CN113305809B - Force sense simulation control method of fully-constrained space rope driving parallel mechanism - Google Patents
Force sense simulation control method of fully-constrained space rope driving parallel mechanism Download PDFInfo
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Abstract
The invention discloses a force sense simulation control method of a fully constrained space rope driven parallel mechanism, which comprises the following steps: step one, determining a motion calculation method; step two, solving a Jacobian matrix; step three, determining a tension distribution method; step four, establishing a dynamic model of the mechanism when the elasticity of the rope is considered; step five, building a closed-loop motion control frame; step six, determining a force sense simulation control scheme; and step seven, completing the construction of the overall control framework. The control frame of the invention is composed of three parts, which can ensure the good position tracking of the mobile platform, ensure the small and adjustable tension on the rope, and increase the man-machine interaction function of the rope parallel mechanism. In the specific control scheme, the dynamic performance of the mechanism is improved by introducing the internal force coordination ring, and the interaction with people is realized by introducing the force sense simulation ring. The force sensing simulation ring can be used or not according to the use requirement, and the rest two parts still have a good control effect.
Description
Technical Field
The invention belongs to the technical field of control, and relates to a force sense simulation control method of a fully-constrained space rope driving parallel mechanism.
Background
The rope-driven parallel mechanism has the advantages of small mechanism mass, large movement space, small movement inertia, adjustable rigidity, strong load capacity and the like, is gradually concerned by numerous scholars, and the research and the start of China on the aspect of the rope parallel mechanism are late, so that the rope-driven parallel mechanism can be applied to numerous fields at present, for example: radio telescopes, wind tunnel tests, rehabilitation robots, industrial cameras, carrying assembly and the like. Due to the characteristic of unidirectional stress of the ropes, the mechanism needs to realize flexible control of n degrees of freedom, the number m of the ropes is equal to or larger than m and is larger than or equal to n +1, namely at least 7 ropes are needed for realizing control of six degrees of freedom, and in order to ensure the symmetry of the mechanism, 8 ropes are mostly adopted for realizing control of a full constraint space. When the rope is controlled to drive the parallel mechanism, the dynamic characteristics of the mechanism are involved, the mechanism is in redundant constraint, and the regulation of the internal force of the rope is also important. Secondly, enabling the mechanism to interact with people is a trend developed in the modern times, which puts higher requirements on the control framework of the rope-driven parallel mechanism, and the research on the control framework of the rope-driven parallel mechanism is very important.
Disclosure of Invention
In order to solve the problems, the invention provides a force sense simulation control method of a rope drive parallel mechanism in a fully constrained space. The rope mechanism has the characteristics of simple structure, large movement range and intrinsic safety, and can stably run on one hand and realize movement on a given track; on the other hand can interact with people, can make corresponding reaction to the force that the external world exerted, has realized the good control to two controlled variables of mechanism moving platform position and rope tension, can be used for simulating people and virtual object interactive power sense simultaneously.
The purpose of the invention is realized by the following technical scheme:
a force sense simulation control method of a fully-constrained space rope driving parallel mechanism comprises the following steps:
step one, determining a motion calculation method:
the motion calculation method considers the influence of the guide pulley on one hand, and solves the relation between the motor rotation angle and the rope length variation in the hoisting structure on the other hand, so that the rope is divided into two parts for analysis: the working space inner part and the driving system inner part solve the swing angle beta for the working space inner partiAngle of wrap alphaiCoordinates of rope outlet pointBSiFinally, the length l of the rope of the working space part is obtainedW,i(ii) a For the inner part of the driving system, obtaining an identity relation through the rope length states at two moments to solve the relation between the rotation angle of the motor and the rope length variable quantity, wherein:
(1) angle of oscillation betaiExpressed as:
in the formula,Bai,xthe component of the dynamic hinge point vector on the x axis of the global coordinate system is shown;Bai,ythe component of the dynamic hinge point vector on the y axis of the global coordinate system is shown;Bbi,xthe component of the vector of the tangent point of the swing axis of the guide pulley and the edge of the guide pulley on the x axis of the global coordinate system is shown;Bbi,ythe component of the vector of the oscillating axis of the guide pulley and the tangent point of the edge of the guide pulley on the y axis of the global coordinate system;
(2) wrap angle alphaiExpressed as:
αi＝π-(αi,1+αi,2)；
in the formula,Bmicentering the guide pulley in a global coordinate systemVector quantity;Bmi,zis the component of the guide pulley center vector on the z axis of the global coordinate system;Baithe vector of the movable hinge point in the global coordinate system is obtained;Bai,zthe component of the dynamic hinge point vector on the z axis of the global coordinate system is shown; ρ is the guide sheave radius.
(3) Coordinates of rope outlet pointBSiExpressed as:
in the formula,Bmi,xis the component of the guide pulley center vector on the x axis of the global coordinate system;Bmi,ythe component of the guide pulley center vector on the y axis of the global coordinate system is shown;
(4) rope length l of working space partW,iExpressed as:
lW,i＝qP+lAS＝ρ·αi+||Bai-BSi||2；
in the formula, qPThe length of the rope wrapped on the guide pulley; lASThe length of the rope between the rope outlet point of the guide pulley and the movable hinge point is determined;
(5) the relationship between the motor rotation angle and the rope length variation is expressed as follows:
in the formula,. DELTA.lWIs the effective variation of the rope; h is the winding pitch of the rope;
is the motor corner; v. ofPGThe transmission ratio between the motor and the winch is set; r is the hoisting radius;
step two, solving a Jacobian matrix:
wherein J is a Jacobian matrix of the mechanism;BRPa rotation matrix of pose change between a global coordinate system and a body coordinate system; lnIs a unit rope length vector;Paiis the vector of the movable hinge point in the body coordinate system,Bai＝BRP Pai；
step three, determining a tension distribution method:
the ropes were tension distributed using Closed-form theory:
fis＝-J+Tw+fm-J+TJTfm；
in the formula (f)isIs the rope tension; j. the design is a square+TIs the pseudo-inverse of the Jacobian matrix; w is an external force; f. ofmThe average value of the maximum value and the minimum value of the tension range;
step four, establishing a dynamic model of the mechanism in consideration of the elasticity of the rope:
assuming that the connections between the ropes and the mobile platform, between the ropes and the guide pulley, and between the ropes and the winch are all in an ideal state, based on the above assumptions, the dynamics modeling includes the mobile platform, the winch and the guide pulley, and the ropes, wherein:
(1) adopting a Newton Euler method to model a mobile platform:
wherein L is a matrix formed by unit direction vectors of each rope;Pa is a movable platform hinge point coordinate matrix; e is a 3 × 3 identity matrix; i is an inertia matrix of the movable platform relative to the fixed platform; omega is an antisymmetric matrix; m is the mobile platform mass; g is a gravity acceleration vector; f. of2iIs the platform side rope tension; t is the moving displacement of the movable platform relative to the fixed platform; ω and
for the angular speed and angle of rotation of the moving platform relative to the stationary platformAcceleration;
(2) a moment balance method is adopted to model a hoisting and guide pulley:
in the formula, JrEquivalent moment of inertia of the winch model and the pulley model;
the rotation angle vector of the ith motor; crAn equivalent damping coefficient matrix of a winch model and a pulley model; lambda [ alpha ]sThe equivalent radius of the winch model and the pulley model; f. of1iThe rope tension of the ith rope driving side; t isact,iIs the torque of the drive;
(3) modeling the rope as a spring damping model;
in the formula, ciFor the stiffness of the rope, diDamping for the rope; Δ liIs the deformation amount of the rope;
the rope deformation speed;
(4) the mathematical model of dynamics is:
wherein F is an external force acting on the mobile platform;
step five, building a closed-loop motion control framework:
the closed-loop motion control framework comprises a joint feedback-based motion control framework and a pose feedback-based motion control framework, wherein:
the motion control frame based on joint feedback and the motion control frame based on pose feedback both comprise an expected pose, moving platform pose feedback, winch corner feedback, internal force coordination, a motor driving system and a dynamic model with an elastic rope;
in the motion control frame based on joint feedback, the expected pose is solved through inverse kinematics to obtain the expected length variation of each rope, the result is converted into an expected motor corner, the expected motor corner is compared with the fed-back actual corner to obtain joint deviation, and the joint deviation is input into a PID controller to realize position control;
in the motion control frame based on pose feedback, a pose error is obtained by comparing an expected pose with a model measurement pose, a rope length error can be obtained according to a Jacobian matrix which is different between the rope length error and the pose error, the conversion from a task space error to a joint space error is realized, and then a rotation angle error of a motor is obtained and input into a PD controller to realize position control;
in the internal force coordination loop, expected tension is solved according to a tension distribution method, and the expected tension and rope tension obtained by model measurement form force internal loop feedback.
Step six, determining a force sense simulation control scheme:
the whole mechanism is equivalent to a mass-spring-damping system by adopting a force sense simulation ring, so that a transfer function between force and motion is obtained, external force is converted into position correction of a platform, the physical characteristics of the mechanism are changed by setting different parameter combinations, namely, a moving platform of the mechanism generates different motion state outputs under the action of the external force F, wherein:
the transfer function between force and motion is expressed as:
in the formula, MdIs equivalent mass; ddEquivalent damping is adopted; kdIs the equivalent stiffness; f is an external force acting on the mobile platform; e is the displacement correction of the mobile platform;
and seventhly, completing the construction of an integral control framework:
the overall control frame comprises at least two parts: a mobile platform position closed loop (two frames) and an internal force coordination loop; if the parallel mechanism needs to realize force sense simulation, the integral control frame also comprises a force sense simulation ring, and the step eight is executed;
and step eight, simulating different force senses and verifying the feasibility of human-computer interaction.
Compared with the prior art, the invention has the following advantages:
the control frame of the invention is composed of three parts, which can ensure the good position tracking of the mobile platform, ensure the small and adjustable tension on the rope, and increase the man-machine interaction function of the rope parallel mechanism. In the specific control scheme, the dynamic performance of the mechanism is improved by introducing the internal force coordination ring, and the interaction with people is realized by introducing the force sense simulation ring. The force sensing simulation ring can be used or not according to the use requirement, and the rest two parts still have a good control effect.
Drawings
FIG. 1 is an overall mechanical schematic;
FIG. 2 is an enlarged view of a portion of FIG. 1;
FIG. 3 is a schematic view of a closed vector of a rope in a workspace;
FIG. 4 is a schematic view of a cord drive;
FIG. 5 is a schematic view of the installation of the hoisting mechanism;
FIG. 6 is a block diagram of a kinetic model;
FIG. 7 is an overall control framework based on pose feedback;
FIG. 8 is an overall control framework based on joint feedback.
Detailed Description
The technical solution of the present invention is further described below with reference to the accompanying drawings, but not limited thereto, and any modification or equivalent replacement of the technical solution of the present invention without departing from the spirit and scope of the technical solution of the present invention shall be covered by the protection scope of the present invention.
The parallel mechanism is driven by eight ropes, the parallel mechanism is connected with a winch through a motor, the winch is wound with the ropes, the ropes are finally connected to a tail end executing mechanism, namely a mobile platform, through the guide of a guide pulley, the motion control of the tail end executing mechanism is completed through controlling the rotating angle of the motor, and a handle is arranged on the mobile platform of the parallel mechanism, so that the interaction between a person and the mechanism is facilitated. Fig. 1 and 2 are diagrammatic views of an overall mechanism with which a person can interact by holding the handle to move the platform. Fig. 4 is a schematic view of the complete transmission of a rope, and fig. 5 is a schematic view of the installation of a hoisting mechanism. The method comprises the following specific steps:
step 1: a motion solution method is determined.
The guide pulleys of the parallel mechanism can influence the rope length, and meanwhile, the transmission structure of the parallel mechanism can cause the rope length loosened by hoisting to be different from the rope length released at the tail end, so that the influence of the guide pulleys is considered on one hand, and on the other hand, the relationship between the motor rotation angle and the rope length variation in the structure is solved.
The rope drive diagram shown in fig. 4 was analyzed in two parts: the working space inner part (a hoisting rope outlet point C-a tangent point B of the guide pulley swinging shaft and the edge of the guide pulley) and the driving system inner part (a tangent point B of the guide pulley swinging shaft and the edge of the guide pulley-a movable hinge point A).
Firstly, a working space inner part: as shown in fig. 3, knowing the pulley radius ρ of the working space, the rope length in the working space is calculated by dividing the rope length into two parts, taking into account the influence of the pulley on the rope length: the first part is the length wrapped on the pulley, namely the arc length between the rope and two tangent points of the pulley, and the second part is the length between the exit rope point and the movable platform connecting point.
(1) Solving for the angle of oscillation betai：
In the formula,Bai,xthe component of the dynamic hinge point vector on the x axis of the global coordinate system is shown;Bai,ythe component of the dynamic hinge point vector on the y axis of the global coordinate system is shown;Bbi,xfor the oscillating axle of the guide pulley and the edge of the guide pulleyThe component of the tangent point vector on the x-axis of the global coordinate system;Bbi,yis the component of the tangent point vector of the swing axis of the guide pulley and the edge of the guide pulley on the y axis of the global coordinate system.
(2) Solving for wrap angle alphai：
In the formula,
a rotation matrix of the guide pulleys about the swing angle; e.g. of the typexIs a unit vector in the H coordinate system along the positive direction of the x axis, ex＝[1 0 0]T。
Angle of wrap alphaiCan be expressed as alphai＝π-(αi,1+αi,2)。
Wherein,
(3) solving coordinates of rope outlet pointBSi：
(4) Solving the rope length l of the working space partW,i：
Adding the lengths of the two parts to obtainW,i＝qP+lAS＝ρ·αi+||Bai-BSi||2。
In the formula, qPThe length of the rope wrapped on the guide pulley; lASThe length of the rope between the rope outlet point of the guide pulley and the movable hinge point is shown.
II, a driving system part: as shown in FIG. 4, s is the length of the straight line between the pulley in the driving system and the guide pulley in the working space, and can be turned by the winch
And the rope winding pitch h:
the rope length of hoisting and loosening is as follows:
in the form of a loose rear drive system
Effective variation of added rope Δ lWEqual to the internal length of the drive system before release plus the length to be released, as follows:
in the formula, cAAnd cBAs shown in FIG. 4 (c)AThe length of the rope from the rope outlet point of the winch to the tangent point of the rope and the left side of the pulley gamma, cBThe length of the rope wrapped on the pulley gamma); lW0,iThe length of the rope is the original length of the working space part.
Finishing to obtain:
step 2: the jacobian matrix is solved.
The Jacobian matrix can be used for describing the relation between the variable speed of the mechanism joint and the speed of the mobile platform and also describing the relation between the joint force and the stress of the tail end mobile platform, so that the Jacobian matrix is solved to lay a foundation for rope tension distribution and conversion from the joint variable to the tail end variable.
In pair type
Two sides are simultaneously derived and simplified:
ignoring the less influential terms, the above equation is simplified:
and step 3: a tension distribution method is determined.
The rope on the parallel mechanism has the characteristics of elasticity and unidirectional stress, the rope is ensured to be always in a tensioning state when the mobile platform moves, and the rope is subjected to tension distribution to ensure that the tension on the rope is within an expected range for the full-constraint mechanism.
The ropes were tension distributed using Closed-form theory:
f＝-J+Tw+fm-J+TJTfm。
wherein f is the rope tension; j. the design is a square+TIs the pseudo-inverse of the Jacobian matrix; w is an external force; f. ofmIs the average of the maximum and minimum values of the tension range.
And 4, step 4: a dynamic model of the mechanism is established taking into account the elasticity of the rope.
The rope-driven parallel mechanism researched by the invention does not need to bear larger load, and the moving platform has lighter weight. The connection between the rope and the moving platform, between the rope and the guide pulley, and between the rope and the winch are all assumed to be in an ideal state, namely, no friction force is generated in the mechanism. Based on the above assumptions, the dynamic modeling includes moving platforms, winches and guide sheaves, and ropes.
Moving platform dynamics: and establishing a dynamic model of the translation process of the terminal platform based on Newton's law, and establishing a dynamic model of the rotation process of the mobile platform based on Euler's equation.
Finishing to obtain:
hoisting and guide sheave dynamics: suppose JrEquivalent moment of inertia of the winch model and the pulley model;
a rotation angle vector of the ith motor, wherein the direction for extending the rope is defined as a positive direction; crAn equivalent damping coefficient matrix of a winch model and a pulley model; lambda [ alpha ]sThe equivalent radius of the winch model and the pulley model; f. of1iThe rope tension of the ith rope driving side; t isact,iIs the torque of the drive. Then the moment balances:
rope dynamics: the rope is equivalent to a spring damping model, and the rigidity of the rope is set to be ciAnd the damping of the rope is diThen, there are:
complete kinetics: when the mechanism interacts with the user, assuming that the force applied by the user is F, the overall mathematical model of the dynamics is,
the constructed dynamic simulation framework is shown in fig. 6.
And 5: and (5) building a closed-loop motion control framework.
The present invention provides two control frameworks: one motion control framework based on pose feedback and the other motion control framework based on joint feedback. The two frames comprise an expected pose, moving platform pose feedback, winch corner feedback, internal force coordination, a motor driving system and a dynamic model with an elastic rope, wherein:
the joint space control method includes the steps that expected rope length variable quantity of each rope is obtained through inverse kinematics solution from an expected pose, the result is converted into an expected motor corner, the expected motor corner is compared with a fed-back actual corner to obtain joint deviation, and the joint deviation is input into a PID controller to achieve position control;
the pose closed loop is a task space control method, a pose error is obtained by comparing an expected pose with a model measurement pose, a rope length error can be obtained according to a Jacobian matrix which is different between the rope length error and the pose error, the conversion from the task space error to a joint space error is realized, and then the rotation angle error of the motor is obtained and input into a PD controller to realize position control;
the control frame also comprises a rope tension control method, namely an internal force coordination loop, the expected tension is solved according to the tension distribution method, and the expected tension and the rope tension obtained by model measurement form force internal loop feedback.
In the invention, a motion control framework based on joint feedback is shown in fig. 7, an expected pose is calculated by inverse kinematics to obtain an expected length change delta l of each rope, the expected length change delta l is converted into an expected motor rotation angle according to the result obtained in the step 1, the expected motor rotation angle is compared with a fed-back actual rotation angle to obtain a joint deviation delta theta, the joint deviation delta theta is input into a PID (proportion integration differentiation) controller, and tension control adopts the tension distribution method in the step 3 to form force inner loop feedback.
In the invention, a motion control frame based on pose feedback is shown in fig. 8, the pose deviation delta q can be obtained by comparing an expected pose with a measurement pose, the rope length error delta l can be obtained as J.delta q according to a jacobian matrix which is different between the rope length error and the pose error, the conversion from a task space error to a joint space error is completed, the rotation angle error of a motor can be obtained and input into a PD controller to realize position control, and tension control adopts the tension distribution method in the step 3 to form force inner loop feedback.
In the invention, the two controls are both realized by outputting driving torque control mechanism motion through a motor driving system.
Step 6: and determining a force sense analog control scheme.
On the basis of realizing motion control, the invention also provides a control scheme for man-machine interaction, wherein the whole mechanism is equivalent to a mass-spring-damping system by adopting a force sense simulation ring, and the physical characteristics of the mechanism are changed by setting different parameter combinations, namely a moving platform of the mechanism can generate different motion state outputs under the action of an external force F. The transfer function between force and motion is:
the external force can be converted into the position correction amount of the platform.
In the invention, the rope tension sensor is adopted, when the mobile platform is acted by external force, the tension on the rope is inevitably changed, and the measured rope tension is converted into the external force through Jacobian matrix and stress analysis and then is input into the controller of the force sensing simulation ring.
Resultant w of forces other than rope tensionisCan be expressed as:
wis＝-JTfis。
in the formula (f)isIs the rope tension.
The inertia force is offset through stress analysis
And the gravity winitExternal force wadmExpressed as:
and 7: and finishing the construction of the overall control framework.
The overall control framework comprises three parts, namely a mobile platform position closed loop (two frameworks), an internal force coordination loop and a force sense simulation loop, as shown in fig. 7 and 8. If the mechanism does not need to realize force sense simulation, only the force sense simulation ring in the control frame needs to be removed, and the rest part can still realize good control on the mechanism.
And 8: and simulating different force senses to verify the feasibility of human-computer interaction.
By simulating several parameter setting situations, the feeling of force when a person interacts with a certain object in reality can be analogized, for example: the force sense of the situations of pushing a wall, pushing a box, beating a ball and the like can be simulated. The specific simulation scenario is as follows:
when the rigidity, the damping and the inertia exist, the mobile platform can show damping oscillation under the action of an instantaneous thrust and is finally stabilized at a balance position; when the damping is 0, the mobile platform can present an elastic effect, people can feel the force feeling when touching the spring, and the platform can be used for simulating a rubber ball; when the rigidity and the inertia are both 0, the mobile platform can show the following movement to the external force, when the external force is removed at a certain moment, the mobile platform can stop at the position where the force disappears, people can feel the force sense like pushing an object with light weight from one position to another position, and at the moment, the platform can be used for simulating a box; when the rigidity is 0, the mobile platform gradually moves away until stopping under the action of an instantaneous thrust, people can feel the force feeling when pushing away a boat on the water surface, and the platform can be used for simulating the boat on the water surface. When infinite rigidity and damping are set at a certain position, the platform cannot be moved under the action of continuously increasing external force, people can feel the force when the platform collides with a wall, and the platform can be used for simulating the wall.
Claims (6)
1. A force sense simulation control method of a rope-driven parallel mechanism in a fully-constrained space is characterized by comprising the following steps of:
step one, determining a motion calculation method:
the rope was divided into two parts for analysis: the working space inner part and the driving system inner part solve the swing angle beta for the working space inner partiAngle of wrap alphaiCoordinates of rope outlet pointBSiFinally, the length l of the rope of the working space part is obtainedW,i(ii) a For the part in the driving system, obtaining an identity relation through the rope length states at two moments to solve the relation between the motor rotation angle and the rope length variation;
step two, solving a Jacobian matrix:
the jacobian matrix is represented as:
J＝[ln T (BRP Pai×ln)T]；
wherein J is a Jacobian matrix of the mechanism;BRPa rotation matrix of pose change between a global coordinate system and a body coordinate system; lnIs a unit rope length vector;Paiis the vector of the movable hinge point in the body coordinate system,Bai＝BRP Pai；
step three, determining a tension distribution method:
the ropes were tension distributed using Closed-form theory:
fis＝-J+Tw+fm-J+TJTfm；
in the formula (f)isIs the rope tension; j. the design is a square+TIs the pseudo-inverse of the Jacobian matrix; w is an external force; f. ofmThe average value of the maximum value and the minimum value of the tension range;
step four, establishing a dynamic model of the mechanism in consideration of the elasticity of the rope:
assuming that the connections between the ropes and the moving platform, between the ropes and the guide pulleys, and between the ropes and the winches are all in an ideal state, the mathematical model of the dynamics is expressed as:
wherein L is a matrix formed by unit direction vectors of each rope;Pa is a movable platform hinge point coordinate matrix; c. CiIs the stiffness of the rope; diDamping for the rope; Δ liIs the deformation amount of the rope;
the rope deformation speed; e is a 3 × 3 identity matrix; i is an inertia matrix of the movable platform relative to the fixed platform; omega is an antisymmetric matrix; m is the mobile platform mass; g is a gravity acceleration vector; t is the moving displacement of the movable platform relative to the fixed platform; ω and
the rotating angular velocity and the angular acceleration of the movable platform relative to the fixed platform are obtained; f is an external force acting on the mobile platform;
step five, building a closed-loop motion control framework:
the closed-loop motion control framework comprises a joint feedback-based motion control framework and a pose feedback-based motion control framework, wherein: the motion control frame based on joint feedback and the motion control frame based on pose feedback both comprise an expected pose, moving platform pose feedback, winch corner feedback, internal force coordination, a motor driving system and a dynamic model with an elastic rope;
step six, determining a force sense simulation control scheme:
the whole mechanism is equivalent to a mass-spring-damping system by adopting a force sense simulation ring, so that a transfer function between force and motion is obtained, external force is converted into position correction of a platform, and the physical characteristics of the mechanism are changed by setting different parameter combinations, namely the moving platform of the mechanism is subjected to external force FextDifferent motion state outputs are generated under the action;
and seventhly, completing the construction of an integral control framework:
the overall control frame comprises at least two parts: a mobile platform position closed loop and an internal force coordination loop.
2. The method for simulating and controlling the force sense of a rope-driven parallel mechanism in a fully constrained space as claimed in claim 1, wherein in the first step, the swing angle β isiAngle of wrap alphaiCoordinates of rope outlet pointBSiLength of rope in working spaceW,iAnd the relation between the motor rotation angle and the rope length variation is expressed as follows:
(1) angle of oscillation betai：
In the formula,Bai,xthe component of the dynamic hinge point vector on the x axis of the global coordinate system is shown;Bai,ythe component of the dynamic hinge point vector on the y axis of the global coordinate system is shown;Bbi,xthe component of the vector of the tangent point of the swing axis of the guide pulley and the edge of the guide pulley on the x axis of the global coordinate system is shown;Bbi,ythe component of the vector of the oscillating axis of the guide pulley and the tangent point of the edge of the guide pulley on the y axis of the global coordinate system;
(2) wrap angle alphai：
αi＝π-(αi,1+αi,2)；
In the formula,Bmithe vector of the center of the guide pulley in the global coordinate system is taken as the vector;Bmi,zis the component of the guide pulley center vector on the z axis of the global coordinate system;Baithe vector of the movable hinge point in the global coordinate system is obtained;Bai,zfor the vector of the pivot point in the z-axis of the global coordinate systemA component; rho is the radius of the guide pulley;
(3) coordinates of rope outlet pointBSi：
In the formula,Bmi,xis the component of the guide pulley center vector on the x axis of the global coordinate system;Bmi,ythe component of the guide pulley center vector on the y axis of the global coordinate system is shown;
(4) rope length l of working space partW,i：
lW,i＝qP+lAS＝ρ·αi+||Bai-BSi||2；
In the formula, qPThe length of the rope wrapped on the guide pulley; lASThe length of the rope between the rope outlet point of the guide pulley and the movable hinge point is determined;
(5) the relationship between the motor rotation angle and the rope length variation is as follows:
in the formula,. DELTA.lWIs the effective variation of the rope; h is the winding pitch of the rope;
is the motor corner; v. ofPGThe transmission ratio between the motor and the winch is set; r is the hoisting radius.
3. The force sense simulation control method of the fully constrained space rope driven parallel mechanism according to claim 1, wherein in the fourth step, the dynamic modeling comprises a moving platform, a hoisting and guiding pulley and a rope, wherein:
(1) adopting a Newton Euler method to model a mobile platform:
in the formula (f)2iIs the platform side rope tension;
(2) a moment balance method is adopted to model a hoisting and guide pulley:
in the formula, JrEquivalent moment of inertia of the winch model and the pulley model;
the rotation angle vector of the ith motor; crAn equivalent damping coefficient matrix of a winch model and a pulley model; lambda [ alpha ]sThe equivalent radius of the winch model and the pulley model; f. of1iThe rope tension of the ith rope driving side; t isact,iIs the torque of the drive;
(3) modeling the rope as a spring damping model;
4. the force sense analog control method of the fully-constrained space rope-driven parallel mechanism according to claim 1, characterized in that in the fifth step, in a motion control frame based on joint feedback, the expected rope length variation of each rope is obtained by inverse kinematics solution from the expected pose, the result is converted into an expected motor rotation angle, and then the expected motor rotation angle is compared with the fed-back actual rotation angle to obtain joint deviation, and the joint deviation is input into a PID controller to realize position control; in a motion control frame based on pose feedback, comparing an expected pose with a model measurement pose to obtain a pose error, obtaining a rope length error according to a Jacobian matrix which is different from the rope length error and the pose error, realizing the conversion from a task space error to a joint space error, further solving a corner error of a motor and inputting the corner error into a PD controller to realize position control; in the internal force coordination loop, expected tension is solved according to a tension distribution method, and the expected tension and rope tension obtained by model measurement form force internal loop feedback.
5. The method for simulating and controlling the force sense of a rope-driven parallel mechanism in the fully constrained space according to claim 1, wherein in the sixth step, the transfer function between the force and the motion is expressed as:
in the formula, MdIs equivalent mass; ddEquivalent damping is adopted; kdIs the equivalent stiffness; and E is the displacement correction quantity of the movable platform.
6. The force sense simulation control method of the fully-constrained space rope-driven parallel mechanism according to claim 1, wherein in the seventh step, if the parallel mechanism needs to realize force sense simulation, the overall control frame further comprises a force sense simulation ring, and the eighth step is executed;
and step eight, simulating different force senses and verifying the feasibility of human-computer interaction.
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