Composite control method and system for mechanical arm with gap joint
By constructing a composite control method of collision force feedforward and PD feedback, the collision force caused by the joint clearance of the robotic arm is compensated in real time, which solves the control accuracy and reliability problems of the robotic arm in complex scenarios and achieves high precision and stable operation.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- TONGJI UNIV
- Filing Date
- 2026-02-02
- Publication Date
- 2026-05-12
AI Technical Summary
Existing technologies are insufficient to effectively cope with nonlinear collision forces caused by the joint gaps of robotic arms, resulting in inadequate control precision and reliability, and making it impossible to achieve high precision and stable operation in complex scenarios.
A composite control method combining collision force feedforward and PD feedback is adopted. By constructing a nonlinear dynamic model, the collision force disturbance caused by joint clearance is compensated in real time, and precise tracking is achieved by combining PD feedback control.
It improves the operating accuracy and stability of the robotic arm, effectively suppresses nonlinear collision forces, and achieves precise motion tracking of the end effector, thus resolving the contradiction between nonlinear suppression and precision tracking in traditional control methods.
Smart Images
Figure CN122008312A_ABST
Abstract
Description
Technical Field
[0001] This invention belongs to the field of engineering equipment control technology, specifically a composite control method and system that combines collision force feedforward and PD feedback. Background Technology
[0002] In complex scenarios such as industrial production and aerospace, six-degree-of-freedom robotic arms need to complete high-precision and high-stability tasks, and their joint performance directly determines the overall operational quality. However, during long-term load operation, the relative friction between bearings and bushings inevitably causes wear, resulting in joint gaps. These gaps can lead to periodic vibrations and jitters during robotic arm operation, not only exacerbating joint fatigue damage and shortening equipment lifespan, but also triggering strong nonlinear collision forces, leading to increased trajectory errors in the end effector. From the current state of control technology, existing control strategies for robotic arms with gaps mainly include traditional PD control, adaptive control, and robust control. Although traditional PD control is simple to implement, it struggles to handle the nonlinearity and parameter perturbations caused by gaps; adaptive control, while possessing some parameter adaptation capabilities, is highly dependent on the accuracy of system modeling, and its performance significantly degrades when modeling errors exist; robust control, while suppressing some disturbances, cannot accurately offset the source of collision forces, making it difficult to balance dynamic response speed and steady-state accuracy. Currently, the core shortcomings of existing technologies are: insufficient consideration of the nonlinear characteristics of joint collision forces; control strategies are mostly single-objective optimizations, lacking a collaborative design of "disturbance suppression-precision tracking"; and control parameter adaptation lags behind dynamic changes in the gap, failing to adapt to changes in system dynamics in real time. Therefore, there is an urgent need to design a composite control method with high precision, strong robustness, and the ability to adapt to gap uncertainties to meet the stable operation requirements of manipulators with gap joints in complex scenarios. Summary of the Invention
[0003] The purpose of this invention is to solve the problems of insufficient control accuracy and reliability of existing technologies in dealing with nonlinear collision forces in joint gaps, and to provide a collision force feedforward-PD feedback composite control method and system suitable for manipulators with joint gaps.
[0004] To achieve the above objectives, the present invention employs the following technical solution: On the one hand, this invention provides a composite control method for a robotic arm with intermittent joints, including... S101: Based on a six-DOF robotic arm with gap joints, a nonlinear dynamic model of the system is constructed; the joint gaps and collision forces of the robotic arm are modeled, and the control boundaries of the collision force feedforward module and the PD feedback module are clarified; S102: Based on the aforementioned nonlinear dynamics model, a composite control structure of "collision force feedforward compensation - PD feedback tracking" is constructed; S103: Based on the composite control structure, the joint position and posture of the robotic arm are accurately tracked, and the collision force disturbance caused by the gap is compensated in real time, thereby improving the operating accuracy and reliability of the robotic arm.
[0005] Preferably, the construction of the nonlinear dynamic model of the robotic arm with gapped joints specifically involves: Define the clearance vector as the bearing geometric center. r ob With the geometric center of the bushing r oj The difference eccentricity The gap size satisfies: (1); in, R b Represented by the bearing radius, R j The values are represented by the bushing radius and the contact deformation. The Lankarani-Nikravesh model was used to calculate the joint normal collision force. (2); The tangential friction force was calculated using the Stribeck model: (3); in n =1.5 is the nonlinear coefficient. For contact deformation rate, The static friction coefficient is The coefficient of kinetic friction is . Stribeck velocity threshold, It is an empirical constant. The coefficient of viscous friction is... The relative angular velocity of the joints is: The total impact force is: (4); Further establish a dynamic model of the robotic arm with clearance: (5); in, q It is a generalized coordinate system. Represents generalized speed. Represents generalized acceleration. M It is a quality matrix. C It is the damping matrix. K Stiffness matrix F e It is the generalized force acting on the system. The system's constraint matrix,F c It represents the force of impact.
[0006] Preferably, the composite control structure of "collision force feedforward compensation - PD feedback tracking" is specifically as follows: The collision force feedforward compensation module is based on the X-axis component of the collision force. Y-axis component The bearing's center of mass coordinates ( x b , y b ), shaft sleeve centroid coordinates ( x i , y j ), calculate the compensating torque of the bearing at the clearance hinge. Compensating torque of bushing Total feedforward compensation torque ;PD control module, control torque is: , (6); in, Indicates the first i Desired angle of each joint and the actual angle of the joint The error between; K p This is the proportionality coefficient. K d These are the differential coefficients; the total control torque is the superposition of the feedforward compensation torque and the feedback tracking torque. (7).
[0007] Preferably, the contact stiffness coefficient in the Lankarani-Nikravesh model K With damping coefficient D The calculation is as follows: Contact stiffness coefficient: (8) (9) (10) in, v b and E b These are the Poisson's ratio and Young's modulus of the bearing. v j and E j These are the Poisson's ratio and Young's modulus of the bushing; Damping coefficient: (11) in, c e The coefficient of recovery is set to 0.9. It is the initial collision velocity at the point of impact.
[0008] On the other hand, the present invention provides a composite control system for a gapped joint robotic arm that can implement the method, comprising: The modeling module is based on a six-degree-of-freedom manipulator with gap joints. It constructs a nonlinear dynamic model of the manipulator system with gap joints. The model includes the joint gap kinematic model, the Lankarani-Nikravesh collision force model, the Stribeck friction force model, and the Lagrange dynamic equations of the manipulator system. The control structure construction module is based on a nonlinear dynamics model and constructs a composite control structure of "collision force feedforward compensation - PD feedback tracking", clarifying the collaborative working logic of the feedforward module and the feedback module. The tracking and compensation module, based on the composite control structure, calculates the total control torque. It can accurately track the joint position and posture of the robotic arm and compensate for the collision force disturbance caused by the gap in real time.
[0009] Compared with the prior art, the present invention has the following beneficial effects: This invention employs the Lankarani-Nikravesh model in the collision force feedforward module to provide real-time compensation for nonlinear collision force disturbances caused by gaps. The PD control method provides stable trajectory tracking and ensures sufficient accuracy. The two control modules work together, and the proposed composite control method, consisting of collision force feedforward compensation and PD feedback tracking, effectively improves the operational accuracy and stability of the manipulator with gap joints. It overcomes the contradiction between nonlinear suppression and accuracy tracking in traditional control methods, achieving precise tracking of the desired motion of the end effector. Attached Figure Description
[0010] To more clearly illustrate the technical solutions of the embodiments of the present invention, the accompanying drawings used in the embodiments will be briefly introduced below. It should be understood that the following drawings only show some embodiments of the present invention and should not be regarded as a limitation on the scope. For those skilled in the art, other related drawings can be obtained based on these drawings without creative effort.
[0011] Figure 1 This is a flowchart illustrating the collision force feedforward-PD feedback composite control method applicable to a manipulator with a gapped joint according to the present invention. Figure 2 This is a schematic diagram of the collision force feedforward-PD feedback composite control system applicable to a manipulator with a gapped joint according to the present invention. Figure 3 This is a schematic diagram of the joint space kinematic model of the present invention; Figure 4 This is a schematic diagram of the DH parameter definition for the robotic arm of the present invention; Figure 5 This is a comparison diagram of joint collision forces under different control strategies of the present invention; Figure 6 This is a comparison chart of the trajectory errors of the robotic arm end effector under different control strategies of the present invention. Detailed Implementation
[0012] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. The components of the embodiments of the present invention described and shown in the accompanying drawings can generally be arranged and designed in various different configurations.
[0013] Therefore, the following detailed description of the embodiments of the invention provided in the accompanying drawings is not intended to limit the scope of the claimed invention, but merely to illustrate selected embodiments of the invention. All other embodiments obtained by those skilled in the art based on the embodiments of the invention without inventive effort are within the scope of protection of the invention.
[0014] It should be noted that similar labels and letters in the following figures indicate similar items. Therefore, once an item is defined in one figure, it does not need to be further defined and explained in subsequent figures.
[0015] In the description of the embodiments of the present invention, it should be noted that if terms such as "upper," "lower," "horizontal," or "inner" indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings, or the orientation or positional relationship commonly used when the product of the invention is in use, they are only for the convenience of describing the present invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation, and therefore should not be construed as a limitation of the present invention. Furthermore, terms such as "first" and "second" are only used to distinguish descriptions and should not be construed as indicating or implying relative importance.
[0016] Furthermore, the use of the term "horizontal" does not imply that the component must be absolutely horizontal, but rather that it can be slightly tilted. For example, "horizontal" simply means that its direction is more horizontal than "vertical," and does not mean that the structure must be completely horizontal, but can be slightly tilted.
[0017] In the description of the embodiments of the present invention, it should also be noted that, unless otherwise explicitly specified and limited, the terms "set," "install," "connect," and "link" should be interpreted broadly. For example, they can refer to a fixed connection, a detachable connection, or an integral connection; they can refer to a mechanical connection or an electrical connection; they can refer to a direct connection or an indirect connection through an intermediate medium; and they can refer to the internal connection of two components. Those skilled in the art can understand the specific meaning of the above terms in the present invention according to the specific circumstances.
[0018] The present invention will now be described in further detail with reference to the accompanying drawings: Based on the nonlinear dynamic model of a manipulator with a gapped joint, the relationship between the drive input and the output motion of the end effector was established. However, the nonlinearity of the joint clearance and the time-varying nature of the collision force of the manipulator can significantly induce control errors. These nonlinear factors prompt the research on corresponding control methods to achieve the required precise motion. To improve control performance, this invention discloses a collision force feedforward-PD feedback composite control method suitable for manipulators with gapped joints, the specific process of which is as follows: Figure 1 As shown.
[0019] S101, based on a six-DOF robotic arm with gapped joints, constructs a nonlinear dynamic model of the system; models the joint clearance and collision force characteristics of the robotic arm, and determines the control boundaries of the collision force feedforward module and the PD feedback module; see [link to documentation]. Figure 3 and 4 A nonlinear dynamic model of a robotic arm with gapped joints is constructed, specifically as follows: 1. Based on the Lagrange equation, establish a nonlinear dynamic model for a robotic arm with a gapped joint. (1) in, q It is a generalized coordinate system. Represents generalized speed. Represents generalized acceleration. M It is a quality matrix. C It is the damping matrix. K Stiffness matrix F e It is the generalized force acting on the system. The system's constraint matrix, F c It represents the force of impact.
[0020] 2. Kinematic modeling of the joint gap, with the gap vector being the geometric center of the bearing. r ob With the geometric center of the bushing r oj The difference eccentricity The gap size satisfies (2) in, R b Represented by the bearing radius, R j This is represented by the bushing radius. Therefore, the contact deformation can be further calculated as follows: .
[0021] 3. Collision force construction: The Lankarani-Nikravesh model was used to calculate the joint normal collision force. (3) Tangential friction force was calculated using the Stribeck model. , (4) in n =1.5 is the nonlinear coefficient. For contact deformation rate, The static friction coefficient is The coefficient of kinetic friction is . Stribeck velocity threshold, It is an empirical constant. The coefficient of viscous friction is... Let be the relative angular velocity of the joints, and the total collision force be... .
[0022] S102, based on a nonlinear dynamics model, constructs a composite control structure of "collision force feedforward compensation - PD feedback tracking"; see [link / reference]. Figure 2 A composite control structure of "collision force feedforward compensation - PD feedback tracking" is constructed, specifically as follows: 1. Sensor module, using a three-dimensional force sensor (sensor 2) to collect collision force. An absolute photoelectric encoder (sensor 1) is used to collect joint angle signals. The sensor signal is filtered and then input to the controller module.
[0023] 2. Control module, feedforward compensation unit based on collision force components and bearing center of mass coordinates ( x b , y b ), shaft sleeve centroid coordinates ( x i , y j ), calculate bearing compensation torque Bushing compensation torque The total feedforward compensation torque is The feedback tracking unit uses a PD control module, and the control torque is... , (5) in, Indicates the first i Desired angle of each joint and the actual angle of the joint The error between them. K p This is the proportionality coefficient. K d The differential coefficients are used; the torque synthesis unit is the superposition of feedforward compensation torque and feedback tracking torque.
[0024] (6) 3. The actuator uses a servo motor as the drive unit, the servo driver is matched with the servo motor model, and the control mode is set to torque mode; the robotic arm body is a six-degree-of-freedom serial structure to meet the requirements of workload and positioning accuracy.
[0025] S103, based on this composite control structure, tracks the joint position and attitude of the robotic arm and compensates for gap collision force disturbances; S103.1, Collision Force Feedforward Disturbance Compensation; Based on the collision force signal collected by sensor 2, the feedforward compensation unit updates the compensation torque according to the set sampling period, through... To counteract the disturbance of joint rotation caused by the impact force, corresponding to Figure 5 The effect of suppressing the amplitude of collision force in the medium-compound control.
[0026] S103.2, PD feedback trajectory correction; based on the angle signal acquired by the encoder, the feedback tracking unit calculates the tracking torque according to the set sampling period, and then... Correcting trajectory deviations ensures the motion accuracy of the end effector. Figure 6 The effect of reducing trajectory error in the composite control system.
[0027] like Figure 5 As shown, traditional PD control strategies do not provide targeted compensation for collision forces, and the amplitude of the collision force fluctuates significantly due to gap nonlinearity. This invention, through feedforward compensation, preemptively offsets collision force disturbances, resulting in a significant reduction in the amplitude of the collision force. Figure 6 As shown, traditional PD control relies solely on single feedback adjustment, making it difficult to balance disturbance suppression and accurate tracking, resulting in a large range of trajectory error fluctuations. This invention combines feedforward compensation and PD feedback into a composite control, which significantly reduces trajectory error and achieves faster error convergence, fully demonstrating the superiority of the composite control structure.
[0028] The above are merely preferred embodiments of the present invention and are not intended to limit the present invention. Various modifications and variations can be made to the present invention by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.
Claims
1. A composite control method for a robotic arm with a gapped joint, characterized in that, include S101: Based on a six-DOF robotic arm with gap joints, a nonlinear dynamic model of the system is constructed; the joint clearance and collision force of the robotic arm are modeled, and the control boundaries of the collision force feedforward module and the PD feedback module are clarified. S102: Based on the aforementioned nonlinear dynamics model, a composite control structure of "collision force feedforward compensation - PD feedback tracking" is constructed; S103: Based on the composite control structure, the joint position and posture of the robotic arm are accurately tracked, and the collision force disturbance caused by the gap is compensated in real time, thereby improving the operating accuracy and reliability of the robotic arm.
2. The composite control method for a robotic arm with a gapped joint according to claim 1, characterized in that, The construction of the nonlinear dynamic model of the robotic arm with gapped joints is specifically as follows: Define the clearance vector as the bearing geometric center. r ob With the geometric center of the bushing r oj The difference eccentricity The gap size is satisfied; （1）； in, R b Represented by the bearing radius, R j The values are represented by the bushing radius and the contact deformation. The Lankarani-Nikravesh model was used to calculate the joint normal collision force. （2）； The tangential friction force was calculated using the Stribeck model: （3）； in n =1.5 is the nonlinear coefficient. For contact deformation rate, The static friction coefficient is The coefficient of kinetic friction is . Stribeck velocity threshold, It is an empirical constant. The coefficient of viscous friction is... The relative angular velocity of the joints is: The total impact force is: （4）； Further establish a dynamic model of the robotic arm with clearance: （5）； in, q It is a generalized coordinate system. Represents generalized speed. Represents generalized acceleration. M It is a quality matrix. C It is the damping matrix. K Stiffness matrix F e It is the generalized force acting on the system. The system's constraint matrix, F c It represents the force of impact.
3. The composite control method for a robotic arm with a gapped joint according to claim 1, characterized in that, The composite control structure of "collision force feedforward compensation - PD feedback tracking" is specifically as follows: The collision force feedforward compensation module is based on the X-axis component of the collision force. Y-axis component The bearing's center of mass coordinates ( x b , y b ), shaft sleeve centroid coordinates ( x i , y j ), calculate the compensating torque of the bearing at the clearance hinge. Compensating torque of bushing Total feedforward compensation torque ;PD control module, control torque is: ,（6）； in, Indicates the first i Desired angle of each joint and the actual angle of the joint The error between; K p This is the proportionality coefficient. K d These are the differential coefficients; the total control torque is the superposition of the feedforward compensation torque and the feedback tracking torque. （7）。 4. The composite control method for a robotic arm with a gapped joint according to claim 2, characterized in that, The contact stiffness coefficient in the Lankarani-Nikravesh model K With damping coefficient D The calculation is as follows: Contact stiffness coefficient: （8）； （9）； （10）； in, v b and E b These are the Poisson's ratio and Young's modulus of the bearing. v j and E j These are the Poisson's ratio and Young's modulus of the bushing; Damping coefficient: （11）； in, c e The coefficient of restitution is set to 0.
9. It is the initial collision velocity at the point of impact.
5. A composite control system for a gapped joint robotic arm that can implement the method described in any one of claims 1-4, characterized in that, include: The modeling module is based on a six-degree-of-freedom manipulator with gap joints. It constructs a nonlinear dynamic model of the manipulator system with gap joints. The model includes the joint gap kinematic model, the Lankarani-Nikravesh collision force model, the Stribeck friction force model, and the Lagrange dynamic equations of the manipulator system. The control structure construction module is based on a nonlinear dynamics model and constructs a composite control structure of "collision force feedforward compensation - PD feedback tracking", clarifying the collaborative working logic of the feedforward module and the feedback module. The tracking and compensation module, based on the composite control structure, calculates the total control torque. It can accurately track the joint position and posture of the robotic arm and compensate for the collision force disturbance caused by the gap in real time.