CN113954079B - Universal mathematical characterization method for homogeneous modular robot - Google Patents
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Abstract
The embodiment of the invention provides a universal mathematical characterization method for a homogeneous modular robot, which realizes the universal mathematical characterization of the homogeneous modular robot and comprises the following steps: obtaining a three-dimensional model of a homogeneous modular robot and a single-module three-dimensional model; then acquiring a matrix set of connection orientation relations between the active components and the passive components, the number, the types and the arrangement of the interfaces and the interfaces in the single module; establishing a single module body center and an interface coordinate system, and obtaining a homogeneous transformation matrix of the interface coordinate system relative to a body center coordinate system; further obtaining a single-module general mathematical representation of the homogeneous modular robot; obtaining mathematical representation results of each single module according to the three-dimensional model of the robot; and finally, constructing a common mathematical characterization method of the homogeneous modular robot to obtain the common mathematical characterization of the homogeneous modular robot. According to the technical scheme provided by the embodiment of the invention, the mathematical characterization of the homogeneous modular robot can be realized, and a mathematical model basis is provided for the follow-up research aiming at the modular robot.
Description
[ technical field ] A method for producing a semiconductor device
The invention relates to a general mathematical characterization method for a homogeneous modular robot, and belongs to the field of robot mathematical characterization.
[ background of the invention ]
With the continuous promotion of industrialization and informatization and the continuous improvement of the cost of human resources, a large number of special robots are widely applied to agriculture, industry and service industry for carrying out the work of repeatability, danger and incapability of direct human intervention. With the maturity of technical conditions, homogeneous modular robots capable of changing configurations according to work tasks are receiving more and more attention and research.
The use of the robot needs to be based on the establishment of a mathematical model, so a mathematical representation method capable of accurately expressing the state information of each module in the modular robot is needed, which is an application premise of the modular robot. Most of the existing modularized robots aim at heterogeneous modularized robots, the characterization mode has no universality, and once module information is changed, a characterization method needs to be redesigned; and a few characterization methods related to the homogeneous modular robot are only suitable for the modular robot with a symmetrical structure and cannot be generalized. Therefore, the research of the universal mathematical characterization method of the homogeneous modular robot has important theoretical research value.
[ summary of the invention ]
In view of this, the present invention provides a general mathematical characterization method for homogeneous modular robots, so as to implement mathematical characterization of homogeneous modular robots.
The embodiment of the invention provides a general mathematical characterization method for a homogeneous modular robot, which comprises the following steps:
obtaining a three-dimensional model of the homogeneous modular robot and forming a single-module three-dimensional model of the homogeneous modular robot;
according to a single-module three-dimensional model forming the homogeneous modular robot, combining a single-module core motor arrangement mode, obtaining the number, the type and the arrangement of interfaces of an active component, a passive component and a single module in the single module;
establishing a single module body center and an interface coordinate system establishing rule according to a single module three-dimensional model forming the homogeneous modular robot, and obtaining a plurality of coordinate systems of the single module body center and the interface thereof and a homogeneous transformation matrix of the interface coordinate system relative to the single module body center coordinate system;
acquiring a single-module interface connection orientation relation matrix set according to a single-module three-dimensional model forming the homogeneous modular robot;
constructing a single-module general mathematical characterization method of the homogeneous modular robot according to the active components and the passive components in the single module, the number of interfaces of the single module, the types of the interfaces, the arrangement of the interfaces, a homogeneous transformation matrix of an interface coordinate system relative to a single-module body center coordinate system and a single-module interface connection orientation relation matrix set, and obtaining a general mathematical characterization of the single module of the homogeneous modular robot;
reading the mathematical characterization result of each single module in the homogeneous modular robot according to the three-dimensional model of the homogeneous modular robot and the general mathematical characterization of the single module of the homogeneous modular robot, constructing a general mathematical characterization method of the homogeneous modular robot, obtaining the general mathematical characterization of the homogeneous modular robot,
the homogeneous modular robot is characterized in that the structures and functions of all modules of the robot are completely the same.
In the method, according to the single-module three-dimensional model forming the homogeneous modular robot, a single-module body center and an interface coordinate system establishing rule are established, and a plurality of coordinate systems of the single-module body center and the interface thereof and a homogeneous transformation matrix of the interface coordinate system relative to the single-module body center coordinate system are obtained:
single module body center coordinate system { C } and interface coordinate system { S } thereof i }(i＝1,2,...,n surf_con ) The establishment rule is as follows:
a body center coordinate system { C }, wherein the origin of the coordinate system is fixed on the intersection point of the output shaft of the single-module spindle motor and the dividing plane; the z axis is collinear with the output shaft of the body core motor, and the direction is the torque output direction of the body core motor; the x axis is parallel to the single module dividing plane, and the direction is selected to be the third quadrant direction as the positive direction; the y-axis is determined according to the right hand rule, y = zxx;
interface coordinate system S i }(i＝1,2,...,n surf_con ) The origin of the coordinate system is fixed at the geometric center of the interface plane; the z-axis is vertical to the interface plane, and the direction points to the outside of the single module; the x axis is parallel to the interface plane, and the direction is selected to be the third quadrant direction as the positive direction; the y-axis is determined according to the right hand rule, y = zxx;
the total number of the interfaces of the single module is n surf_con 。
In the method, according to the single-module three-dimensional model forming the homogeneous modular robot, the single-module body center and the interface coordinate system establishing rule are established, a plurality of coordinate systems of the single-module body center and the interface thereof and a homogeneous transformation matrix of the interface coordinate system relative to the single-module body center coordinate system are obtained
Wherein, the first and the second end of the pipe are connected with each other,
representing an interface coordinate system S i }(i＝1,2,...,n surf_con ) A rotation transformation matrix relative to the body center coordinate system { C }, based on the transformation matrix>
Representing the interface coordinate system S i }(i＝1,2,...,n surf_con ) And (3) reading parameters in a translation transformation matrix relative to the body center coordinate system { C } through the three-dimensional model parameters of the single module.
In the method, a single-module interface connection orientation relation matrix set is obtained according to a single-module three-dimensional model forming the homogeneous modular robot:
sequentially determining a rotation transformation homogeneous transformation matrix relative to an initial interface coordinate system by determining the arrangement mode of positioning devices on the interface according to the single-module three-dimensional model;
and reading the rotation parameters of the interface positioning device in the three-dimensional model to obtain each element in the matrix.
In the method, a homogeneous modular robot single-module general mathematical characterization method is constructed according to the number of the active components and the passive components in the single module, the number of the interfaces of the single module, the types of the interfaces, the arrangement of the interfaces, a homogeneous transformation matrix of an interface coordinate system relative to a single module body center coordinate system, and a single-module interface connection orientation relation matrix set, so as to obtain a general mathematical characterization of the homogeneous modular robot single module:
wherein, the ID represents the design number of the current module; n is surf_con Representing the number of face interfaces of a single module; a is a i (i＝1,2,...,n surf_con ) Indicates the component type, a, to which the interface i belongs i =0 denotes that the component type of the interface i is a passive component and cannot actively output torque, a i =1 denotes that the type of component to which the interface i belongs is active component, which can be activeOutputting the torque; b i (i＝1,2,...,n surf_con ) Indicates the type of interface i, b i =0 denotes that interface i is a female interface and cannot actively output torque, b i =1 indicates that the interface i is a male interface and can actively output torque; d is a radical of i (i＝1,2,...,n surf_con ) Indicating the state of interface i, d i =0 denotes that the interface i is in idle state, d i =1 indicates that the state of the interface i is connected; e.g. of the type i (i＝1,2,...,n surf_con ) A module number indicating a state of connection with the interface i; f. of i (i＝1,2,...,n surf_con ) A module interface number indicating a state of connection with the interface i; g i (i＝1,2,...,n surf_con ) Representing the connection orientation relation of the interface i; and all parameters in the matrix are obtained by reading parameters of the single-module three-dimensional model.
In the method, the mathematical characterization results of the single modules in the homogeneous modular robot are read according to the homogeneous modular robot three-dimensional model and the universal mathematical characterization of the single modules of the homogeneous modular robot, and a universal mathematical characterization method of the homogeneous modular robot is constructed to obtain the universal mathematical characterization of the homogeneous modular robot:
the mathematical characterization result of each single module in the homogeneous modular robot is as follows:
wherein n is topo_num Representing the number of modules, in a homogeneous modular robot i (i＝1,2,...,n topo_module ) The method is characterized in that a single-module general mathematical characterization method of the homogeneous modular robot is used for describing results obtained by a three-dimensional model of the homogeneous modular robot;
the general mathematical characterization method of the homogeneous modular robot comprises the following steps:
by sequential extraction
Numbering each module in the set to obtain momentsArray M:
wherein m is i (i＝1,2,...,n topo_module ) Representing the serial numbers of all modules in the three-dimensional model of the homogeneous modular robot;
by sequential extraction
D for each interface in the set i (i＝1,2,...,n surf_con )、e i (i＝1,2,...,n surf_con )、f i (i＝1,2,...,n surf_con ) Obtaining a matrix C:
wherein, c ij (i＝1,2,...,n topo_module ；j＝1,2,...,n topo_module )∈{1，...，n surf_con Denotes the module m i And module m j Connected interface number, when i = j, c ij ＝0(i＝1,2,...,n topo_module ；j＝1,2,...,n topo_module )，n surf_con Representing the number of face interfaces of a single module;
by extracting { module in order 1 ,module 1 ,...,module topo_module G for each interface in the set i (i＝1,2,...,n surf_con ) Obtaining a matrix CO:
wherein, co ij (i＝1,2,...,n topo_module ；j＝1,2,...,n topo_module ) A representation module m i And module m j When i = j, co ij ＝0(i＝1,2,...,n topo_module ；j＝1,2,...,n topo_module )。
According to the technical scheme, the embodiment of the invention has the following beneficial effects:
according to the technical scheme of the embodiment of the invention, a homogeneous modular robot three-dimensional model and a single-module three-dimensional model forming the homogeneous modular robot are obtained; according to a single-module three-dimensional model forming the homogeneous modular robot, combining a single-module core motor arrangement mode, obtaining the number, the type and the arrangement of interfaces of an active component, a passive component and a single module in the single module; establishing a single module body center and an interface coordinate system establishing rule according to a single module three-dimensional model forming the homogeneous modular robot, and obtaining a plurality of coordinate systems of the single module body center and the interface thereof and a homogeneous transformation matrix of the interface coordinate system relative to the single module body center coordinate system; acquiring a single-module interface connection orientation relation matrix set according to a single-module three-dimensional model forming the homogeneous modular robot; constructing a single-module general mathematical characterization method of the homogeneous modular robot according to the active components and the passive components in the single module, the number of interfaces of the single module, the types of the interfaces, the arrangement of the interfaces, a homogeneous transformation matrix of an interface coordinate system relative to a single-module body center coordinate system and a single-module interface connection orientation relation matrix set, and obtaining a general mathematical characterization of the single module of the homogeneous modular robot; according to the three-dimensional model of the homogeneous modular robot and the universal mathematical characterization of the single modules of the homogeneous modular robot, the mathematical characterization results of the single modules in the homogeneous modular robot are read, a universal mathematical characterization method of the homogeneous modular robot is constructed, and the universal mathematical characterization of the homogeneous modular robot is obtained, so that the mathematical characterization of the homogeneous modular robot can be realized, and a mathematical model basis is provided for the follow-up research aiming at the modular robot.
[ description of the drawings ]
In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings needed to be used in the embodiments will be briefly described below, and it is obvious that the drawings in the following description are only some embodiments of the present invention, and it is obvious for those skilled in the art to obtain other drawings without creativity and labor.
FIG. 1 is a schematic flow chart of a general mathematical characterization method for a homogeneous modular robot according to an embodiment of the present invention;
FIG. 2 is a schematic diagram of a three-dimensional model of a homogeneous modular robot according to an embodiment of the present invention;
FIG. 3 is a schematic diagram of a single-module three-dimensional model of a homogeneous modular robot according to an embodiment of the present invention;
FIG. 4 is a diagram illustrating the result of partitioning between active and passive components of a single module according to an embodiment of the present invention;
FIG. 5 is a schematic diagram illustrating the result of establishing the coordinate system of the single module body core and the interface in the embodiment of the present invention.
[ EXAMPLES ]
For better understanding of the technical solutions of the present invention, the following detailed descriptions of the embodiments of the present invention are provided with reference to the accompanying drawings.
It should be understood that the described embodiments are only some embodiments of the invention, and not all embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
An embodiment of the present invention provides a general mathematical characterization method for a homogeneous modular robot, please refer to fig. 1, which is a flow diagram of the general mathematical characterization method for a homogeneous modular robot according to the embodiment of the present invention, and as shown in fig. 1, the method includes the following steps:
101, obtaining a three-dimensional model of a homogeneous modular robot and a single-module three-dimensional model forming the homogeneous modular robot;
specifically, a schematic diagram of a three-dimensional model of a homogeneous modular robot is shown in fig. 2, a schematic diagram of a three-dimensional model of a single module constituting the homogeneous modular robot is shown in fig. 3, numbers 1, 9, 16, and 17 denote interface planes, numbers 2, 8, 15, and 18 denote interfaces, numbers 3, 6, 10, and 14 denote positioning devices, numbers 4 and 13 denote interface motor bodies, numbers 5 and 12 denote interface motor output shafts, number 7 denotes a single module division plane, number 11 denotes a body center motor body, and number 19 denotes a body center motor output shaft.
102, obtaining the number, the type and the arrangement of interfaces of an active component and a passive component in a single module and the single module according to a single module three-dimensional model forming the homogeneous modular robot and by combining a single module body core motor arrangement mode;
specifically, the connecting portion of the single module core motor main body is an active component, the connecting portion of the single module core motor output shaft is defined as a passive component, and the dividing result of the active component and the passive component of the single module is shown in fig. 4.
According to the single-module three-dimensional model diagram shown in fig. 3, interface information is read to obtain:
the interface 2 is positioned on the passive component, is a public interface and is idle at the current state;
the interface 8 is positioned on the active component, is a female interface and is idle at the current state;
the interface 15 is positioned on the active component, is a female interface and is idle at the current state;
the interface 18 is positioned in the passive component and is a public interface, and the current state of the interface is idle;
103, constructing a single module body center and an interface coordinate system establishing rule according to a single module three-dimensional model forming the homogeneous modular robot, and obtaining a plurality of coordinate systems of the single module body center and the interface thereof and a homogeneous transformation matrix of the interface coordinate system relative to the single module body center coordinate system;
specifically, a single module body center coordinate system { C } and an interface coordinate system { S } thereof i }(i＝1,2,...,n surf_con ) The establishment rule is as follows:
a body center coordinate system { C }, wherein the origin of the coordinate system is fixed on the intersection point of the output shaft of the single-module spindle motor and the dividing plane; the z axis is collinear with the output shaft of the body core motor, and the direction is the torque output direction of the body core motor; the x axis is parallel to the single module dividing plane, and the direction is selected to be the third quadrant direction as the positive direction; the y-axis is determined according to the right hand rule, y = zxx;
interface coordinate system S i }(i＝1,2,...,n surf_con ) The origin of the coordinate system is fixed at the geometric center of the interface plane; the z-axis is vertical to the interface plane, and the direction points to the outside of the single module; the x axis is parallel to the interface plane, and the direction is selected to be the third quadrant direction as the positive direction; the y-axis is determined according to the right hand rule, y = zxx;
the total number of the interfaces of the single module is n surf_con ；
The result of establishing the single module body center and the interface coordinate system is shown in fig. 5.
Homogeneous transformation matrix of interface coordinate system relative to single module body center coordinate system
Wherein the content of the first and second substances,
representing the interface coordinate system S i }(i＝1,2,...,n surf_con ) A rotation transformation matrix with respect to the body-centered coordinate system C, device for selecting or keeping>
Representing the interface coordinate system S i }(i＝1,2,...,n surf_con ) The parameters in the translation transformation matrix corresponding to the body center coordinate system { C } are obtained by reading the parameters of the three-dimensional model of the single module;
according to the single-module three-dimensional model schematic diagram shown in fig. 3, the homogeneous transformation matrix result is obtained as follows:
104, acquiring a single-module interface connection orientation relation matrix set according to a single-module three-dimensional model forming the homogeneous modular robot;
specifically, according to the single-module three-dimensional model, a rotation transformation homogeneous transformation matrix relative to an initial interface coordinate system is sequentially determined by determining the arrangement mode of positioning devices on the interface;
reading each element in the matrix through the rotation parameters of an interface positioning device in the three-dimensional model;
according to the single module three-dimensional model schematic diagram shown in fig. 3, the set of the single module interface connection orientation relation matrixes is read as follows:
there are 2 kinds of connection orientation relations, and the corresponding homogeneous transformation matrix is S T O1 、 S T O2 ，
105, constructing a single-module general mathematical characterization method of the homogeneous modular robot according to the number, types and arrangement of interfaces of the single module, a homogeneous transformation matrix of an interface coordinate system relative to a single-module body center coordinate system and a single-module interface connection orientation relation matrix set of active components and passive components in the single module, and obtaining a general mathematical characterization of the single module of the homogeneous modular robot;
specifically, the universal mathematical characterization of the homogeneous modular robot single module is as follows:
wherein, the ID represents the design number of the current module; n is surf_con Representing the number of face interfaces of a single module; a is i (i＝1,2,...,n surf_con ) Indicates the component type, a, to which the interface i belongs i =0 denotes that the component type of the interface i is a passive component and cannot actively output torque, a i =1 represents that the type of the component to which the interface i belongs is an active component, and can actively output torque;b i (i＝1,2,...,n surf_con ) Indicates the type of interface i, b i =0 denotes that interface i is a female interface and cannot actively output torque, b i =1 indicates that the interface i is a male interface and can actively output torque; d i (i＝1,2,...,n surf_con ) Indicating the state of interface i, d i =0 denotes that the interface i is in idle state, d i =1 indicates that the state of the interface i is connected; e.g. of the type i (i＝1,2,...,n surf_con ) A module number indicating a state of connection with the interface i; f. of i (i＝1,2,...,n surf_con ) A module interface number indicating a state of connection with the interface i; g is a radical of formula i (i＝1,2,...,n surf_con ) Representing the connection orientation relation of the interface i; all parameters in the matrix are obtained by reading parameters of the single-module three-dimensional model;
according to the schematic diagram of the single-module three-dimensional model shown in fig. 3, the corresponding mathematical characterization result is as follows:
106, reading mathematical characterization results of each single module in the homogeneous modular robot according to the homogeneous modular robot three-dimensional model and the universal mathematical characterization of the single modules of the homogeneous modular robot, and constructing a universal mathematical characterization method of the homogeneous modular robot to obtain the universal mathematical characterization of the homogeneous modular robot;
specifically, according to the three-dimensional model diagram of the homogeneous modular robot shown in fig. 2, the mathematical characterization result of each module in the diagram can be obtained as follows:
the mathematical characterization result of each single module in the homogeneous modular robot is as follows:
wherein n is topo_num Representing the number of modules, in a homogeneous modular robot i (i＝1,2,...,n topo_module ) The method is characterized in that a single-module general mathematical characterization method of the homogeneous modular robot is used for describing results obtained by a three-dimensional model of the homogeneous modular robot;
the general mathematical characterization method of the homogeneous modular robot comprises the following steps:
by sequential extraction
Numbering each module in the set to obtain a matrix M:
wherein m is i (i＝1,2,...,n topo_module ) Representing the serial numbers of all modules in the three-dimensional model of the homogeneous modular robot;
by sequential extraction
D of each interface in the set i (i＝1,2,...,n surf_con )、e i (i＝1,2,...,n surf_con )、f i (i＝1,2,...,n surf_con ) Obtaining a matrix C: />
Wherein, c ij (i＝1,2,...,n topo_module ；j＝1,2,...,n topo_module )∈{1，...，n surf_con Denotes the module m i And module m j Connected interface number, when i = j, c ij ＝0(i＝1,2,...,n topo_module ；j＝1,2,...,n topo_module )，n surf_con Representing the number of face interfaces of a single module;
by extracting { module in order 1 ,module 1 ,...,module topo_module G of each interface in the set i (i＝1,2,...,n surf_con ) Obtaining a matrix CO:
wherein, co ij (i＝1,2,...,n topo_module ；j＝1,2,...,n topo_module ) A representation module m i And module m j When i = j, co ij ＝0(i＝1,2,...,n topo_module ；j＝1,2,...,n topo_module )；
According to the schematic diagram of the three-dimensional model of the homogeneous modular robot shown in fig. 2, the mathematical characterization result of the robot can be obtained as follows:
M＝[3,6,1]
the technical scheme of the embodiment of the invention has the following beneficial effects:
according to the technical scheme of the embodiment of the invention, a homogeneous modular robot three-dimensional model and a single-module three-dimensional model forming the homogeneous modular robot are obtained; according to a single-module three-dimensional model forming the homogeneous modular robot, combining a single-module core motor arrangement mode, obtaining the number, the type and the arrangement of interfaces of an active component, a passive component and a single module in the single module; establishing a single module body center and an interface coordinate system establishing rule according to a single module three-dimensional model forming the homogeneous modular robot, and obtaining a plurality of coordinate systems of the single module body center and the interface thereof and a homogeneous transformation matrix of the interface coordinate system relative to the single module body center coordinate system; acquiring a single-module interface connection orientation relation matrix set according to a single-module three-dimensional model forming the homogeneous modular robot; constructing a single-module general mathematical characterization method of the homogeneous modular robot according to the active components and the passive components in the single module, the number of interfaces of the single module, the types of the interfaces, the arrangement of the interfaces, a homogeneous transformation matrix of an interface coordinate system relative to a single-module body center coordinate system and a single-module interface connection orientation relation matrix set, and obtaining a general mathematical characterization of the single module of the homogeneous modular robot; according to the three-dimensional model of the homogeneous modular robot and the universal mathematical characterization of the single modules of the homogeneous modular robot, the mathematical characterization results of the single modules in the homogeneous modular robot are read, a universal mathematical characterization method of the homogeneous modular robot is constructed, and the universal mathematical characterization of the homogeneous modular robot is obtained, so that the mathematical characterization of the homogeneous modular robot can be realized, and a mathematical model basis is provided for the follow-up research aiming at the modular robot.
The above description is only for the purpose of illustrating the preferred embodiments of the present invention and is not to be construed as limiting the invention, and any modifications, equivalents, improvements and the like made within the spirit and principle of the present invention should be included in the scope of the present invention.
Those skilled in the art will appreciate that those matters not described in detail in the present specification are well known in the art.
Claims (6)
1. A method for universal mathematical characterization of a homogeneous modular robot, the method comprising:
obtaining a three-dimensional model of the homogeneous modular robot and forming a single-module three-dimensional model of the homogeneous modular robot;
according to a single-module three-dimensional model forming the homogeneous modular robot, combining a single-module body core motor arrangement mode, obtaining the number, the type and the arrangement of interfaces of active components and passive components, and single modules in the single module;
establishing a single module body center and an interface coordinate system establishing rule according to a single module three-dimensional model forming the homogeneous modular robot, and obtaining a plurality of coordinate systems of the single module body center and the interface thereof and a homogeneous transformation matrix of the interface coordinate system relative to the single module body center coordinate system;
acquiring a single-module interface connection orientation relation matrix set according to a single-module three-dimensional model forming the homogeneous modular robot;
constructing a single-module general mathematical characterization method of the homogeneous modular robot according to the active components and the passive components in the single module, the number of interfaces of the single module, the types of the interfaces, the arrangement of the interfaces, a homogeneous transformation matrix of an interface coordinate system relative to a single-module body center coordinate system and a single-module interface connection orientation relation matrix set, and obtaining a general mathematical characterization of the single module of the homogeneous modular robot;
reading the mathematical characterization result of each single module in the homogeneous modular robot according to the three-dimensional model of the homogeneous modular robot and the universal mathematical characterization of the single module of the homogeneous modular robot, constructing a universal mathematical characterization method of the homogeneous modular robot, obtaining the universal mathematical characterization of the homogeneous modular robot,
the homogeneous modular robot is characterized in that the structures and functions of all modules of the robot are completely the same.
2. The method according to claim 1, wherein a single module body center and an interface coordinate system establishing rule are established according to a single module three-dimensional model forming the homogeneous modular robot, a plurality of coordinate systems of the single module body center and the interface thereof and a homogeneous transformation matrix of the interface coordinate system relative to the single module body center coordinate system are obtained:
single module body center coordinate system { C } and interface coordinate system { S } thereof i }(i＝1,2,...,n surf_con ) The establishment rule is as follows:
a body center coordinate system { C }, wherein the origin of the coordinate system is fixed on the intersection point of the output shaft of the single-module spindle motor and the dividing plane; the z axis is collinear with the output shaft of the body core motor, and the direction is the torque output direction of the body core motor; the x axis is parallel to the single module dividing plane, and the direction is selected to be the third quadrant direction as the positive direction; the y-axis is determined according to the right hand rule, y = zxx;
interface coordinate system S i }(i＝1,2,...,n surf_con ) The origin of the coordinate system is fixed at the geometric center of the interface plane; the z-axis is vertical to the interface plane, and the direction points to the outside of the single module; the x axis is parallel to the interface plane, and the direction is selected to be the third quadrant direction as the positive direction; the y-axis is determined according to the right hand rule, y = zxx;
the total number of the interfaces of the single module is n surf_con 。
3. The method according to claim 1, wherein the establishing rule of the single module body center and the interface coordinate system is established according to the single module three-dimensional model forming the homogeneous modular robot, and a plurality of coordinate systems of the single module body center and the interface and a homogeneous transformation matrix of the interface coordinate system relative to the single module body center coordinate system are obtained
Wherein the content of the first and second substances,
representing the interface coordinate system S i }(i＝1,2,...,n surf_con ) A rotation transformation matrix with respect to the body center coordinate system C,
representing the interface coordinate system S i }(i＝1,2,...,n surf_con ) And (3) obtaining the parameters in the translation transformation matrix relative to the body center coordinate system { C } through reading the parameters of the three-dimensional model of the single module.
4. The method of claim 1, wherein the set of single-module interface connection orientation relationship matrices is obtained from a single-module three-dimensional model of the homogeneous modular robot:
sequentially determining a rotation transformation homogeneous transformation matrix relative to an initial interface coordinate system by determining the arrangement mode of positioning devices on the interface according to the single-module three-dimensional model;
and reading the rotation parameters of the interface positioning device in the three-dimensional model to obtain each element in the matrix.
5. The method of claim 1, wherein a single-module universal mathematical characterization method of the homogeneous modular robot is constructed according to the number of the active components and the passive components in the single module, the number of the interfaces of the single module, the types of the interfaces, the arrangement of the interfaces, a homogeneous transformation matrix of an interface coordinate system relative to a body center coordinate system of the single module, and a single-module interface connection orientation relation matrix set, so as to obtain a universal mathematical characterization of the single module of the homogeneous modular robot:
wherein, the ID represents the design number of the current module; n is surf_con Representing the number of face interfaces of a single module; a is a i (i＝1,2,...,n surf_con ) Indicates the component type, a, to which the interface i belongs i =0 denotes that the component type of the interface i is a passive component and cannot actively output torque, a i =1 represents that the type of the component to which the interface i belongs is an active component, and can actively output torque; b i (i＝1,2,...,n surf_con ) Indicates the type of interface i, b i =0 denotes that interface i is a female interface and cannot actively output torque, b i =1 indicates that the interface i is a male interface and can actively output torque; d i (i＝1,2,...,n surf_con ) Indicates the state of the interface i, d i =0 denotes that the interface i is in idle state, d i =1 for interface iThe state is connection; e.g. of the type i (i＝1,2,...,n surf_con ) A module number indicating a state of connection with the interface i; f. of i (i＝1,2,...,n surf_con ) A module interface number indicating a state of connection with the interface i; g i (i＝1,2,...,n surf_con ) Representing the connection orientation relation of the interface i; and all parameters in the matrix are obtained by reading parameters of the single-module three-dimensional model.
6. The method of claim 1, wherein the mathematical characterization results of the individual modules in the homogeneous modular robot are read according to the homogeneous modular robot three-dimensional model and the common mathematical characterization of the individual modules of the homogeneous modular robot, and a common mathematical characterization method for the homogeneous modular robot is constructed to obtain the common mathematical characterization of the homogeneous modular robot:
the mathematical characterization result of each single module in the homogeneous modular robot is as follows:
wherein n is topo_module Represents the number of modules in the homogeneous modular robot,
representing a representation result obtained by each module by using a homogeneous modular robot single-module general mathematical representation method, wherein ID represents the design number of the current module; n is surf_con Representing the number of face interfaces of a single module; a is a i (i＝1,2,...,n surf_con ) Indicates the component type, a, to which the interface i belongs i =0 denotes that the component type of the interface i is a passive component and cannot actively output torque, a i =1 represents that the type of the component to which the interface i belongs is an active component, and can actively output torque; b i (i＝1,2,...,n surf_con ) Indicates the type of interface i, b i =0 denotes a connectionThe port i is a female port and cannot actively output torque, b i =1 indicates that the interface i is a male interface and can actively output torque; d i (i＝1,2,...,n surf_con ) Indicates the state of the interface i, d i =0 denotes that the interface i is in idle state, d i =1 indicates that the state of the interface i is connected; e.g. of the type i (i＝1,2,...,n surf_con ) A module number indicating a state of connection with the interface i; f. of i (i＝1,2,...,n surf_con ) A module interface number indicating a state of connection with the interface i; g i (i＝1,2,...,n surf_con ) Representing the connection orientation relation of the interface i; all parameters in the matrix are obtained by reading parameters of the single-module three-dimensional model;
the general mathematical characterization method of the homogeneous modular robot comprises the following steps:
by sequential extraction
Numbering each module in the set to obtain a matrix M:
wherein m is i (i＝1,2,...,n topo_module ) Representing the serial numbers of all modules in the three-dimensional model of the homogeneous modular robot;
by sequential extraction
D of each interface in the set i (i＝1,2,...,n surf_con )、e i (i＝1,2,...,n surf_con )、f i (i＝1,2,...,n surf_con ) Obtaining a matrix C:
wherein, c ij (i＝1,2,...,n topo_module ；j＝1,2,...,n topo_module )∈{1，...，n surf_con Denotes the module m i And module m j Connected interface number, when i = j, c ij ＝0(i＝1,2,...,n topo_module ；j＝1,2,...,n topo_module )，n surf_con Representing the number of face interfaces of a single module;
by extracting { module in order 1 ,module 1 ,...,module topo_module G of each interface in the set i (i＝1,2,...,n surf_con ) Obtaining a matrix CO:
wherein, co ij (i＝1,2,...,n topo_module ；j＝1,2,...,n topo_module ) A representation module m i And module m j When i = j, co ij ＝0(i＝1,2,...,n topo_module ；j＝1,2,...,n topo_module )。
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