CN110909479B - Compliance calculation method for continuous robot - Google Patents
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Abstract
The invention discloses a method for calculating flexibility of a continuous robot, which comprises the following steps: the rope of the continuous robot is arranged into a plurality of sections, and each section is provided with a plurality of supporting disks and elastic tubes; acquiring the force born by the support wafers and the distance between the support wafers, and obtaining a moment relation formula according to the relation between the force and the direction vector; according to the force balance formula, the moment balance formula and the bending curvature calculation formula, the moment relation formula is used for obtaining the bending curvature through an optimization algorithm; obtaining the relative rotation angle of the supporting wafer through a calculation formula according to the bending curvature; obtaining a homogeneous transformation matrix through a homogeneous transformation algorithm according to the relative rotation angle of the support wafer, and obtaining the coordinates of the support wafer according to the homogeneous transformation matrix; and obtaining the flexibility matrix by differentiating the strives partial through the homogeneous transformation matrix. By comparing the flexibility values of different configurations, a path with the flexibility meeting the requirement in the space can be obtained. The method is high in calculation efficiency and can be widely applied to flexibility modeling of the continuous robot.
Description
Technical Field
The invention relates to the field of mobile robot collaborative operation, in particular to a method for calculating flexibility of a continuous robot.
Background
The continuous robot is used as a novel bionic robot and has great difference in structure with the traditional robot. The continuous robot employs an invertebrate structure similar to octopus tentacles, elephant noses, animal tongues, etc., without discrete joints and rigid links. Since the flexibility of a continuous robot directly affects its accuracy, it is important to study its flexibility.
In the existing flexible robot compliance research, deformation of a flexible arm under unidirectional load is concentrated in many ways. The method comprises the steps of deducing a continuous robot statics model analytical solution by using a Cosseread-Rod method in research, further defining an analytical solution model of a flexibility matrix, and simplifying the flexibility matrix during calculation due to complex solution. When the compliance calculation assumes no drive and only a load of a tip force is applied, the compliance matrix is a small displacement divided by the load causing the displacement, and the accuracy of calculating the compliance of the robot is not high, so that the calculation accuracy of the operation model of the whole continuous robot is not high.
Disclosure of Invention
The present invention aims to at least solve the technical problems existing in the prior art. Therefore, the invention provides a method for calculating the flexibility of the continuous robot, which can accurately calculate the value of the flexibility matrix, so that the calculation accuracy of the running model of the continuous robot is high.
One embodiment of the present invention provides a method for calculating compliance of a continuous robot, comprising: comprising the following steps:
the rope of the continuous robot is arranged into a plurality of sections, and each section consists of a plurality of supporting disks and an elastic tube;
acquiring the force born by the support wafers and the distance between the support wafers, and obtaining a moment relation according to the relation between the force and the direction vector;
according to a force balance formula, a moment balance formula and a bending curvature calculation formula, the moment relation is used for obtaining the bending curvature through an optimization algorithm;
obtaining the relative rotation angle of the supporting wafer according to the bending curvature and a calculation formula;
obtaining a homogeneous transformation matrix according to the relative rotation angle of the supporting wafer and through a homogeneous transformation algorithm, and obtaining coordinates in a global coordinate system of the supporting wafer according to the homogeneous transformation matrix;
and obtaining a flexibility matrix by differentiating the sought partial through the homogeneous transformation matrix.
The method for calculating the flexibility of the continuous robot has the following advantages: the flexibility modeling is subdivided into three steps of kinematic modeling, statics modeling and flexibility calculation, the relative rotation angle of each supporting wafer is calculated according to force balance, moment balance and bending curvature, a homogeneous transformation matrix is calculated after the relative rotation angle is obtained, the flexibility matrix can be obtained by differentiating the received force according to the homogeneous transformation matrix, the flexibility value in the working space can be calculated efficiently, a path with smaller flexibility value can be planned by comparing the flexibility values under different arm shapes, and the corresponding path has larger rigidity and higher precision.
According to further embodiments of the present invention, a method for calculating compliance of a continuous robot, the force includes: upper rope driving forceLower rope driving force +.>Support wafer gravity->Gravity of central elastic tube>Contact force->The moment in the moment relation comprises the following steps: driving moment generated by upper rope +.>Driving moment generated by the lower rope +.>Moment generated by supporting the wafer gravity>Moment generated by gravity of central elastic tube>Moment generated by contact forceThe relationship between the force and the moment is:
driving moment:
generated by gravityMoment:
moment generated by contact force:
wherein,for fixing at->Origin of the coordinate system of the center of the individual support discs, < >>And->Respectively +.>The upper and lower rope holes on the round piece are +.>、/>、/>、/>、/>The direction vector is the upper rope driving force, the lower rope driving force, the gravity of the supporting disc, the gravity of the central elastic tube and the contact force.
According to the method for calculating the flexibility of the continuous robot, the force balance in the force balance formula comprises the end force balance and other support disc force balances, the moment balance in the moment balance formula comprises the end moment balance and other support disc moment balances, and the equations of the end force balance and the end moment balance are as follows:
for external forces in the coordinate system->In (a) representation of->Is the external force is about>Moment produced->；
The equation of the force balance of the other support wafer and the moment balance of the other support wafer is as follows:
in the method, in the process of the invention,and->Respectively +.>Segment Joint Unit pair->The forces and moments generated by the segment joint units,for force->Point->Moment produced->And->Respectively +.>The contact force and the contact moment to which the support wafer is subjected are in a coordinate system +.>Is represented by (a).
According to the method for calculating the flexibility of the continuous robot, the bending curvature formula is an euler-bernoulli equation, and the equation is:
in the method, in the process of the invention,is->Bending curvature of the segment elastic tube->Is->Moment of force exerted on the segment unit->And->Young's modulus and moment of inertia of the elastic tube, respectively.
According to the method for calculating the flexibility of the continuous robot according to other embodiments of the present invention, the step-by-step obtaining the bending radius and the relative rotation angle of the support wafer according to the bending curvature and by a calculation formula specifically includes:
according to the bending curvature through the formulaObtaining the bending radius r of the calculation robot;
according to the bending radius and the length l between two supporting discs, the formula is adoptedAnd obtaining the relative rotation angle of the supporting wafer.
According to the compliance calculation method of the continuous robot of other embodiments of the present invention, the optimization algorithm is a nonlinear least square method.
According to the compliance calculation method of the continuous robot of other embodiments of the present invention, a homogeneous transformation matrix is obtained according to a homogeneous transformation algorithm according to a relative rotation angle of the support wafer, and coordinates in a global coordinate system of the support wafer are specifically obtained according to the homogeneous transformation matrix:
obtaining a rotation matrix according to the relative rotation angle of the support wafer；
According to the rotation matrixObtaining a homogeneous transformation matrix by homogeneous transformation>The specific calculation formula of the homogeneous transformation matrix is as follows:
，/>a rotation matrix and P a translation matrix;
according to the theory in robotics, the robot's representation of the coordinates of a certain said support disk in the global coordinate system is
。
According to the method for calculating the flexibility of the continuous robot in other embodiments of the present invention, the method for obtaining the flexibility matrix by differentiating the strives for partial through the homogeneous transformation matrix specifically includes:
wherein,for a homogeneous transformation matrix represented by the robot's end coordinate system in the global coordinate system, +.>For the tip contact force is +>The component in the axial direction, i.e. the component of the end load force in the x-axis, +.>For the component of the tip contact force in the y-axis direction, i.e. the component of the tip load force in the y-axis,/>For the component of the tip contact force in the z-axis direction, i.e. the component of the tip load force in the z-axis,/>For the end contact moment +.>Component of axial direction, ++>For the component of the tip contact moment in the y-axis direction, +.>Is the component of the tip contact torque in the z-axis direction.
According to the method for calculating the flexibility of the continuous robot of other embodiments of the present invention, the method for obtaining the rotation matrix according to the relative rotation angle of the support wafer specifically includes:
the rotation matrix is obtained from the relative rotation angle by the following formula:
。
according to further embodiments of the present invention, the robot tip has 2 degrees of freedom and each support wafer has one degree of rotational freedom.
Drawings
FIG. 1 is a schematic view of a continuous robot in an embodiment of the present invention;
FIG. 2 is a schematic view showing the relative positions of two adjacent joint units of the continuous robot according to an embodiment of the present invention;
FIG. 3 is a schematic view of the displacement of the end of the continuous robot when a small force is applied to the end in an embodiment of the present invention;
FIG. 4 is a diagram of a static simulation of a continuous robot under different rope driving forces in an embodiment of the invention;
fig. 5 is a schematic diagram of a continuous robot dual-segment rope-driven continuous robot in a working space under no-load condition and the magnitude of different direction compliance values in the working space according to an embodiment of the present invention.
Detailed Description
The conception and the technical effects produced by the present invention will be clearly and completely described in conjunction with the embodiments below to fully understand the objects, features and effects of the present invention. It is apparent that the described embodiments are only some embodiments of the present invention, but not all embodiments, and that other embodiments obtained by those skilled in the art without inventive effort are within the scope of the present invention based on the embodiments of the present invention.
In the description of the present invention, if an orientation description such as "upper", "lower", "front", "rear", "left", "right", etc. is referred to, it is merely for convenience of description and simplification of the description, and does not indicate or imply that the apparatus or element referred to must have a specific orientation, be configured and operated in a specific orientation, and thus should not be construed as limiting the invention. If a feature is referred to as being "disposed," "secured," "connected," or "mounted" on another feature, it can be directly disposed, secured, or connected to the other feature or be indirectly disposed, secured, connected, or mounted on the other feature.
In the description of the embodiments of the present invention, if "several" is referred to, it means more than one, if "multiple" is referred to, it is understood that the number is not included if "greater than", "less than", "exceeding", and it is understood that the number is included if "above", "below", "within" is referred to. If reference is made to "first", "second" it is to be understood as being used for distinguishing technical features and not as indicating or implying relative importance or implicitly indicating the number of technical features indicated or implicitly indicating the precedence of the technical features indicated.
The embodiment of the invention discloses a method for calculating the flexibility of a continuous robot, which comprises the following steps:
the rope of the continuous robot is arranged into a plurality of sections, and each section consists of a plurality of supporting disks and an elastic tube;
acquiring the force born by the support wafers and the distance between the support wafers, and obtaining a moment relation formula according to the relation between the force and the direction vector;
according to a force balance formula, a moment balance formula and a bending curvature calculation formula, the moment relation formula obtains the bending curvature through an optimization algorithm;
obtaining the relative rotation angle of the supporting wafer according to the bending curvature and a calculation formula;
obtaining a homogeneous transformation matrix according to the relative rotation angle of the supporting wafer and through a homogeneous transformation algorithm, and obtaining coordinates in a global coordinate system of the supporting wafer according to the homogeneous transformation matrix;
and obtaining the flexibility matrix by differentiating the strives partial through the homogeneous transformation matrix.
Referring to fig. 1, where a is the drive rope, B is the support disc, C is the central elastic tube, L1 is the first length of rope, and L2 is the second length of rope. The rope-driven continuous robot consists of a central elastic tube, a supporting circular plate, a driving rope and a base (not shown). This embodiment is a two-stage planar continuous robot. In this embodiment, the method for calculating the compliance of the continuous robot uses newton-euler method for modeling to obtain the compliance matrix of the continuous robot, and the modeling includes: kinematic modeling, statics modeling, and compliance modeling. Firstly, a rope of a continuous robot is set to be 2 sections, each section is provided with a plurality of supporting disks and a central elastic tube, and as the single-section robot can only control one degree of freedom of the tail end, namely the rotation angle, the degree of freedom of the robot can be controlled, and if the robot is multi-section, more degrees of freedom of the robot can be controlled, and a more complex track can be obtained through the mode. In this embodiment, the robot tip has 2 degrees of freedom, and each support wafer has one degree of rotational freedom. The driving force of the robot rope, the distance between the adjacent supporting disks and the distance between each supporting disk are equal as the supporting disks are equidistantly arranged. And obtaining a moment relation formula of a certain elastic tube according to the relation between the force and the moment, obtaining the bending curvature through an optimization algorithm by using a force balance formula, a moment balance formula and a bending curvature calculation formula, and obtaining the relative rotation angle of the supporting wafer through the bending curvature because the moment relation formula is related to the relative rotation angle of the supporting wafer, so that the relative rotation angle of the elastic tube is obtained after elimination. And obtaining the relative rotation angle of the rest support wafer and the relative rotation angle of the tail end of the robot according to the statics of the robot, namely force balance and/or moment balance. According to the kinematics of the continuous robot, a secondary transformation matrix is obtained through each relative corner according to homogeneous transformation, and the homogeneous transformation matrix is used for obtaining the representation in a global coordinate system after the coordinates of a certain supporting wafer can be obtained. The partial differentiation of the load is then sought according to the homogeneous transformation matrix to obtain the overall compliance matrix. In one aspect, the compliance matrix represents compliance characteristics of the robot to external forces. On the other hand, the compliance matrix is the inverse of the stiffness matrix. By obtaining the flexibility matrix, the flexibility of the continuous robot in the working space can be mastered, when a larger load is needed, the place with small flexibility can be selected in the track planning, and when a larger flexibility is needed, the place with large flexibility is selected.
Wherein the forces in the force balance include: upper rope driving forceLower rope driving force +.>Support wafer gravity->Gravity of central elastic tube>Contact force->. The moment in the moment relation includes: driving moment generated by upper rope +.>Driving moment generated by the lower rope +.>Moment generated by supporting the wafer gravity>Moment generated by gravity of central elastic tube>Moment due to contact force->. Wherein about the upper rope driving force +>Lower rope driving forceSupport wafer gravity->Gravity of central elastic tube>Are known, and the contact force +.>And can be obtained by measurement. The moment can be determined from the known forces. The calculation formula of the moment and the force is specifically as follows:
wherein the calculation formula of the driving moment and the driving force is as follows:
（1）
the calculation formulas of the gravity and the gravity moment of the supporting disc and the central elastic tube are as follows:
（2）
the calculation formulas of the contact force and the contact moment are as follows:
（3）
wherein,for fixing at->Origin of the coordinate system of the center of the individual support discs, < >>And->Respectively +.>The upper and lower rope holes on each disc are related to the relative rotation angle between the two support discs, and the direction vector between the upper and lower rope holes from the support disc to the support disc is related to the relative rotation angle between the two support discs. In this embodiment, the arc formed by the two support disks is assumed to be an equal arc, and the curve is considered to be an arc when only the rope driving force is applied under no external force, so that the two support disks are assumed to be equal arcs. Because the distance between the two support wafers is equal, the arc length between the two support wafers is the same, and therefore, the direction vector between the support wafer and the upper rope hole and the lower rope hole of the support wafer can be obtained only by knowing the included angle. The moment relation can thus be obtained by known forces.
Referring to fig. 2, fig. 2 is a schematic diagram of the relative positions of the continuous robot rope. In which the relative rotation angle between the support wafers is shown、/>Each support wafer is provided with a movable coordinate system, and the origin of the movable coordinate system is as far as +.>At the center of the supporting wafer. Since the rope will pass through the upper and lower rope holes of a certain disc +.>And->Therefore, there is an upper rope driving force +>And lower rope driving force +>The representation of a certain dynamic coordinate system in the global coordinate system can be obtained by matrix multiplication.
And the force and moment of other support wafers and the tail end of the robot can be obtained according to the force balance and the moment balance, so that the moment relation between other elastic tubes and the tail end of the robot is obtained. The force balance comprises the balance of the tail end of the robot and other support wafer force balances, and the moment balance comprises the tail end moment balance of the robot and other support wafer moment balances. The relation between the end force balance and the end moment balance of the robot is as follows:
（4）/>for external forces in the coordinate system->In (a) representation of->Is the external force is about>Moment produced->；
The equations for other support disc force balance and other support disc moment balance are:
（5）
in the method, in the process of the invention,and->Respectively the first/>Segment Joint Unit pair->The forces and moments generated by the segment joint units,for force->Point->Moment produced->And->Respectively +.>The contact force and the contact moment to which the support wafer is subjected are in a coordinate system +.>Is represented by (a). Wherein->And->Respectively +.>Segment Joint Unit pair->The force and moment generated by the segment joint unit can be solved by the known driving force, gravity and contact force, and the moment is related to the direction vector, so that each support wafer and each robot can be obtainedMoment relation at the end.
After the moment expressions of each supporting wafer and each terminal are obtained, the bending curvature can be solved according to a bending curvature formula, wherein the bending curvature formula is Euler-Bernoulli equation, and the expression of the equation is:
（6）
in the method, in the process of the invention,is->Bending curvature of a segment-shaped elastic tube, i.e. between two supporting discs, +.>Is->Moment of force exerted on the segment unit->And->The young's modulus and moment of inertia of the elastic tube are respectively, where moment of inertia is i=1/2 m (r1×r1+r2×r2), m is mass, R1 is the inner radius of the elastic tube, and R2 is the outer radius of the elastic tube, and since the elastic tube is equally linear in this embodiment, r1=r2=r. The moment applied to a certain section of elastic tube is obtained through the moment of two supporting discs and is a moment relation. The curvature of the curve can be solved by an optimization algorithm that in this embodiment uses a least squares method.
The known bending curvature is obtained step by step through a calculation formula, and the bending radius and the relative rotation angle of the supporting wafer are specifically as follows:
according to the bending curvature through the formulaObtaining the bending radius r of the calculated robot, and according to the bending radius and the length l between the two support wafers, namely the distance between the two support wafers, then passing through the formula +.>And obtaining the relative rotation angle of the support wafer, calculating the bending curvature according to the relation between the relative rotation angle and the direction vector of the elastic tube, and then calculating the relative rotation angle. The bending radius r of the robot can be calculated according to a calculation formula by the bending curvature of the robot, and the rotation angle of the next wafer relative to the previous wafer can be obtained by knowing the bending radius r and the original length of the robot as l.
The rotation matrix of the robot is provided according to the wanted relative rotation angle of the supporting waferWherein ∈m about rotation matrix>The relative rotation angle is obtained by mainly adopting the following calculation formula:
（7）
homogeneous transformation matrix of robotComprising a rotation matrix->And a translation matrix p, wherein the rotation of the continuous robot is around the Z axis, and the rotation matrix can be obtained through a formula (7) after knowing the rotation angle according to the robotics theory. The specific calculation formula of homogeneous transformation is as follows:
（8）
after the homogeneous transformation matrix is obtained, according to the theory in robotics, the coordinates of a certain wafer of the robot are expressed as
=/>X/>。（9）
After the homogeneous transformation matrix is obtained, partial differentiation can be obtained according to the homogeneous transformation matrix to obtain a flexibility matrix, and the specific calculation mode of the flexibility matrix is as follows:
（10）
wherein,for a homogeneous transformation matrix represented by the robot's end coordinate system in the global coordinate system, +.>For the tip contact force is +>The component in the axial direction, i.e. the component of the end load force in the x-axis, +.>For the component of the tip contact force in the y-axis direction, i.e. the component of the tip load force in the y-axis,/>For the component of the tip contact force in the z-axis direction, i.e. the component of the tip load force in the z-axis,/>For the end contact moment +.>The component of the axial direction is,
for the component of the tip contact moment in the y-axis direction, +.>Is the component of the tip contact torque in the z-axis direction.
Wherein the compliance matrix is calculated specifically as follows, exemplified by the first column of the compliance matrix:
（11）
wherein the method comprises the steps ofA direction matrix which is a homogeneous transformation matrix, a table end direction,/->The position vector of the matrix is uniformly transformed, and the end position of the table is obtained. The 4X4 homogeneous transformation matrix is equivalent to a 6X1 vector by the "V" operation of the lie group algebra. The relative rotation angle is calculated in the mode, the obtained homogeneous transformation matrix is related to the position vector, and the flexibility of each section of elastic tube can be obtained by partial differentiation, so that the movement shape of the robot is calculated more accurately.
Embodiment two: referring to fig. 3, an embodiment of the present invention is a schematic view of the displacement of the end of a continuous robot when a small force is applied. Compliance at this point is the compliance of displacement in all directions when a small external load is applied. Note that the compliance matrixIn the simulation calculation and experimental research, we only consider the main diagonal elementsThe element is just enough, and the point can be clearly seen in the schematic diagram. To->And->For example, a->Is indicated at->The end position under the action of directional force load is +.>Trend of change of direction,/->Is indicated at->The end position under the action of directional force load is +.>Trend of change in direction.
（12）
The equation is a theoretical basis of the embodiment, and the compliance value of each direction is obtained through partial differentiation.
Referring to fig. 4, four graphs in fig. 4 are (a) in fig. 4, (b) in fig. 4, (c) in fig. 4, and (d) in fig. 4, and (a) in fig. 4, (b) in fig. 4, (c) in fig. 4, and (d) in fig. 4 are statics simulations of the robot under different rope driving forces, and are within an error allowable range compared with experiments, so that the modeling of the compliance matrix is established correctly.
Referring to fig. 5, fig. 5 includes (a) in fig. 5, (b) in fig. 5, (c) in fig. 5, (a) in fig. 5, (b) in fig. 5, and (c) in fig. 5 as the working space under no load, and the magnitude of the compliance value in the working space in different directions, wherein (a) in fig. 5 is the working space under no load, (b) in fig. 5 is the compliance value in the X direction, and (c) in fig. 5 is the compliance value in the Y direction. Referring to fig. 5 (b), it is understood that the compliance characteristic in the X-direction is near the X-axis, and the compliance value is small, and the compliance in the X-direction increases as it moves away from the X-axis. Referring to fig. 5 (c), the Y-direction compliance characteristic is that compliance near the Y-axis is small, and compliance in the Y-direction increases with distance from the Y-axis.
In conclusion, the flexibility value in the working space can be calculated very efficiently by subdividing the flexibility modeling into three steps of kinematic modeling, statics modeling and flexibility calculation. By comparing the flexibility under different arm shapes, a path with smaller flexibility value can be planned, and the corresponding path has larger rigidity and higher precision.
The embodiments of the present invention have been described in detail with reference to the accompanying drawings, but the present invention is not limited to the above embodiments, and various changes can be made within the knowledge of one of ordinary skill in the art without departing from the spirit of the present invention. Furthermore, embodiments of the invention and features of the embodiments may be combined with each other without conflict.
Claims (8)
1. A method for calculating compliance of a continuous robot, comprising:
the rope of the continuous robot is arranged into a plurality of sections, and each section consists of a plurality of supporting disks and an elastic tube;
acquiring the force born by the support wafers and the distance between adjacent support wafers, and constructing a moment relation between the two support wafers according to the relation between the force and the direction vector;
according to a force balance formula, a moment balance formula and a bending curvature calculation formula, the moment relation formula obtains the bending curvature through an optimization algorithm, and the method specifically comprises the following steps: obtaining a moment relation between each supporting wafer and the tail end of the robot based on the force balance formula, the moment balance formula, the force of the supporting wafer and the moment relation; solving based on an optimization algorithm, the moment relation type back and bending curvature formulas of each supporting wafer and the tail end to obtain bending curvature;
calculating the relative rotation angle of the supporting wafer through a calculation formula and the bending curvature; wherein the calculation formula is as follows，/>For relative rotation angle->To support the distance between discs->Is a bending radius, and the bending radius is +.>，/>Is a bending curvature; performing homogeneous transformation on the relative rotation angle of the support wafer through a homogeneous transformation algorithm to obtain a homogeneous transformation matrix, wherein the homogeneous transformation matrix comprises coordinates in a global coordinate system of the support wafer; the method comprises the steps of obtaining a homogeneous transformation matrix through a homogeneous transformation algorithm according to the relative rotation angle of the supporting wafer, and obtaining coordinates in a global coordinate system of the supporting wafer according to the homogeneous transformation matrix, wherein the coordinates are specifically as follows:
obtaining a rotation matrix according to the relative rotation angle of the support wafer；
According to the rotation matrixObtaining a homogeneous transformation matrix by homogeneous transformation>The specific calculation formula of the homogeneous transformation matrix is as follows:
，/>a rotation matrix and P a translation matrix;
according to the theory in robotics, the robot's representation of the coordinates of a certain said support disk in the global coordinate system is
；
Obtaining a flexibility matrix by partial differentiation of the homogeneous transformation matrix; wherein the compliance matrix characterizes a magnitude of compliance of the continuous robot within a workspace; wherein, the obtaining the flexibility matrix by differentiating the strives for partial through the homogeneous transformation matrix specifically comprises:
wherein (1)>For a homogeneous transformation matrix represented by the robot's end coordinate system in the global coordinate system, +.>For the tip contact force is +>The component in the axial direction, i.e. the component of the end load force in the x-axis, +.>In the y-axis direction for tip contact forceComponent (a) of the end load force in the y-axis,/-component (a)>For the component of the tip contact force in the z-axis direction, i.e. the component of the tip load force in the z-axis,/>For the end contact moment +.>Component of axial direction, ++>For the component of the tip contact moment in the y-axis direction, +.>Is the component of the tip contact torque in the z-axis direction.
2. The method of calculating compliance of a continuous robot of claim 1, wherein the force comprises: upper rope driving forceLower rope driving force +.>Support wafer gravity->Gravity of central elastic tube>Contact force->The moment in the moment relation comprises the following steps: driving moment generated by upper rope +.>Driving moment generated by the lower rope +.>Moment generated by supporting the wafer gravity>Moment generated by gravity of central elastic tube>Moment generated by contact forceThe relationship between the force and the moment is:
driving moment:
moment generated by gravity:
moment generated by contact force:
wherein,for fixing at->Origin of the coordinate system of the center of the individual support discs, < >>And->Respectively +.>The upper and lower rope holes on the round piece are +.>、/>、/>、/>、/>The direction vector is the upper rope driving force, the lower rope driving force, the gravity of the supporting disc, the gravity of the central elastic tube and the contact force.
3. The method of claim 1, wherein the force balance in the force balance formula includes an end force balance and other support disk force balances, and the torque balance in the torque balance formula includes an end torque balance and other support disk torque balances, and the equations of the end force balance and the end torque balance are:
for external forces in the coordinate system->In (a) representation of->Is the external force is about>Moment produced->；
The equation of the force balance of the other support wafer and the moment balance of the other support wafer is as follows:
in the method, in the process of the invention,and->Respectively +.>Segment Joint Unit pair->Forces and moments generated by the segment joint unit, < ->For force->Point->Moment produced->And->Respectively +.>The contact force and the contact moment to which the support wafer is subjected are in a coordinate system +.>Is represented by (a).
4. The method of claim 1, wherein the bending curvature formula is an euler-bernoulli equation, and the equation is:
in the method, in the process of the invention,is->Bending curvature of the segment elastic tube->Is->Moment of force exerted on the segment unit->And->Young's modulus and moment of inertia of the elastic tube, respectively.
5. The method for calculating the compliance of a continuous robot according to claim 1, wherein the step-by-step obtaining the bending radius and the relative rotation angle of the support wafer according to the bending curvature and by a calculation formula is specifically:
according to the bending curvature through the formulaObtaining the bending radius r of the calculation robot;
according to the bending radius and the length l between two supporting discs, the formula is adoptedAnd obtaining the relative rotation angle of the supporting wafer.
6. The method of claim 1, wherein the optimization algorithm is a nonlinear least squares method.
7. The method for calculating the compliance of a continuous robot according to claim 1, wherein the rotation matrix obtained from the relative rotation angle of the support wafer is specifically:
the rotation matrix is obtained from the relative rotation angle by the following formula:
。
8. the method of claim 1, wherein the robot tip has 2 degrees of freedom and each support wafer has one degree of rotational freedom.
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