CN111590567B - Space manipulator teleoperation planning method based on Omega handle - Google Patents

Space manipulator teleoperation planning method based on Omega handle Download PDF

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CN111590567B
CN111590567B CN202010398024.2A CN202010398024A CN111590567B CN 111590567 B CN111590567 B CN 111590567B CN 202010398024 A CN202010398024 A CN 202010398024A CN 111590567 B CN111590567 B CN 111590567B
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omega
mechanical arm
handle
joints
wrist
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CN111590567A (en
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徐拴锋
张海博
段文杰
王勇
胡海东
孙鲲
魏春岭
何英姿
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Beijing Institute of Control Engineering
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Beijing Institute of Control Engineering
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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
    • B25J9/1679—Programme controls characterised by the tasks executed
    • B25J9/1689—Teleoperation

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Abstract

The invention relates to a space manipulator teleoperation planning method based on an Omega handle, which decomposes the motion of a manipulator into a translational motion of a wrist and a rotational motion of the last three joints for controlling, so that the degree of freedom of the manipulator related to the translational motion of the wrist is less than that of the whole manipulator, thereby reducing the probability of occurrence of kinematic singularity. The movement of the mechanical arm is divided into the rotation of the last three joints and the translation of the wrist, the movement of the other joints except the last three joints generates the translation of the wrist, the translation and the rotation are decoupled mutually, the movement control is simple and reliable, the physical significance is clear, and the occupied resources are less. The gesture of the tail end of the space manipulator is mapped into the motion of the last three joints in the joint space, and compared with a traditional gesture mapping method, the gesture motion of the space manipulator does not have a singular problem.

Description

Space manipulator teleoperation planning method based on Omega handle
Technical Field
The invention relates to a teleoperation planning method for a space manipulator based on an Omega handle, and belongs to the field of teleoperation motion planning of space manipulators.
Background
In-orbit servicing is typically accomplished by a robotic arm equipped on the tracking spacecraft. Teleoperation of space manipulators by an operator via a handle is the primary means of performing on-orbit servicing tasks in the current state of the art. The Omega handle is a relatively common teleoperation device, has six degrees of freedom, and is respectively used for controlling the position and the posture of an end effector of a mechanical arm.
The motion mapping relation between the various degrees of freedom of the Omega handle and the mechanical arm directly determines the use experience and the work efficiency of an operator. Among them, the position mapping between the Omega handle and the space manipulator is relatively simple, but the posture mapping between the Omega handle and the space manipulator is relatively complicated. The current common attitude mapping method is to use the angular speed of a mechanical arm tail end fixed connection coordinate system relative to a mechanical arm base coordinate system as the attitude control output of an Omega handle. The physical meaning of the method is clear, but the following disadvantages exist:
(1) the posture mapping mode is not intuitive enough, and the operation experience is not good;
(2) the tail end attitude control of the space manipulator has a singular problem at certain configurations;
(3) the algorithm is complex and not beneficial to on-orbit application.
Disclosure of Invention
The invention aims to overcome the defects of the prior art, provides a space manipulator teleoperation planning method based on an Omega handle and solves the problem that the posture mapping between the Omega handle and the space manipulator is not intuitive.
The invention is realized by the following technical scheme:
a teleoperation planning method of a space manipulator based on an Omega handle comprises the following steps:
(1) establishing translation mapping between an Omega handle and a mechanical arm wrist;
(2) establishing a rotation mapping between three rotation joints of the Omega handle and the last three joints of the mechanical arm;
(3) generating the rotating speeds of the last three joints of the mechanical arm according to the Omega handle rotating output; and according to the Omega handle translation output, generating the rotation speeds of n-3 joints in front of the mechanical arm corresponding to the translation speed of the mechanical arm wrist, wherein n is the number of the degrees of freedom of the mechanical arm.
(4) The speed of each joint of the space manipulator can be integrated to obtain the position of each joint, and after the speed or the position of each joint is obtained, teleoperation planning of the space manipulator can be completed.
Preferably, the method for establishing the translation mapping between the Omega handle and the mechanical arm wrist in the step (1) comprises the following steps:
three translational degrees of freedom of an Omega handle relative to a zero position p0Output p oftrans∈R3×1Is marked as
ptrans＝pt-p0
Wherein p ist∈R3×1Is the current translational output of the Omega handle.
Translation instruction p of Omega handle to mechanical armcmd∈R3×1Is marked as
pcmd＝robotTomegaptrans
Wherein the content of the first and second substances,robotTomega∈R3×3is a conversion matrix from an Omega handle coordinate system to a mechanical arm base system.
Preferably, the robot arm base coordinate system and the handle coordinate system are arranged in parallel with each other in the same or opposite directions.
Preferably, the method for establishing the rotational mapping of the three rotational joints of the Omega handle and the last three joints of the mechanical arm comprises the following steps:
2.1 the rolling, yawing and pitching freedom degrees of the Omega handle respectively correspond to the rotation motions of a wrist rolling joint, a wrist yawing joint and a wrist pitching joint of the mechanical arm;
2.2 three rotational degrees of freedom of Omega handle with respect to zero position
Figure BDA0002488396240000021
Is output as
Figure BDA0002488396240000022
Figure BDA0002488396240000023
Wherein the content of the first and second substances,
Figure BDA0002488396240000024
is the current rotational output of the Omega handle;
2.3Omega handle rotation command to arm
Figure BDA0002488396240000025
Figure BDA0002488396240000026
Wherein the content of the first and second substances,robotRomega∈R3×3the method is a mapping matrix between the rotational freedom degrees of the Omega handle and the rotational freedom degrees of the last three joints of the mechanical arm.
Preferably, if the rolling, pitching and yawing of the last three joints of the mechanical arm are consistent with the layout of the three rotating joints of the Omega handle, the layout of the three rotating joints of the mechanical arm is as followsrobotRomegaIs an identity matrix.
Preferably, the method for generating the rotation speeds of the last three joints of the mechanical arm according to the Omega handle rotation output comprises the following steps:
the angular speed control commands of the Omega handle corresponding to the last three joints of the mechanical arm are as follows
Figure BDA0002488396240000031
Then
Figure BDA0002488396240000032
Wherein k isω∈R3×3For the scale factor diagonal matrix corresponding to the rotational degree of freedom,
Figure BDA0002488396240000033
kω1、kω2、kω3the three rotational degrees of freedom of the wrist of the mechanical arm are respectively corresponding to the scaling quantities of the Omega handle in the rolling, pitching and yawing directions;
rotational speed of last three joints of mechanical arm
Figure BDA0002488396240000034
Is composed of
Figure BDA0002488396240000035
Preferably, the method for generating the rotation speeds of the front n-3 joints of the mechanical arm corresponding to the translation speed of the mechanical arm wrist according to the translation of the Omega handle comprises the following steps:
let the control command of the translation speed of the wrist of the mechanical arm corresponding to the Omega handle be vcmd∈R3×1Then, then
vcmd＝kvpcmd
Wherein k isv∈R3×3For the scale factor diagonal matrix corresponding to the translational degree of freedom,
Figure BDA0002488396240000036
kv1、kv2、kv3respectively the zooming amount of the mechanical arm wrist translation relative to the Omega handle translation direction;
speed of front n-3 joints of mechanical arm
Figure BDA0002488396240000037
Is composed of
Figure BDA0002488396240000041
Wherein, Jfor∈R(n-3)×6Is a jacobian matrix corresponding to the wrist of the robot arm,
Figure BDA0002488396240000042
is JforThe classical pseudo-inverse of (c).
Preferably, the robot joint speed command is generated
Figure BDA0002488396240000043
And then, generating a mechanical arm joint position instruction according to the mechanical arm joint speed instruction:
the space manipulator joint speed instruction is
Figure BDA0002488396240000044
Based on the mechanical arm joint speed instruction, a position instruction is generated, and the specific method comprises the following steps:
space manipulator at time tk+1The joint position of
Figure BDA0002488396240000045
At time tk+1The space manipulator joint position is approximately given by
Figure BDA0002488396240000046
Wherein q (t)k) For space the arm at time tkThe joint position of (a).
In conclusion, after the joint speed or the joint position is obtained, the teleoperation planning of the space manipulator can be completed.
Preferably, pedals are provided to enable the Omega handle to teleoperate the output of control commands to the robotic arms.
The teleoperation system comprises an on-board mechanical arm, a satellite-ground communication link, a ground measurement and control system, a vision processing and analyzing subsystem, a telemetering data processing subsystem, a teleoperation planning control subsystem, a control instruction automatic generation subsystem and a three-dimensional view and prediction display simulation subsystem;
the on-satellite mechanical arm executes a space operation task, collects the motion state of the mechanical arm and the hand-eye camera image and sends the motion state and the hand-eye camera image to the ground measurement and control system through a satellite-ground communication link; the ground measurement and control system demodulates and then sends the image to the vision processing and analyzing subsystem, and sends the motion state of the mechanical arm to the telemetering data processing subsystem; the vision processing and analyzing subsystem sends the processed images to the three-dimensional visual and prediction display simulation subsystem and the teleoperation planning control subsystem for display respectively; the remote measurement data processing subsystem removes the field of the motion state data of the mechanical arm and then sends the data to the teleoperation planning control subsystem, and the teleoperation planning control subsystem generates a mechanical arm control instruction based on a space mechanical arm teleoperation planning method of an Omega handle and sends the mechanical arm control instruction to the three-dimensional view and the prediction display simulation subsystem to update the simulation scene; the teleoperation planning control subsystem displays hand-eye camera images of the mechanical arm, receives operation input of an Omega handle and a pedal of an operator, and generates a speed and position instruction of the mechanical arm based on motion state data of the mechanical arm; under the condition that a pedal is stepped on, the control instruction automatic generation subsystem carries out protocol conversion based on the speed and position instructions of the mechanical arm and then sends the converted data to the three-dimensional view and prediction display simulation subsystem, the three-dimensional view and prediction display simulation subsystem carries out safety test on the speed and position instructions of the mechanical arm and carries out virtual display of the instructions executed by the mechanical arm, whether collision exists or not is judged, and if no collision exists, the command is sent to the on-satellite mechanical arm through the satellite-ground communication link for execution.
Compared with the prior art, the invention has the following advantages:
(1) according to the method disclosed by the invention, the posture of the Omega handle is mapped into the motion of the last three joints of the space manipulator in the joint space, and compared with the traditional posture mapping method, the space manipulator does not have a singular problem in posture motion.
(2) The method disclosed by the invention controls the motion of the mechanical arm by dividing the motion of the mechanical arm into two parts, namely the translation of the wrist and the rotation of the last three joints, so that the degree of freedom of the mechanical arm related to the translation of the wrist is less than that of the whole arm, thereby reducing the probability of occurrence of kinematic singularity.
(3) The invention divides the movement of the mechanical arm into the rotation of the last three joints and the translation of the wrist, the movement of the other joints generates the translation of the wrist, and the translation and the rotation are mutually decoupled, the movement control is simple and reliable, the physical meaning is clear, and the occupied resource is less.
(4) The time complexity of the method disclosed by the invention is low, the space manipulator is controlled to operate after the ground generates the instruction, and the requirement on hardware configuration of a ground operating system is low.
Drawings
FIG. 1 is a schematic view of the structure and coordinate system of an Omega handle;
FIG. 2 is a schematic diagram of a robot arm structure and a base coordinate system according to an embodiment;
fig. 3 is a teleoperation test system composition and signal flow diagram.
Detailed Description
Based on the constructed teleoperation ground test system, the mechanical arm teleoperation planning method disclosed by the invention is used. The arm adopts series connection structure, and the terminal hand eye binocular camera of installation. In the teleoperation test, an enabling device, namely a pedal, is introduced in consideration of safety. It can control whether the operation command generated by the Omega handle is sent to the mechanical arm to execute: when an operator steps on the pedal, an operation instruction can be sent to the mechanical arm to be executed; when the operator releases the pedal, a stop command is sent to the mechanical arm, and the mechanical arm stops running. After the state of each device is confirmed to be correct, the test is started: based on the images returned by the binocular camera, an operator operates the Omega handle to control the mechanical arm to move towards the target star, and when the target star butting ring is positioned in the gripper at the tail end of the mechanical arm, the gripper is closed, so that the target star butting ring is grabbed.
The invention discloses a space manipulator teleoperation planning method based on an Omega handle, which comprises the following steps:
(1) establishing translation mapping between an Omega handle and a mechanical arm;
(2) establishing a rotation mapping between an Omega handle and a mechanical arm;
(3) generating a joint speed instruction for operating and controlling the mechanical arm according to the Omega handle output;
(4) the speed of each joint of the space manipulator can be integrated to obtain the position of each joint, and after the speed or the position of each joint is obtained, teleoperation planning of the space manipulator can be completed.
The specific method of the step (1) comprises the following steps:
establishing translation mapping between an Omega handle and a mechanical arm, which specifically comprises the following steps:
the translation of the wrist of the mechanical arm is controlled through three translation degrees of freedom of the Omega handle. In connection with fig. 2, the wrist is defined here as the root of the third last joint from the end of the robot arm, the specific position of the root being based on the position obtained by the DH modeling method. The position mapping relationship between the Omega handle and the mechanical arm is defined as: the three translational degrees of freedom of the Omega handle correspond to the translational degrees of freedom of the wrist part of the mechanical arm one by one.
Three translational degrees of freedom of an Omega handle relative to a zero position p0Output p oftrans∈R3×1Is marked as
ptrans＝pt-p0
Wherein p ist∈R3×1For the current translational output of the Omega handle, the unit: mm, the position of the wrist of the handle under the coordinate system of the handle is given by the encoder of the handle, and the wrist of the handle is defined as the combination part of the parallel part of the Omega handle and the rolling joint of the handle. p is a radical of0∈R3×1The unit is the translation output of the Omega handle at a certain zero position: mm, e.g. (0,0,0) of the handle coordinate systemT。
Translation instruction p of Omega handle to mechanical armcmd∈R3×1Is marked as
pcmd＝robotTomegaptrans
Wherein the content of the first and second substances,robotTomega∈R3×3the transformation matrix from the Omega handle coordinate system to the robot arm base system is the one in which the robot arm coordinate system and the handle coordinate system are arranged in parallel and in the same or opposite directions. In one embodiment, since the robot arm base coordinate system is opposite to X, Y of the Omega handle coordinate system, the Z direction is coincident, then:
Figure BDA0002488396240000071
if the axes of the mechanical arm and the translational direction X, Y, Z of the handle are all consistent
Figure BDA0002488396240000072
The specific method of the step (2) is as follows:
establishing a rotation mapping between an Omega handle and a mechanical arm, which specifically comprises the following steps:
the rotation of the last three joints of the mechanical arm, namely the wrist, is controlled through three rotational degrees of freedom of the three joints of the Omega handle. The posture mapping relationship between the Omega handle and the mechanical arm is defined as: the degree of freedom of the Omega handle corresponds to the rolling rotation of the end of the mechanical arm, and the degrees of freedom of the Omega handle in yaw and pitch correspond to the rotational movement of the wrist yaw and pitch joints of the mechanical arm, respectively.
Output of three rotary joints of Omega handle relative to a certain zero position
Figure BDA0002488396240000073
(corresponding to roll, pitch, yaw, respectively) and is recorded as
Figure BDA0002488396240000074
Wherein the content of the first and second substances,
Figure BDA0002488396240000075
for the current rotational output of the Omega handle, the unit: deg;
Figure BDA0002488396240000076
the unit is the rotation output of the Omega handle at a certain zero position: deg, e.g. (0,0,0)T。
Rotation instruction of Omega handle to mechanical arm
Figure BDA0002488396240000077
Is marked as
Figure BDA0002488396240000078
Wherein the content of the first and second substances,robotRomega∈R3×3the method is a mapping matrix between the rotational freedom degrees of the Omega handle and the rotational freedom degrees of the last three joints of the mechanical arm. In one embodiment, the layout of the last three joints of the mechanical arm is pitch, yaw and roll in sequence, that is, the three joints perform roll, pitch and yaw in sequence. The layout of the three rotating joints of the Omega handle is rolling, pitching and yawing in sequence, and the directions of the mechanical arm and the Omega handle are opposite and consistent, so that the Omega handle has the advantages of simple structure, convenient operation, low cost and the like
Figure BDA0002488396240000081
The specific method of the step (3) is as follows:
generating a joint speed instruction for operating and controlling the mechanical arm according to the Omega handle output, which specifically comprises the following steps:
the Omega handle controls the mechanical arm in a speed mode, namely, the deviation of the Omega handle relative to a certain zero position configuration is used as the speed control input of the mechanical arm, the first three components are the translation speed of the wrist, and the last three components are the rotation speed of the wrist. I.e. the greater the offset of a certain degree of freedom of the Omega handle with respect to the zero position, the greater the corresponding control speed. When the target configuration differs significantly from the current configuration, the operator may apply a greater speed control input, and conversely decrease the speed control input until the robotic arm reaches the target configuration.
Let the control command of the translation speed of the wrist of the mechanical arm corresponding to the Omega handle be vcmd∈R3×1Then, then
vcmd＝kvpcmd
Wherein k isv∈R3×3For the scale factor diagonal matrix corresponding to the translational degree of freedom,
Figure BDA0002488396240000082
kv1、kv2、kv3respectively the amount of the robot arm wrist translation relative to the Omega handle X, Y, Z direction.
The angular speed control instruction corresponding to the Omega handle is
Figure BDA0002488396240000083
Then
Figure BDA0002488396240000084
Wherein k isω∈R3×3For the scale factor diagonal matrix corresponding to the rotational degree of freedom,
Figure BDA0002488396240000091
kω1、kω2、kω3the three rotational degrees of freedom of the wrist of the mechanical arm are respectively the scaling amount of the Omega handle in the rolling direction, the pitching direction and the yawing direction.
Velocity of the last three joints of the arm
Figure BDA0002488396240000092
Is composed of
Figure BDA0002488396240000093
Let the degree of freedom of the mechanical arm be n, the speeds of other joints except the last three joints, namely the front n-3 joints of the mechanical arm
Figure BDA0002488396240000094
Is composed of
Figure BDA0002488396240000095
Wherein, Jfor∈R(n-3)×6Is a jacobian matrix corresponding to the wrist of the robot arm,
Figure BDA0002488396240000096
is JforThe classical pseudo-inverse of (c).
The specific method of the step (4) comprises the following steps:
the space manipulator can obtain each joint position by integrating each joint speed, and the teleoperation planning of the space manipulator can be completed after the joint speed or the joint position is obtained, and the method specifically comprises the following steps:
space manipulator joint speed command
Figure BDA0002488396240000097
Is composed of
Figure BDA0002488396240000098
The space manipulator joint speed instruction is
Figure BDA0002488396240000099
Based on the mechanical arm joint speed instruction, a position instruction is generated, and the specific method comprises the following steps:
space manipulator at time tk+1The joint position of
Figure BDA00024883962400000910
At time tk+1The space manipulator joint position is approximately given by
Figure BDA00024883962400000911
Wherein q (t)k) For space the arm at time tkThe joint position of (a).
And after the joint speed or the joint position is obtained, the teleoperation planning of the space manipulator can be completed.
With reference to fig. 1 and 3, the present invention is applied to a teleoperation system of an on-orbit mechanical arm, and includes an on-board mechanical arm, a satellite-ground communication link, a ground measurement and control system, a vision processing and analyzing subsystem, a telemetry data processing subsystem, a teleoperation control subsystem, a control instruction automatic generation subsystem, and a three-dimensional view and prediction display simulation subsystem.
The on-satellite mechanical arm executes a space operation task, collects the motion state of the mechanical arm and the hand-eye camera image and sends the motion state and the hand-eye camera image to the ground measurement and control system through a satellite-ground communication link; the ground measurement and control system demodulates and then sends the image to the vision processing and analyzing subsystem, and sends the motion state of the mechanical arm to the telemetering data processing subsystem; the vision processing and analyzing subsystem sends the processed images to the three-dimensional visual and prediction display simulation subsystem and the teleoperation planning control subsystem for display respectively; the remote measurement data processing subsystem removes the field of the motion state data of the mechanical arm and then sends the data to the teleoperation planning control subsystem, and the teleoperation planning control subsystem generates a mechanical arm control instruction based on a space mechanical arm teleoperation planning method of an Omega handle and sends the mechanical arm control instruction to the three-dimensional view and the prediction display simulation subsystem to update the simulation scene; the teleoperation planning control subsystem displays hand-eye camera images of the mechanical arm, receives operation input of an Omega handle and a pedal of an operator, and generates a speed and position instruction of the mechanical arm based on motion state data of the mechanical arm; under the condition that a pedal is stepped on, the control instruction automatic generation subsystem carries out protocol conversion based on the speed and position instructions of the mechanical arm and then sends the converted data to the three-dimensional view and prediction display simulation subsystem, the three-dimensional view and prediction display simulation subsystem carries out safety test on the speed and position instructions of the mechanical arm and carries out virtual display of the instructions executed by the mechanical arm, whether collision exists or not is judged, and if no collision exists, the command is sent to the on-satellite mechanical arm through the satellite-ground communication link for execution.
The test system related to the embodiment of the method comprises an Omega handle, a pedal and a fixed base six-degree-of-freedom mechanical arm, wherein a binocular hand-eye camera is mounted at the tail end of the mechanical arm, and visual feedback information is provided for teleoperation of the mechanical arm.
The above description is only for the best mode of the present invention, but the scope of the present invention is not limited thereto, and any changes or substitutions that can be easily conceived by those skilled in the art within the technical scope of the present invention are included in the scope of the present invention.

Claims (1)

1. A teleoperation planning method of a space manipulator based on an Omega handle is characterized by comprising the following steps:
(1) establishing translation mapping between an Omega handle and a mechanical arm wrist;
(2) establishing a rotation mapping between three rotation joints of the Omega handle and the last three joints of the mechanical arm;
(3) generating the rotating speeds of the last three joints of the mechanical arm according to the Omega handle rotating output; according to the Omega handle translation output, the rotation speeds of n-3 joints in front of the mechanical arm corresponding to the translation speed of the mechanical arm wrist are generated, wherein n is the number of the degrees of freedom of the mechanical arm;
(4) integrating the speed of each joint of the space manipulator to obtain the position of each joint, namely finishing teleoperation planning of the space manipulator;
the method for establishing the translation mapping between the Omega handle and the mechanical arm wrist in the step (1) comprises the following steps:
three translational degrees of freedom of an Omega handle relative to a zero position p0Output p oftrans∈R3×1Is marked as
ptrans＝pt-p0
Wherein p ist∈R3×1Is the current translational output of the Omega handle;
translation instruction p of Omega handle to mechanical armcmd∈R3×1Is marked as
pcmd＝robotTomegaptrans
Wherein the content of the first and second substances,robotTomega∈R3×3a conversion matrix from an Omega handle coordinate system to a mechanical arm base system;
the specific method for establishing the rotation mapping of the three rotation joints of the Omega handle and the last three joints of the mechanical arm in the step (2) is as follows:
2.1 enabling the rolling, yawing and pitching freedom degrees of the Omega handle to respectively correspond to the rotation motions of a wrist rolling joint, a wrist yawing joint and a wrist pitching joint of the mechanical arm;
2.2 three rotational degrees of freedom of Omega handle with respect to zero position
Figure FDA0003260154520000011
Is output as
Figure FDA0003260154520000012
Figure FDA0003260154520000013
Wherein the content of the first and second substances,
Figure FDA0003260154520000014
is the current rotational output of the Omega handle;
2.3Omega handle rotation command to arm
Figure FDA0003260154520000021
Is marked as
Figure FDA0003260154520000022
Wherein the content of the first and second substances,robotRomega∈R3×3a mapping matrix between the rotational freedom degree of the Omega handle and the rotational freedom degrees of the last three joints of the mechanical arm is formed;
a pedal is arranged for enabling the Omega handle to remotely operate and control the output of the command to the mechanical arm;
the coordinate system of the mechanical arm base and the coordinate system of the handle are arranged in parallel and in the same or opposite directions;
if the rolling, pitching and yawing freedom degrees of the last three joints of the mechanical arm are consistent with the layout of the three rotating joints of the Omega handle, the mechanical arm is provided with a plurality of jointsrobotRomegaIs an identity matrix;
the method for generating the rotating speeds of the last three joints of the mechanical arm according to the Omega handle rotating output in the step (3) comprises the following steps:
the angular speed control commands of the Omega handle corresponding to the last three joints of the mechanical arm are as follows
Figure FDA0003260154520000023
Then
Figure FDA0003260154520000024
Wherein k isω∈R3×3For the scale factor diagonal matrix corresponding to the rotational degree of freedom,
Figure FDA0003260154520000025
kω1、kω2、kω3the three rotational degrees of freedom of the wrist of the mechanical arm are respectively corresponding to the scaling quantities of the Omega handle in the rolling, pitching and yawing directions;
rotational speed of last three joints of mechanical arm
Figure FDA0003260154520000026
Is composed of
Figure FDA0003260154520000027
The method for generating the rotation speeds of the front n-3 joints of the mechanical arm corresponding to the translation speed of the mechanical arm wrist according to the translation of the Omega handle in the step (3) comprises the following steps:
let the control command of the translation speed of the wrist of the mechanical arm corresponding to the Omega handle be vcmd∈R3×1Then, then
vcmd＝kvpcmd
Wherein k isv∈R3×3For the scale factor diagonal matrix corresponding to the translational degree of freedom,
Figure FDA0003260154520000031
kv1、kv2、kv3respectively the zooming amount of the mechanical arm wrist translation relative to the Omega handle translation direction;
speed of front n-3 joints of mechanical arm
Figure FDA0003260154520000032
Is composed of
Figure FDA0003260154520000033
Wherein, Jfor∈R(n-3)×6Is a jacobian matrix corresponding to the wrist of the robot arm,
Figure FDA0003260154520000034
is JforThe classical pseudo-inverse of (1);
generating a mechanical arm joint velocity command
Figure FDA0003260154520000035
And then, generating a mechanical arm joint position instruction according to the mechanical arm joint speed instruction:
the space manipulator joint speed instruction is
Figure FDA0003260154520000036
Based on the mechanical arm joint speed instruction, a position instruction is generated, and the specific method comprises the following steps:
space manipulator at time tk+1The joint position of
Figure FDA0003260154520000037
At time tk+1The space manipulator joint position is approximately given by
Figure FDA0003260154520000038
Wherein q (t)k) For space the arm at time tkThe joint position of (a).
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