CN107256284A - A kind of many gait dynamic modeling methods of real-time interactive quadruped robot and system - Google Patents
A kind of many gait dynamic modeling methods of real-time interactive quadruped robot and system Download PDFInfo
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Abstract
The present invention relates to a kind of many gait dynamic modeling methods of real-time interactive quadruped robot and system, the graph visualization model of many gait dynamic systems, quadruped robot and the landform of quadruped robot is built；Information transfer is carried out using multi-threading correspondence between many gait dynamic systems and the quadruped robot and the graph visualization model of landform.The present invention carries out dynamics real-time resolving based on Vortex Dynamics Engines, based on udp protocol by way of client service end communicates in real time to graphics engine multiplexed transport robot status information, platform visual analyzing is carried out, the modeling of the dynamic system of many gait pattern insertions is completed.
Description
Technical field
The present invention relates to Dynamic Modeling in Robotics technical field, and in particular to a kind of real-time interactive quadruped robot is more
Gait dynamics modeling method and system.
Background technology
Dynamic Modeling in Robotics method is calculated to derive manually and solved using dynamics software, and the former is for simple
Robot system it is feasible, but for complicated robot system, the kinetics equation of structure is very complicated, it is difficult to obtain correct
Analytic solutions；It is relatively easy using dynamics software modeling.Current quadruped robot Dynamic Modeling mainly using ADAMS,
The dynamics softwares such as RECURDYN are modeled and some Dynamics Engines for increasing income such as ODE, although the former modeling method precision is high,
But calculate very complicated, it is difficult to ensure that the real-time of control, therefore be difficult that the control parameter correction for matching actual model machine is required, and
And expansibility is poor, secondary development is not easy to；Although the latter's expansibility is stronger, the high counting accuracy of dynamics is real with height
What when property had both not enough protrudes.
The content of the invention
To solve above-mentioned deficiency of the prior art, it is an object of the invention to provide a kind of real-time interactive quadruped robot
Many gait dynamic modeling methods and system, carry out dynamics real-time resolving based on Vortex Dynamics Engines, make full use of
Vortex pinpoint accuracy, high real-time, interactive, the high-quality modeling characteristic of high expansion, the cycle that resolves are realized using system clock frequency
Accurate timing, based on UDP (User Datagram Protocol) agreement by way of client-server end communicates in real time to
The status information of graphics engine multiplexed transport robot, carries out platform visual analyzing, completes the power of many gait pattern insertions
The modeling of system.
The purpose of the present invention is realized using following technical proposals：
The present invention provides a kind of many gait dynamic modeling methods of real-time interactive quadruped robot, and its improvements exists
In：
Build the graph visualization model of many gait dynamic systems, quadruped robot and the landform of quadruped robot；
Using many between many gait dynamic systems and the quadruped robot and the graph visualization model of landform
Thread communication carries out information transfer.
Further：The many gait dynamic systems for building quadruped robot, including：
Build quadruped robot single legged model；
The kinetic model and morphodynamics model of quadruped robot are built based on Vortex；
Joint control is set up, the expectation dynamic behavior that many gait Controlling models are produced is performed.
Further：The structure quadruped robot single legged model includes：
Build single leg kinematics model, including leg positive kinematics and inverse kinematics；
According to single leg kinematics model, leg joint force Jacobian matrix J is calculated；
Joint power model under being acted on without external force is built using Lagrangian method；
The torque that sufficient end power maps to joint is incorporated into joint power model；
It is preferred that, the leg positive kinematics formula is：
Leg inverse kinematics formula is：
θ1=atan2 (py,px)
Leg positive kinematics are to obtain homogeneous transform matrix T of the foot coordinate system relative to hip joint coordinate system, and foot is sat
Mark means the coordinate system where the rotary shaft z4 of joint, the coordinate system where the joint rotary shaft z1 that hip joint coordinate is meant；
Leg inverse kinematics is the position p=(p with respect to hip joint coordinate system by footx,py,pz) solve joint angles；
In formula：aiRepresent leg joint link lever length, si=sin θi, ci=cos θi, sij=sin (θi+θj), cij=cos
(θi+θj),θiThe joint angles in the i-th joint are represented, i represents the sequence number in joint, i=1,2,3；kfhAccorded with for front and rear leg on angle
Number the configuration factor, the corresponding k of forelegfh=1, the corresponding k of back legfh=-1；a1Represent the length of leg joint connecting rod 1 from top to bottom
Degree, a2Represent the length of leg joint link lever 2, a3Represent the length of leg joint link lever 3；c1=cos θ1,s1=sin θ1,c23=
cos(θ2+θ3),s23=sin (θ2+θ3)；θ1、θ2、θ3Respectively represent the 1st, 2, the joint angles in 3 joints；px,py,pzRepresent respectively
Foot position corresponding with respect to hip joint coordinate system x, y, z axle；
It is preferred that, the joint power model is：
The torque that sufficient end power maps to joint incorporates joint power model：
τf=JTF
Wherein：Q is joint angles, and M is joint mass matrix, and C is coriolis force matrix, and G is gravitational moment battle array, and τ drives for joint
Kinetic moment, F is sufficient end power, τfThe torque mapped for sufficient end power to joint；Joint angular acceleration, joint angle speed are represented respectively
Degree.
Further：The kinetic model and morphodynamics model that quadruped robot is built based on Vortex, bag
Include：
Based on quadruped robot three-dimensional entity model, with reference to the physical dimension and barycenter, quality of three-dimensional entity model, and assign
Quality, rotary inertia and material properties are given, the dynamic behavior of quadruped robot kinetic model is assigned；
Using constraint is hinged between the rod member of quadruped robot kinetic model, foot uses spring constraint with knee joint,
According to rod member quality, barycenter and rotary inertia information, with reference to the movement relation between rod member, auxiliary connection restriction relation is built, is based on
Relief model kinetic parameter, sets up typical step, slope operating mode, assigns landform material properties, and for different operating modes
It is reduced to collide solid accordingly, while robot foot section is reduced into capsule collision body, collision detection, shape is carried out with landform
Into quadruped robot and landform can real-time, interactive dynamic system.
Further：It is described to set up joint control, the expectation dynamic behavior that many gait Controlling models are produced is performed, bag
Include：
The real-time that dynamics is resolved is ensured using computer clock frequency, for accurate timing, and multithreading skill is used
Art is communicated；
Many gait control algolithms based on c++ object-oriented way are used in many gait dynamic systems；
Joint control is built, the robot motion that many gait dynamic systems are produced is performed；
It is preferred that, the structure joint control is：
Wherein：Joint control represents to build the drive signal in joint, θ according to the position and feedforward force information in jointdFor
Desired joint angles are calculated by single leg inverse kinematics model, θ is the position signalling for gathering joint in real time by kinetic model, profit
Resolved with Vortex Dynamics Engines real-time iterative and obtain actual joint angles；
According to dynamic system sample frequency,WithThe desired speed and actual speed in calculating joint in real time are represented respectively,
kpFor joint control scale factor；kvFor joint control differential divisor, joint decoupling is independently controlled, according to leg
The kinetic model in each joint, and joint desired locations and physical location, build joint PD control device；τffTo expect foot
Hold power FdArthrotropic mapping feedforward torque, expression formula is τff=-JTFd, J is joint force Jacobian matrix, and u is that controller is defeated
Enter；
It is preferred that, the joint PD control device is：
In formula：μpdRepresent the input of joint PD control device.
Further：The construction force scholarship and moral conduct is the graph visualization model of reproducible quadruped robot and landform,
Including：
Based on robot three-dimensional physical model, using the graphics engine module built in Vortex, quadruped robot is built
Graphical model；
Based on landform three-dimensional entity model, using the graphics engine module built in Vortex, the graphical model of landform is built；
Multithreading is used in the graph visualization task of quadruped robot and landform, and using client-server end
Mode and quadruped robot and landform kinetic model real-time Communication for Power, by the quadruped robot of dynamics real-time resolving and ground
The dynamic behavior of shape interaction is sent to by way of client-server end in graphics engine module, and dynamic behavior reproduce
Quadruped robot and landform graph visualization model.
Further：Many gait dynamic systems and the quadruped robot and the graph visualization model of landform it
Between using multi-threading correspondence carry out information transfer, including：
Using many gait dynamic systems as client, the client set based on udp protocol is built in multithreading
Connect word；
Using quadruped robot and the graph visualization model of landform as service end, build and be based in multithreading
The ServerSocket of udp protocol；
Information transfer between many gait dynamic systems and quadruped robot and the graph visualization model of landform.
A kind of dynamic (dynamical) modeling of many gaits of real-time interactive quadruped robot, it is theed improvement is that, the system
System includes：
Build module, the figure of many gait dynamic systems, quadruped robot and landform for building quadruped robot
Visualization Model；
Information transmission modular, it is visual for many gait dynamic systems and the figure of the quadruped robot and landform
Information transfer is carried out using multi-threading correspondence between change model.
Further, the structure module, including：
First builds submodule, many gait dynamic systems for building quadruped robot；
Second builds submodule, the graph visualization model for building quadruped robot and landform；
It is preferred that, first builds submodule, further comprises：
First builds subelement, for building quadruped robot single legged model；
Second builds subelement, kinetic model and morphodynamics mould for building quadruped robot based on Vortex
Type；
3rd builds subelement, for setting up joint control, performs the expectation dynamics that many gait Controlling models are produced
Behavior；
It is preferred that, second builds submodule, further comprises：
4th builds subelement, for based on robot three-dimensional physical model, using the graphics engine mould built in Vortex
Block, builds the graphical model of quadruped robot；
5th builds subelement, for based on landform three-dimensional entity model, using the graphics engine module built in Vortex,
Build the graphical model of landform；
6th builds subelement, for using multithreading skill in the graph visualization task of quadruped robot and landform
Art, and the kinetic model real-time Communication for Power by the way of client-server end with quadruped robot and landform, dynamics is real-time
The dynamic behavior that the quadruped robot of resolving is interacted with landform is sent to graphics engine module by way of client-server end
In, the graph visualization model of the reproducible quadruped robot of Cambium periodicity behavior and landform；
It is preferred that, information transmission modular, including：
Client modules：For, as client, being built in multithreading using many gait dynamic systems and being based on UDP
The client socket of agreement；
Server module, for using quadruped robot and topographical pattern Visualization Model as service end, in multithreading skill
The ServerSocket based on udp protocol is built in art；
Communication module, between many gait dynamic systems and quadruped robot and the graph visualization model of landform
Information transfer.
Further, described first subelement is built, be additionally operable to：
Determine leg positive kinematics and inverse kinematics；
According to single leg kinematics model, leg joint force Jacobian matrix is calculated；
Joint power model under being acted on without external force is built using Lagrangian method；
The torque that sufficient end power maps to joint is incorporated into joint power model；
It is preferred that：Second builds subelement, is additionally operable to：
Based on quadruped robot three-dimensional entity model, with reference to the physical dimension and barycenter, quality of three-dimensional entity model, and assign
Quality, rotary inertia and material properties are given, the dynamic behavior of quadruped robot kinetic model is assigned；
Using constraint is hinged between the rod member of quadruped robot kinetic model, foot uses spring constraint with knee joint,
According to rod member quality, barycenter and rotary inertia information, with reference to the movement relation between rod member, auxiliary connection restriction relation is built, is based on
Relief model kinetic parameter, sets up typical step, slope operating mode, assigns landform material properties, and for different operating modes
It is reduced to collide solid accordingly, while robot foot section is reduced into capsule collision body, collision detection, shape is carried out with landform
Into quadruped robot and landform can real-time, interactive dynamic system；
It is preferred that, the 3rd builds subelement, is additionally operable to：
The real-time that dynamics is resolved is ensured using computer clock frequency, for accurate timing, and multithreading skill is used
Art is communicated；
Many gait control algolithms based on c++ object-oriented way are used in many gait dynamic systems；
Joint control is built, the robot motion that many gait dynamic systems are produced is performed.
Compared with immediate prior art, the technical scheme that the present invention is provided has an advantageous effect in that：
(1) using the timing mode of computer clock frequency, timing accuracy is high, and many gait control algolithm controlling cycles are with adopting
The sample cycle, which is guaranteed, realizes the communication of client and service end using multithreading, reduces EMS memory occupation, communication reliability
It is high；By client and the real-time Communication for Power of service end, the visualization of quadruped robot and landform real-time, interactive is realized, multistep is completed
The modeling of the dynamic system of states model insertion, and personnel can realize the manipulation to robot, man-machine friendship by data-interface
Mutual property is strong, and is easy to diagnostic message failure.
(2) by merging joint PD control and torque feedforward control, the compliance control device in joint, quadruped robot are set up
There is preferably compliance when foot is contacted with ground, different gaits, highly versatile are applicable to.
(3) Dynamics Engine based on Vortex is developed, and real-time is high, and dynamics calculation accuracy is high；
(4) modeled by the way of C++ object-orienteds, expansibility is strong, is easy to secondary development.
Brief description of the drawings
Fig. 1 is the quadruped robot single legged model schematic diagram that the present invention is provided；
Fig. 2 is the quadruped robot and morphodynamics modeling procedure figure that the present invention is provided；
Fig. 3 is the quadruped robot and topographical pattern model visualization schematic diagram that the present invention is provided；
Fig. 4 is many gait patterns and dynamic (dynamical) embedded block diagram that the present invention is provided；
Fig. 5 is the structural frames for the dynamic (dynamical) modeling of many gaits of real-time interactive quadruped robot that the present invention is provided
Figure.
Embodiment
The embodiment to the present invention is described in further detail below in conjunction with the accompanying drawings.
The following description and drawings fully show specific embodiments of the present invention, to enable those skilled in the art to
Put into practice them.Other embodiments can include structure, logic, electric, process and other changes.Embodiment
Only represent possible change.Unless explicitly requested, otherwise single component and function are optional, and the order operated can be with
Change.The part of some embodiments and feature can be included in or replace part and the feature of other embodiments.This hair
The scope of bright embodiment includes the gamut of claims, and claims is all obtainable equivalent
Thing.Herein, these embodiments of the invention can individually or generally be represented that this is only with term " invention "
For convenience, and if in fact disclosing the invention more than one, it is not meant to automatically limit the scope of the application to appoint
What single invention or inventive concept.
Embodiment one,
The present invention provides a kind of many gait dynamic modeling methods of the real-time interactive quadruped robot of object-oriented, including
The structure of dynamic system, the insertion of many gait patterns, many gaits expect the execution of dynamic behavior, dynamic behavior it is visual
Change, many gait Controlling models produce desired walking motion, based on single legged model, utilize the collision detection module built in Vortex
Real-time dynamics resolve iteration and obtain joint angles, power, joint control driving are built on this basis, so as to realize four-footed machine
The desired dynamic behavior of device people, the dynamic behavior of generation is reproduced in graphical model, and can be described as with power scholarship and moral conduct
For quadruped robot virtual prototype.
S1, the graph visualization model for building many gait dynamic systems of quadruped robot, quadruped robot and landform；
The step S1 further comprises：
Step 1, quadruped robot single legged model is built；
Step 2, quadruped robot and morphodynamics model are built based on Vortex；
Used between S2, many gait dynamic systems and the quadruped robot and the graph visualization model of landform
Multi-threading correspondence carries out information transfer.
Specific steps content is as follows：
As shown in figure 1, step 1, builds quadruped robot single legged model.Specifically include：
Step 11：Single leg kinematics model, including leg positive kinematics and inverse kinematics are built, by the seat for building single leg
Mark system, using the method for coordinate homogeneous transformation, and the layout of the physical dimension, geometrical relationship and hip joint according to leg, obtain
Sufficient end is relative to the homogeneous transform matrix of hip joint and the inverse solution of sufficient end position.
Leg positive kinematics are to obtain homogeneous transform matrix T of the foot coordinate system relative to hip joint coordinate system, and foot is sat
Mark the coordinate system as where the joint rotary shaft z4 in Fig. 1 that means, hip joint coordinate mean such as the joint rotary shaft in Fig. 1
Coordinate system where z1,
In formula, aiRepresent leg joint link lever length, si=sin θi, ci=cos θi, sij=sin (θi+θj), cij=
cos(θi+θj),θiThe joint angles in the i-th joint are represented, i represents the sequence number in joint, i=1,2,3；kfhIt is front and rear leg on angle
The configuration factor of symbol, the corresponding k of forelegfh=1, the corresponding k of back legfh=-1；a1Represent leg joint connecting rod 1 from top to bottom
Length, a2Represent the length of leg joint link lever 2, a3Represent the length of leg joint link lever 3；c1=cos θ1,s1=sin θ1,c23
=cos (θ2+θ3),s23=sin (θ2+θ3)；θ1、θ2、θ3Respectively represent the 1st, 2, the joint angles in 3 joints；px,py,pzDifference table
Show foot position corresponding with respect to hip joint coordinate system x, y, z axle；
Leg inverse kinematics is the position p=(p with respect to hip joint coordinate system by footx,py,pz) joint angles are solved, ask
Solve result as follows：
θ1=atan2 (py,px)
In formula, kfhThe configuration factor for front and rear leg on angle symbol, the corresponding k of forelegfh=1, the corresponding k of back legfh
=-1.
Step 12：According to leg exercise relation, leg joint force Jacobian matrix J is solved.
Leg joint force Jacobian matrix is the power/speed and joint power/speed that foot is described based on hip joint coordinate system
Mapping relations, solving result：
Step 13：According to joint angles q, joint mass matrix M, coriolis force Matrix C, gravity matrix G, joint driven torque
τ, the joint Lagrange's dynamical equations under being acted on without external force are built using Lagrangian method.
Step 14：Foot end power F is considered to the mapping relations of joint space, the torque τ that sufficient end power is mapped to jointfIncorporate
Joint power model.
τf=JTF (3)
As shown in Figure 2 and Figure 3, step 2, quadruped robot and morphodynamics model are built based on Vortex.Vortex is
Rigid multibody dynamics engine, and be the kinetic modeling tools based on C++ object-orienteds, multi-freedom robot can be carried out
Rigid multibody dynamics is modeled and terrain modeling, and the high-quality characteristic with high accuracy, high real-time, high expansion, quadruped robot is moved
Mechanical modeling is equivalent to the virtual prototype with dynamics is built, to replace actual model machine, the actual power in its joint and position
Iteration completion can be resolved as the collision detection module Real-time dynamics built in Vortex by putting, and complete quadruped robot virtual prototype
A variety of gaits walking modeling, need to be by quadruped robot power of many gait Controlling model insertions based on Vortex secondary development
In system, and many gait Controlling models are converted into joint drive signal, complete the hoofing part of virtual prototype, it is dynamic to ensure
The real-time of mechanical system, quadruped robot Dynamic Modeling, many gait patterns, joint drive are built by multithreading
Real-time task (client), is clear analysis, the validity of diagnosis Dynamic Modeling, based on the figure module built in Vortex,
Landform and robot graph visualization analysis task (service end) are built using multithreading, being communicated by UDP in real time will be dynamic
Mechanical signal is transmitted to figure module, realizes many gait dynamic behaviors of quadruped robot in graph visualization task again
It is existing, form the complete many gait dynamic systems of quadruped robot.
Specifically include：
Step 21：Based on existing quadruped robot three-dimensional entity model, physical dimension and barycenter, the matter of reference entity
Amount, does some simplification processing, and assigns the attributes such as quality, rotary inertia, material, assigns the power of quadruped robot simulation model
Learn attribute.
Step 22：Using constraint is hinged between rod member, foot uses spring constraint with knee joint, according to rod member quality, matter
The information such as the heart, rotary inertia, with reference to the movement relation between rod member, build auxiliary connection restriction relation, realize quadruped robot mechanism
The modeling of physical model and graphical model.
Step 23：Typical walking operating mode is built according to duty requirements, by building the typical condition physics such as step, slope
Model and graphical model, and then test the landform adaptability of a variety of gait control algorithms.
Step 24：Between quadruped robot and the physical model and graphical model of landform by the way of client-server end
Real-time Communication for Power is carried out, the behavior of the robot of dynamics real-time resolving is sent to figure by way of client-server end and drawn
Graph visualization is realized in holding up.
Fig. 4 is many gait patterns and dynamic (dynamical) embedded block diagram, includes insertion, the structure of joint control of many gait patterns
Build, the introducing of multithreading, controlling cycle and the timing of the precision clock in sampling period, and the client in multithreading task
The communication of end-service end.Specifically include following steps：
Step 31：Realize that accurate timing ensures controlling cycle and sampling period using computer clock frequency.
Step 32：Multithreading is introduced in client and service end, the occupancy to main thread task internal memory is reduced, with
Ensure the reliability of communication.
Step 33：Several typical gait control algorithms are incorporated into dynamic system in the way of c++ object-orienteds, constituted
Many gait dynamic systems.
Step 34：Joint control is built, is specially：By single leg inverse kinematics model, desired joint angles θ is solvedd,
And gather the position signalling θ in joint in real time by joint position sensor, and according to system sampling frequency, the phase in Real-time solution joint
Hope speedWith actual speedIntroduce joint control scale factor kp, differential divisor kv, joint decoupling is subjected to independent control
System, according to the desired locations and physical location of the kinetic model in each joint of leg, and joint, builds joint PD control
Device, utilizes joint force Jacobian matrix J, it would be desirable to sufficient end power FdArthrotropic mapping torque τff=-JTFdFeedovered as joint
Power, builds joint control, controller input is u, realizes the control of joint position/power, and then realize the position/force control of foot
System.
It is described structure joint control be：
Wherein：Joint control represents to build the drive signal in joint, θ according to the position in joint and force informationdFor by list
Leg inverse kinematics model calculates desired joint angles, and θ is the position signalling for gathering joint in real time by kinetic model, is utilized
Vortex Dynamics Engines real-time iterative, which is resolved, obtains actual joint angles；
It is preferred that, the joint PD control device is：
Above-mentioned four step resolves (kinetic model) with reproducing necessity of dynamic behavior (graphical model) to perform dynamics
Work, the first step is to ensure the real-time that dynamics is resolved, and second step ensures the structure of client and service end communication task, the
Three steps are to produce desired robot motion using many gait Controlling models, and the 4th step is to perform many gait dynamic systems to produce
Robot motion, first two steps are the structure frameworks of kinetic model and graphical model, are concurrency relations, and rear two step is dynamics
Many gait action executings of model and graphical model, are ordinal relations.
Step 4, the communication at client-server end is built in multithreading task based on udp protocol, dynamic system is completed
Information transfer between graph visualization.Specifically include：
Step 41：Using many gait dynamic systems as client, the visitor based on udp protocol is built in multithreading task
Family end socket.
Step 42：Using quadruped robot and topographical pattern visualization tasks as service end, built in multithreading task
ServerSocket based on udp protocol.
Embodiment two,
Based on same inventive concept, it is dynamic (dynamical) that the present invention also provides a kind of many gaits of real-time interactive quadruped robot
Modeling, its structure chart as shown in figure 5, including：
Build module, the figure of many gait dynamic systems, quadruped robot and landform for building quadruped robot
Visualization Model；
Information transmission modular, it is visual for many gait dynamic systems and the figure of the quadruped robot and landform
Information transfer is carried out using multi-threading correspondence between change model.
Further, the structure module, including：
First builds submodule, many gait dynamic systems for building quadruped robot；
Second builds submodule, the graph visualization model for building quadruped robot and landform；
It is preferred that, first builds submodule, further comprises：
First builds subelement, for building quadruped robot single legged model；
Second builds subelement, kinetic model and morphodynamics mould for building quadruped robot based on Vortex
Type；
3rd builds subelement, for setting up joint control, performs the expectation dynamics that many gait Controlling models are produced
Behavior；
It is preferred that, second builds submodule, further comprises：
4th builds subelement, for based on robot three-dimensional physical model, using the graphics engine mould built in Vortex
Block, builds the graphical model of quadruped robot；
5th builds subelement, for based on landform three-dimensional entity model, using the graphics engine module built in Vortex,
Build the graphical model of landform；
6th builds subelement, for using multithreading skill in the graph visualization task of quadruped robot and landform
Art, and the kinetic model real-time Communication for Power by the way of client-server end with quadruped robot and landform, dynamics is real-time
The dynamic behavior that the quadruped robot of resolving is interacted with landform is sent to graphics engine module by way of client-server end
In, the graph visualization model of the reproducible quadruped robot of Cambium periodicity behavior and landform；
It is preferred that, information transmission modular, including：
Client modules：For, as client, being built in multithreading using many gait dynamic systems and being based on UDP
The client socket of agreement；
Server module, for using quadruped robot and topographical pattern Visualization Model as service end, in multithreading skill
The ServerSocket based on udp protocol is built in art；
Communication module, between many gait dynamic systems and quadruped robot and the graph visualization model of landform
Information transfer.
Further, described first subelement is built, be additionally operable to：
Determine leg positive kinematics and inverse kinematics；
According to single leg kinematics model, leg joint force Jacobian matrix is calculated；
Joint power model under being acted on without external force is built using Lagrangian method；
The torque that sufficient end power maps to joint is incorporated into joint power model；
It is preferred that：Second builds subelement, is additionally operable to：
Based on quadruped robot three-dimensional entity model, with reference to the physical dimension and barycenter, quality of three-dimensional entity model, and assign
Quality, rotary inertia and material properties are given, the dynamic behavior of quadruped robot kinetic model is assigned；
Using constraint is hinged between the rod member of quadruped robot kinetic model, foot uses spring constraint with knee joint,
According to rod member quality, barycenter and rotary inertia information, with reference to the movement relation between rod member, auxiliary connection restriction relation is built, is based on
Relief model kinetic parameter, sets up typical step, slope operating mode, assigns landform material properties, and for different operating modes
It is reduced to collide solid accordingly, while robot foot section is reduced into capsule collision body, collision detection, shape is carried out with landform
Into quadruped robot and landform can real-time, interactive dynamic system；
It is preferred that, the 3rd builds subelement, is additionally operable to：
The real-time that dynamics is resolved is ensured using computer clock frequency, for accurate timing, and multithreading skill is used
Art is communicated；
Many gait control algolithms based on c++ object-oriented way are used in many gait dynamic systems；
Joint control is built, the robot motion that many gait dynamic systems are produced is performed.
A kind of quadruped robot for object-oriented that the present invention is provided and the graph visualization model modelling approach of landform and
System.Dynamics real-time resolving is carried out based on Vortex Dynamics Engines, Vortex pinpoint accuracy, high friendship in real time is made full use of
Mutually, the high-quality modeling characteristic of high expansion, the resolving cycle realizes accurate timing using system clock frequency, based on UDP (User
Datagram Protocol) agreement by way of client-server end communicates in real time to graphics engine multiplexed transport robot
Status information, carry out platform visual analyzing, complete the modeling of the dynamic system of many gait patterns insertion.
It should be understood by those skilled in the art that, embodiments herein can be provided as method, system or computer program
Product.Therefore, the application can be using the reality in terms of complete hardware embodiment, complete software embodiment or combination software and hardware
Apply the form of example.Moreover, the application can be used in one or more computers for wherein including computer usable program code
The computer program production that usable storage medium is implemented on (including but is not limited to magnetic disk storage, CD-ROM, optical memory etc.)
The form of product.
The application is the flow with reference to method, equipment (system) and computer program product according to the embodiment of the present application
Figure and/or block diagram are described.It should be understood that can be by every first-class in computer program instructions implementation process figure and/or block diagram
Journey and/or the flow in square frame and flow chart and/or block diagram and/or the combination of square frame.These computer programs can be provided
The processor of all-purpose computer, special-purpose computer, Embedded Processor or other programmable data processing devices is instructed to produce
A raw machine so that produced by the instruction of computer or the computing device of other programmable data processing devices for real
The device for the function of being specified in present one flow of flow chart or one square frame of multiple flows and/or block diagram or multiple square frames.
These computer program instructions, which may be alternatively stored in, can guide computer or other programmable data processing devices with spy
Determine in the computer-readable memory that mode works so that the instruction being stored in the computer-readable memory, which is produced, to be included referring to
Make the manufacture of device, the command device realize in one flow of flow chart or multiple flows and/or one square frame of block diagram or
The function of being specified in multiple square frames.
These computer program instructions can be also loaded into computer or other programmable data processing devices so that in meter
Series of operation steps is performed on calculation machine or other programmable devices to produce computer implemented processing, thus in computer or
The instruction performed on other programmable devices is provided for realizing in one flow of flow chart or multiple flows and/or block diagram one
The step of function of being specified in individual square frame or multiple square frames.
The above embodiments are merely illustrative of the technical scheme of the present invention and are not intended to be limiting thereof, although with reference to above-described embodiment pair
The present invention is described in detail, and those of ordinary skill in the art can still enter to the embodiment of the present invention
Row modification or equivalent substitution, these any modifications or equivalent substitution without departing from spirit and scope of the invention, in application
Within pending claims of the invention.
Claims (10)
1. a kind of many gait dynamic modeling methods of real-time interactive quadruped robot, it is characterised in that：
Build the graph visualization model of many gait dynamic systems, quadruped robot and the landform of quadruped robot；
Multithreading is used between many gait dynamic systems and the quadruped robot and the graph visualization model of landform
Communication carries out information transfer.
2. many gait dynamic modeling methods as claimed in claim 1, it is characterised in that：It is described to build many of quadruped robot
Gait dynamics system, including：
Build quadruped robot single legged model；
The kinetic model and morphodynamics model of quadruped robot are built based on Vortex；
Joint control is set up, the expectation dynamic behavior that many gait Controlling models are produced is performed.
3. many gait dynamic modeling methods as claimed in claim 2, it is characterised in that：The structure quadruped robot list leg
Model includes：
Build single leg kinematics model, including leg positive kinematics and inverse kinematics；
According to single leg kinematics model, leg joint force Jacobian matrix J is calculated；
Joint power model under being acted on without external force is built using Lagrangian method；
The torque that sufficient end power maps to joint is incorporated into joint power model；
It is preferred that, the leg positive kinematics formula is：
<mrow>
<mi>T</mi>
<mo>=</mo>
<mfenced open = "[" close = "]">
<mtable>
<mtr>
<mtd>
<mrow>
<msub>
<mi>c</mi>
<mn>1</mn>
</msub>
<msub>
<mi>c</mi>
<mn>23</mn>
</msub>
</mrow>
</mtd>
<mtd>
<mrow>
<mo>-</mo>
<msub>
<mi>c</mi>
<mn>1</mn>
</msub>
<msub>
<mi>s</mi>
<mn>23</mn>
</msub>
</mrow>
</mtd>
<mtd>
<mrow>
<mo>-</mo>
<msub>
<mi>s</mi>
<mn>1</mn>
</msub>
</mrow>
</mtd>
<mtd>
<mrow>
<msub>
<mi>c</mi>
<mn>1</mn>
</msub>
<mrow>
<mo>(</mo>
<msub>
<mi>a</mi>
<mn>1</mn>
</msub>
<mo>+</mo>
<msub>
<mi>a</mi>
<mn>2</mn>
</msub>
<msub>
<mi>c</mi>
<mn>2</mn>
</msub>
<mo>+</mo>
<msub>
<mi>a</mi>
<mn>3</mn>
</msub>
<msub>
<mi>c</mi>
<mn>23</mn>
</msub>
<mo>)</mo>
</mrow>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<msub>
<mi>s</mi>
<mn>1</mn>
</msub>
<msub>
<mi>s</mi>
<mn>23</mn>
</msub>
</mrow>
</mtd>
<mtd>
<mrow>
<mo>-</mo>
<msub>
<mi>s</mi>
<mn>1</mn>
</msub>
<msub>
<mi>s</mi>
<mn>23</mn>
</msub>
</mrow>
</mtd>
<mtd>
<msub>
<mi>c</mi>
<mn>1</mn>
</msub>
</mtd>
<mtd>
<mrow>
<msub>
<mi>s</mi>
<mn>1</mn>
</msub>
<mrow>
<mo>(</mo>
<msub>
<mi>a</mi>
<mn>1</mn>
</msub>
<mo>+</mo>
<msub>
<mi>a</mi>
<mn>2</mn>
</msub>
<msub>
<mi>c</mi>
<mn>2</mn>
</msub>
<mo>+</mo>
<msub>
<mi>a</mi>
<mn>3</mn>
</msub>
<msub>
<mi>c</mi>
<mn>23</mn>
</msub>
<mo>)</mo>
</mrow>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<mo>-</mo>
<msub>
<mi>s</mi>
<mn>23</mn>
</msub>
</mrow>
</mtd>
<mtd>
<mrow>
<mo>-</mo>
<msub>
<mi>c</mi>
<mn>23</mn>
</msub>
</mrow>
</mtd>
<mtd>
<mn>0</mn>
</mtd>
<mtd>
<mrow>
<mo>-</mo>
<mrow>
<mo>(</mo>
<msub>
<mi>a</mi>
<mn>2</mn>
</msub>
<msub>
<mi>s</mi>
<mn>2</mn>
</msub>
<mo>+</mo>
<msub>
<mi>a</mi>
<mn>3</mn>
</msub>
<msub>
<mi>s</mi>
<mn>23</mn>
</msub>
<mo>)</mo>
</mrow>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mn>0</mn>
</mtd>
<mtd>
<mn>0</mn>
</mtd>
<mtd>
<mn>0</mn>
</mtd>
<mtd>
<mn>1</mn>
</mtd>
</mtr>
</mtable>
</mfenced>
</mrow>
Leg inverse kinematics formula is：
θ1=atan2 (py,px)
<mrow>
<msub>
<mi>&theta;</mi>
<mn>3</mn>
</msub>
<mo>=</mo>
<mo>-</mo>
<msub>
<mi>k</mi>
<mrow>
<mi>f</mi>
<mi>h</mi>
</mrow>
</msub>
<mo>&lsqb;</mo>
<mi>&pi;</mi>
<mo>-</mo>
<mi>arccos</mi>
<mrow>
<mo>(</mo>
<mfrac>
<mrow>
<msubsup>
<mi>a</mi>
<mn>2</mn>
<mn>2</mn>
</msubsup>
<mo>+</mo>
<msubsup>
<mi>a</mi>
<mn>3</mn>
<mn>2</mn>
</msubsup>
<mo>-</mo>
<msup>
<mrow>
<mo>(</mo>
<msqrt>
<mrow>
<msubsup>
<mi>p</mi>
<mi>x</mi>
<mn>2</mn>
</msubsup>
<mo>+</mo>
<msubsup>
<mi>p</mi>
<mi>y</mi>
<mn>2</mn>
</msubsup>
</mrow>
</msqrt>
<mo>-</mo>
<msub>
<mi>a</mi>
<mn>1</mn>
</msub>
<mo>)</mo>
</mrow>
<mn>2</mn>
</msup>
<mo>-</mo>
<msubsup>
<mi>p</mi>
<mi>z</mi>
<mn>2</mn>
</msubsup>
</mrow>
<mrow>
<mn>2</mn>
<msub>
<mi>a</mi>
<mn>2</mn>
</msub>
<msub>
<mi>a</mi>
<mn>3</mn>
</msub>
</mrow>
</mfrac>
<mo>)</mo>
</mrow>
<mo>&rsqb;</mo>
</mrow>
<mrow>
<msub>
<mi>&theta;</mi>
<mn>2</mn>
</msub>
<mo>=</mo>
<msub>
<mi>k</mi>
<mrow>
<mi>f</mi>
<mi>h</mi>
</mrow>
</msub>
<mrow>
<mo>{</mo>
<mrow>
<mi>arcsin</mi>
<mrow>
<mo>&lsqb;</mo>
<mfrac>
<mrow>
<msub>
<mi>a</mi>
<mn>3</mn>
</msub>
<mi>sin</mi>
<mrow>
<mo>(</mo>
<mrow>
<mi>&pi;</mi>
<mo>+</mo>
<msub>
<mi>k</mi>
<mrow>
<mi>f</mi>
<mi>h</mi>
</mrow>
</msub>
<msub>
<mi>&theta;</mi>
<mn>3</mn>
</msub>
</mrow>
<mo>)</mo>
</mrow>
</mrow>
<msqrt>
<mrow>
<msup>
<mrow>
<mo>(</mo>
<mrow>
<msqrt>
<mrow>
<msubsup>
<mi>p</mi>
<mi>x</mi>
<mn>2</mn>
</msubsup>
<mo>+</mo>
<msubsup>
<mi>p</mi>
<mi>y</mi>
<mn>2</mn>
</msubsup>
</mrow>
</msqrt>
<mo>-</mo>
<msub>
<mi>a</mi>
<mn>1</mn>
</msub>
</mrow>
<mo>)</mo>
</mrow>
<mn>2</mn>
</msup>
<mo>+</mo>
<msubsup>
<mi>p</mi>
<mi>z</mi>
<mn>2</mn>
</msubsup>
</mrow>
</msqrt>
</mfrac>
<mo>&rsqb;</mo>
</mrow>
</mrow>
<mo>}</mo>
</mrow>
<mo>-</mo>
<mi>a</mi>
<mi>tan</mi>
<mn>2</mn>
<mrow>
<mo>(</mo>
<mrow>
<msub>
<mi>p</mi>
<mi>z</mi>
</msub>
<mo>,</mo>
<msqrt>
<mrow>
<msubsup>
<mi>p</mi>
<mi>x</mi>
<mn>2</mn>
</msubsup>
<mo>+</mo>
<msubsup>
<mi>p</mi>
<mi>y</mi>
<mn>2</mn>
</msubsup>
</mrow>
</msqrt>
<mo>-</mo>
<msub>
<mi>a</mi>
<mn>1</mn>
</msub>
</mrow>
<mo>)</mo>
</mrow>
</mrow>
Leg positive kinematics are to obtain foot coordinate system relative to the homogeneous transform matrix T of hip joint coordinate system, foot coordinate system
Coordinate system where articulations digitorum manus rotary shaft z4, the coordinate system where the joint rotary shaft z1 that hip joint coordinate is meant；
Leg inverse kinematics is the position p=(p with respect to hip joint coordinate system by footx,py,pz) solve joint angles；
In formula：aiRepresent leg joint link lever length, si=sin θi, ci=cos θi, sij=sin (θi+θj), cij=cos (θi+
θj),θiThe joint angles in the i-th joint are represented, i represents the sequence number in joint, i=1,2,3；kfhIt is front and rear leg on angle symbol
Configure the factor, the corresponding k of forelegfh=1, the corresponding k of back legfh=-1；a1The length of leg joint connecting rod 1 from top to bottom is represented,
a2Represent the length of leg joint link lever 2, a3Represent the length of leg joint link lever 3；c1=cos θ1,s1=sin θ1,c23=cos
(θ2+θ3),s23=sin (θ2+θ3)；θ1、θ2、θ3Respectively represent the 1st, 2, the joint angles in 3 joints；px,py,pzFoot is represented respectively
Portion position corresponding with respect to hip joint coordinate system x, y, z axle；
It is preferred that, the joint power model is：
<mrow>
<mi>M</mi>
<mover>
<mi>q</mi>
<mo>&CenterDot;&CenterDot;</mo>
</mover>
<mo>+</mo>
<mi>C</mi>
<mover>
<mi>q</mi>
<mo>&CenterDot;</mo>
</mover>
<mo>+</mo>
<mi>G</mi>
<mo>=</mo>
<mi>&tau;</mi>
</mrow>
1
The torque that sufficient end power maps to joint incorporates joint power model：
<mrow>
<mi>M</mi>
<mover>
<mi>q</mi>
<mo>&CenterDot;&CenterDot;</mo>
</mover>
<mo>+</mo>
<mi>C</mi>
<mover>
<mi>q</mi>
<mo>&CenterDot;</mo>
</mover>
<mo>+</mo>
<mi>G</mi>
<mo>=</mo>
<mi>&tau;</mi>
<mo>+</mo>
<msub>
<mi>&tau;</mi>
<mi>f</mi>
</msub>
</mrow>
τf=JTF
Wherein：Q is joint angles, and M is joint mass matrix, and C is coriolis force matrix, and G is gravitational moment battle array, and τ is joint drive power
Square, F is sufficient end power, τfThe torque mapped for sufficient end power to joint；Joint angular acceleration, joint angular speed, J are represented respectively
For Jacobian matrix.
4. many gait dynamic modeling methods as claimed in claim 2, it is characterised in that：It is described that four-footed is built based on Vortex
Kinetic model and the morphodynamics model of robot, including：
Based on quadruped robot three-dimensional entity model, with reference to the physical dimension and barycenter, quality of three-dimensional entity model, and matter is assigned
Amount, rotary inertia and material properties, assign the dynamic behavior of quadruped robot kinetic model；
Using constraint is hinged between the rod member of quadruped robot kinetic model, foot uses spring constraint with knee joint, according to
Rod member quality, barycenter and rotary inertia information, with reference to the movement relation between rod member, build auxiliary connection restriction relation, based on landform
Model kinetic parameter, sets up typical step, slope operating mode, assigns landform material properties, and simplify for different operating modes
For corresponding collision solid, while robot foot section is reduced into capsule collision body, collision detection is carried out with landform, four are formed
Biped robot and landform can real-time, interactive dynamic system.
5. many gait dynamic modeling methods as claimed in claim 2, it is characterised in that：It is described to set up joint control, hold
The expectation dynamic behavior that many gait Controlling models of row are produced, including：
The real-time that dynamics is resolved is ensured using computer clock frequency, entered for accurate timing, and using multithreading
Row communication；
Many gait control algolithms based on c++ object-oriented way are used in dynamic system；
Joint control is built, the robot motion that dynamic system is produced is performed；
It is preferred that, the structure joint control is：
<mrow>
<mi>u</mi>
<mo>=</mo>
<msub>
<mi>k</mi>
<mi>p</mi>
</msub>
<mrow>
<mo>(</mo>
<msub>
<mi>&theta;</mi>
<mi>d</mi>
</msub>
<mo>-</mo>
<mi>&theta;</mi>
<mo>)</mo>
</mrow>
<mo>+</mo>
<msub>
<mi>k</mi>
<mi>v</mi>
</msub>
<mrow>
<mo>(</mo>
<msub>
<mover>
<mi>&theta;</mi>
<mo>&CenterDot;</mo>
</mover>
<mi>d</mi>
</msub>
<mo>-</mo>
<mover>
<mi>&theta;</mi>
<mo>&CenterDot;</mo>
</mover>
<mo>)</mo>
</mrow>
<mo>+</mo>
<msub>
<mi>&tau;</mi>
<mrow>
<mi>f</mi>
<mi>f</mi>
</mrow>
</msub>
</mrow>
Wherein：Joint control represents to build the drive signal in joint, θ according to the position and feedforward force information in jointdFor by single leg
Inverse kinematics model calculates desired joint angles, and θ is the position signalling for gathering joint in real time by kinetic model, is utilized
Vortex Dynamics Engines real-time iterative, which is resolved, obtains actual joint angles；
According to dynamic system sample frequency,WithThe desired speed and actual speed in calculating joint in real time, k are represented respectivelypFor
Joint control scale factor；kvFor joint control differential divisor, joint decoupling is independently controlled, according to leg each
The kinetic model in joint, and joint desired locations and physical location, build joint PD control device；τffTo expect sufficient end power
FdArthrotropic mapping feedforward torque, expression formula is τff=-JTFdJ is joint force Jacobian matrix, and u inputs for controller；
It is preferred that, the joint PD control device is：
<mrow>
<msub>
<mi>&mu;</mi>
<mrow>
<mi>p</mi>
<mi>d</mi>
</mrow>
</msub>
<mo>=</mo>
<msub>
<mi>k</mi>
<mi>p</mi>
</msub>
<mrow>
<mo>(</mo>
<msub>
<mi>&theta;</mi>
<mi>d</mi>
</msub>
<mo>-</mo>
<mi>&theta;</mi>
<mo>)</mo>
</mrow>
<mo>+</mo>
<msub>
<mi>k</mi>
<mi>v</mi>
</msub>
<mrow>
<mo>(</mo>
<msub>
<mover>
<mi>&theta;</mi>
<mo>&CenterDot;</mo>
</mover>
<mi>d</mi>
</msub>
<mo>-</mo>
<mover>
<mi>&theta;</mi>
<mo>&CenterDot;</mo>
</mover>
<mo>)</mo>
</mrow>
</mrow>
In formula：μpdRepresent the input of joint PD control device.
6. many gait dynamic modeling methods as claimed in claim 1, it is characterised in that：The construction force scholarship and moral conduct is can be again
Existing quadruped robot and the graph visualization model of landform, including：
Based on robot three-dimensional physical model, using the graphics engine module built in Vortex, the figure of quadruped robot is built
Model；
Based on landform three-dimensional entity model, using the graphics engine module built in Vortex, the graphical model of landform is built；
Multithreading is used in the graph visualization task of quadruped robot and landform, and using the side at client-server end
Formula and quadruped robot and the graphical model real-time Communication for Power of landform, the quadruped robot of dynamics real-time resolving is interacted with landform
Dynamic behavior be sent to by way of client-server end in graphics engine module, the reproducible four-footed of dynamic behavior
The graph visualization model of robot and landform.
7. many gait dynamic modeling methods as claimed in claim 1, it is characterised in that：Many gait dynamic systems with
Information transfer is carried out using multi-threading correspondence between the quadruped robot and the graph visualization model of landform, including：
Using many gait dynamic systems as client, the client socket based on udp protocol is built in multithreading；
Using quadruped robot and the graph visualization model of landform as service end, built in multithreading based on UDP associations
The ServerSocket of view；
Information transfer between many gait dynamic systems and quadruped robot and the graph visualization model of landform.
8. the dynamic (dynamical) modeling of a kind of many gaits of real-time interactive quadruped robot, it is characterised in that the system includes：
Module is built, it is visual for building the figure of many gait dynamic systems, quadruped robot and landform of quadruped robot
Change model；
Information transmission modular, for many gait dynamic systems and the quadruped robot and the graph visualization mould of landform
Information transfer is carried out using multi-threading correspondence between type.
9. modeling as claimed in claim 8, it is characterised in that the structure module, including：
First builds submodule, many gait dynamic systems for building quadruped robot；
Second builds submodule, the graph visualization model for building quadruped robot and landform；
It is preferred that, first builds submodule, further comprises：
First builds subelement, for building quadruped robot single legged model；
Second builds subelement, kinetic model and morphodynamics model for building quadruped robot based on Vortex；
3rd builds subelement, for setting up joint control, performs the expectation dynamic behavior that many gait Controlling models are produced；
It is preferred that, second builds submodule, further comprises：
4th builds subelement, for based on robot three-dimensional physical model, using the graphics engine module built in Vortex, structure
Build the graphical model of quadruped robot；
5th builds subelement, for based on landform three-dimensional entity model, using the graphics engine module built in Vortex, builds
The graphical model of landform；
6th builds subelement, for using multithreading in the graph visualization task of quadruped robot and landform, and
With quadruped robot and the kinetic model real-time Communication for Power of landform by the way of client-server end, by dynamics real-time resolving
The dynamic behavior that is interacted with landform of quadruped robot be sent to by way of client-server end in graphics engine module,
The graph visualization model of the reproducible quadruped robot of Cambium periodicity behavior and landform；
It is preferred that, information transmission modular, including：
Client modules：For, as client, being built in multithreading using many gait dynamic systems and being based on udp protocol
Client socket；
Server module, for using quadruped robot and topographical pattern Visualization Model as service end, in multithreading
Build the ServerSocket based on udp protocol；
Communication module, for the information between many gait dynamic systems and quadruped robot and the graph visualization model of landform
Transmission.
10. modeling as claimed in claim 9, it is characterised in that described first builds subelement, is additionally operable to：
Determine leg positive kinematics and inverse kinematics；
According to single leg kinematics model, leg joint force Jacobian matrix is calculated；
Joint power model under being acted on without external force is built using Lagrangian method；
The torque that sufficient end power maps to joint is incorporated into joint power model；
It is preferred that：Second builds subelement, is additionally operable to：
Based on quadruped robot three-dimensional entity model, with reference to the physical dimension and barycenter, quality of three-dimensional entity model, and matter is assigned
Amount, rotary inertia and material properties, assign the dynamic behavior of quadruped robot kinetic model；
Using constraint is hinged between the rod member of quadruped robot kinetic model, foot uses spring constraint with knee joint, according to
Rod member quality, barycenter and rotary inertia information, with reference to the movement relation between rod member, build auxiliary connection restriction relation, based on landform
Model kinetic parameter, sets up typical step, slope operating mode, assigns landform material properties, and simplify for different operating modes
For corresponding collision solid, while robot foot section is reduced into capsule collision body, collision detection is carried out with landform, four are formed
Biped robot and landform can real-time, interactive dynamic system；
It is preferred that, the 3rd builds subelement, is additionally operable to：
The real-time that dynamics is resolved is ensured using computer clock frequency, entered for accurate timing, and using multithreading
Row communication；
Many gait control algolithms based on c++ object-oriented way are used in many gait dynamic systems；
Joint control is built, the robot motion that many gait dynamic systems are produced is performed.
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| CN108614427A (en) * | 2018-06-07 | 2018-10-02 | 中国北方车辆研究所 | A kind of quadruped robot stress control method and device |
| CN108860360A (en) * | 2018-08-01 | 2018-11-23 | 清华大学深圳研究生院 | A kind of system of quadruped robot obstacle jump |
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| CN113705049A (en) * | 2021-08-26 | 2021-11-26 | 哈尔滨工业大学 | Soft robot dynamics simulation method |
| CN113821935A (en) * | 2021-09-30 | 2021-12-21 | 合肥工业大学 | Method and system for establishing dynamic model based on symmetric constraint |
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| CN114879711A (en) * | 2022-05-23 | 2022-08-09 | 中国北方车辆研究所 | Modularized motion control system of legged bionic robot |
| CN114879711B (en) * | 2022-05-23 | 2024-05-28 | 中国北方车辆研究所 | Modularized motion control system of leg-foot type bionic robot |
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