A method for analyzing the kinematic posture of a robot arm connection assembly

Abstract

The present application belongs to the field of space combination motion analysis, and particularly relates to a mechanical arm connecting combination attitude analysis method. The specific steps are as follows: 1, obtaining the position, velocity, attitude and angular velocity of the manipulated target in the body coordinate system. 2, according to the relative position, calculating the combination center of mass and establishing the combination coordinate system parallel to the body layout system; according to the relative attitude, calculating the combination inertia tensor in the combination coordinate system. 3, analyzing the combination angular momentum kinematics formula when the target rotates relatively, and deducing the reaction torque generated by the relative rotation. 4, analyzing the combination angular momentum when the configuration changes, and deducing the torque generated by the configuration change. 5, after superimposing the torque, calculating the combination attitude angular velocity according to the inertia tensor, and performing integration to obtain the attitude angle of the body parallel to the combination system. The present application can improve the simulation accuracy and reliability of the kinematics analysis system based on the angular momentum conservation, and has been applied in the on-orbit satellite ground test.

Description

Technical Field

[0001] This invention relates to a kinematic attitude analysis method for a robotic arm connection assembly, belonging to the field of spatial assembly motion analysis technology. Background Technology

[0002] Space attitude control in the aerospace field requires simulation verification and analysis of various ground-based control systems and dynamic components. Ground-based simulation analysis systems are large, and their associated kinematic analysis requires both high computational speed and high accuracy. However, matching commercial dynamics software with the overall dynamics interface of the co-simulation system is difficult, and the computational accuracy of traditional kinematic analysis methods is significantly affected by data packet loss during transmission. Therefore, a method for analyzing the kinematic attitude of a combined body with strong interface adaptability, high computational speed, and reliable results is required.

[0003] The main theories of motion analysis for composite bodies include the Newton-Euler equations, the Lagrange equations, and the Kane method. The Newton-Euler equations, based on vector mechanics, model the dynamics by decoupling all rigid body elements in the system, deriving the motion equations of the center of mass of each element, obtaining the kinematic equations of different elements within the system, and recursively calculating the interaction forces between the elements. The Lagrange equations, based on analytical mechanics, use a generalized coordinate system to represent the spatial position of the system of particles and describe the interaction relationships between objects using energy and work. The Kane method improves upon d'Alembert's principle and the principle of virtual displacement, using generalized velocity as an independent variable and incorporating related variables such as partial velocity to solve for the generalized inertial force of the system.

[0004] For assemblies with large configuration variations, high degrees of freedom in the robotic arm, and a body mass not significantly greater than the target, the motion processes of the body and the target are strongly coupled, making it difficult for existing analysis methods to accurately analyze the body's attitude changes. The Newton-Euler method accumulates recursive errors during the closed-loop recursive motion results of the assemblies, leading to significant computational errors. The Lagrange equation method is computationally intensive, and during the high-degree-of-freedom motion of the robotic arm, it requires high efficiency in transmitting target pose information, and its accuracy is greatly affected by data quality. The Kane method, when the body and target masses are similar and the motion is strongly coupled, requires the introduction of additional constraint equations, resulting in complex derivations and low reliability of the results. Summary of the Invention

[0005] The technical problem solved by this invention is to overcome the shortcomings of existing technologies and provide a kinematic attitude analysis method for strongly coupled combined bodies with large configuration changes, high degrees of freedom of the robotic arm, and body mass characteristics not much greater than the target. This method is simple to implement in engineering and provides reliable calculation results.

[0006] The technical solution of this invention is:

[0007] This invention discloses a method for kinematic attitude analysis of a robotic arm assembly, comprising:

[0008] This invention discloses a method for kinematic attitude analysis of a robotic arm assembly, comprising:

[0009] Calculate the inertia tensor of the target in a system parallel to the body layout with the target's center of mass as the origin;

[0010] Calculate the positions of the body and the target relative to the centroid of the combined body in the combined body coordinate system;

[0011] Calculate the combined body inertia tensor in the combined body coordinate system based on the inertia tensor and position.

[0012] Calculate the rotational angular momentum of the composite body based on its inertia tensor;

[0013] Calculate the target rotational reaction torque based on the rotational angular momentum of the combined body;

[0014] Based on the target rotational reaction torque and the changes in the robotic arm configuration, the translational angular momentum of the assembly is calculated.

[0015] Calculate the reaction torque of configuration change based on the translational angular momentum of the composite body;

[0016] Based on the target rotation reaction torque and configuration change reaction torque, the dynamic differential equation of the composite body is obtained;

[0017] Based on the differential equation of the combined body dynamics, by integrating the angular velocity, the body attitude angle parallel to the combined body coordinate system is obtained.

[0018] Furthermore, in the above method, the calculation of the inertial tensor of the target object in the body layout system with the target's centroid as the origin is specifically as follows:

[0019]

[0020] Among them, C SfromB The transformation matrix from the target centroid coordinate system to the body layout system; Let I be the target's moment of inertia matrix in the target's center-of-mass coordinate system; T Let be the inertial tensor with the target centroid as the origin and parallel to the body layout system.

[0021] Furthermore, in the above method, the calculation of the position of the main body and the target relative to the centroid of the combined body in the combined body coordinate system specifically involves:

[0022]

[0023] Where, m T For target quality; m SP is the mass of the body; P is the position vector from the center of mass of the body to the center of mass of the target; P S P is the position vector from the center of mass of the composite body to the center of mass of the solid body; T The vector pointing from the center of mass of the composite body to the center of mass of the target body.

[0024] Furthermore, in the above method, the calculation of the combined body inertia tensor in the combined body coordinate system specifically involves:

[0025]

[0026] Among them, I S I is the body inertia tensor in the body layout system; ZHT Let be the inertial tensor of the composite body with its origin at the center of mass parallel to the body layout system.

[0027] Furthermore, in the above method, the calculation of the rotational angular momentum of the assembly specifically involves:

[0028]

[0029] Among them, I T Let I be the inertial tensor parallel to the body layout system with the target centroid as its origin. ZHT Let Ω be the inertial tensor of the composite body with its origin parallel to the body's center of mass in the overall layout system; T Let w be the angular velocity of the target attitude relative to the body attitude. ZHT ω represents the angular velocity of the combined body; rot is a subscript indicating the rotational component.

[0030] Furthermore, in the above method, the calculation of the target rotational reaction torque specifically involves:

[0031]

[0032] Among them, T rot The reaction torque for the rotation of the target.

[0033] Furthermore, in the above method, the calculation of the translational angular momentum of the combined body specifically involves:

[0034]

[0035] Among them, v T Let I be the translational velocity of the target relative to the body. ZHT Let w be the inertial tensor of the composite body with its origin parallel to the body's layout system at its center of mass; ZHT P represents the attitude angular velocity of the combined body. T Let m be the position vector from the center of mass of the composite body to the center of mass of the target body. T For target quality.

[0036] Furthermore, in the above method, the calculation of the reaction torque for configuration change specifically involves:

[0037]

[0038] Among them, T tran This is the reaction torque for configuration changes.

[0039] Furthermore, in the above method, the differential equation of the combined body dynamics is specifically as follows:

[0040]

[0041] in, Angular momentum during the configurational manipulation of the combined body; T rot The reaction torque for the target rotation; T tran The translational reaction moment of the configuration; T control +T distrurbance It refers to the external torque generated by the flywheel, thruster, light pressure, and gravity gradient in the dynamic system.

[0042] The advantages of this invention over the prior art are as follows:

[0043] (1) The present invention adopts a technical solution based on the conservation of angular momentum to solve the interaction torque, which achieves the technical effect of simple derivation formula and physical intuitiveness for the motion of strongly coupled combined bodies with large configuration changes, and solves the technical problem of high reliability requirements for motion analysis results.

[0044] (2) The present invention adopts the technical solution of decoupling translation and rotation analysis, which realizes the technical effect of simple and fast analysis when manipulating the robot arm with high degree of freedom, and solves the technical problem of high calculation accuracy when the configuration of the combined body changes rapidly.

[0045] (3) The present invention adopts a technical solution that unifies all vectors and tensors under the body coordinate system and makes the combined body coordinate system parallel to the system, thereby achieving the technical effect that the obtained combined body angular acceleration is the desired body angular acceleration, and solving the technical problem of combining with other dynamics in the joint simulation system. Attached Figure Description

[0046] Figure 1 This is a flowchart of the kinematic attitude analysis method for the robotic arm connection assembly of the present invention. Detailed Implementation

[0047] The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0048] like Figure 1 As shown, this invention provides a method for kinematic attitude analysis of a robotic arm assembly, comprising the following steps:

[0049] like Figure 1 The diagram shows a block diagram of the kinematic attitude analysis method for a robotic arm connected assembly. By treating the manipulated target as a component capable of six degrees of freedom of motion within the assembly, the relative pose change is obtained based on the joint angle changes of the robotic arm. Then, rotational and translational analyses are performed on the assembly. The reaction torque generated by the relative motion of the manipulated target on the assembly is calculated using the conservation of angular momentum. The angular velocity of the assembly is obtained by superimposing other dynamic torque terms from the GNC simulation system, thus yielding the motion results of the assembly. Finally, the attitude motion state of the body in the body coordinate system parallel to the assembly coordinate system is derived, thereby achieving attitude dynamics support for the co-simulation system of spatially variable configuration assemblies.

[0050] The specific implementation steps are as follows:

[0051] Step 1: Obtain the joint rotation motion state of the robotic arm and calculate the position P of the manipulated target's center of mass relative to the body's center of mass in the body coordinate system; calculate the velocity v of the target's center of mass projected onto the body's center of mass in the body coordinate system. T The pose transformation matrix C from target pose to body pose. SfromB ; The angular velocity of the target relative to the body in the body coordinate system ΩT .

[0052] Step 2: Based on the known target and body mass and relative position, the coordinates O of the composite body's center of mass in the body layout system can be obtained. zht ; with O zht Establish an O parallel to the body layout system at the origin. zht X b Y b Z b Combined body coordinate system; calculate the combined body inertia in the combined body coordinate system based on the inertia of the two bodies and their relative attitude. The specific algorithm is as follows:

[0053] 1. Calculate the inertia tensor of the target in a system parallel to the body layout with the target's center of mass as the origin:

[0054]

[0055] in,

[0056] C SfromB Transformation matrix from target centroid coordinate system to body layout system

[0057] Target moment of inertia matrix in target center of mass coordinate system

[0058] I T : The inertial tensor parallel to the body layout system with the target's center of mass as the origin.

[0059] 2. Calculate the position vectors of the body and the target relative to the centroid of the combined body in the combined body coordinate system:

[0060]

[0061] in,

[0062] m T Target quality

[0063] m S Body mass

[0064] P: Vector pointing from the centroid of the body to the centroid of the target.

[0065] P S : Vector pointing from the center of mass of the composite body to the center of mass of the solid body

[0066] P T : Vector pointing from the center of mass of the composite body to the center of mass of the target body

[0067] 3. Calculate the inertia tensor of the composite body:

[0068]

[0069] in,

[0070] I S : Body inertia tensor under body layout system

[0071] I ZHT The inertial tensor of the composite body with its origin at the center of mass parallel to the body's layout system.

[0072] Step 3: Analyze the angular momentum of the combined body when the target rotates relative to the target and differentiate it with respect to time to derive the reaction torque generated by the rotation. The specific algorithm is as follows:

[0073] 1. Rotational angular momentum H of the combined body rot =(I ZHT w ZHT ) (rot) +I T Ω T

[0074] 2. Differentiate the angular momentum with respect to time in an inertial frame of reference:

[0075]

[0076] 3. Place the kinematics of the combined body on the left side of the equation, and the right side represents the reaction torque:

[0077]

[0078] in,

[0079] ΩT : Angular velocity of the target attitude relative to the body attitude.

[0080] w ZHT : Assemblies' attitude angular velocity

[0081] Step 4: Calculate the reaction torque generated by the change in the manipulated target configuration of the combined body. The specific algorithm is as follows:

[0082] 1. Translational angular momentum H of the particle in the combined configuration tran =(I ZHT w ZHT ) (tran) +m T (P T ×v T )

[0083] 2. Differentiate the angular momentum with respect to time in an inertial frame of reference:

[0084]

[0085] 3. Place the kinematics of the combined body on the left side of the equation, and the right side represents the reaction torque:

[0086]

[0087] in,

[0088] v T : The translational velocity of the target relative to the body.

[0089] Step 5: Combine the relative rotational and translational motions. The specific analysis steps are as follows.

[0090] 1. The torque of the combined body acting on the reaction force of the target relative to its motion.

[0091]

[0092] 2. Conservation of angular momentum of the combined body The differential equation of the combined body dynamics is obtained.

[0093]

[0094] in,

[0095] Angular momentum during configuration maneuvering of the combined system;

[0096] Target rotational reaction torque;

[0097] Configurational translational reaction moment;

[0098] T control +Tdistrurbance External torque generated by flywheels, thrusters, light pressure, gravity gradients, etc. in a dynamic system.

[0099] Step Six: Combined Coordinate System O zht X b Y b Z b Parallel to the body layout system O b X b Y b Z b All the above vectors are projected in the body layout coordinate system. The body angular velocity is equal to the combined body angular velocity. The body attitude angle is obtained by solving the angular velocity according to the combined body dynamics differential equation and integrating it.

[0100] Although the present invention has been described in detail through the preferred embodiments above, it should be understood that the above description should not be considered as a limitation of the present invention. Various modifications and substitutions to the present invention will be apparent to those skilled in the art after reading the above description. Therefore, the scope of protection of the present invention should be defined by the appended claims.

[0101] The contents not described in detail in this specification are common knowledge to those skilled in the art.

Claims

1. A method for kinematic attitude analysis of a robotic arm assembly, characterized in that, include: Calculate the inertia tensor of the target in a system parallel to the body layout with the target's center of mass as the origin; Calculate the positions of the body and the target relative to the centroid of the combined body in the combined body coordinate system; Calculate the combined body inertia tensor in the combined body coordinate system based on the inertia tensor and position. Calculate the rotational angular momentum of the composite body based on its inertia tensor; Calculate the target rotational reaction torque based on the rotational angular momentum of the combined body; Based on the target rotational reaction torque and the changes in the robotic arm configuration, the translational angular momentum of the assembly is calculated. Calculate the reaction torque of configuration change based on the translational angular momentum of the composite body; Based on the target rotation reaction torque and configuration change reaction torque, the dynamic differential equation of the composite body is obtained; Based on the differential equation of the combined body dynamics, by integrating the angular velocity, the body attitude angle parallel to the combined body coordinate system is obtained.

2. The method for kinematic attitude analysis of a robotic arm connection assembly according to claim 1, characterized in that, The calculation of the inertial tensor of the target object in a system parallel to the body layout with the target's centroid as the origin is specifically as follows: Among them, C SfromB The transformation matrix from the target centroid coordinate system to the body layout system; Let I be the target's moment of inertia matrix in the target's center-of-mass coordinate system; T Let be the inertial tensor with the target centroid as the origin and parallel to the body layout system.

3. The method for kinematic attitude analysis of a robotic arm connection assembly according to claim 1, characterized in that, The calculation of the positions of the main body and the target relative to the centroid of the combined body in the combined body coordinate system is as follows: Where, m T For target quality; m S P is the mass of the body; P is the position vector from the center of mass of the body to the center of mass of the target; P S P is the position vector from the center of mass of the composite body to the center of mass of the solid body; T The vector pointing from the center of mass of the composite body to the center of mass of the target body.

4. The method for kinematic attitude analysis of a robotic arm connection assembly according to claim 1, characterized in that, The calculation of the combined body inertia tensor in the combined body coordinate system is specifically as follows: Among them, I S I is the body inertia tensor in the body layout system; ZHT Let be the inertial tensor of the composite body with its origin at the center of mass parallel to the body layout system.

5. The method for kinematic attitude analysis of a robotic arm connection assembly according to claim 1, characterized in that, The calculation of the rotational angular momentum of the assembly is specifically as follows: Among them, I T Let I be the inertial tensor parallel to the body layout system with the target centroid as its origin. ZHT Let be the inertial tensor of the composite body with its origin parallel to the body's layout system at the center of mass of the composite body; ΩT Let w be the angular velocity of the target attitude relative to the body attitude. ZHT ω represents the angular velocity of the combined body; rot is a subscript indicating the rotational component.

6. The method for kinematic attitude analysis of a robotic arm connection assembly according to claim 5, characterized in that, The calculation of the target rotational reaction torque is specifically as follows: Among them, T rot The reaction torque for the rotation of the target.

7. The method for kinematic attitude analysis of a robotic arm connection assembly according to claim 1, characterized in that, The calculation of the translational angular momentum of the composite body is specifically as follows: Among them, v T Let I be the translational velocity of the target relative to the body. ZHT Let w be the inertial tensor of the composite body with its origin parallel to the body's layout system at its center of mass; ZHT P represents the attitude angular velocity of the combined body. T Let m be the position vector from the center of mass of the composite body to the center of mass of the target body. T For target quality.

8. The method for kinematic attitude analysis of a robotic arm connection assembly according to claim 7, characterized in that, The calculation of the reaction torque for configuration change is specifically as follows: Among them, T tran This is the reaction torque for configuration changes.

9. The method for kinematic attitude analysis of a robotic arm connection assembly according to claim 1, characterized in that, The differential equations of the combined dynamics are as follows: in, Angular momentum during the configurational manipulation of the combined body; T rot The reaction torque for the target rotation; T tran The translational reaction moment of the configuration; T control +T distrurbance It refers to the external torque generated by the flywheel, thruster, light pressure, and gravity gradient in the dynamic system.

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