CN113608451A - Simulation control platform based on ROS and exoskeleton robot simulation control system - Google Patents

Simulation control platform based on ROS and exoskeleton robot simulation control system Download PDF

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CN113608451A
CN113608451A CN202110792420.8A CN202110792420A CN113608451A CN 113608451 A CN113608451 A CN 113608451A CN 202110792420 A CN202110792420 A CN 202110792420A CN 113608451 A CN113608451 A CN 113608451A
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exoskeleton
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魏巍
林西川
章鹏程
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Maybe Intelligent Technology Suzhou Co ltd
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Abstract

The invention provides a simulation control platform based on ROS and a simulation control system of an exoskeleton robot, wherein the simulation control platform based on ROS comprises: a control module; the data acquisition module acquires data fed back by the exoskeleton robot and transmits the data with the control module; the simulation display module is used for constructing the exoskeleton robot model and carrying out simulation display on the exoskeleton robot model based on the feedback data under the control of the control system; an athletic intent detection module, comprising: and the plurality of movement intention detection units subscribe data fed back by the exoskeleton robot and identify the movement intention of the human body. The invention provides an exoskeleton robot simulation control system based on ROS, which can shorten the development period of an exoskeleton software control algorithm, can realize experimental verification on the exoskeleton robot control algorithm by simulating a real exoskeleton robot model, and can also provide debugging of controller parameters.

Description

Simulation control platform based on ROS and exoskeleton robot simulation control system
Technical Field
The invention relates to the technical field of exoskeleton robots, in particular to a simulation control platform based on ROS and a simulation control system of an exoskeleton robot.
Background
The power-assisted lower limb exoskeleton robot is a wearable man-machine integrated mechanical device, can provide power assistance in an electric mode and the like to enhance the strength output of a human body, and is suitable for assisting heavy-body-strength workers to work or assisting the old and the disabled and other scenes. Meanwhile, the exoskeleton robot can be applied to the special fields of individual combat, emergency rescue and the like, and is used for assisting rescue workers or soldiers to carry related equipment to walk for a long distance under the condition that conventional vehicles cannot drive into the scene. Therefore, the exoskeleton robot technology has important significance and value in the fields of future intelligent human-computer interaction and human-computer co-fusion.
The motion control of the lower limb exoskeleton robot is a premise and guarantee that a wearer can be assisted to complete a bearing transportation task, and is one of key technologies of the exoskeleton robot. Due to the complexity of the exoskeleton robot wearing personnel in the ring and the operation environment, identifying the movement intention of the wearer and improving the control performance of the wearer become keys for overcoming the exoskeleton robot technology. However, in the development and operation of exoskeletal robots, the conventional off-line programming and debugging method is difficult to ensure in terms of efficiency and safety due to the presence of the operator in the loop. Therefore, it is necessary to provide a further solution to the above problems.
Disclosure of Invention
The invention aims to provide a simulation control platform based on ROS and an exoskeleton robot simulation control system, so as to overcome the defects in the prior art.
In order to achieve the above object, the present invention provides an ROS-based simulation control platform for simulation control of an exoskeleton robot, comprising:
a control module;
the data acquisition module acquires data fed back by the exoskeleton robot and transmits the data with the control module;
the simulation display module is used for constructing an exoskeleton robot model and carrying out simulation display on the exoskeleton robot model under the control of the control system based on feedback data;
an athletic intent detection module, comprising: a plurality of movement intention detection units which subscribe the data fed back by the exoskeleton robot and carry out human movement intention identification.
As an improvement of the ROS-based simulation control platform, the data acquisition module acquires data of the exoskeleton robot end in real time by means of the PCI-CAN board card.
As an improvement of the ROS-based simulation control platform, the data acquisition module issues the acquired data in the form of ROS topics, simultaneously subscribes joint control information of the control module, and sends the joint control information to the exoskeleton robot.
As an improvement of the ROS-based simulation control platform, the control module supports a self-defined exoskeleton dynamics mathematical model or an open-source three-dimensional physical simulation platform.
As an improvement of the ROS-based simulation control platform, when the control module supports an open-source three-dimensional physical simulation platform, a simulation control flow is executed according to the following steps:
importing the exoskeleton three-dimensional structure chart into the open source three-dimensional physical simulation platform, then adjusting and optimizing the information parameters of the constructed exoskeleton robot model, and simultaneously performing control simulation on the model and the actual system in the platform by using a low-order control algorithm by means of control algorithm nodes of the open source three-dimensional physical simulation platform;
verifying a related moment depth control algorithm, observing a simulation operation effect in a simulation platform, and performing online algorithm verification test at an actual system end by means of control information sent to a lower exoskeleton end after the control algorithm is verified;
after the algorithm verification is passed, an exoskeleton dynamics optimization model is automatically constructed based on computational power configuration of an actual system, and comparison verification is carried out on a simulation platform.
As an improvement of the ROS-based simulation control platform, the PC simulation control platform disassembles the motion state into: a left foot soaring right foot support state, a two foot support state, and a right foot soaring left foot support state.
As an improvement of the ROS-based simulation control platform of the present invention,
single leg support kinetic model:
Figure 473538DEST_PATH_IMAGE001
in the formula:
Figure DEST_PATH_IMAGE002
the sum of kinetic energy of each rod piece of the exoskeleton;
Figure 984153DEST_PATH_IMAGE003
the sum of the gravitational potential energy of each rod piece of the exoskeleton;
Figure DEST_PATH_IMAGE004
the sum of the elastic potential energy of the exoskeleton knee joint;
l is a Lagrange function and is equal to the difference between the total kinetic energy, the gravitational potential energy and the total elastic potential energy of the system;
Figure 232732DEST_PATH_IMAGE005
respectively representing the generalized angular velocities of the knee and ankle joints;
Figure DEST_PATH_IMAGE006
respectively representing the generalized coordinates of a sagittal plane system and a frontal plane system;
Figure 221417DEST_PATH_IMAGE007
respectively representing the resultant force of the knee and ankle joints, namely the joint motor driving force and the human-computer interaction force.
As an improvement of the ROS-based simulation control platform of the present invention,
the 6-link kinetic equation of the exoskeleton support phase is as follows:
Figure DEST_PATH_IMAGE008
in the formula (I), the compound is shown in the specification,
Figure 753898DEST_PATH_IMAGE009
an inertia tensor array representing the robot in a sagittal plane;
Figure DEST_PATH_IMAGE010
is a matrix of coriolis forces and centrifugal forces of 6x 6;
Figure 700994DEST_PATH_IMAGE011
is a 6x1 gravity matrix;
Figure DEST_PATH_IMAGE012
is an elastic force matrix;
Figure 561503DEST_PATH_IMAGE013
Figure DEST_PATH_IMAGE014
Figure 229245DEST_PATH_IMAGE015
respectively representing a generalized position, a generalized velocity and a generalized acceleration in 6x1 dimensions.
As an improvement of the simulation control platform based on ROS, in a two-foot supporting state, the output torque of the left hip joint and the right hip joint can be in accordance with the distance between the projection point of the whole gravity center of the exoskeleton on the connecting line of the landing points of the two feet and the two feet
Figure DEST_PATH_IMAGE016
,
Figure 819495DEST_PATH_IMAGE017
The proportion distribution is as follows:
Figure DEST_PATH_IMAGE018
,
Figure 203072DEST_PATH_IMAGE019
the total torque required by the left hip joint and the right hip joint of the exoskeleton system;
other joint torques were derived from 5-bar linkage dynamics:
Figure DEST_PATH_IMAGE020
in the formula (I), the compound is shown in the specification,
Figure 550876DEST_PATH_IMAGE021
the kinetic energy sum of each connecting rod of the exoskeleton comprises a left shank, a right shank, a left thigh, a right thigh and a body;
Figure DEST_PATH_IMAGE022
the potential energy sum of each connecting rod of the exoskeleton comprises a left shank, a right shank, a left thigh and a right thigh and a body;
es is the elastic potential energy of the system knee joint.
In order to achieve the above object, the present invention provides a lower extremity exoskeleton robot simulation control system based on ROS, comprising:
a lower exoskeleton end, the ROS-based simulation control platform as described above;
the lower exoskeleton end comprises: the simulation control platform based on the ROS can receive data fed back by the human body posture sensing module and the interaction force detection module;
the human body posture sensing module comprises: six-axis inertial measurement sensors arranged on a back frame, angle sensors arranged at knee joints of left and right legs and pressure sensors arranged on left and right soles.
Compared with the prior art, the invention has the beneficial effects that: the invention provides a simulation control platform based on ROS and an exoskeleton robot simulation control system, which can shorten the development period of an exoskeleton software control algorithm, can realize experimental verification on the exoskeleton robot control algorithm by simulating a real exoskeleton robot model, and can also provide debugging of controller parameters.
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In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the embodiments or the prior art will be briefly described below, it is obvious that the drawings in the following description are only some embodiments described in the present invention, and for those skilled in the art, other drawings can be obtained according to the drawings without creative efforts.
FIG. 1 is a block diagram of one embodiment of a ROS based exoskeleton robot simulation control system of the present invention;
FIG. 2 is a flow chart of simulation control when the control module supports an open-source three-dimensional physical simulation platform.
Detailed Description
The present invention is described in detail below with reference to various embodiments, but it should be understood that these embodiments are not intended to limit the present invention, and those skilled in the art should be able to make modifications and substitutions on the functions, methods, or structures of these embodiments without departing from the scope of the present invention.
As shown in fig. 1, an embodiment of the present invention provides an ROS-based exoskeleton robot simulation control system, which employs a modular distributed master-slave control hardware architecture. The exoskeleton robot simulation control system comprises: an upper ROS-based simulation control platform 100 and a lower exoskeleton end 200. The upper-layer simulation control platform 100 based on ROS performs simulation control and task decision, the lower-layer exoskeleton end 200 performs control according to instructions of the control platform, and the whole system has the characteristics of high cohesion and low coupling.
Specifically, the PC emulation control platform is built by relying on the ROS environment running in a real-time Linux operating system, and the method comprises the following steps: a control module 101, a data acquisition module 102, a simulation display module 103, and an exercise intention detection module 104.
The control module 101 may be a PC host, and is mainly responsible for acquiring sensing data, simulating motion, and controlling the exoskeleton robot system. Meanwhile, in order to guarantee real-time performance, the ROS2 system is operated on the PC host, and the version system communication adopts a communication framework based on Data Distribution Services (DDS).
And the data acquisition module 102 acquires data fed back by the lower exoskeleton end 200 and transmits the data with the control module 101. The data acquisition module 102 acquires data of the exoskeleton robot end in real time by means of a PCI-CAN board card. Meanwhile, the data acquisition module 102 issues the acquired data in the form of ROS topics, subscribes to the joint control information of the control module 101, and sends the joint control information to the lower exoskeleton end 200.
The simulation display module 103 is used for constructing an exoskeleton robot model and performing simulation display on the exoskeleton robot model under the control of the control system based on the feedback data. Specifically, the simulation display module 103 may compile a URDF file based on an actual exoskeleton robot physical model, construct an exoskeleton robot model, then introduce exoskeleton sensing information into a robot simulation environment RVIZ in the ROS system, and directly display a motion simulation picture of the current exoskeleton robot in the exoskeleton debugging and running process.
The exercise intention detection module 104 is used for human body exercise state detection and exercise intention identification. The athletic intent detection module 104 includes: a plurality of movement intention detection units which subscribe the data fed back by the exoskeleton robot and carry out human movement intention identification.
Further, control module 101 supports custom exoskeleton dynamics mathematical models or open source three-dimensional physical simulation platforms (Gazebo). The Gazebo is provided with a simulated real physical engine ODE, wherein the ODE is a rigid body dynamics library with industrial quality and can create a virtual simulation environment for the operation of the exoskeleton robot; in addition, the Gazebo supports sensor simulation and is provided with abundant extensible plug-ins.
As shown in fig. 2, when the control module 101 supports the open-source three-dimensional physical simulation platform, the simulation control flow is executed according to the following steps:
and S1, directly importing the exoskeleton three-dimensional structure diagram into a Gazebo simulation platform through an SW2URDF plug-in unit, and then adjusting and optimizing information parameters such as the quality of the exoskeleton model and the like based on an actual exoskeleton system. Meanwhile, a control algorithm node can be opened, a model and an actual system in the platform are controlled and simulated by using a low-order control algorithm, and model parameters are identified and corrected based on an operation effect, so that a rigid body dynamics model in the simulation platform is closer to the actual exoskeleton system.
S2, the ros _ control of the Gazebo can be directly used for verification research of the related moment depth control algorithm, and meanwhile, the simulation operation effect is observed in the simulation platform. After the control algorithm verification is completed, the user can enable the control information sent to the lower exoskeleton end 200 to perform an online algorithm verification test at the actual system end.
And S3, after the algorithm verification is passed, automatically constructing an exoskeleton dynamics optimization model to replace a Gazebo node based on the computational power configuration of an actual system so as to reduce the load requirement of the system, and performing comparison verification on a simulation platform.
In the exoskeletal man-machine coupling motion process, based on the rhythmicity of human walking, the motion state can be disassembled into three basic motion configurations: a left foot soaring right foot supporting state, a double foot supporting state and a right foot soaring left foot supporting state. The man-machine coupling motion process is the switching process of the three typical motion configurations. Along with the movement and the switching of the movement configuration, the dynamic structure of the system is changed. Therefore, the exoskeleton robot dynamic equations need to be respectively established according to different motion configurations.
For the single-leg support kinetic model:
Figure 756730DEST_PATH_IMAGE001
in the formula:
Figure 670328DEST_PATH_IMAGE002
the sum of kinetic energy of each rod piece of the exoskeleton;
Figure 631331DEST_PATH_IMAGE003
the sum of the gravitational potential energy of each rod piece of the exoskeleton;
Figure 810639DEST_PATH_IMAGE004
the sum of the elastic potential energy of the exoskeleton knee joint;
l is a Lagrange function and is equal to the difference between the total kinetic energy, the gravitational potential energy and the total elastic potential energy of the system;
Figure 272714DEST_PATH_IMAGE005
respectively representing the generalized angular velocities of the knee and ankle joints;
Figure 119447DEST_PATH_IMAGE006
respectively representing the generalized coordinates of a sagittal plane system and a frontal plane system;
Figure 110406DEST_PATH_IMAGE007
respectively representing the resultant force of the knee and ankle joints, namely joint motor driving force and human-computer interaction force;
in the single-leg supporting phase link, the system can be regarded as a 6-link model which comprises a left lower leg rod, a right lower leg rod, a left upper leg rod, a right upper leg rod, a trunk and supporting leg feet, and 4 active degrees of freedom are positioned at the left hip knee joint and the right hip knee joint.
The 6-link kinematic equation for the exoskeleton support phase is thus:
Figure 777010DEST_PATH_IMAGE008
in the formula (I), the compound is shown in the specification,
Figure 121404DEST_PATH_IMAGE009
an inertia tensor array representing the robot in a sagittal plane;
Figure 275174DEST_PATH_IMAGE010
is a matrix of coriolis forces and centrifugal forces of 6x 6;
Figure 250083DEST_PATH_IMAGE011
is a 6x1 gravity matrix;
Figure 466301DEST_PATH_IMAGE012
is an elastic force matrix;
Figure 801336DEST_PATH_IMAGE013
Figure 560344DEST_PATH_IMAGE014
Figure 768472DEST_PATH_IMAGE015
respectively representing a generalized position, a generalized velocity and a generalized acceleration of 6x1 dimensions;
the force exerted by the body on the exoskeleton is
Figure 658936DEST_PATH_IMAGE023
Measured by system human-computer interaction force sensing, the matrix is a 6x1 matrix;
j is a 6x6 matrix representing the mapping of Cartesian space forces experienced on the exoskeleton sagittal plane to the robot joint space.
For both feet support state:
the output torque of the left hip joint and the right hip joint can be based on the distance between the projected point of the exoskeleton's whole gravity center on the connecting line of the landing points of the two feet and the two feet
Figure 17236DEST_PATH_IMAGE016
,
Figure 676757DEST_PATH_IMAGE017
The proportion distribution is as follows:
Figure 931152DEST_PATH_IMAGE018
Figure 308912DEST_PATH_IMAGE019
the total torque required by the left hip joint and the right hip joint of the exoskeleton system;
other joint torques were derived from 5-bar linkage dynamics:
Figure 798800DEST_PATH_IMAGE020
in the formula (I), the compound is shown in the specification,
Figure 63559DEST_PATH_IMAGE021
the kinetic energy sum of each connecting rod of the exoskeleton comprises a left shank, a right shank, a left thigh, a right thigh and a body;
Figure 738123DEST_PATH_IMAGE022
the potential energy sum of each connecting rod of the exoskeleton comprises a left shank, a right shank, a left thigh and a right thigh and a body;
es is the elastic potential energy of the system knee joint.
The lower exoskeleton end 200 comprises an exoskeleton hip and knee joint motor module control system, drivers of all joint motors are integrated in a joint control node board, and the position, speed and moment mode operation setting of the joint motors can be realized at the bottom layer. The lower exoskeleton end 200 and the upper simulation control platform 100 based on ROS are connected by a CAN bus, and a protocol layer uses a CANopen protocol to support flexible increase and decrease of hip and knee active joint motor nodes.
Specifically, the lower exoskeleton end 200 includes: the human body posture sensing module 201, the joint driving motor module 202 and the interaction force detection module 203.
The ROS-based simulation control platform can receive data fed back by the human body posture sensing module 201 and the interaction force detection module 203. The human body posture sensing module 201 includes: six-axis inertial measurement sensors arranged on a back frame, angle sensors arranged at knee joints of left and right legs and pressure sensors arranged on left and right soles. Each sensor correspondingly feeds back to a plurality of motion intention detection units in the motion intention detection module 104 to be used as a data basis for human motion state detection and motion intention identification. The joint drive motor modules 202 may be arranged in multiple groups as desired.
In one embodiment, one IMU six-axis inertial measurement sensor is arranged on the back of the back and used for detecting the spatial attitude information of the upper torso; the knee ankle joints of the left leg and the right leg are respectively internally provided with an absolute encoder, the total number of the absolute encoders is 6, and the absolute encoders can be used for detecting the angle information of the knee ankle joints; meanwhile, the left and right pelma of the exoskeleton are provided with 1 pelma pressure sensor, and the total number of the pelma pressure sensors is 2, so that the exoskeleton can be used for detecting the state of lifting and dropping the leg. Based on the method, developers can collect the exoskeleton end sensing information on line to perform state analysis of sitting, walking, bending and the like of the wearable exoskeleton system.
In summary, the invention provides a simulation control platform based on ROS and a simulation control system of an exoskeleton robot, which can shorten the development period of exoskeleton software control algorithms, can realize experimental verification of exoskeleton robot control algorithms by simulating real exoskeleton robot models, and can also provide debugging of controller parameters.
It will be evident to those skilled in the art that the invention is not limited to the details of the foregoing illustrative embodiments, and that the present invention may be embodied in other specific forms without departing from the spirit or essential attributes thereof. The present embodiments are therefore to be considered in all respects as illustrative and not restrictive, the scope of the invention being indicated by the appended claims rather than by the foregoing description, and all changes which come within the meaning and range of equivalency of the claims are therefore intended to be embraced therein.
Furthermore, it should be understood that although the present description refers to embodiments, not every embodiment may contain only a single embodiment, and such description is for clarity only, and those skilled in the art should integrate the description, and the embodiments may be combined as appropriate to form other embodiments understood by those skilled in the art.

Claims (10)

1. An ROS-based simulation control platform for simulation control of an exoskeleton robot, the ROS-based simulation control platform comprising:
a control module;
the data acquisition module acquires data fed back by the exoskeleton robot and transmits the data with the control module;
the simulation display module is used for constructing an exoskeleton robot model and carrying out simulation display on the exoskeleton robot model under the control of the control system based on feedback data;
an athletic intent detection module, comprising: a plurality of movement intention detection units which subscribe the data fed back by the exoskeleton robot and carry out human movement intention identification.
2. The ROS-based simulation control platform of claim 1, wherein the data acquisition module acquires data of the exoskeleton robot end in real time by means of an existing PCI-CAN board.
3. The ROS-based simulation control platform of claim 2, wherein the data collection module publishes the collected data in the form of ROS topics, and at the same time, subscribes to joint control information of the control module and sends the information to the exoskeleton robot.
4. The ROS-based simulation control platform of claim 1, wherein the control module supports custom exoskeleton dynamics mathematical models or open source three-dimensional physical simulation platforms.
5. The ROS-based simulation control platform of claim 1, wherein when the control module supports an open-source three-dimensional physical simulation platform, a simulation control flow is executed according to the following steps:
importing the exoskeleton three-dimensional structure chart into the open source three-dimensional physical simulation platform, then adjusting and optimizing the information parameters of the constructed exoskeleton robot model, and simultaneously performing control simulation on the model and the actual system in the platform by using a low-order control algorithm by means of control algorithm nodes of the open source three-dimensional physical simulation platform;
verifying a related moment depth control algorithm, observing a simulation operation effect in a simulation platform, and performing online algorithm verification test at an actual system end by means of control information sent to a lower exoskeleton end after the control algorithm is verified;
after the algorithm verification is passed, an exoskeleton dynamics optimization model is automatically constructed based on computational power configuration of an actual system, and comparison verification is carried out on a simulation platform.
6. The ROS-based simulation control platform of claim 1, wherein the PC simulation control platform disassembles motion states during exoskeleton man-machine coupling motion as: a left foot soaring right foot support state, a two foot support state, and a right foot soaring left foot support state.
7. The ROS-based simulation control platform of claim 6,
single leg support kinetic model:
Figure DEST_PATH_IMAGE001
in the formula:
Figure 865081DEST_PATH_IMAGE002
the sum of kinetic energy of each rod piece of the exoskeleton;
Figure DEST_PATH_IMAGE003
for the weight of each rod of the exoskeletonThe sum of force potential energy;
Figure 752135DEST_PATH_IMAGE004
the sum of the elastic potential energy of the exoskeleton knee joint;
l is a Lagrange function and is equal to the difference between the total kinetic energy, the gravitational potential energy and the total elastic potential energy of the system;
Figure DEST_PATH_IMAGE005
respectively representing the generalized angular velocities of the knee and ankle joints;
Figure 58351DEST_PATH_IMAGE006
respectively representing the generalized coordinates of a sagittal plane system and a frontal plane system;
Figure DEST_PATH_IMAGE007
respectively representing the resultant force of the knee and ankle joints, namely the joint motor driving force and the human-computer interaction force.
8. The ROS-based simulation control platform of claim 7,
the 6-link kinetic equation of the exoskeleton support phase is as follows:
Figure DEST_PATH_IMAGE009
in the formula (I), the compound is shown in the specification,
Figure 310341DEST_PATH_IMAGE010
an inertia tensor array representing the robot in a sagittal plane;
Figure DEST_PATH_IMAGE011
is a matrix of coriolis forces and centrifugal forces of 6x 6;
Figure 787327DEST_PATH_IMAGE012
is a 6x1 gravity matrix;
Figure DEST_PATH_IMAGE013
is an elastic force matrix;
Figure 212492DEST_PATH_IMAGE014
Figure DEST_PATH_IMAGE015
Figure 904374DEST_PATH_IMAGE016
respectively representing a generalized position, a generalized velocity and a generalized acceleration in 6x1 dimensions.
9. The ROS-based simulation control platform of claim 6, wherein in the two-leg support state, the output torque of the left and right hip joints is based on the distance between the projected point of the exoskeleton's overall center of gravity on the line connecting the two-leg landing points and the two-leg
Figure DEST_PATH_IMAGE017
,
Figure 468210DEST_PATH_IMAGE018
The proportion distribution is as follows:
Figure DEST_PATH_IMAGE019
,
Figure 245542DEST_PATH_IMAGE020
the total torque required by the left hip joint and the right hip joint of the exoskeleton system;
other joint torques were derived from 5-bar linkage dynamics:
Figure DEST_PATH_IMAGE021
in the formula (I), the compound is shown in the specification,
Figure 943240DEST_PATH_IMAGE022
the kinetic energy sum of each connecting rod of the exoskeleton comprises a left shank, a right shank, a left thigh, a right thigh and a body;
Figure DEST_PATH_IMAGE023
the potential energy sum of each connecting rod of the exoskeleton comprises a left shank, a right shank, a left thigh and a right thigh and a body;
es is the elastic potential energy of the system knee joint.
10. An exoskeleton robot simulation control system based on ROS, comprising:
a lower exoskeleton end, the ROS-based simulation control platform of any one of claims 1 to 9;
the lower exoskeleton end comprises: the simulation control platform based on the ROS can receive data fed back by the human body posture sensing module and the interaction force detection module;
the human body posture sensing module comprises: six-axis inertial measurement sensors arranged on a back frame, angle sensors arranged at knee joints of left and right legs and pressure sensors arranged on left and right soles.
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