BDA0002475972440000082
The integral of these two equations can be written as
Figure BDA0002475972440000083
Figure BDA0002475972440000084
If the robot end effector is able to track the desired cartesian velocity of
Figure BDA0002475972440000085
And
Figure BDA0002475972440000086
accurate force control of the manipulator can be achieved; the relation between the Cartesian velocity and the joint velocity should be based on inverse priority control; thus, the equation for the inverse priority control strategy for the manipulator can be derived:
Figure BDA0002475972440000087
the joint velocity required by the above equation will ensure force control of the manipulator; it is worth mentioning that the force control law is only a speed step control law, which relies on an inner speed loop control; if the internal position control effect is good, accurate force control can be realized; because the inner speed ring control can realize low-frequency position tracking, the outer force ring can realize low-frequency force tracking.
Preferably, the relationship between the external force and the joint acceleration in the inverse-priority impedance control of the manipulator is solved by using the joint velocity, so that the inverse-priority impedance control of the manipulator is ensured in the following manner:
when the manipulator implements force control, the manipulator functions as an initiator to some extent, that is, the manipulator is ready to respond to the external environment; when the mechanical arm works as an impedance control model, the mechanical arm passively responds to an external force;
the corresponding impedance relationship between the external force and the joint acceleration can be expressed as
Figure BDA0002475972440000088
Figure BDA0002475972440000089
The reference speed can be expressed as
Figure BDA00024759724400000810
Figure BDA00024759724400000811
Therefore, the inverse priority impedance control of the manipulator guarantees the expression:
Figure BDA0002475972440000091
preferably, the overall framework implementation of extending the inverse-priority computation of the position control space to the inverse-priority computation of the force control space to obtain the manipulator velocity-level inverse-priority impedance control is as follows:
hybrid impedance applications are a combination of the two strategies mentioned above, i.e. the cartesian task can be divided into two cases: the first is a position control subspace, in which the impedance control is implemented; the second is a force control subspace in which force control is implemented;
thus selecting a selection matrix; the relationship between the external force and the position response is as follows
Figure BDA0002475972440000092
Figure BDA0002475972440000093
So a simplified form of the desired speed can be expressed as
Figure BDA0002475972440000094
Figure BDA0002475972440000095
Then we get a solution based on reverse priority
Figure BDA0002475972440000096
Considering n-layer tasks, the corresponding impedance control task also belongs to n-layer framework, therefore, the overall framework expression of the manipulator speed level inverse priority impedance control is as follows
Figure BDA0002475972440000097
The expression (52) solves the problem that the reverse priority calculation of the position control space is expanded to the manipulator reverse priority mixed impedance control of the reverse priority calculation of the force control space, so that the redundant manipulator of the manipulator can realize the expected impedance control task under different hierarchical structures.
The invention can achieve the following effects:
the invention can control the balance of the manipulator, the manipulator is convenient to move, and the redundant manipulator of the manipulator can realize the expected impedance control task under different hierarchical structures.
Drawings
FIG. 1 is a schematic representation of the dynamics of force control of the present invention.
FIG. 2 is a schematic diagram of the dynamics of the impedance control of the present invention.
FIG. 3 is a schematic diagram of the dynamics of the hybrid impedance control of the present invention.
Fig. 4 is a schematic diagram of a seven-degree-of-freedom robot connection structure according to an embodiment of the present invention.
Fig. 5 is a schematic block diagram of a circuit principle connection structure according to an embodiment of the present invention.
Detailed Description
The invention is further described with reference to the following figures and examples.
An embodiment, a mobile robot redundant robot arm inverse priority impedance control system, see fig. 4, 5, includes a robot and a console S31 for controlling the robot; also includes a movable moving platform S41; the manipulator comprises a mechanical arm, a mounting seat S1, a vertical column S2, an output gripper S12 and a vertical cylinder S23; the mounting seat is fixed on the mobile platform;
the mechanical arm comprises a vertical lifting mobile platform S3, a first arm section S6, a second arm section S7, a third arm section S8 and a fourth arm section S10;
a vertical rail S24 is arranged on the left surface of the vertical column, and the vertical lifting mobile platform is vertically arranged on the vertical rail in a sliding manner; the lower end of the vertical column is fixedly connected to the upper surface of the mounting seat, the cylinder seat S21 of the vertical cylinder is fixedly connected to the upper surface of the mounting seat positioned on the left side of the vertical track, the telescopic rod S22 of the vertical cylinder is vertically arranged upwards, and the upper end of the telescopic rod of the vertical cylinder is fixedly connected to the lower surface of the vertical lifting mobile platform; the vertical lifting mobile platform can move up and down along a vertical track under the driving of a telescopic rod of a vertical cylinder to form a first degree of freedom;
the first arm section comprises an A1 section pipe S13 and an A2 section pipe S14 which is telescopically connected in a left pipe orifice of the A1 section pipe, a first air cylinder S25 with a telescopic rod horizontally arranged towards the left is fixedly arranged at the right end in the A1 section pipe, and the telescopic rod of the first air cylinder is fixedly connected at the right end of the A2 section pipe;
the arm section II comprises a section B1 of pipe S16 and a section B2 of pipe S17 which is telescopically connected into a left pipe orifice of a section B1 of pipe, a second cylinder 37 with a telescopic rod horizontally arranged towards the left is fixedly arranged at the right end in the section B1 of pipe, and the telescopic rod of the second cylinder is fixedly connected to the right end of the section B2 of pipe;
the left end of the vertical lifting moving platform is provided with a first horizontal rotating shaft S4 driven by a first speed reducing motor S26, and the right end of the A1 section of pipe is fixedly connected to the first horizontal rotating shaft, so that the first arm section can horizontally rotate to form a second degree of freedom; a first electromagnetic brake S32 capable of controlling the rotation of the first horizontal rotating shaft is also arranged on the first horizontal rotating shaft;
the left end of the section A2 of the tube is provided with a second horizontal rotating shaft S15 driven by a second speed reducing motor S27, and the right end of the section B1 of the tube is fixedly connected to the second horizontal rotating shaft, so that the arm section II can horizontally rotate to form a third degree of freedom; a second electromagnetic brake S33 capable of controlling the second horizontal rotating shaft to rotate is also arranged on the second horizontal rotating shaft;
the left end of the B2 section pipe is provided with a third horizontal rotating shaft S18 driven by a third speed reducing motor S28, and the right end of the arm section III is fixedly connected to the third horizontal rotating shaft, so that the arm section III can horizontally rotate to form a fourth degree of freedom; a third electromagnetic brake S34 capable of controlling the third horizontal rotating shaft to rotate is also arranged on the third horizontal rotating shaft;
a first transverse vertical rotating shaft S9 which is driven by a fourth speed reducing motor S29 and can rotate on the left vertical surface and the right vertical surface is arranged at the left end of the arm section III, and the right end of the arm section IV is fixedly connected to the first transverse vertical rotating shaft, so that the arm section IV can vertically rotate on the left vertical surface and the right vertical surface to form a fifth degree of freedom; a fourth electromagnetic brake S35 capable of controlling the first transverse vertical rotating shaft to rotate is further arranged on the first transverse vertical rotating shaft;
a first longitudinal vertical rotating shaft S11 which is driven by a fifth speed reducing motor S30 and can rotate on the front vertical surface and the rear vertical surface is arranged at the left end of the arm section four, and the right end of the output gripper is fixedly connected to the first longitudinal vertical rotating shaft, so that the right end of the output gripper can vertically rotate on the front vertical surface and the rear vertical surface to form a sixth degree of freedom; a fifth electromagnetic brake S36 capable of controlling the first vertical rotating shaft to rotate is further arranged on the first vertical rotating shaft;
the section A2 of the pipe can be driven by the telescopic rod of the first cylinder to move in a telescopic manner from side to side in the section A1 of the pipe to form a seventh degree of freedom;
the B2 section of pipe can be driven by the telescopic rod of the second cylinder to move in the B1 section of pipe in a left-right telescopic manner to form an eighth degree of freedom;
the left end of a first horizontal pipe S39 is horizontally and fixedly connected to the right surface of the vertical column, a balance adjusting block S40 is arranged in the first horizontal pipe in a left-right sliding mode, a balance adjusting cylinder S38 with a telescopic rod facing horizontally is fixedly connected to the left end of the first horizontal pipe, and the right end of the telescopic rod of the balance adjusting cylinder is fixedly connected to the balance adjusting block;
the control end of No. one electromagnetic brake, the control end of No. two electromagnetic brakes, the control end of No. three electromagnetic brakes, the control end of No. four electromagnetic brakes, the control end of No. five electromagnetic brakes, the control end of a gear motor, the control end of No. two gear motor, the control end of No. three gear motor, the control end of No. four gear motor, the control end of No. five gear motor, the control end of a cylinder, the control end of No. two cylinders, the control end of balance adjustment cylinder and the control end of vertical cylinder are respectively control connection on the control cabinet. The seventh degree of freedom can enable the mechanical arm to extend freely, and the eighth degree of freedom can enable the mechanical arm to extend freely, so that the operation range and flexibility are greatly increased.
The balance adjusting cylinder controls the balance of the vertical column by moving the balance adjusting block left and right, and then the balance of the manipulator is controlled. The manipulator is convenient to move. The mobile platform comprises an automobile.
Because some mechanical arms of the invention have eight degrees of freedom, the invention has good flexibility and high reliability and is easy to complete control tasks.
A method for controlling the inverse priority impedance of a redundant mechanical arm of a mobile manipulator is shown in figures 1-3. The method comprises the following steps:
step 1, establishing a redundant mechanical arm kinematics model, and giving a gradient direction strategy implementation process of a redundant mechanical arm zero space vector as follows:
the pose and the speed of the end effector in the Cartesian space are defined as x,
Figure BDA0002475972440000111
The angular position and angular velocity of the joint space are q,
Figure BDA0002475972440000112
J is a Jacobian matrix of the n-degree-of-freedom robot, where x ∈ Rn，
Figure BDA0002475972440000113
Figure BDA0002475972440000114
J∈Rm-n(ii) a The positive kinematic equation for a redundant degree of freedom robotic arm can be described by:
Figure BDA0002475972440000115
equation (1) is also referred to as a robot arm kinematics velocity model;
considering the solution of the least squares method, the optimal problem can be listed as:
Figure BDA0002475972440000116
the solution of formula (1) can be optimized by finding the best
Figure BDA0002475972440000117
To solve the problem;
Figure BDA0002475972440000118
thus, the pseudo-inverse solution of equation (1) can be expressed as:
Figure BDA0002475972440000121
in the formula J+Pseudo-inverse of the Jacobian matrix
I-identity matrix
Figure BDA0002475972440000122
-arbitrary null space vector
Figure BDA0002475972440000123
Minimum norm solution, defining hand movements
Figure BDA0002475972440000124
Homogeneous solution, no action at the end
Equation (4) represents the position and attitude control of the end effector; adding any residual error into the formula (4) to obtain a general expression containing a null space; the multi-task optimization can be realized on a zero vector by using the equation;
however, the above equation ignores the ill-conditioned state of the jacobian matrix; the regularization equation may be modified by adding additional regularization values,
Figure BDA0002475972440000125
where λ ≧ 0 is the weighting matrix,
Figure BDA0002475972440000126
is a weighting coefficient, and satisfies
Figure BDA0002475972440000127
The solution to the above equation can be expressed as:
Figure BDA0002475972440000128
equation (7) is also referred to as a redundant manipulator kinematics model;
the joint limit function of the joint limit gradient direction of the position-dependent scalar index of the null-space vector of the redundant manipulator is as follows:
Figure BDA0002475972440000129
step 2, establishing a task priority solving strategy for obtaining a singularity elimination algorithm through a singular robust solution as follows:
in the solution of the redundant mechanical arm of the Jacobian matrix, an optimization task is realized in a null space of a main task; the reverse task kinematics is established on the basis of the forward task kinematics:
Figure BDA00024759724400001210
wherein
Figure BDA00024759724400001211
And
Figure BDA00024759724400001212
representation task1 and task2
The inverse kinematics equation of the redundant manipulator is obtained from expression (5) as follows:
Figure BDA00024759724400001213
task1 as the main Task and Task2 as the auxiliary Task; that is to say that the position of the first electrode,
Figure BDA00024759724400001214
is that
Figure BDA00024759724400001215
Is implemented in the null space of (1); the final inverse kinematics expression for the redundant manipulator is as follows:
Figure BDA00024759724400001216
wherein
Figure BDA00024759724400001217
Figure BDA00024759724400001218
Is a projection matrix which gives the applicable range of the secondary task to the primary task;
Figure BDA00024759724400001219
and
Figure BDA00024759724400001220
is the desired commanded speed;
Figure BDA0002475972440000131
is the main task of the method, and the method comprises the following steps of,
Figure BDA0002475972440000132
is a secondary task;
if two related tasks are interdependent, then the corresponding Jacobian matrix is singular; if the task jacobian matrix is singular, the corresponding task is not satisfied; in this case, the jacobian correlation matrix will be singularities, defined as algorithmic singularities;
that is, if
Figure BDA0002475972440000133
Where ρ (·) is the rank of the matrix;
it is clear that the singularity of the algorithm is caused by task conflicts between the secondary tasks and the primary task; in addition, task priority based redundant robotic arm inverse kinematics aims to provide better control over the effectiveness of the primary tasks;
therefore, the position control direction is used as a main task, so that the position ensures the accuracy of the control direction task; then, establishing a task priority solving strategy equation for obtaining a singularity elimination algorithm through singular robust solution:
Figure BDA0002475972440000134
step 3, establishing a singular robust solution inverse kinematics analysis model as follows:
the motion singularity can occur based on the Jacobian pseudo-inverse solution, which is caused by the secondary matrix; for the motion singularity problem, a DLS (damped least squares) solution should also be given;
the cost function for the DLS solution can be modified to:
Figure BDA0002475972440000135
thus, the singular robust pseudo-inverse solution of the above equation can be expressed as:
Figure BDA0002475972440000136
equation (15) is a singular robust solution inverse kinematics analysis model, where λ is η2I, the DLS solution is equivalent to an additional regularization solution, and the scalar value η balances the task precision and singularity;
for the calculation of the pseudo-inverse solution of the Jacobian matrix, the singular value SVD decomposition form of the Jacobian matrix can be given
J＝U∑VT(16)
Wherein U ∈ Rm×m，V∈Rn×n，∑∈Rm×nU is a column vector UiA unitary matrix of V is formed by column vectors ViThe constituent unary matrix, ∑, is a block matrix of m × n diagonal matrices containing the singular values σ of JiMore than or equal to 0 contains n-m zero column vectors in descending order;
Figure BDA0002475972440000137
wherein r is less than or equal to m is the rank of the matrix J;
for motion singularity, with reference to the singular value decomposition SVD required to compute the pseudo-inverse solution, the large resulting joint velocity is due to the smallest singular value rapidly approaching 0, as follows:
Figure BDA0002475972440000138
factor lambda0Will affect the singularity, λ0The higher the value is, the larger the damping is, and the closer the joint velocity is to the singular point; in addition, the strategy for defining the variable damping factor is also different; we can get
Figure BDA0002475972440000141
From the above equation, we can see that the parameter > 0 monitors the smallest singular value.
Step 4, establishing a reverse priority control strategy of the multi-task redundant mechanical arm as follows;
introducing an inverse-priority projection matrix
Figure BDA0002475972440000142
The matrix comprises a null space of corresponding elements of the lowest priority l-k-1 task independent of the kth task, so derived
Figure BDA0002475972440000143
Wherein JijIs a jacobian matrix associated with all components of the i-th task that are linearly independent of the j-th task;
therefore, the priority derivation formula is as follows:
Figure BDA0002475972440000144
in the above derivation, k ═ l, l-1, …, 1; initial value
Figure BDA0002475972440000145
To give a general form of computation of the linear independent Jacobian matrix J, the inverse augmented Jacobian matrix is defined as:
Figure BDA0002475972440000146
have therein
Figure BDA0002475972440000147
Wherein
Figure BDA0002475972440000148
To represent
Figure BDA0002475972440000149
A row of (2);
therefore, the method is not to be taken,
Figure BDA00024759724400001410
the pseudo-inverse solution of (a) can be expressed as:
Figure BDA00024759724400001411
and
Figure BDA00024759724400001412
wherein, TkRepresentation matrix
Figure BDA00024759724400001413
Expansion of (2);
the final inverse priority projection can be written as:
Figure BDA00024759724400001414
thus, we can derive the expression of the pseudo-inverse solution:
Figure BDA0002475972440000151
the reverse priority control strategy equation of the multi-task redundant mechanical arm is established as follows:
Figure BDA0002475972440000152
and 5, simplifying the reverse control equation of the redundant mechanical arm with the primary task and the secondary task as follows:
for a six-degree-of-freedom or seven-degree-of-freedom redundant manipulator, there are not enough six-degree-of-freedom DOF to complete multiple levels of tasks; it is necessary to carry out a dual task priority control; that is, the motion control of the manipulator is a primary task and a secondary task;
the equations for the inverse control of a redundant robotic arm having primary and secondary tasks are as follows
Figure BDA0002475972440000153
The above formula is very different from the previous expression (11), but the algorithmic framework is similar; in the above-mentioned equations, the process of the present invention,
Figure BDA0002475972440000154
is a secondary task that is to be performed,
Figure BDA0002475972440000155
is the main task; the main task is realized in a designated null space of the main task; the core point of reverse priority being a projection matrix
Figure BDA0002475972440000156
Calculating (1);
Figure BDA0002475972440000157
is expressed as formula (30):
Figure BDA0002475972440000158
using similar guides as in previous equations (22) - (28), a simplified inverse control equation for a redundant robotic arm having a primary task and a secondary task can be obtained:
Figure BDA0002475972440000159
and 6, establishing a reverse priority control strategy of the manipulator as follows:
the dynamics of the manipulator in force control space can be written as:
Figure BDA00024759724400001510
where X is the position in Cartesian space, M (X) is an inertial matrix,
Figure BDA00024759724400001511
non-linear force, F input control force, FeIs the contact force;
furthermore, the input joint moments are obtained on the basis of a conversion of the Jacobian matrix
τ＝JT(q)F (33)
The desired equation of motion of the manipulator in force control space may be defined as follows:
Figure BDA00024759724400001512
wherein M isdAnd BdIs an inertia and damping matrix; fdIs a command force, FeIs the contact force;
the kinetic profile of force control is shown in FIG. 1;
thus, the relationship between the environment and the manipulator response can be written as
Figure BDA00024759724400001513
The combination of the above two equations is as follows
Figure BDA0002475972440000161
As can be seen from the above equation, if M ise、BeAnd KeKnown, then MdAnd BdWill affect the system response;
force control enables the manipulator to interact with the environment or human; in addition, in some cases, it is not necessary to implement omnidirectional force control and guarantee omnidirectional force control, that is, sometimes we only want to guarantee the force tracking control accuracy in a certain direction;
for example, when the manipulator interacts with the planer, only precise force tracking control needs to be maintained in the vertical direction, while precise force tracking control is not needed in the other direction; in other cases, position direction force control is more important than attitude direction force control;
it is therefore necessary to perform a hierarchical force control of the manipulator; that is, it is necessary to provide a new hierarchical force control framework; from the above equation we can derive the desired hierarchical force control relationship as follows
Figure BDA0002475972440000162
Figure BDA0002475972440000163
The integral of these two equations can be written as
Figure BDA0002475972440000164
Figure BDA0002475972440000165
If the robot end effector is able to track the desired cartesian velocity of
Figure BDA0002475972440000166
And
Figure BDA0002475972440000167
accurate force control of the manipulator can be achieved; the relation between the Cartesian velocity and the joint velocity should be based on inverse priority control; thus, the equation for the inverse priority control strategy for the manipulator can be derived:
Figure BDA0002475972440000168
the joint velocity required by the above equation will ensure force control of the manipulator; it is worth mentioning that the force control law is only a speed step control law, which relies on an inner speed loop control; if the internal position control effect is good, accurate force control can be realized; because the inner speed ring control can realize low-frequency position tracking, the outer force ring can realize low-frequency force tracking.
And 7, solving the relation between the external force and the joint acceleration in the reverse priority impedance control of the manipulator by adopting the joint speed, so as to obtain the realization mode of ensuring the reverse priority impedance control of the manipulator, wherein the realization mode comprises the following steps:
when the manipulator implements force control, the manipulator functions as an initiator to some extent, that is, the manipulator is ready to respond to the external environment; when the mechanical arm works as an impedance control model, the mechanical arm passively responds to an external force; the kinetic scheme of impedance control is shown in fig. 2;
the corresponding impedance relationship between the external force and the joint acceleration can be expressed as
Figure BDA0002475972440000169
Figure BDA0002475972440000171
The reference speed can be expressed as
Figure BDA0002475972440000172
Figure BDA0002475972440000173
Therefore, the inverse priority impedance control of the manipulator guarantees the expression:
Figure BDA0002475972440000174
and 8, expanding the reverse priority calculation of the position control space to the reverse priority calculation of the force control space, so as to obtain the overall framework implementation mode of the manipulator speed-level reverse priority impedance control, wherein the overall framework implementation mode comprises the following steps:
hybrid impedance applications are a combination of the two strategies mentioned above, i.e. the cartesian task can be divided into two cases: the first is a position control subspace, in which the impedance control is implemented; the second is a force control subspace in which force control is implemented;
thus selecting a selection matrix; the relationship between the external force and the position response is as follows
Figure BDA0002475972440000175
So a simplified form of the desired speed can be expressed as
Figure BDA0002475972440000177
Figure BDA0002475972440000178
Then we get a solution based on reverse priority
Figure BDA0002475972440000179
The kinetic scheme of the hybrid impedance control is shown in FIG. 3;
considering n-layer tasks, the corresponding impedance control task also belongs to n-layer framework, therefore, the overall framework expression of the manipulator speed level inverse priority impedance control is as follows
Figure BDA00024759724400001710
Expression (52) solves the problem of extending the reverse-priority computation of the position control space into manipulator reverse-priority hybrid impedance control of the reverse-priority computation of the force control space; the redundant mechanical arm of the manipulator can realize the expected impedance control task under different hierarchical structures.

Claims (10)

1. A redundant robot arm inverse priority impedance control system for a mobile robot, comprising a robot and a console for controlling the robot (S31); characterized in that the device also comprises a movable moving platform (S41); the robot includes a robot arm, a mounting seat (S1), a vertical column (S2), an output gripper (S12), and a vertical cylinder (S23); the mounting seat is fixed on the mobile platform;
the mechanical arm comprises a vertical lifting mobile platform (S3), a first arm section (S6), a second arm section (S7), a third arm section (S8) and a fourth arm section (S10);
a vertical rail (S24) is arranged on the left surface of the vertical column, and the vertical lifting mobile platform is vertically arranged on the vertical rail in a sliding manner; the lower end of the vertical column is fixedly connected to the upper surface of the mounting seat, a cylinder seat (S21) of the vertical cylinder is fixedly connected to the upper surface of the mounting seat positioned on the left side of the vertical track, a telescopic rod (S22) of the vertical cylinder is vertically arranged upwards, and the upper end of the telescopic rod of the vertical cylinder is fixedly connected to the lower surface of the vertical lifting mobile platform; the vertical lifting mobile platform can move up and down along a vertical track under the driving of a telescopic rod of a vertical cylinder to form a first degree of freedom;
the first arm section comprises an A1 section of pipe (S13) and an A2 section of pipe (S14) which is telescopically connected in a left pipe orifice of the A1 section of pipe, a first air cylinder (S25) with a telescopic rod horizontally arranged towards the left is fixedly arranged at the right end in the A1 section of pipe, and the telescopic rod of the first air cylinder is fixedly connected at the right end of the A2 section of pipe;
the arm section II comprises a section B1 pipe (S16) and a section B2 pipe (S17) which is telescopically connected in a left pipe orifice of the section B1 pipe, a second cylinder (37) with a telescopic rod horizontally arranged towards the left is fixedly arranged at the right end in the section B1 pipe, and the telescopic rod of the second cylinder is fixedly connected at the right end of the section B2 pipe;
the left end of the vertical lifting mobile platform is provided with a first horizontal rotating shaft (S4) driven by a first speed reducing motor (S26), and the right end of the A1 section of pipe is fixedly connected to the first horizontal rotating shaft, so that the first arm section can horizontally rotate to form a second degree of freedom; a first electromagnetic brake (S32) capable of controlling the rotation of the first horizontal rotating shaft is also arranged on the first horizontal rotating shaft;
the left end of the A2 section of pipe is provided with a second horizontal rotating shaft (S15) driven by a second speed reducing motor (S27), and the right end of the B1 section of pipe is fixedly connected to the second horizontal rotating shaft, so that the second arm section can horizontally rotate to form a third degree of freedom; a second electromagnetic brake (S33) capable of controlling the second horizontal rotating shaft to rotate is also arranged on the second horizontal rotating shaft;
the left end of the B2 section pipe is provided with a third horizontal rotating shaft (S18) driven by a third speed reducing motor (S28), and the right end of the arm section III is fixedly connected to the third horizontal rotating shaft, so that the arm section III can horizontally rotate to form a fourth degree of freedom; a third electromagnetic brake (S34) capable of controlling the third horizontal rotating shaft to rotate is also arranged on the third horizontal rotating shaft;
a first transverse vertical rotating shaft (S9) which is driven by a fourth speed reducing motor (S29) and can rotate on the left vertical surface and the right vertical surface is arranged at the left end of the arm section III, and the right end of the arm section IV is fixedly connected to the first transverse vertical rotating shaft, so that the arm section IV can vertically rotate on the left vertical surface and the right vertical surface to form a fifth degree of freedom; a fourth electromagnetic brake (S35) capable of controlling the first transverse vertical rotating shaft to rotate is further arranged on the first transverse vertical rotating shaft;
a first longitudinal vertical rotating shaft (S11) which is driven by a fifth speed reducing motor (S30) and can rotate on the front vertical surface and the rear vertical surface is arranged at the left end of the arm section four, and the right end of the output gripper is fixedly connected to the first longitudinal vertical rotating shaft, so that the right end of the output gripper can vertically rotate on the front vertical surface and the rear vertical surface to form a sixth degree of freedom; a fifth electromagnetic brake (S36) capable of controlling the first vertical rotating shaft to rotate is further arranged on the first vertical rotating shaft;
the section A2 of the pipe can be driven by the telescopic rod of the first cylinder to move in a telescopic manner from side to side in the section A1 of the pipe to form a seventh degree of freedom;
the B2 section of pipe can be driven by the telescopic rod of the second cylinder to move in the B1 section of pipe in a left-right telescopic manner to form an eighth degree of freedom;
the left end of a first horizontal pipe (S39) is horizontally and fixedly connected to the right surface of the vertical column, a balance adjusting block (S40) is arranged in the first horizontal pipe in a sliding mode from left to right, a balance adjusting cylinder (S38) with a telescopic rod facing horizontally is fixedly connected to the left end of the first horizontal pipe, and the right end of the telescopic rod of the balance adjusting cylinder is fixedly connected to the balance adjusting block;
the control end of No. one electromagnetic brake, the control end of No. two electromagnetic brakes, the control end of No. three electromagnetic brakes, the control end of No. four electromagnetic brakes, the control end of No. five electromagnetic brakes, the control end of a gear motor, the control end of No. two gear motor, the control end of No. three gear motor, the control end of No. four gear motor, the control end of No. five gear motor, the control end of a cylinder, the control end of No. two cylinders, the control end of balance adjustment cylinder and the control end of vertical cylinder are respectively control connection on the control cabinet.
2. A reverse priority impedance control method for a redundant mechanical arm of a mobile manipulator is characterized by comprising the following steps:
step 1, establishing a kinematic model of the redundant mechanical arm, and giving a gradient direction strategy of a zero space vector of the redundant mechanical arm;
step 2, establishing a task priority solving strategy for obtaining a singularity elimination algorithm through a singular robust solution;
step 3, establishing a singular robust solution inverse kinematics analysis model;
step 4, establishing a reverse priority control strategy of the multi-task redundant mechanical arm;
step 5, simplifying a reverse control equation of the redundant mechanical arm with the main task and the secondary task;
step 6, establishing a reverse priority control strategy of the manipulator;
step 7, solving the relation between the external force and the joint acceleration in the reverse priority impedance control of the manipulator by adopting the joint speed, thereby obtaining the reverse priority impedance control guarantee of the manipulator;
and 8, expanding the reverse priority calculation of the position control space to the reverse priority calculation of the force control space, thereby obtaining the overall framework of the speed-level reverse priority impedance control of the manipulator.
3. The reverse priority impedance control method for the redundant manipulator of the mobile manipulator according to claim 2, wherein the implementation process of establishing a kinematic model of the redundant manipulator and giving a gradient direction strategy of a zero space vector of the redundant manipulator is as follows:
the pose and the speed of the end effector in the Cartesian space are defined as x,
Figure FDA0002475972430000041
The angular position and angular velocity of the joint space are q,
Figure FDA0002475972430000042
J is a Jacobian matrix of the n-degree-of-freedom robot, where x ∈ Rn，
Figure FDA0002475972430000043
J∈Rm-n(ii) a The positive kinematic equation for a redundant degree of freedom robotic arm can be described by:
Figure FDA0002475972430000044
equation (1) is also referred to as a robot arm kinematics velocity model;
considering the solution of the least squares method, the optimal problem can be listed as:
Figure FDA0002475972430000045
the solution of formula (1) can be optimized by finding the best
Figure FDA0002475972430000046
To solve the problem;
Figure FDA0002475972430000047
thus, the pseudo-inverse solution of equation (1) can be expressed as:
Figure FDA0002475972430000048
in the formula J+Pseudo-inverse of the Jacobian matrix
I-identity matrix
Figure FDA0002475972430000051
-arbitrary null space vector
Figure FDA0002475972430000052
Minimum norm solution, defining hand movements
Figure FDA0002475972430000053
Homogeneous solution, no action at the end
Equation (4) represents the position and attitude control of the end effector; adding any residual error into the formula (4) to obtain a general expression containing a null space; the multi-task optimization can be realized on a zero vector by using the equation;
however, the above equation ignores the ill-conditioned state of the jacobian matrix; the regularization equation may be modified by adding additional regularization values,
Figure FDA0002475972430000054
where λ ≧ 0 is the weighting matrix,
Figure FDA0002475972430000055
is a weighting coefficient, and satisfies
Figure FDA0002475972430000056
The solution to the above equation can be expressed as:
Figure FDA0002475972430000057
equation (7) is also referred to as a redundant manipulator kinematics model;
the joint limit function of the joint limit gradient direction of the position-dependent scalar index of the null-space vector of the redundant manipulator is as follows:
Figure FDA0002475972430000058
4. the inverse priority impedance control method for the redundant manipulator of the mobile manipulator according to claim 3, wherein a task priority solving strategy for obtaining the singularity elimination algorithm through a singular robust solution is established as follows:
in the solution of the redundant mechanical arm of the Jacobian matrix, an optimization task is realized in a null space of a main task; the reverse task kinematics is established on the basis of the forward task kinematics:
Figure FDA0002475972430000061
wherein
Figure FDA0002475972430000062
And
Figure FDA0002475972430000063
representation task1 and task2
The inverse kinematics equation of the redundant manipulator is obtained from expression (5) as follows:
Figure FDA0002475972430000064
task1 as the main Task and Task2 as the auxiliary Task; that is, task2
Figure FDA0002475972430000065
Is at task1
Figure FDA0002475972430000066
Is implemented in the null space of (1); the final inverse kinematics expression for the redundant manipulator is as follows:
Figure FDA0002475972430000067
wherein
Figure FDA00024759724300000615
Figure FDA0002475972430000069
Is a projection matrix which gives the applicable range of the secondary task to the primary task;
Figure FDA00024759724300000610
and
Figure FDA00024759724300000611
is the desired commanded speed;
Figure FDA00024759724300000612
is the main task of the method, and the method comprises the following steps of,
Figure FDA00024759724300000613
is a secondary task;
if two related tasks are interdependent, then the corresponding Jacobian matrix is singular; if the task jacobian matrix is singular, the corresponding task is not satisfied; in this case, the jacobian correlation matrix will be singularities, defined as algorithmic singularities;
that is, if
Figure FDA00024759724300000614
Where ρ (·) is the rank of the matrix;
it is clear that the singularity of the algorithm is caused by task conflicts between the secondary tasks and the primary task; in addition, task priority based redundant robotic arm inverse kinematics aims to provide better control over the effectiveness of the primary tasks;
therefore, the position control direction is used as a main task, so that the position ensures the accuracy of the control direction task; then, establishing a task priority solving strategy equation for obtaining a singularity elimination algorithm through singular robust solution:
Figure FDA0002475972430000071
5. the method for controlling the inverse priority impedance of the redundant manipulator of the mobile manipulator according to claim 4, wherein a singular robust solution inverse kinematics analysis model is established as follows:
the motion singularity can occur based on the Jacobian pseudo-inverse solution, which is caused by the secondary matrix; for the motion singularity problem, a DLS (damped least squares) solution should also be given;
the cost function for the DLS solution can be modified to:
Figure FDA0002475972430000072
thus, the singular robust pseudo-inverse solution of the above equation can be expressed as:
Figure FDA0002475972430000073
equation (15) is a singular robust solution inverse kinematics analysis model, where λ is η2I, the DLS solution is equivalent to an additional regularization solution, and the scalar value η balances the task precision and singularity;
for the calculation of the pseudo-inverse solution of the Jacobian matrix, the singular value SVD decomposition form of the Jacobian matrix can be given
J＝U∑VT(16)
Wherein U ∈ Rm×m，V∈Rn×n，∑∈Rm×nU is a column vector UIA unitary matrix of V is formed by column vectors VIThe constituent unary matrix, ∑, is a block matrix of m × n diagonal matrices containing the singular values σ of JiMore than or equal to 0 contains n-m zero column vectors in descending order;
Figure FDA0002475972430000074
wherein r is less than or equal to m is the rank of the matrix J;
for motion singularity, with reference to the singular value decomposition SVD required to compute the pseudo-inverse solution, the large resulting joint velocity is due to the smallest singular value rapidly approaching 0, as follows:
Figure FDA0002475972430000081
factor lambda0Will affect the singularity, λ0The higher the value is, the larger the damping is, and the closer the joint velocity is to the singular point; in addition, the definition canThe strategy of varying the damping factor is also different; we can get
Figure FDA0002475972430000082
From the above equation, we can see that the parameter > 0 monitors the smallest singular value.
6. The method according to claim 5, wherein a reverse priority control strategy for the multitasking redundant robot is established as follows;
introducing an inverse-priority projection matrix
Figure FDA0002475972430000083
The matrix comprises a null space of corresponding elements of the lowest priority l-k-1 task independent of the kth task, so derived
Figure FDA0002475972430000084
Figure FDA0002475972430000085
Wherein Ji|jIs a jacobian matrix associated with all components of the i-th task that are linearly independent of the j-th task;
therefore, the priority derivation formula is as follows:
Figure FDA0002475972430000086
in the above derivation, k ═ l, l-1, …, 1; initial value
Figure FDA0002475972430000087
To give a general form of computation of the linear independent Jacobian matrix J, the inverse augmented Jacobian matrix is defined as:
Figure FDA0002475972430000091
have therein
Figure FDA0002475972430000092
Wherein
Figure FDA0002475972430000093
To represent
Figure FDA0002475972430000094
A row of (2);
therefore, the method is not to be taken,
Figure FDA0002475972430000095
the pseudo-inverse solution of (a) can be expressed as:
Figure FDA0002475972430000096
and
Figure FDA0002475972430000097
wherein, TkRepresentation matrix
Figure FDA0002475972430000098
Expansion of (2);
the final inverse priority projection can be written as:
Figure FDA0002475972430000099
thus, we can derive the expression of the pseudo-inverse solution:
Figure FDA00024759724300000910
the reverse priority control strategy equation of the multi-task redundant mechanical arm is established as follows:
Figure FDA00024759724300000911
7. the method according to claim 6, wherein the inverse control equation of the redundant robot having the primary task and the secondary task is simplified as follows:
for a six-degree-of-freedom or seven-degree-of-freedom redundant manipulator, there are not enough six-degree-of-freedom DOF to complete multiple levels of tasks; it is necessary to carry out a dual task priority control; that is, the motion control of the manipulator is a primary task and a secondary task;
the equations for the inverse control of a redundant robotic arm having primary and secondary tasks are as follows
Figure FDA0002475972430000101
The above formula is very different from the previous expression (11), but the algorithmic framework is similar; in the above-mentioned equations, the process of the present invention,
Figure FDA0002475972430000102
is a secondary task that is to be performed,
Figure FDA0002475972430000103
is the main task; the main task is realized in a designated null space of the main task; the core point of reverse priority being a projection matrix
Figure FDA0002475972430000104
Calculating (1);
Figure FDA0002475972430000105
is expressed as formula (30):
Figure FDA0002475972430000106
using similar guides as in previous equations (22) - (28), a simplified inverse control equation for a redundant robotic arm having a primary task and a secondary task can be obtained:
Figure FDA0002475972430000107
8. the method of claim 7, wherein the reverse priority impedance control strategy for the redundant robot arm of the transfer robot is established as follows:
the dynamics of the manipulator in force control space can be written as:
Figure FDA0002475972430000108
where X is the position in Cartesian space, M (X) is an inertial matrix,
Figure FDA0002475972430000109
non-linear force, F input control force, FeIs the contact force;
furthermore, the input joint moments are obtained on the basis of a conversion of the Jacobian matrix
τ＝JT(q)F (33)
The desired equation of motion of the manipulator in force control space may be defined as follows:
Figure FDA0002475972430000111
wherein M isdAnd BdIs an inertia and damping matrix; fdIs a command force, FeIs the contact force;
thus, the relationship between the environment and the manipulator response can be written as
Figure FDA0002475972430000112
The combination of the above two equations is as follows
Figure FDA0002475972430000113
As can be seen from the above equation, if M ise、BeAnd KeKnown, then MdAnd BdWill affect the system response;
force control enables the manipulator to interact with the environment or human; in addition, in some cases, it is not necessary to implement omnidirectional force control and guarantee omnidirectional force control, that is, sometimes we only want to guarantee the force tracking control accuracy in a certain direction;
it is therefore necessary to perform a hierarchical force control of the manipulator; that is, it is necessary to provide a new hierarchical force control framework; from the above equation we can derive the desired hierarchical force control relationship as follows
Figure FDA0002475972430000114
Figure FDA0002475972430000115
The integral of these two equations can be written as
Figure FDA0002475972430000116
Figure FDA0002475972430000117
If the robot end effector is able to track the desired cartesian velocity of
Figure FDA0002475972430000121
And
Figure FDA0002475972430000122
accurate force control of the manipulator can be achieved; the relation between the Cartesian velocity and the joint velocity should be based on inverse priority control; thus, the equation for the inverse priority control strategy for the manipulator can be derived:
Figure FDA0002475972430000123
the joint velocity required by the above equation will ensure force control of the manipulator; it is worth mentioning that the force control law is only a speed step control law, which relies on an inner speed loop control; if the internal position control effect is good, accurate force control can be realized; because the inner speed ring control can realize low-frequency position tracking, the outer force ring can realize low-frequency force tracking.
9. The method according to claim 8, wherein the relationship between an external force and a joint acceleration in the reverse priority impedance control of the manipulator is solved by using a joint velocity, and the reverse priority impedance control of the manipulator is ensured by:
when the manipulator implements force control, the manipulator functions as an initiator to some extent, that is, the manipulator is ready to respond to the external environment; when the mechanical arm works as an impedance control model, the mechanical arm passively responds to an external force;
the corresponding impedance relationship between the external force and the joint acceleration can be expressed as
Figure FDA0002475972430000124
Figure FDA0002475972430000125
The reference speed can be expressed as
Figure FDA0002475972430000126
Figure FDA0002475972430000131
Therefore, the inverse priority impedance control of the manipulator guarantees the expression:
Figure FDA0002475972430000132
10. the method of claim 9, wherein the overall framework for achieving the manipulator velocity-level inverse-priority impedance control by extending the inverse-priority computation of the position control space to the inverse-priority computation of the force control space is implemented as follows:
hybrid impedance applications are a combination of the two strategies mentioned above, i.e. the cartesian task can be divided into two cases: the first is a position control subspace, in which the impedance control is implemented; the second is a force control subspace in which force control is implemented;
thus selecting a selection matrix; the relationship between the external force and the position response is as follows
Figure FDA0002475972430000133
Figure FDA0002475972430000134
So a simplified form of the desired speed can be expressed as
Figure FDA0002475972430000135
Figure FDA0002475972430000136
Then we get a solution based on reverse priority
Figure FDA0002475972430000141
Considering n-layer tasks, the corresponding impedance control task also belongs to n-layer framework, therefore, the overall framework expression of the manipulator speed level inverse priority impedance control is as follows
Figure FDA0002475972430000142
Expression (52) solves the problem of extending the reverse-priority computation of the position control space into manipulator reverse-priority hybrid impedance control of the reverse-priority computation of the force control space; the redundant mechanical arm of the manipulator can realize the expected impedance control task under different hierarchical structures.
CN202010369760.5A 2020-04-30 2020-04-30 System and method for controlling reverse priority impedance of redundant mechanical arm of mobile mechanical arm Active CN111687834B (en)

Priority Applications (1)

Application Number Priority Date Filing Date Title
CN202010369760.5A CN111687834B (en) 2020-04-30 2020-04-30 System and method for controlling reverse priority impedance of redundant mechanical arm of mobile mechanical arm

Applications Claiming Priority (1)

Application Number Priority Date Filing Date Title
CN202010369760.5A CN111687834B (en) 2020-04-30 2020-04-30 System and method for controlling reverse priority impedance of redundant mechanical arm of mobile mechanical arm

Publications (2)

Publication Number Publication Date
CN111687834A true CN111687834A (en) 2020-09-22
CN111687834B CN111687834B (en) 2023-06-02

Family

ID=72476984

Family Applications (1)

Application Number Title Priority Date Filing Date
CN202010369760.5A Active CN111687834B (en) 2020-04-30 2020-04-30 System and method for controlling reverse priority impedance of redundant mechanical arm of mobile mechanical arm

Country Status (1)

Country Link
CN (1) CN111687834B (en)

Cited By (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN114800527A (en) * 2022-06-06 2022-07-29 山东大学 Force application control method and system for tail end of mobile operation mechanical arm

Citations (27)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
JPS6416389A (en) * 1987-07-11 1989-01-19 Agency Ind Science Techn Control system of multi-joint type arm robot having redundancy
US4999553A (en) * 1989-12-28 1991-03-12 The United States Of America As Represented By The Administrator Of The National Aeronautics And Space Administration Method and apparatus for configuration control of redundant robots
EP1854425A1 (en) * 2006-05-11 2007-11-14 BrainLAB AG Position determination for medical devices with redundant position measurement and weighting to prioritise measurements
JP2009066685A (en) * 2007-09-11 2009-04-02 Sony Corp Robot device, and control method for robot device
US20100161127A1 (en) * 2008-12-18 2010-06-24 Gm Global Technology Operations, Inc. Multiple priority operational space impedance control
US20100234999A1 (en) * 2006-06-26 2010-09-16 Yuichiro Nakajima Multi-joint robot and control program thereof
CN101947786A (en) * 2009-04-30 2011-01-19 通用汽车环球科技运作公司 Be used for the humanoid robot method and apparatus of control automatically
JP2011183527A (en) * 2010-03-10 2011-09-22 Toyota Motor Corp Joint target value determining method of redundant robot and control device of redundant robot
CN105676636A (en) * 2016-01-11 2016-06-15 北京邮电大学 NSGA-II algorithm-based multi-objective optimization method for mechanical arm in redundant space
CN205363898U (en) * 2015-12-31 2016-07-06 中国科学院沈阳自动化研究所 Open -ended modularity arm
CN106708069A (en) * 2017-01-19 2017-05-24 中国科学院自动化研究所 Coordinated planning and control method of underwater mobile operation robot
CN107290956A (en) * 2017-08-01 2017-10-24 浙江大学 A kind of position control method of the simple joint flexible mechanical arm based on feedback of status
CN107351085A (en) * 2017-08-21 2017-11-17 西北工业大学 A kind of robot for space collision avoidance method based on multiple control points
CN107650120A (en) * 2016-07-26 2018-02-02 深圳华清精密科技有限公司 Method for determining all singular configurations of 9-degree-of-freedom mechanical arm
DE102016222255B3 (en) * 2016-11-14 2018-04-12 Kuka Roboter Gmbh Robotic arm, mobile robot and logistics system
CN108098786A (en) * 2017-12-19 2018-06-01 扬州大学 Fusion reactor peeps mechanical arm in
CN108153153A (en) * 2017-12-19 2018-06-12 哈尔滨工程大学 A kind of study impedance control system and control method
CN108241339A (en) * 2017-12-27 2018-07-03 北京航空航天大学 The movement solution of apery mechanical arm and configuration control method
CN108247631A (en) * 2017-12-06 2018-07-06 西北工业大学 A kind of autonomous robust of mechanical arm for improving path trace performance keeps away unusual method
CN108621163A (en) * 2018-05-10 2018-10-09 同济大学 A kind of redundancy tow-armed robot cooperation control method towards remittance tenon technique
CN108839025A (en) * 2018-07-12 2018-11-20 杭州电子科技大学 A kind of motion planning method and device of mobile mechanical arm
CN109079780A (en) * 2018-08-08 2018-12-25 北京理工大学 Distributed mobile mechanical arm task hierarchy optimization control method based on generalized coordinates
CN110104216A (en) * 2019-01-28 2019-08-09 西北工业大学深圳研究院 A kind of collaboration paths planning method for kinematic redundancy dual-arm space robot
CN209631457U (en) * 2018-12-17 2019-11-15 清研同创机器人（天津）有限公司 A kind of Omni-mobile formula robot spraying system
CN110497378A (en) * 2019-09-04 2019-11-26 上海海事大学 A kind of automatic loading and unloading robot for part processing
CN110524522A (en) * 2019-09-19 2019-12-03 浙江工业大学 A kind of series-parallel anthropomorphous machine's arm of multiple degrees of freedom redundancy
US20220009093A1 (en) * 2020-07-08 2022-01-13 Ubtech Robotics Corp Ltd Task hierarchical control method, and robot and computer readable storage medium using the same

Patent Citations (27)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
JPS6416389A (en) * 1987-07-11 1989-01-19 Agency Ind Science Techn Control system of multi-joint type arm robot having redundancy
US4999553A (en) * 1989-12-28 1991-03-12 The United States Of America As Represented By The Administrator Of The National Aeronautics And Space Administration Method and apparatus for configuration control of redundant robots
EP1854425A1 (en) * 2006-05-11 2007-11-14 BrainLAB AG Position determination for medical devices with redundant position measurement and weighting to prioritise measurements
US20100234999A1 (en) * 2006-06-26 2010-09-16 Yuichiro Nakajima Multi-joint robot and control program thereof
JP2009066685A (en) * 2007-09-11 2009-04-02 Sony Corp Robot device, and control method for robot device
US20100161127A1 (en) * 2008-12-18 2010-06-24 Gm Global Technology Operations, Inc. Multiple priority operational space impedance control
CN101947786A (en) * 2009-04-30 2011-01-19 通用汽车环球科技运作公司 Be used for the humanoid robot method and apparatus of control automatically
JP2011183527A (en) * 2010-03-10 2011-09-22 Toyota Motor Corp Joint target value determining method of redundant robot and control device of redundant robot
CN205363898U (en) * 2015-12-31 2016-07-06 中国科学院沈阳自动化研究所 Open -ended modularity arm
CN105676636A (en) * 2016-01-11 2016-06-15 北京邮电大学 NSGA-II algorithm-based multi-objective optimization method for mechanical arm in redundant space
CN107650120A (en) * 2016-07-26 2018-02-02 深圳华清精密科技有限公司 Method for determining all singular configurations of 9-degree-of-freedom mechanical arm
DE102016222255B3 (en) * 2016-11-14 2018-04-12 Kuka Roboter Gmbh Robotic arm, mobile robot and logistics system
CN106708069A (en) * 2017-01-19 2017-05-24 中国科学院自动化研究所 Coordinated planning and control method of underwater mobile operation robot
CN107290956A (en) * 2017-08-01 2017-10-24 浙江大学 A kind of position control method of the simple joint flexible mechanical arm based on feedback of status
CN107351085A (en) * 2017-08-21 2017-11-17 西北工业大学 A kind of robot for space collision avoidance method based on multiple control points
CN108247631A (en) * 2017-12-06 2018-07-06 西北工业大学 A kind of autonomous robust of mechanical arm for improving path trace performance keeps away unusual method
CN108098786A (en) * 2017-12-19 2018-06-01 扬州大学 Fusion reactor peeps mechanical arm in
CN108153153A (en) * 2017-12-19 2018-06-12 哈尔滨工程大学 A kind of study impedance control system and control method
CN108241339A (en) * 2017-12-27 2018-07-03 北京航空航天大学 The movement solution of apery mechanical arm and configuration control method
CN108621163A (en) * 2018-05-10 2018-10-09 同济大学 A kind of redundancy tow-armed robot cooperation control method towards remittance tenon technique
CN108839025A (en) * 2018-07-12 2018-11-20 杭州电子科技大学 A kind of motion planning method and device of mobile mechanical arm
CN109079780A (en) * 2018-08-08 2018-12-25 北京理工大学 Distributed mobile mechanical arm task hierarchy optimization control method based on generalized coordinates
CN209631457U (en) * 2018-12-17 2019-11-15 清研同创机器人（天津）有限公司 A kind of Omni-mobile formula robot spraying system
CN110104216A (en) * 2019-01-28 2019-08-09 西北工业大学深圳研究院 A kind of collaboration paths planning method for kinematic redundancy dual-arm space robot
CN110497378A (en) * 2019-09-04 2019-11-26 上海海事大学 A kind of automatic loading and unloading robot for part processing
CN110524522A (en) * 2019-09-19 2019-12-03 浙江工业大学 A kind of series-parallel anthropomorphous machine's arm of multiple degrees of freedom redundancy
US20220009093A1 (en) * 2020-07-08 2022-01-13 Ubtech Robotics Corp Ltd Task hierarchical control method, and robot and computer readable storage medium using the same

Non-Patent Citations (5)

* Cited by examiner, † Cited by third party
Title
ANTONIO PENALVER: "A Multi-Task Priority Framework for Redundant Robots with Multiple Kinematic Chains under Hard Joint and Cartesian Constraints", 《2018 IEEE/RSJ INTERNATIONAL CONFERENCE ON INTELLIGENT ROBOTS AND SYSTEMS》 *
FABRIZIO FLACCO: "A Reverse Priority Approach to Multi-Task Control of Redundant Robots", 《2014 IEEE/RSJ INTERNATIONAL CONFERENCE ON INTELLIGENT ROBOTS AND SYSTEMS》 *
OUSSAMA KANOUN: "Kinematic Control of Redundant Manipulators:Generalizing the Task-Priority Framework to Inequality Task", 《IEEE TRANSACTIONS ON ROBOTICS》 *
华磊等: "一种七自由度冗余机械臂阻抗控制研究", 《华中科技大学学报(自然科学版)》 *
黄水华: "多约束下的机械臂运动控制算法研究", 《中国博士学位论文全文数据库 信息科技辑》 *

Cited By (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN114800527A (en) * 2022-06-06 2022-07-29 山东大学 Force application control method and system for tail end of mobile operation mechanical arm

Also Published As

Publication number Publication date
CN111687834B (en) 2023-06-02

Similar Documents

Publication Publication Date Title
EP1728600B1 (en) Controlling the trajectory of an effector
US8600554B2 (en) System and method for robot trajectory generation with continuous accelerations
Peng et al. Compliant motion control of kinematically redundant manipulators
CN111702753B (en) Redundant mechanical arm inverse priority impedance control system and control method
Chen et al. Optimal, fault-tolerant mappings to achieve secondary goals without compromising primary performance
Li et al. Enhanced IBVS controller for a 6DOF manipulator using hybrid PD-SMC method
CN111687835B (en) System and method for controlling reverse priority impedance of redundant mechanical arm of underwater mechanical arm
Yan et al. A 5-DOF redundantly actuated parallel mechanism for large tilting five-face machining
Nemec et al. Force control of redundant robots in unstructured environment
KR20220148857A (en) robot control
Chung et al. Torque optimizing control with singularity-robustness for kinematically redundant robots
CN109623812A (en) Consider the mechanical arm method for planning track of spacecraft ontology attitude motion
CN111687834B (en) System and method for controlling reverse priority impedance of redundant mechanical arm of mobile mechanical arm
CN111687832B (en) System and method for controlling inverse priority impedance of redundant mechanical arm of space manipulator
Wimböck et al. Experimental study on dynamic reactionless motions with DLR's humanoid robot Justin
Nemec et al. Null space velocity control with dynamically consistent pseudo-inverse
Uzunoğlu et al. A multi-priority controller for industrial macro-micro manipulation
CN111687833B (en) System and method for controlling impedance of inverse priority of manipulator
Wen et al. Motion Planning for Image-based Visual Servoing of an Underwater Vehicle-Manipulator System in Task-Priority Frameworks
Yang et al. Dynamic compensation control of flexible macro–micro manipulator systems
Cao et al. Performance analysis of 3-PPRU parallel mechanism with a completely/partially/non constant Jacobian matrix
Pajak et al. Planning of a point to point collision-free trajectory for mobile manipulators
Hishinuma et al. Singularity-consistent vibration suppression control with a redundant manipulator mounted on a flexible base
Lu et al. Mechatronic design of dynamically decoupled manipulators based on the control performance improvement
Carmichael et al. Preliminary Analysis of a Redundancy Resolution Method for Mobile Manipulators used in Physical Human Robot Interaction

Legal Events

Date Code Title Description
PB01 Publication
PB01 Publication
SE01 Entry into force of request for substantive examination
SE01 Entry into force of request for substantive examination
GR01 Patent grant
GR01 Patent grant