SS-ALE modeling method and simulation control system of rope cluster driven space agile manipulator

Abstract

The present application provides an SS-ALE modeling method and simulation control system for a rope cluster driven space agile manipulator, and relates to the technical field of space manipulators. The SS-ALE modeling method includes: using a multi-rigid body model to model the rigid structure in the rope cluster driven space agile manipulator; using an ALE cable unit model to model the non-contact segment of the rope that is not in contact with the pulley in the rope cluster driven space agile manipulator; using a rope-pulley system constraint equation to model the contact segment of the rope that is in contact with the pulley in the rope cluster driven space agile manipulator; using a Coulomb dry friction model to model the sliding friction between the rope driving the wrist and elbow joints and the fixed pulley in the rope cluster driven space agile manipulator; this method can simulate the elastic deformation and contact friction of the rope, realize the open-loop and closed-loop control modes of rope length input and force input, and simulate the rope drive with high fidelity, so as to more accurately present the dynamic characteristics of the system.

Description

Technical Field

[0001] The present application relates to the technical field of space manipulators, and in particular to an SS-ALE modeling method and a simulation control system for a rope cluster driven space agile manipulator. Background Art

[0002] The space manipulator is the core equipment for spacecraft on-orbit services, and plays a key role in on-orbit tasks such as equipment maintenance, refueling, material transportation, and emergency rescue. Traditional rigid space manipulators use modular joints and motors are installed at the joints, resulting in large mass inertia and large size, making it difficult to achieve high compliance and high agility. In recent years, rope cluster-driven agile space manipulators have received widespread attention. Rope cluster-driven agile space manipulators are remotely driven by ropes, and have the characteristics of electromechanical separation, light weight and low inertia, inherent compliance, agility, etc., which is an innovation in space manipulator technology.

[0003] Traditional space rigid manipulators can establish accurate dynamic equations based on Lagrange equations or Newton-Euler method, but for rope cluster driven space agile manipulators, the driving mode of flexible ropes introduces complex characteristics such as large hysteresis, non-smoothness, and strong coupling, which significantly increases the difficulty of modeling and control. At present, there is a complete kinematic analysis for the modeling research of rope cluster driven space agile manipulators. By using the rope length as the medium, a kinematic model of "driving space-joint space-task space" is established to provide a basis for control; while there are few studies on the dynamic modeling of rope cluster driven space agile manipulators. The existing dynamic models are generally based on Lagrange equations or Newton-Euler method. For example, Tu Mingzheng et al. used the Lagrange equations and the principle of virtual work to establish a dynamic model for the control design of a four-degree-of-freedom rope-driven rigid manipulator; Chen Weihai et al. used the iterative Newton-Euler method to establish a dynamic model, and analyzed the tension of the rope based on the tension distribution algorithm of the dynamic minimum preload; Wu Hongtao et al. used the Newton-Euler method to establish a dynamic model and analyzed the influence of the rope preload on the system force.

[0004] The current dynamic modeling methods for rope-driven rigid manipulators focus on the modeling of multi-rigid body systems. When dealing with rope modeling problems, the ropes are usually simplified as rigid ropes, and the effects of the elastic deformation and contact friction of the ropes on the dynamic characteristics of the system are ignored. However, the rope cluster-driven agile space manipulator is designed to improve the agility of movement. When performing on-orbit tasks at a high speed, the inertial force may cause a large rope deformation, resulting in a significant deviation between the actual motion trajectory and the planned trajectory. The rope deformation problem cannot be ignored. In addition, the contact friction between the rope and the pulley will also affect the tension distribution of the rope, thereby affecting the rope deformation and the force of the system. In particular, the stick-slip friction of the rope in reciprocating motion will significantly affect the driving effect of the rope on the joint. In order to solve the rope modeling problem and simulate the contact friction between the rope and the pulley that changes dynamically with the configuration, research on replacing the mechanical model with a neural network model has emerged in recent years. For example, the KoreaTech team in South Korea has developed a hybrid model that combines a multi-rigid body dynamics model based on mechanics with a neural network learning model to improve the applicability of the model. However, this method requires a lot of training on real data and is difficult to generalize to different tasks that are different from the training scenario. Summary of the invention

[0005] In order to solve at least one of the above problems, the present application proposes a SS-ALE modeling method and a simulation control system for a rope cluster driven space agile robotic arm.

[0006] According to the first aspect of the present application, at least one embodiment of the present application provides an SS-ALE modeling method for a rope cluster driven space agile manipulator, comprising: adopting a multi-rigid body model to model the rigid structure in the rope cluster driven space agile manipulator; adopting an ALE cable unit model to model the non-contact segment of the rope that is not in contact with the pulley in the rope cluster driven space agile manipulator; adopting a rope-pulley system constraint equation to model the contact segment of the rope that is in contact with the pulley in the rope cluster driven space agile manipulator; adopting a Coulomb dry friction model to model the sliding friction between the rope driving the wrist joint and the elbow joint and the fixed pulley in the rope cluster driven space agile manipulator; the multi-rigid body model, the ALE cable unit model, the rope-pulley system constraint equation and the Coulomb dry friction model are used to build a dynamic model of the rope cluster driven space agile manipulator, so as to input the generated motor torque into the dynamic model for rope drive simulation.

[0007] For example, in some embodiments of the present application, the non-contact segment of the rope that is not in contact with the pulley in the rope cluster driven spatial agile manipulator is modeled using an ALE rope unit model, including: modeling the non-contact segment of the rope that is not in contact with the pulley based on the generalized coordinates and control equations of the ALE variable length rope unit; wherein the ALE variable length rope unit includes a first node and a second node, and the generalized coordinates of the ALE variable length rope unit are calculated according to the following formula:

[0008]

[0009] in, are the generalized coordinates of the ALE variable length cable element, , are the position coordinates of the first node and the second node, , are the material coordinates of the first node and the second node;

[0010] The control equation of the ALE variable length cable element satisfies the following formula:

[0011]

[0012] in, is the generalized mass of the ALE variable length cable element, is a generalized external force, is the additional inertial force caused by material flow, is the generalized elastic force caused by elastic deformation.

[0013] For example, in some embodiments of the present application, the contact segment of the rope in contact with the pulley in the rope cluster driven space agile manipulator is modeled using the rope-pulley system constraint equation, including: establishing the rope-pulley system constraint equation according to position constraints, tangency constraints and length constraints, and modeling the contact segment of the rope in contact with the pulley in the rope cluster driven space agile manipulator.

[0014] For example, in some embodiments of the present application, the position constraint condition satisfies the following formula:

[0015]

[0016]

[0017] in, , are the position coordinates of the first and second tangent points of the contact segment rope and the pulley in the global coordinate system, represents the position coordinates of the pulley center in the global coordinate system, is the attitude transformation matrix from the pulley center of mass coordinate system to the global coordinate system, , are the position coordinates of the first tangent point and the second tangent point in the pulley center of mass coordinate system.

[0018] For example, in some embodiments of the present application, the tangency constraint condition satisfies the following formula:

[0019]

[0020]

[0021] in, , is the tangent vector of the contact segment rope at the first tangent point and the second tangent point in the global coordinate system.

[0022] For example, in some embodiments of the present application, the dynamic material length of the rope is calculated according to the material coordinates of the first tangent point and the second tangent point, and the wrap angle of the first tangent point and the second tangent point and the contact segment rope to the pulley; the length constraint condition satisfies the following formula:

[0023]

[0024] in, is the initial material length of the rope, is the dynamic material length of the rope, are the material coordinates of the first tangent point and the second tangent point, It is the wrap angle between the first tangent point, the second tangent point and the contact section rope and the pulley.

[0025] For example, in some embodiments of the present application, the sliding friction between the ropes driving the wrist joint and the elbow joint and the fixed pulley in the rope cluster driven spatial agile manipulator is modeled using a Coulomb dry friction model, including: calculating the friction force between the rope and the fixed pulley according to the following formula:

[0026]

[0027] in, , are respectively the rope tensions at both ends of the contact section rope in contact with the fixed pulley, is the coefficient of kinetic friction, is the wrap angle of the contact section rope to the fixed pulley, is the static friction.

[0028] According to the second aspect of the present application, at least one embodiment of the present application provides a simulation control system, including: a planning module, used to generate the expected motion trajectory of each joint angle of the rope cluster driven space agile robotic arm; a motor three-ring control module, connected to the planning module, used to generate the motor torque of the driving rope according to the error between the actual value and the expected motion trajectory; a dynamic modeling module, used to execute the SS-ALE modeling method as described in any one of the first aspects to build a dynamic model of the rope cluster driven space agile robotic arm; the dynamic modeling module is connected to the motor three-ring control module, inputs the motor torque into the dynamic model for rope drive simulation, and feeds back the output result to the motor three-ring control module, so that the motor three-ring control module further adjusts the motor torque to form a closed-loop control.

[0029] According to the third aspect of the present application, at least one embodiment of the present application provides an electronic device, comprising: one or more processors; a memory for storing one or more programs; when the one or more programs are executed by the one or more processors, the one or more processors execute a method as described in any one of the first aspects.

[0030] According to a fourth aspect of the present application, at least one embodiment of the present application provides a computer-readable storage medium having a computer program stored thereon, wherein the program is executed by a processor to implement a method as described in any one of the first aspects.

[0031] This application proposes a stick-slip arbitrary Lagrangian-Eulerian (SS-ALE) dynamic modeling method for a rope-cluster driven space agile manipulator. This method uses a variable length cable unit based on ALE description to simulate the driving rope, and uses the Coulomb dry friction model to describe the stick-slip friction of the driving rope passing through the pulley. By establishing the constraint equation between the rope and the pulley to simulate the rope passing through the pulley system, the number of degrees of freedom introduced by the dynamic modeling is reduced, and the over-dense division of the rope nodes and the accompanying large number of contact collision detections in the traditional finite element method are avoided, so as to realize the dynamic simulation of the rigid-flexible coupling system. Compared with the current rope-driven rigid manipulator dynamic model, which usually simplifies the rope into a rigid rope and ignores the influence of the elastic deformation and contact friction of the rope on the dynamic characteristics of the system, this method can simulate the elastic deformation and contact friction of the rope, realize the open-loop and closed-loop control modes of the rope length input and force input, and simulate the rope drive with high fidelity, so as to more accurately present the dynamic characteristics of the system.

[0032] In order to systematically study the rope length input and force input modes, this application also proposes a simulation control system for building a rope cluster-driven space agile manipulator based on the SS-ALE dynamic modeling method, adding a motor three-loop control model, and then building a rope cluster-driven space agile manipulator dynamic simulation control system. The motor three-loop control model establishes a three-loop control of the "position loop-speed loop-current loop" for the joint motor. In this way, precise control of the motor is achieved, providing input for the SS-ALE dynamic model, which will help to carry out parameter analysis and control strategy research, thereby guiding the optimization of mechanism design, effectively improving motion accuracy and other performance, and providing technical support for ground tests and on-orbit services.

[0033] It should be understood that the foregoing general description and the following detailed description are exemplary only and are not restrictive of the present application. BRIEF DESCRIPTION OF THE DRAWINGS

[0034] By describing in detail exemplary embodiments thereof with reference to the accompanying drawings, the above and other objects, features and advantages of the present application will become more apparent. The accompanying drawings described below are only some embodiments of the present application, and are not intended to limit the present application.

[0035] Figure 1 An exemplary rope cluster driven space agile manipulator configuration and joint schematic diagram are shown;

[0036] Figure 2A , Figure 2B A schematic diagram showing an exemplary transmission method of a rope-driven elbow joint and a wrist joint;

[0037] Figure 3 A schematic diagram showing an exemplary SS-ALE modeling method for a rope cluster driven space agile manipulator;

[0038] Figure 4 A dynamic three-dimensional model of a rope cluster driven space agile manipulator according to an exemplary embodiment is shown;

[0039] Figure 5A , Figure 5B An exemplary schematic diagram of a multi-rigid body model kinematic pair is shown;

[0040] Figure 6 Schematic diagram of an exemplary ALE cable unit is shown;

[0041] Figure 7 A schematic diagram of an exemplary rope-pulley system is shown;

[0042] Fig. 8A , Figure 8B A schematic diagram showing an exemplary point contact friction and friction angle of an elbow joint;

[0043] Fig. 9A schematic diagram of an exemplary Coulomb dry friction model is shown;

[0044] Fig.10 A schematic diagram of a simulation control system showing an exemplary embodiment;

[0045] Fig.11 A schematic diagram of an exemplary motor three-loop control model is shown;

[0046] Figure 12A-12C A schematic diagram showing rope tension verification of an exemplary rope cluster driven space agile manipulator acceleration condition;

[0047] Figures 13A-13D A schematic diagram showing an exemplary effect of elastic deformation of a rope on motion accuracy;

[0048] Figures 14A-14H A schematic diagram showing an exemplary effect of rope contact friction on motion accuracy;

[0049] Fig.15 A structural diagram of an electronic device provided by the present application is shown. DETAILED DESCRIPTION

[0050] Example embodiments will now be described more fully with reference to the accompanying drawings. However, example embodiments can be implemented in many forms and should not be construed as limited to the embodiments set forth herein; rather, these embodiments are provided so that this application will be comprehensive and complete and will fully convey the concepts of the example embodiments to those skilled in the art. The same reference numerals in the figures represent the same or similar parts, and thus their repeated description will be omitted.

[0051] The described features, structures or characteristics may be combined in one or more embodiments in any suitable manner. In the following description, many specific details are provided to provide a full understanding of the embodiments of the present disclosure. However, those skilled in the art will appreciate that the technical solutions of the present disclosure may be practiced without one or more of these specific details, or other modes, components, materials, devices, etc. may be adopted. In these cases, known structures, methods, devices, implementations, materials or operations will not be shown or described in detail.

[0052] The flowcharts shown in the accompanying drawings are only exemplary and do not necessarily include all the contents and operations / steps, nor must they be executed in the order described. For example, some operations / steps can be decomposed, and some operations / steps can be combined or partially combined, so the actual execution order may change according to actual conditions.

[0053] The terms "first", "second", etc. in the specification and claims of this application and the above-mentioned drawings are used to distinguish different objects, rather than to describe a specific order. In addition, the terms "including" and "having" and any variations thereof are intended to cover non-exclusive inclusions. For example, a process, method, system, product or device that includes a series of steps or units is not limited to the listed steps or units, but optionally includes steps or units that are not listed, or optionally includes other steps or units inherent to these processes, methods, products or devices.

[0054] Those skilled in the art will appreciate that the drawings are merely schematic diagrams of example embodiments, and the modules or processes in the drawings are not necessarily necessary for implementing the present application, and therefore cannot be used to limit the scope of protection of the present application.

[0055] Figure 1 An exemplary rope-cluster-driven space agile robotic arm configuration and joint schematic diagram are shown.

[0056] The SS-ALE modeling method of the rope cluster driven space agile manipulator provided in this application is used to simulate objects such as Figure 1 As shown, the rope cluster driven spatial agile robotic arm includes shoulder, elbow and wrist joints, with a total of 7 degrees of freedom, among which shoulder joint 1 and shoulder joint 2 are driven by traditional motor + reducer, and control rotation and pitch with 1 degree of freedom respectively; the elbow and wrist joints are remotely driven by ropes, elbow joint 1 and elbow joint 2 have pitch freedom, and the wrist joint has rotation, pitch and yaw, with a total of 3 degrees of freedom.

[0057] Among them, the transmission method of rope-driven elbow and wrist joints is as follows Figure 2A and Figure 2B As shown in the figure, each elbow joint is driven by a set of ropes, and pure rolling occurs in the plane under the constraint of the mechanism; the pitch and yaw degrees of freedom of the wrist joint are coupled and driven by two sets of ropes in coordination, and pure rolling occurs in space under the constraint of the mechanism, and another set of ropes drives the rotational degree of freedom of the wrist joint alone. The five sets of ropes driving the elbow and wrist joints are initially wound around the corresponding winding wheels located on the shoulders, and reach the elbow and wrist joints through several steering pulleys. The motor located on the shoulder controls the winding wheels to retract and release the ropes, thereby driving the elbow and wrist joints to rotate.

[0058] The rope cluster driven spatial agile manipulator is a complex rigid-flexible coupling system, which includes multiple flexible ropes that take deformation into account and have a large range of motion, as well as rigid components such as arm rods and pulleys installed thereon that do not take deformation into account. In the system, the ropes pass through several steering pulleys to reach the driving joints, and the topological relationship between the ropes and the pulleys is very complex. If the traditional finite element method is used to model this rigid-flexible coupling system, the flexible ropes are discretized with rope units and the contact between the rope unit nodes and the pulleys is established, then the rope unit nodes need to be divided densely enough to ensure the calculation accuracy. This method will greatly increase the number of system degrees of freedom and the difficulty of contact and collision detection, making it difficult to achieve dynamic simulation. In addition, compared with traditional rigid transmission mechanisms, rope drives inevitably have contact friction with the pulleys because the ropes pass through a large number of pulley guide transmissions, which affects the transmission efficiency to a certain extent. Figure 2A and Figure 2B As shown, the rope passes through several movable pulleys and fixed pulleys, wherein the rope passing through the movable pulley overcomes the bearing friction of the pulley itself, and the transmission efficiency loss is small or negligible; while the rope passing through the fixed pulley has sliding friction with the pulley, and the transmission efficiency loss is significant, and its size is related to the wrapping angle of the rope to the pulley, and changes dynamically with the configuration during the transmission process, and cannot be ignored.

[0059] Therefore, in order to analyze the influence of elastic deformation and contact friction of the rope on the dynamic characteristics of the system, the present application provides a stick-slip arbitrary Lagrangian-Eulerian (SS-ALE) dynamic modeling method for a rope cluster driven space agile manipulator, which uses a variable length cable unit described by arbitrary Lagrangian-Eulerian Formulation (ALE) to simulate the driving rope, and uses a Coulomb dry friction model to describe the stick-slip (SS) friction generated by the driving rope passing through the pulley. At the same time, the rigid arm and the control system are modeled, thereby realizing high-fidelity dynamic modeling and simulation of the rope cluster driven space agile manipulator, which is used to construct a set of dynamic models such as Figure 1 The dynamic model of the rope cluster driven space agile manipulator is shown in FIG. Figure 4 shown.

[0060] Figure 3 A schematic diagram of the SS-ALE modeling method of a rope cluster driven space agile manipulator according to an exemplary embodiment is shown.

[0061] like Figure 3 As shown, the SS-ALE modeling method of the rope cluster driven space agile manipulator includes steps S301-S304:

[0062] In step S301, a multi-rigid body model is used to model the rigid structure in the rope cluster driven space agile manipulator.

[0063] In step S302, the non-contact section of the rope that is not in contact with the pulley in the rope cluster driven spatial agile manipulator is modeled using the ALE rope unit model.

[0064] In step S303, the contact section of the rope in the rope cluster driven space agile manipulator that is in contact with the pulley is modeled using the rope-pulley system constraint equation.

[0065] In step S304, the sliding friction between the ropes driving the wrist joint and the elbow joint and the fixed pulley in the rope cluster driven spatial agile manipulator is modeled using the Coulomb dry friction model.

[0066] The arm, pulley and other components in the rope-cluster driven space agile robotic arm are rigid structures that are not easy to bend. The internal structure can be ignored and only the mass and inertia need to be considered. Therefore, the modeling can be based on a multi-rigid body model.

[0067] In step S301: the rigid body model adopts the traditional modeling method to describe the rigid structure posture according to the center of mass position and posture, and based on Newton's second law of center of mass translation and the center of mass fixed-point rotation equation, the rigid structure in the rope cluster driven space agile manipulator is modeled.

[0068] Among them, the center of mass position of the rigid body adopts the component of the center of mass in the global coordinate system As generalized coordinates, the posture of the rigid body uses the Euler rotation vector As generalized coordinates, the center of mass position and posture constitute the rigid body generalized coordinates :

[0069]

[0070] The governing equations of a rigid body include translation and rotation. Newton's second law based on the translation of the center of mass is:

[0071]

[0072] The center of mass fixed point rotation equation is:

[0073]

[0074] in, is the mass of the rigid body, is the equivalent external force applied on the center of mass, is the inertia tensor of the rigid body, is the angular velocity of the rigid body in the local coordinate system of the center of mass, is the equivalent moment applied to the center of mass in the local coordinate system of the center of mass. The vector can be rotated by Euler Calculated.

[0075] According to the example embodiment, when modeling the rigid structure in the rope cluster driven space agile manipulator, the kinematic pairs between the rigid arm bars and between the arm bars and components such as pulleys need to satisfy the constraint equations. The kinematic pairs between the rigid arm bars and between the arm bars and components such as pulleys include fixed pairs connecting the arm bars and components such as pulleys fixed thereon, and rotation pairs connecting the rotation joint components at various locations.

[0076] Among them, the fixed joints between rigid bodies need to constrain all 6 degrees of freedom to keep the global position and global posture consistent. The constraint equation is:

[0077]

[0078] The revolute joint between rigid bodies needs to constrain the five degrees of freedom except the direction of the axis of rotation. The constraint equation is:

[0079]

[0080] in, , is the constraint point on the two rigid bodies connected by the kinematic joint, , , Represents the global component of the local coordinate axis of the constraint point, such as Figure 5A and Figure 5B shown.

[0081] In order to analyze the influence of elastic deformation of the rope on the dynamic characteristics of the system, the variable length rope element based on ALE description is used to simulate the non-contact rope segment.

[0082] In step S302, a non-contact section of the rope that is not in contact with the pulley is modeled based on the generalized coordinates and control equations of the ALE variable-length rope unit.

[0083] like Figure 6 As shown, the ALE variable-length cable unit includes a first node and a second node, and the two ALE nodes constitute a variable-length ALE virtual unit to describe a straight cable that is non-contact with the pulley.

[0084] The generalized coordinates of the ALE variable length cable element are calculated according to the following formula:

[0085]

[0086] in, is the generalized coordinate of the ALE variable length cable element, , are the position coordinates of the first node and the second node, , are the material coordinates of the first node and the second node. The physical meaning of the material coordinates is that the nodes can slide along the rope, that is, the unit has a variable length and there is material flow inside.

[0087] The control equation of the ALE variable length cable element satisfies the following formula:

[0088]

[0089] in, is the generalized mass of the ALE variable length cable element, is a generalized external force, is the additional inertial force caused by material flow, is the generalized elastic force caused by elastic deformation.

[0090] The rope transmission of the rope cluster driven space agile manipulator passes through a large number of pulleys, which complete the steering or tensioning of the rope and guide the rope to move along a predetermined path. According to whether it contacts and wraps around the pulley, the rope can be divided into non-contact section rope and contact section rope, such as Figure 7 As shown in the figure, the non-contact rope segment is modeled using the above-mentioned ALE variable length rope unit model. Since the length of the contact rope segment accounts for a small proportion of the total rope length, the elastic deformation has little effect on the total rope length. The arc length of the contact rope segment tangent to the pulley is used to represent its length. The contact rope segment and the non-contact rope segment are tangent to the edge of the pulley. The contact rope segment and the non-contact rope segment are associated through the rope-pulley system constraint equation. The rope-pulley system constraint equation includes position constraint, length constraint and tangency constraint. The above-mentioned geometric constraints are established through the ALE rope unit nodes at the tangent point, instead of dividing a large number of rope units and performing collision detection to avoid dragging down the calculation process.

[0091] In step S303, the contact segment of the rope in contact with the pulley in the rope cluster driven space agile manipulator is modeled using the rope-pulley system constraint equation, including: establishing the rope-pulley system constraint equation according to the position constraint condition, the tangency constraint condition and the length constraint condition, and modeling the contact segment of the rope in contact with the pulley in the rope cluster driven space agile manipulator.

[0092] The physical meaning of the position constraint is the first tangent point between the contact segment and the non-contact segment of the rope. A , second tangent point B Always located at the boundary contour of the pulley, the position constraint satisfies the following formula:

[0093]

[0094]

[0095] in, , The first tangent point between the contact rope and the pulleyA and the second tangent point B The position coordinates in the global coordinate system, represents the position coordinates of the pulley center in the global coordinate system, is the attitude transformation matrix from the pulley center of mass coordinate system to the global coordinate system, , First tangent point A and the second tangent point B Position coordinates in the pulley center of mass coordinate system.

[0096] The physical meaning of the tangency constraint is that the rope and the pulley remain tangent at the boundary. The tangency constraint condition satisfies the following formula:

[0097]

[0098]

[0099] in, , The contact segment rope at the first tangent point in the global coordinate system A and the second tangent point B The tangent vector at .

[0100] The physical meaning of the length constraint is that the material length of the entire rope remains constant, and the length constraint condition satisfies the following formula:

[0101]

[0102] in, is the initial material length of the rope, is the dynamic material length of the rope, First tangent point A and the second tangent point B The material coordinates of First tangent point A and the second tangent point B The angle of the rope wrapped around the pulley at the contact section. The dynamic material length of the rope can be calculated based on the first tangent point. A and the second tangent point B The material coordinates of A and the second tangent point B Calculation of the wrap angle of the contact section rope wrapped around the pulley.

[0103] According to some embodiments, when considering a scenario where the starting point of the rope is wound around a motor winding wheel, it can be considered that one end of the rope is fixedly connected to the pulley, and the second tangent point B Degenerates to a fixed boundary, only for the first tangent point A Create a one-sided constraint equation.

[0104] The ropes of the rope cluster-driven agile manipulator need to pass through fixed pulleys when driving the elbow and wrist joints. Sliding friction occurs between the rope and the fixed pulley. The magnitude of the friction force is related to the wrap angle of the rope passing through the pulley and changes dynamically with the rotation of the joint. Considering that sliding friction has a great influence on the transmission efficiency and the rope has a stick-slip state in reciprocating motion, it is necessary to introduce a Coulomb dry friction model to describe it. By establishing a Coulomb dry friction model, the rope tension on both sides of the ALE node is dynamically distributed to describe the stick-slip friction loss of the rope passing through the pulley.

[0105] In the rope cluster driven space agile manipulator system, the change in length of the rope when the joint is driven to rotate depends on the center distance of the pulley at the joint, but has nothing to do with the shape of the pulley. Therefore, the shapes of the fixed pulley and the movable pulley at the joint are ignored during modeling. Fig. 8A As shown in Figure 1, the line contact friction between the rope and the fixed pulley is simplified to the point contact friction through the ALE node.

[0106] In step S304, the sliding friction between the ropes driving the wrist joint and the elbow joint and the fixed pulley in the rope cluster driven spatial agile manipulator is modeled using a Coulomb dry friction model, including:

[0107] Coulomb dry friction model Fig. 9 As shown, according to the relative sliding speed between the rope and the fixed pulley The friction force of point contact friction is different from It can be expressed as:

[0108]

[0109] in, , , , are dynamic and static friction, respectively. , are the dynamic and static friction coefficients, represents the normal force, Represents external force. When the friction Equal to the dynamic friction ;when When the friction Depends on external force .

[0110] According to some embodiments, Less than speed limit hour, .

[0111] According to the exemplary embodiment, the friction force of the contact section rope passing through the fixed pulley is related to the wrap angle of the rope to the fixed pulley. The friction force of the contact area between the rope and the fixed pulley can be obtained by integration as follows:

[0112]

[0113] in, 、 are the rope tensions at both ends of the rope in contact with the fixed pulley, is the coefficient of kinetic friction, is the wrap angle of the contact section rope to the fixed pulley, is the static friction.

[0114] Angle of the rope around the pulley It is calculated by considering the real configuration of the fixed pulley shape. Taking the elbow joint as an example, Figure 8B As shown, when the elbow joint angle is When the contact angles between the rope and the fixed pulley are 、 ,and 、 The following relationship is satisfied and can be used in the above formula to obtain the friction force in the contact area between the rope and the two fixed pulleys.

[0115]

[0116]

[0117] in, , Elbow joint rotation The initial wrap angle.

[0118] The present application proposes a stick-slip arbitrary Lagrangian-Eulerian (SS-ALE) dynamic modeling method for a rope-cluster driven spatial agile manipulator. This method uses a variable-length cable unit based on the ALE description to simulate the driving rope, and uses the Coulomb dry friction model to describe the stick-slip friction of the driving rope passing over the pulley. Compared with the current rope-driven rigid manipulator dynamics model, which usually simplifies the rope into a rigid rope and ignores the influence of the elastic deformation and contact friction of the rope on the dynamic characteristics of the system, this method can simulate the elastic deformation and contact friction of the rope, realize the open-loop and closed-loop control modes of the rope length input and the force input, and simulate the rope drive with high fidelity, thereby more accurately presenting the dynamic characteristics of the system.

[0119] In order to systematically study the rope length input and force input modes, the SS-ALE dynamics model of the rope cluster driven space agile manipulator is combined with the motor three-loop control model. This application also provides a simulation control system, such as Fig.10 As shown, the simulation control system includes: a planning module 101 , a motor three-loop control module 102 and a dynamic modeling module 103 .

[0120] Among them, the planning module 101 is used to generate the expected motion trajectory of each joint angle of the rope cluster driven space agile manipulator. The motor three-loop control module 102 is connected to the planning module 101, and completes the three-loop control of the joint motor position, speed, and current according to the actual value and the expected motion trajectory, that is, the error between the actual joint angle and the expected joint angle, to obtain the motor torque of the driving rope. The dynamic modeling module 103 is connected to the motor three-loop control module 102, and by executing the SS-ALE modeling method as described above, a dynamic model of the rope cluster driven space agile manipulator is built; the motor torque is input into the dynamic model for rope drive simulation, and the output result is fed back to the motor three-loop control module 102, so that the motor three-loop control module further adjusts the motor torque to form a closed-loop control.

[0121] According to some embodiments, in order to provide more accurate input to the dynamics model, the actual task of driving a space agile manipulator with a rope cluster is used as a research scenario to construct a joint control method system. The control architecture of the motor three-ring control module is as follows: Fig.11 As shown in the figure, the joint motor position control adopts the typical "position loop-speed loop-current loop" three-closed loop control method, which is position loop-speed loop-current loop-SVPWM-three-phase inverter drive from the outside to the inside. Compared with open-loop control, the motor three-loop control module adopts a closed-loop control method, which can eliminate the positioning accuracy deviation caused by factors such as rope elastic deformation and contact friction, making the system's dynamic behavior more accurate.

[0122] Compared with the existing modeling method of rope-driven rigid manipulator, this application adopts SS-ALE dynamic modeling method. One important advantage is that it can simulate the elastic deformation of rope and realize closed-loop control of the whole arm. Figure 4 and Fig. 12A The rope cluster driven space agile manipulator model shown in the figure is used for dynamic simulation. The initial preload of each rope is given as 200N, and the manipulator is made to rotate around the shoulder joint at a certain angular acceleration. Rotation. According to the momentum theorem, the torque provided by the drive ropes of the elbow and wrist joints under this working condition can be theoretically solved, and then the tension difference of each set of drive ropes can be solved. Fig. 12B and Fig. 12C As shown in the figure, the simulation results of the dynamic model are in good agreement with the theoretical solution results, thus verifying the correctness of the rope model.

[0123] In order to reflect the influence of elastic deformation of rope on motion accuracy, friction is not considered first, and the rope and pulley are in smooth contact. The rope cluster drives the end of the spatial agile manipulator to perform circular motion in the plane, such as Fig.13A As shown in the figure, open-loop and closed-loop control methods are used as comparison. The open-loop control method uses the rope length input and the winding wheel trajectory corresponding to the expected joint angle trajectory calculated based on the kinematic relationship as input; the closed-loop control method uses the force input and the Fig.11 The simulation process shown in the figure is input by the motor three-loop control model. T The smaller it is, the greater the inertia force of the system, and the greater the strain and elastic deformation of the rope. Fig. 13B For open loop control, the rope diameter is 1 mm, such as Fig. 13B As shown in the figure, under open-loop control, as the movement speed increases, the elastic deformation of the rope increases, resulting in a gradual increase in the deviation of the circular trajectory; if a thinner rope is used, the rope diameter is reduced from 1mm to 0.5mm, as shown in the figure. Fig. 13C As shown, Fig. 13C For open-loop control, the rope diameter is 0.5 mm. The same inertial force will cause the rope strain and elastic deformation to be amplified by square, and the deviation of the motion trajectory will be further increased. Under closed-loop control, Fig.13D As shown, Fig.13D For closed-loop control, the rope diameter is 0.5mm. Thanks to the real-time feedback of the joint angle, the motion accuracy of the circular trajectory at the end is significantly improved, making it more suitable for performing actual tasks.

[0124] In order to reflect the influence of the contact friction between the rope and the pulley on the motion accuracy, the Coulomb dry friction model is used to describe the contact friction of the rope passing through the fixed pulley of the elbow and wrist joints, such as Fig.14A As shown, the dynamic model of the rope cluster driven space agile manipulator built by the present application is used for simulation, and the end of the rope cluster driven space agile manipulator performs circular motion in the plane. The open-loop control method of rope length input is adopted. The rope diameter is 0.5 mm and the circular motion period is . Fig. 14B is the terminal trajectory corresponding to different friction coefficients, such as Fig. 14B As shown, if friction is not considered, , the end motion trajectory of the robot arm is close to the expected circular trajectory. When the friction coefficient is increased to , the end trajectory obviously deviates from the circular trajectory. This is because the contact friction affects the tension distribution of the rope and aggravates the elastic deformation of the rope.

[0125] In order to illustrate the impact of contact friction on the elbow and wrist joints, contact friction is applied to elbow joint 1, elbow joint 2, and wrist joint respectively. , while the other joints maintain smooth contact, i.e. ,in, Fig. 14C is the friction coefficient of elbow 1 joint The terminal trajectory at ; Fig.14D is the friction coefficient of elbow 1 joint The joint angle at Fig.14E is the friction coefficient of elbow 2 joint The terminal trajectory at ; Fig.14F is the friction coefficient of elbow 2 joint The joint angle at Figure 14G is the friction coefficient of wrist joint The terminal trajectory at ; Fig.14H is the friction coefficient of wrist joint The joint rotation angle and the rope friction of the elbow and wrist joints will affect the end motion accuracy, especially in the reciprocating motion stage. At this time, the relative motion speed of the rope is close to zero, and there will be obvious viscosity, resulting in a significant plateau period of the joint angle under open-loop control.

[0126] This application proposes a simulation control system for building a rope-cluster driven space agile robotic arm based on the SS-ALE dynamic modeling method, which will help to carry out parameter analysis and control strategy research, thereby guiding the design optimization of the mechanism, effectively improving the motion accuracy and other performance, and providing technical support for ground tests and on-orbit services.

[0127] Fig.15 A structural diagram of an electronic device provided by the present application is shown.

[0128] See also Fig.15 , Fig.15 An electronic device is provided, comprising a processor and a memory. The memory stores computer instructions. When the computer instructions are executed by the processor, the processor executes the computer instructions to achieve the following Figure 3 or Fig.11 The method and refinement scheme shown.

[0129] It should be understood that the above-mentioned device embodiments are only illustrative, and the device disclosed in the present application can also be implemented in other ways. For example, the division of units / modules in the above-mentioned embodiments is only a logical function division, and there may be other division methods in actual implementation. For example, multiple units, modules or components can be combined, or can be integrated into another system, or some features can be ignored or not executed.

[0130] In addition, unless otherwise specified, each functional unit / module in each embodiment of the present application may be integrated into one unit / module, each unit / module may exist physically separately, or two or more units / modules may be integrated together. The above-mentioned integrated unit / module may be implemented in the form of hardware or in the form of a software program module.

[0131] If the integrated unit / module is implemented in the form of hardware, the hardware may be a digital circuit, an analog circuit, etc. The physical implementation of the hardware structure includes but is not limited to transistors, memristors, etc. Unless otherwise specified, the processor or chip may be any appropriate hardware processor, such as CPU, GPU, FPGA, DSP, and ASIC, etc. Unless otherwise specified, the on-chip cache, off-chip memory, and storage may be any appropriate magnetic storage medium or magneto-optical storage medium, such as Resistive Random Access Memory (RRAM), Dynamic Random Access Memory (DRAM), Static Random-Access Memory (SRAM), Enhanced Dynamic Random Access Memory (EDRAM), High-Bandwidth Memory (HBM), Hybrid Memory Cube (HMC), etc.

[0132] If the integrated unit / module is implemented in the form of a software program module and sold or used as an independent product, it can be stored in a computer-readable memory. Based on this understanding, the technical solution of the present application, or the part that contributes to the prior art, or all or part of the technical solution can be embodied in the form of a software product, which is stored in a memory and includes several instructions for a computer device (which can be a personal computer, server or network device, etc.) to execute all or part of the steps of the various embodiments of the present disclosure. The aforementioned memory includes: U disk, read-only memory (ROM, Read-Only Memory), random access memory (RAM, Random Access Memory), mobile hard disk, disk or optical disk and other media that can store program codes.

[0133] The present application also provides a non-transitory computer storage medium storing a computer program. When the computer program is executed by multiple processors, the processors execute the following Figure 3 or Fig.11 The method and refinement scheme shown.

[0134] It should be clearly understood that the present application describes how to form and use specific examples, but the present application is not limited to any details of these examples. On the contrary, based on the teaching of the content disclosed in the present application, these principles can be applied to many other embodiments.

[0135] In addition, it should be noted that the above figures are only schematic illustrations of the processes included in the method according to the exemplary embodiments of the present application, and are not intended to be limiting. It is easy to understand that the processes shown in the above figures do not indicate or limit the time sequence of these processes. In addition, it is also easy to understand that these processes can be performed synchronously or asynchronously, for example, in multiple modules.

[0136] The exemplary embodiments of the present application are specifically shown and described above. It should be understood that the present application is not limited to the detailed structures, configurations or implementations described herein; on the contrary, the present application is intended to cover various modifications and equivalent configurations included in the spirit and scope of the appended claims.

Claims

1. A SS-ALE modeling method for a rope cluster driven space agile manipulator, characterized in that: include: A multi-rigid body model is used to model the rigid structure in the rope cluster driven space agile manipulator; The non-contact section of the rope that is not in contact with the pulley in the rope cluster driven space agile manipulator is modeled using an ALE rope unit model; The contact section of the rope in contact with the pulley in the rope cluster driven space agile manipulator is modeled using the rope-pulley system constraint equation, including: The constraint equation of the rope-pulley system is established according to the position constraint condition, the tangency constraint condition and the length constraint condition, and the contact section rope in contact with the pulley in the rope cluster driven space agile manipulator is modeled; The position constraint condition satisfies the following formula: in, , are the position coordinates of the first and second tangent points of the contact segment rope and the pulley in the global coordinate system, represents the position coordinates of the pulley center in the global coordinate system, is the attitude transformation matrix from the pulley center of mass coordinate system to the global coordinate system, , are the position coordinates of the first tangent point and the second tangent point in the pulley center of mass coordinate system; The tangency constraint condition satisfies the following formula: in, , is the tangent vector of the contact segment rope at the first tangent point and the second tangent point in the global coordinate system; Calculate the dynamic material length of the rope according to the material coordinates of the first tangent point and the second tangent point, and the wrap angle of the first tangent point and the second tangent point and the contact section rope to the pulley; The length constraint condition satisfies the following formula: in, is the initial material length of the rope, is the dynamic material length of the rope, are the material coordinates of the first tangent point and the second tangent point, is the wrap angle between the first tangent point and the second tangent point and the contact section rope and the pulley; The sliding friction between the ropes driving the wrist joint and the elbow joint and the fixed pulley in the rope cluster driven space agile manipulator is modeled by using the Coulomb dry friction model; The multi-rigid body model, the ALE cable unit model, the rope-pulley system constraint equations and the Coulomb dry friction model are used to build a dynamic model of the rope cluster driven spatial agile robotic arm, so that the generated motor torque is input into the dynamic model for rope drive simulation.

2. The SS-ALE modeling method according to claim 1, characterized in that: The non-contact section of the rope in the rope cluster driven space agile manipulator that is not in contact with the pulley is modeled using an ALE rope unit model, including: Modeling the non-contact rope segment not in contact with the pulley based on the generalized coordinates and control equations of the ALE variable length rope unit; The ALE variable length cable element includes a first node and a second node, and the generalized coordinates of the ALE variable length cable element are calculated according to the following formula: in, are the generalized coordinates of the ALE variable length cable element, , are the position coordinates of the first node and the second node, , are the material coordinates of the first node and the second node; The control equation of the ALE variable length cable element satisfies the following formula: in, is the generalized mass of the ALE variable length cable element, is a generalized external force, is the additional inertial force caused by material flow, is the generalized elastic force caused by elastic deformation.

3. The SS-ALE modeling method according to claim 1, characterized in that: The sliding friction between the ropes driving the wrist joint and the elbow joint and the fixed pulley in the rope cluster driven space agile manipulator is modeled using a Coulomb dry friction model, including: The friction force between the rope and the fixed pulley is calculated according to the following formula: in, is the friction between the rope and the fixed pulley, is the relative sliding speed between the rope and the fixed pulley, , are respectively the rope tensions at both ends of the contact section rope in contact with the fixed pulley, is the coefficient of kinetic friction, is the wrap angle of the contact section rope to the fixed pulley, is the static friction.

4. A simulation control system, characterized in that: include: A planning module is used to generate the desired motion trajectory of each joint angle of the rope cluster-driven spatial agile manipulator; A motor three-loop control module, connected to the planning module, for generating a motor torque for driving the rope according to an error between an actual value and the desired motion trajectory; A dynamic modeling module is used to execute the SS-ALE modeling method as described in any one of claims 1 to 3 to build a dynamic model of the rope cluster driven space agile manipulator; the dynamic modeling module is connected to the motor three-ring control module, the motor torque is input into the dynamic model for rope drive simulation, and the output result is fed back to the motor three-ring control module, so that the motor three-ring control module further adjusts the motor torque to form a closed-loop control.

5. An electronic device, characterized in that: include: one or more processors; A memory for storing one or more programs; When the one or more programs are executed by the one or more processors, the one or more processors execute the method according to any one of claims 1 to 3.

6. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the program is executed by a processor, the method according to any one of claims 1 to 3 is implemented.

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