A method for designing a suspension force for ground testing gravity compensation of a space manipulator

Abstract

A kind of hanging force design method for space manipulator ground test gravity compensation, comprising the following steps: obtaining kinematics parameters and dynamics parameters of manipulator;Obtain the installation parameters and mass parameters of the hanging tooling of gravity compensation system;Derive the mathematical model of the torque of each rotary joint of manipulator under the action of gravity environment and gravity compensation system in any arm type;Select several typical task configurations of manipulator;According to the mathematical model of joint torque of manipulator and the typical task configuration of manipulator, design the objective function, and determine the optimal hanging force of gravity compensation system by using mathematical optimization method.

Description

Technical Field

[0001] This invention relates to a method for designing the hanging force for gravity compensation in ground testing of a space robotic arm, belonging to the field of space robotic arm technology. Background Technology

[0002] Ground-based gravity compensation systems are a key technology for space robotic arms. If the space robotic arm is tested directly on the ground, the weight of its components would cause it to malfunction. Therefore, when conducting functional tests of the space robotic arm on the ground, a microgravity experimental environment needs to be established using a gravity compensation system to verify the system's functionality and feasibility. The purpose of gravity compensation is to simulate the microgravity environment of space on the ground, enabling control of the space robotic arm and simulating the space environment.

[0003] When conducting ground tests on space robotic arms, effective design methods are needed to guide the setting of the hanging force parameters of the gravity compensation system. Otherwise, excessive or insufficient hanging forces will bring large bending moments and torques to the rotating joints of the robotic arm, affecting the normal movement of the rotating joints and even causing some damage to the rotating joints.

[0004] The search revealed that the information on gravity compensation systems for ground tests of space robotic arms mainly focuses on hardware implementations such as gravity balancing devices and follow-up suspension devices, but no design methods for the balancing force or suspension force of ground test gravity compensation systems were found. Summary of the Invention

[0005] The technical problem solved by this invention is: addressing the lack of design methods for the balancing force or suspension force of ground test gravity compensation systems in the existing technology, this invention proposes a suspension force design method for gravity compensation in ground tests of space robotic arms.

[0006] The present invention solves the above-mentioned technical problem through the following technical solution:

[0007] A method for designing the suspension force for gravity compensation in ground testing of a space robotic arm, comprising:

[0008] Determine the kinematic and dynamic parameters of the robotic arm structure;

[0009] Determine the installation and mass parameters of the gravity compensation system suspension fixture;

[0010] Considering the gravitational environment, a mathematical model of the joint torque of the robotic arm is derived to calculate the torque of each rotating joint of the robotic arm under any set of hanging forces and with any arm shape.

[0011] Determine the typical task configuration of the robotic arm, and based on the obtained mathematical model of the joint torque of the robotic arm, calculate the joint torque matrix of the robotic arm under any set of hanging forces for the typical task configuration;

[0012] Using the joint moment matrix of a typical task configuration of a robotic arm as input, an objective function is designed. After discretization optimization by enumeration method, the optimal hanging force of the gravity compensation system is calculated.

[0013] The robotic arm structure is mounted on an external base, which is set on a simulated wall or an air-floating platform.

[0014] The kinematic parameters of the robotic arm are DH coordinates, and the dynamic parameters of the robotic arm are the mass and center of mass position of each link of the robotic arm.

[0015] The specific steps for deriving the mathematical model are as follows:

[0016] Based on the kinematic and dynamic parameters of the robotic arm structure, calculate the torque exerted by the gravity of each link on each rotary joint of the robotic arm in any arm configuration.

[0017] Based on the installation and mass parameters of the gravity compensation system hanging fixtures, calculate the torque exerted by the gravity of each hanging fixture on each rotating joint of the robotic arm in any arm configuration;

[0018] Based on the installation parameters and hanging force parameters of the gravity compensation system hanging fixture, calculate the torque of each hanging force on each rotating joint of the robotic arm in any arm shape;

[0019] By superimposing all the calculated torques, a mathematical model of the joint torques of the robotic arm under the action of gravity environment and gravity compensation system is determined.

[0020] The specific steps for calculating the torque exerted by the weight of each link of the robotic arm on each rotary joint when the robotic arm is in any arm configuration are as follows:

[0021] For a serial robotic arm with n degrees of freedom, including n+1 links, specifically link 0, link 1, ..., link n, the pose relationship between adjacent link coordinate systems {i} and {i-1} can be represented by DH coordinates as follows:

[0022]

[0023] cθ i =cos(θ) i ),sθ i =sin(θ) i ),cα i =cos(α) i ),sα i =sin(α) i )

[0024] In the formula, i-1 T i Let a be the homogeneous transformation matrix between the coordinate systems {i} and {i-1} of adjacent links. i d i α i and θ i The improved DH coordinates for link i;

[0025] For any homogeneous transformation matrix T, the attitude transformation matrix R and position vector p contained therein are specifically as follows:

[0026] R = T(1:3, 1:3), p = T(1:3, 4)

[0027] When the two coordinate systems described by T have the same direction, R = I 3×3 I 3×3 Represents a 3×3 identity matrix;

[0028] For any arm shape θ of the robotic arm, the joint variable θ is determined through the DH coordinate. i Represented as:

[0029] θ=[θ1 θ2…θ i …θ n ]

[0030] The homogeneous transformation matrix of the link coordinate system {i} relative to the base coordinate system {0} is calculated as follows:

[0031]

[0032] Define the orientation of the global coordinate system {A} according to actual needs, and determine the attitude transformation matrix of the base coordinate system {0} relative to the global coordinate system {A} as follows: A R0;

[0033] When the direction of gravity is along the -Y axis of the global coordinate system {A}, the gravitational acceleration vector in the global coordinate system is determined as follows:

[0034] The gravity vector of link i in the global coordinate system {A} is determined as follows:

[0035]

[0036] Where, m i Let i be the mass of link i;

[0037] The homogeneous transformation matrix of the centroid coordinate system {icm} of link i relative to the link coordinate system {i} is determined as follows:

[0038]

[0039] in,i d icm Let {icm} be the position vector of the centroid coordinate system of link i relative to the link coordinate system {i}.

[0040] The homogeneous transformation matrix of the centroid coordinate system {icm} of link i relative to the base coordinate system {0} is calculated as follows:

[0041]

[0042] The homogeneous transformation matrix of the centroid coordinate system {icm} of link i relative to the link coordinate system {j} is calculated as follows:

[0043]

[0044] The way to express the gravity vector of link i in the base coordinate system {0} is as follows:

[0045]

[0046] The way to express the gravity vector of link i in the link coordinate system {j} is as follows:

[0047]

[0048] Representing the rotary joint j as the link coordinate system {j}, determine the torque exerted by gravity on the rotary joint j at the center of mass coordinate system {icm} of link i. for:

[0049]

[0050]

[0051] Define a calculation factor as:

[0052]

[0053] For any arm shape θ, determine the torque exerted by the gravity of each link of the robotic arm on the rotary joint j. for:

[0054]

[0055] The specific steps for calculating the torque exerted by the weight of each hanging fixture on each rotary joint of the robotic arm in any arm configuration are as follows:

[0056] Determine the number of lifting fixtures as q, and the lifting fixture k is connected to the connecting rod i. Record the sequence of the connecting rod numbers connected to the q lifting fixtures as r.

[0057] The hanging force F kThe intersection point with link i is denoted as lifting point k, where the position of the lifting point is consistent with the installation parameters of the lifting fixture; the center of mass of the lifting fixture k is located at the lifting force F. k On the axis, the weight of the suspended fixture k and the suspension force F k They are collinear in opposite directions, and their points of action are all in the lifting point coordinate system {k}.

[0058] The gravity vector of the hanging fixture k in the global coordinate system {A} is determined as follows:

[0059]

[0060] Among them, M k For the mass of the hanging fixture k;

[0061] The homogeneous transformation matrix of the lifting point coordinate system {k} relative to the link coordinate system {i} is determined as follows:

[0062]

[0063] in, i d kdd Let {k} be the position vector of the lifting point coordinate system relative to the link coordinate system {i}.

[0064] The homogeneous transformation matrix of the lifting point coordinate system {k} relative to the base coordinate system {0} is calculated as follows:

[0065]

[0066] The homogeneous transformation matrix of the lifting point coordinate system {k} relative to the link coordinate system {j} is calculated as follows:

[0067]

[0068] Transform the gravity vector of the suspended fixture k into the base coordinate system {0} as follows:

[0069]

[0070] Transform the gravity vector of the hanging fixture k into the link coordinate system {j} as follows:

[0071]

[0072] Determine the torque exerted by the gravity of the lifting fixture k on the rotary joint j at the lifting point coordinate system {k}. for:

[0073]

[0074]

[0075] Define a calculation factor as:

[0076]

[0077] For any boom type θ, determine the torque exerted by the gravity of each hanging fixture on the rotary joint j. for:

[0078] The specific steps for calculating the torques exerted by each hanging force on each rotary joint of the robotic arm in any arm configuration are as follows: Determine the hanging force F. k The size is F k Determine the suspension force F in the global coordinate system {A} k The vector is:

[0079]

[0080] Determine the hanging force F k The vector transformed into the base coordinate system {0} is:

[0081] 0 F k =( A R0) -1 · A F k

[0082] Determine the hanging force F k The vector transformed into the link coordinate system {j} is:

[0083] j F k =( 0 R j ) -1 · 0 F k =( 0 R j ) -1 ·( A R0) -1 · A F k

[0084] Determine the hanging force F at point {k} in the coordinate system of the lifting point. k Torque on rotary joint j for:

[0085]

[0086]

[0087] For any boom type θ, determine the torque exerted by each suspension force on the rotation joint j. for:

[0088]

[0089] For any arm type θ, determine the weight of each link of the robotic arm, the weight of each hanging fixture, and the torque τ exerted by each hanging force on the rotational joint j of the robotic arm. j for:

[0090]

[0091] The magnitudes of the joint torques are represented as row vectors:

[0092] τ=[τ1 τ2…τ j …τ n ]

[0093] The magnitudes of each suspension force are represented as row vectors:

[0094] F = [F1 F2…F] k …F q ]

[0095] Given any set of arm types θ, and with the robotic arm mass parameters, hoisting fixture installation parameters, and mass parameters determined, the mathematical model for the joint torque τ generated by the hoisting force F is:

[0096] τ = f1(F,θ).

[0097] The typical task configuration of the robotic arm consists of w arm angles θ. i Composition, specifically described as follows:

[0098]

[0099] In the formula, θ represents any arm shape of the robotic arm. i Let n be a 1×n row vector, where n is the degree of freedom of the robotic arm.

[0100] The method for determining the optimal hanging force of the gravity compensation system's hanging fixture is as follows:

[0101] The joint moment matrix τs generated by the suspension force F in the typical mission configuration Θ is determined as follows:

[0102]

[0103] In the formula, τ j It is the sequence of torques acting on joint j in a typical mission configuration Θ under the action of the suspension force F, and is a column vector of w×1.

[0104] Extract the joint moment τ in the j-th column of the joint moment matrix τs j The maximum value τ jmax and minimum value τ jmin Design the objective function, specifically:

[0105]

[0106] Through the objective function τ f Evaluate the effect of a set of suspension forces F on the gravity compensation of the robotic arm;

[0107] The hanging forces are discretized using an enumeration method to construct different combinations of hanging forces. The objective function value of each group of hanging forces is calculated, and the values ​​are arranged in ascending order from smallest to largest. The group of hanging forces with the smallest objective function value is selected as the optimal hanging force F for the gravity compensation system. best .

[0108] The advantages of this invention compared to the prior art are:

[0109] (1) The present invention provides a hanging force design method for gravity compensation of space robotic arm ground test. Through detailed mathematical derivation, a mathematical model of the joint torque of the robotic arm under the action of gravity compensation system is obtained. This model is used to calculate the torque of each rotating joint of the robotic arm under any set of hanging forces in any arm shape. This provides an efficient solution object for the optimization design of hanging force parameters.

[0110] (2) When the present invention calculates the objective function value to quantitatively evaluate the effect of a set of hanging force parameters on the gravity compensation of the robotic arm, it does not consider the joint torque information of the entire process of the ground test operation task of the robotic arm, but only considers the joint torque information corresponding to several typical task configurations. This can significantly reduce the number of calls to the mathematical model of the joint torque of the robotic arm and significantly improve the calculation efficiency.

[0111] (3) The present invention uses an enumeration method to discretize and optimize the hanging force parameters, and designs a set of discrete optimal hanging force parameters as the force input of the gravity compensation system for the ground test of the space manipulator, ensuring that the rotating joint of the manipulator does not bear excessive bending moment and torque during typical tasks. It is easy to implement and has significant effects. Attached Figure Description

[0112] Figure 1 A flowchart of a design method for gravity compensation suspension force in ground testing of a space robotic arm, provided for the invention.

[0113] Figure 2 A schematic diagram of a space robotic arm and ground-based gravity compensation for the invention;

[0114] Figure 3 A schematic diagram of the coordinate system of the seven-degree-of-freedom robotic arm and linkage provided for the invention;

[0115] Figure 4 A schematic diagram of the installation parameters for the hanging fixture provided for the invention;

[0116] Figure 5A schematic diagram of a typical task configuration of a robotic arm provided for the invention;

[0117] Figure 6 A schematic diagram of the angle curves of each joint of the robotic arm during a typical task provided for the invention.

[0118] Figure 7 A schematic diagram of the torque curves of each joint of the robotic arm during a typical task provided for the invention; Detailed Implementation

[0119] A method for designing the suspension force for gravity compensation in ground testing of a space robotic arm is presented. Through mathematical modeling and optimization, suitable suspension force parameters are designed and used as the force input for the gravity compensation system in ground testing of the space robotic arm. This ensures that the rotary joints of the robotic arm do not experience excessive bending moments and torques during typical tasks. The specific steps are as follows:

[0120] Determine the kinematic and dynamic parameters of the robotic arm structure;

[0121] Determine the installation and mass parameters of the gravity compensation system suspension fixture;

[0122] Under the action of the gravity supplementation system, a mathematical model of the torque on each rotary joint of the robotic arm in an arbitrary arm shape under gravity is derived.

[0123] Determine the typical task configuration of the robotic arm;

[0124] Based on the obtained mathematical model of the joint torque of the robotic arm and the typical task configuration of the robotic arm, an objective function is designed. After optimization by an intelligent algorithm, the optimal hanging force of the gravity compensation system hanging fixture is calculated.

[0125] The robotic arm structure is set on an external base, which is set on a simulated wall or air-floating platform. The kinematic parameters of the robotic arm are DH coordinates, and the dynamic parameters of the robotic arm are the mass and center of mass position of each link of the robotic arm.

[0126] Specifically, the steps for deriving the mathematical model are as follows:

[0127] Based on the kinematic and dynamic parameters of the robotic arm structure, calculate the torque exerted by the gravity of each link on each rotary joint of the robotic arm in any arm configuration.

[0128] Based on the installation and mass parameters of the gravity compensation system hanging fixtures, calculate the torque exerted by the gravity of each hanging fixture on each rotating joint of the robotic arm in any arm configuration;

[0129] Based on the installation parameters and hanging force parameters of the gravity compensation system hanging fixture, calculate the torque of each hanging force on each rotating joint of the robotic arm in any arm shape;

[0130] By superimposing all the calculated torques, a mathematical model of the joint torques of the robotic arm under the action of gravity environment and gravity compensation system is determined;

[0131] The specific steps for calculating the torque exerted by the weight of each link of the robotic arm on each rotary joint when the robotic arm is in any arm configuration are as follows:

[0132] Using a series of robotic arms with n degrees of freedom, determine the link coordinate system {i}, the global coordinate system {A}, the base coordinate system {0}, and the centroid coordinate system {icm} of link i.

[0133] For a serial robotic arm with n degrees of freedom, including n+1 links, specifically link 0, link 1, ..., link n, the pose relationship between adjacent link coordinate systems {i} and {i-1} can be represented by the DH coordinate rule as follows:

[0134]

[0135] cθ i =cos(θ) i ),sθ i =sin(θ) i ),cα i =cos(α) i ),sα i =sin(α) i )

[0136] In the formula, i-1 T i Let a be the homogeneous transformation matrix between the coordinate systems {i} and {i-1} of adjacent links. i d i α i and θ i The improved DH coordinates for link i;

[0137] When the direction of gravity is along the -Y axis of the global coordinate system {A}, the gravitational acceleration vector in the global coordinate system is determined as follows:

[0138] The gravity vector of link i in the global coordinate system {A} is determined as follows:

[0139]

[0140] The homogeneous transformation matrix of the centroid coordinate system {icm} of link i relative to the link coordinate system {i} is determined as follows:

[0141]

[0142] The homogeneous transformation matrix of the centroid coordinate system {icm} of link i relative to the base coordinate system {0} is calculated as follows:

[0143]

[0144] The homogeneous transformation matrix of the centroid coordinate system {icm} of link i relative to the link coordinate system {j} is calculated as follows:

[0145]

[0146] The way to express the gravity vector of link i in the base coordinate system {0} is as follows:

[0147]

[0148] The way to express the gravity vector of link i in the link coordinate system {j} is as follows:

[0149]

[0150] Representing the rotary joint j as the link coordinate system {j}, determine the torque exerted by gravity on the rotary joint j at the center of mass coordinate system {icm} of link i. for:

[0151]

[0152]

[0153] The defining factor is:

[0154]

[0155] For any arm shape θ, determine the torque exerted by the gravity of each link of the robotic arm on the rotary joint j. for:

[0156]

[0157] For any homogeneous transformation matrix T, the attitude transformation matrix R and position vector p contained therein are specifically as follows:

[0158] R = T(1:3, 1:3), p = T(1:3, 4)

[0159] When the two coordinate systems described by T have the same direction, R = I 3×3 I 3×3 Represents a 3×3 identity matrix;

[0160] For any arm shape θ of the robotic arm, the joint variable θ is determined by the DH coordinate rule. i Represented as:

[0161] θ=[θ1 θ2…θ i …θ n ]

[0162] The homogeneous transformation matrix of the link coordinate system {i} relative to the base coordinate system {0} is:

[0163]

[0164] The attitude transformation matrix of the base coordinate system {0} relative to the global coordinate system {A} is: A R0;

[0165] The specific steps for calculating the torque exerted by the weight of each hanging fixture on each rotary joint of the robotic arm in any arm configuration are as follows:

[0166] Determine the number of lifting fixtures as q, and the lifting fixture k is connected to the connecting rod i. Record the sequence of the connecting rod numbers connected to the q lifting fixtures as r.

[0167] The hanging force F k The intersection with link i is denoted as lifting point k, where the position of the lifting point is consistent with the installation parameters of the lifting fixture; the center of mass of the lifting fixture k is located at the lifting force F. k On the axis, the weight of the suspended fixture k and the suspension force F k They are collinear in opposite directions, and their points of action are all in the lifting point coordinate system {k}.

[0168] The gravity vector of the hanging fixture k in the global coordinate system {A} is determined as follows:

[0169]

[0170] The mass of the hanging fixture k is M. k The position vector of the lifting point coordinate system {k} relative to the connecting rod coordinate system {i} is: i d kdd ;

[0171] The homogeneous transformation matrix of the lifting point coordinate system {k} relative to the link coordinate system {i} is determined as follows:

[0172]

[0173] The homogeneous transformation matrix of the lifting point coordinate system {k} relative to the base coordinate system {0} is calculated as follows:

[0174]

[0175] The homogeneous transformation matrix of the lifting point coordinate system {k} relative to the link coordinate system {j} is calculated as follows:

[0176]

[0177] Transform the gravity vector of the suspended fixture k into the base coordinate system {0} as follows:

[0178]

[0179] Transform the gravity vector of the hanging fixture k into the link coordinate system {j} as follows:

[0180]

[0181] Determine the torque exerted by the gravity of the lifting fixture k on the rotary joint j at the lifting point coordinate system {k}. for:

[0182]

[0183]

[0184] The defining factor is:

[0185]

[0186] Based on the defined factors, determine the torque exerted by the gravity of each hoisting fixture on the rotary joint j for any boom type θ. for:

[0187]

[0188] The specific steps for calculating the torque exerted by each hanging force on each rotary joint of the robotic arm in any arm configuration are as follows:

[0189] Determine the hanging force F k The size is F k Determine the suspension force F in the global coordinate system {A} k The vector is:

[0190]

[0191] Determine the hanging force F k The vector transformed into the base coordinate system {0} is:

[0192] 0 F k =( A R0) -1 · A F k

[0193] Determine the hanging force F k The vector transformed into the link coordinate system {j} is:

[0194] j F k =( 0 R j ) -1 · 0 F k=( 0 R j ) -1 ·( A R0) -1 · A F k

[0195] The suspension force F at the lifting point coordinate system {k} is determined by the link coordinate system {j}. k Torque on rotary joint j for:

[0196]

[0197]

[0198] Determine the torque exerted by each suspension force on the rotary joint j under any boom type θ. for:

[0199]

[0200] Given an arbitrary arm shape θ, determine the weight of each link of the robotic arm, the weight of each hanging fixture, and the torque τ exerted by each hanging force on the rotational joint j of the robotic arm. j for:

[0201]

[0202] The magnitudes of the joint torques are represented as row vectors:

[0203] τ=[τ1 τ2…τ j …τ n ]

[0204] The magnitudes of each suspension force are represented as row vectors:

[0205] F = [F1 F2…F] k …F q ]

[0206] Given any set of arm types θ, and with the robotic arm mass parameters, hoisting fixture installation parameters, and mass parameters determined, the mathematical model for the joint torque τ generated by the hoisting force F is:

[0207] τ = f1(F,θ);

[0208] A typical robotic arm configuration consists of w arm angles θ. i Composition, specifically described as follows:

[0209]

[0210] In the formula, θ represents any arm shape of the robotic arm. iLet n be a 1×n row vector, where n is the degree of freedom of the robotic arm;

[0211] The method for determining the optimal hanging force of the gravity compensation system's hanging fixture is as follows:

[0212] The joint moment matrix τs generated by the suspension force F in the typical mission configuration Θ is determined as follows:

[0213]

[0214] In the formula, τ j It is the sequence of torques acting on joint j in a typical mission configuration Θ under the action of the suspension force F, and is a column vector of w×1.

[0215] Extract the joint moment τ in the j-th column of the joint moment matrix τs j The maximum value τ jmax and minimum value τ jmin Design the objective function, specifically:

[0216]

[0217] For the objective function τ f During the evaluation test, the effect of the hanging force F on the gravity compensation of the robotic arm was determined.

[0218] The hanging forces are discretized using an enumeration method to construct different combinations of hanging forces. The objective function value of each group of hanging forces is calculated, and the values ​​are arranged in ascending order from smallest to largest. The group of hanging forces with the smallest objective function value is selected as the optimal hanging force F for the gravity compensation system. best .

[0219] The following description, based on the accompanying drawings and specific embodiments, provides further details:

[0220] In the current embodiment, such as Figure 1 The diagram shows a flowchart of the design method for the suspension force of the gravity compensation system in a ground test of a space robotic arm. The method includes the following steps: obtaining the kinematic and dynamic parameters of the robotic arm; obtaining the installation and mass parameters of the suspension fixtures for the gravity compensation system; deriving the mathematical model of the torques acting on each rotary joint of the robotic arm under gravity and the gravity compensation system in any arm configuration; selecting several typical task configurations of the robotic arm; designing an objective function based on the mathematical model of the joint torques and the typical task configurations of the robotic arm; and using a mathematical optimization method to determine the suspension force of the gravity compensation system. The base of the robotic arm is mounted on a simulated wall, and the end effector of the robotic arm is free. The mathematical model of the joint torques of the robotic arm is obtained by superimposing the gravity of each link of the robotic arm, the gravity of each suspension fixture, and the torques exerted by each suspension force on each rotary joint. The mathematical optimization method involves constructing combinations of suspension forces through enumeration and selecting the set of suspension forces that minimizes the objective function value.

[0221] like Figure 2 As shown, the space robotic arm and the ground test gravity compensation system are the objects. The base of the robotic arm is installed on the simulation wall, and the end of the robotic arm is free.

[0222] The steps of the suspension force design method include:

[0223] Step A: Obtain the kinematic and dynamic parameters of the robotic arm.

[0224] The spatial robotic arm is a seven-DOF serial robotic arm. The kinematic parameters (improved DH coordinates) and dynamic parameters required for modeling the robotic arm are shown as 0 and 0, respectively. Following the rules of the improved DH coordinates, a link coordinate system is established, as follows: Figure 3 As shown.

[0225] Table 1. Kinematic parameters of the robotic arm (improved DH coordinates)

[0226] Serial Number <![CDATA[a i (mm)]]> <![CDATA[α i (°)]]> <![CDATA[d i (mm)]]> <![CDATA[θ i (°)]]> 1 0 90 <![CDATA[d1(210)]]> 0 2 0 90 <![CDATA[d2(250)]]> 0 3 0 -90 <![CDATA[d3(240)]]> -90 4 <![CDATA[a4(1500)]]> 0 <![CDATA[d4(230)]]> 0 5 <![CDATA[a5(1500)]]> 0 <![CDATA[d5(240)]]> 90 6 0 90 <![CDATA[d6(250)]]> 0 7 0 -90 <![CDATA[d7(370)]]> 0

[0227] Table 2 Dynamic parameters of the robotic arm

[0228] rod Mass (kg) Centroid (mm) 1 7.0 0.2,-26.1,-57.8 2 7.5 5.3,27.4,-54.7 3 24.6 608.5,1.9,-0.3 4 21.8 1009.9,-2.6,8.7 5 7.6 7.2,-56.8,-24.5 6 7.1 -0.2,57.4,-26.3 7 13.7 1.2,-26.9,-93.9

[0229] Step B: Obtain the installation parameters and quality parameters of the gravity compensation system hanging fixture.

[0230] like Figure 2 As shown, the gravity compensation system has three hanging fixtures. Fixture 1 is connected to link 3, fixture 2 is connected to link 4, and fixture 3 is connected to link 7. The installation parameters of each hanging fixture on the robotic arm are as follows: Figure 4 As shown in Table 3, the quality parameters of the hanging fixture are as follows.

[0231] Table 3 Quality parameters of the hanging fixture

[0232]

[0233]

[0234] Step C: Derive the mathematical model of the torques on each rotary joint of the robotic arm under the action of gravity environment and gravity compensation system in any arm shape.

[0235] Step C1: Based on the kinematic and dynamic parameters of the robotic arm, calculate the torque exerted by the gravity of each link on each rotary joint of the robotic arm in any arm configuration.

[0236] The specific process of step C1 is as follows:

[0237] For a serial robotic arm with n degrees of freedom, there are n+1 links, which are link 0 (base), link 1, ..., link n in sequence. In this embodiment, n = 7.

[0238] An improved DH coordinate rule is used to describe the pose relationship between adjacent link coordinate systems {i} and {i-1}.

[0239]

[0240] i-1 T i Let a be the homogeneous transformation matrix between the coordinate systems {i} and {i-1} of adjacent links, where a i d i α i and θ i Let cθ be the improved DH coordinate of link i. i =cos(θ) i ),sθ i =sin(θ) i ),cα i =cos(α) i ),sα i =sin(α) i );

[0241] For any homogeneous transformation matrix T, the included attitude transformation matrix R and position vector p are as follows:

[0242] R = T(1:3, 1:3), p = T(1:3, 4)

[0243] When the two coordinate systems described by T have the same direction, R = I 3×3 I 3×3 Represents a 3×3 identity matrix;

[0244] For any arm shape θ of the robotic arm, the joint variable θ in the DH coordinate system can be used. i Represented as:

[0245] θ=[θ1 θ2…θ i …θ n ]

[0246] The homogeneous transformation matrix of the link coordinate system {i} relative to the base coordinate system {0}, calculated using forward kinematics, is as follows:

[0247]

[0248] The attitude transformation matrix of the base coordinate system {0} relative to the global coordinate system {A} is: A R0, in this embodiment

[0249] Assume the direction of gravity is along the -Y axis of the global coordinate system {A}, that is, the gravitational acceleration vector in the global coordinate system is... The gravitational acceleration constant is g = 9.8 m / s². 2 ;

[0250] From the dynamic parameters of the robotic arm, we know that the mass of link i is m. i The position vector of the centroid coordinate system {icm} of link i relative to the link coordinate system {i} is: i d icm Then we have:

[0251] The gravity vector of link i in the global coordinate system {A} is:

[0252]

[0253] The homogeneous transformation matrix of the centroid coordinate system {icm} of link i relative to the link coordinate system {i} is:

[0254]

[0255] The homogeneous transformation matrix of the centroid coordinate system {icm} of link i relative to the base coordinate system {0} is calculated as follows:

[0256]

[0257] The homogeneous transformation matrix of the centroid coordinate system {icm} of link i relative to the link coordinate system {j} is calculated as follows:

[0258]

[0259] The gravity vector of link i can be represented in the base coordinate system {0} as follows:

[0260]

[0261] The gravity vector of link i can be transformed into the link coordinate system {j} as follows:

[0262]

[0263] For a rotary joint j, which can be represented by the link coordinate system {j}, the torque exerted by gravity at the center of mass coordinate system {icm} of link i on the rotary joint j is... for:

[0264]

[0265]

[0266] Define factor:

[0267]

[0268] For any arm shape θ, the torque exerted by the gravity of each link of the robotic arm on the rotary joint j for:

[0269]

[0270] Step C2: Based on the installation and mass parameters of the gravity compensation system's hanging fixtures, calculate the torque exerted by the gravity of each hanging fixture on each rotating joint of the robotic arm in any arm configuration.

[0271] The specific process of step C2 is as follows:

[0272] The number of hanging fixtures is q. The hanging fixture k is connected to the connecting rod i. The sequence of the connecting rods connected to the q hanging fixtures is recorded as r. In this embodiment, q = 3, r = [3 4 7];

[0273] Hanging force F k The point where it intersects with link i is a fixed point, called lifting point k. The position of the lifting point is consistent with the installation parameters of the lifting fixture.

[0274] Assume the center of mass of the suspending fixture k is at the suspending force F. k On the axis, the weight of the suspended fixture k and the suspension force F are related. k They are collinear and in opposite directions, and the point of application of both forces is the lifting point coordinate system {k}.

[0275] Based on the installation and mass parameters of the gravity compensation system's hanging fixture, the mass of the hanging fixture k is M. k The position vector of the lifting point coordinate system {k} relative to the connecting rod coordinate system {i} is: i d kdd In this embodiment, 3 d 1dd =[608 0 0], 4 d 2dd =[1016 0 0], 7 d 3dd =[0 0 -243.2], then:

[0276] The gravity vector of the hanging fixture k in the global coordinate system {A} is:

[0277]

[0278] The homogeneous transformation matrix of the lifting point coordinate system {k} relative to the link coordinate system {i} is:

[0279]

[0280] The homogeneous transformation matrix of the lifting point coordinate system {k} relative to the base coordinate system {0} is calculated as follows:

[0281]

[0282] The homogeneous transformation matrix of the lifting point coordinate system {k} relative to the link coordinate system {j} is calculated as follows:

[0283]

[0284] The gravity vector of the suspended fixture k can be represented in the base coordinate system {0} as follows:

[0285]

[0286] The gravity vector of the suspended fixture k can be transformed into the link coordinate system {j} as follows:

[0287]

[0288] For a rotary joint j, which can be represented by a link coordinate system {j}, the torque exerted by the gravity of the hoisting fixture k at the lifting point coordinate system {k} on the rotary joint j is... for:

[0289]

[0290]

[0291] Define factor:

[0292]

[0293] For any boom type θ, the torque exerted by the gravity of each hanging fixture on the rotary joint j for:

[0294]

[0295] Step C3: Based on the installation parameters and hanging force parameters of the gravity compensation system hanging fixture, calculate the torque of each hanging force on each rotating joint of the robotic arm in any arm configuration.

[0296] The specific process of step C3 is as follows:

[0297] Hanging force F k The size is F k The hanging force F in the global coordinate system {A} k The vector is:

[0298]

[0299] The hanging force F kThe vector transformation into the base coordinate system {0} can be represented as:

[0300] 0 F k =( A R0) -1 · A F k

[0301] The hanging force F k The vector transformation into the link coordinate system {j} can be expressed as:

[0302] j F k =( 0 R j ) -1 · 0 F k =( 0 R j ) -1 ·( A R0) -1 · A F k

[0303] For a rotary joint j, which can be represented by the link coordinate system {j}, the suspension force F at the suspension point coordinate system {k} is... k Torque on rotary joint j for:

[0304]

[0305]

[0306] For any boom type θ, the torques exerted by each suspension force on the rotational joint j for:

[0307]

[0308] Step C4: Superimpose the weight of each link of the robotic arm, the weight of each hanging fixture, and the torque of each hanging force on each rotating joint of the robotic arm in any arm shape to obtain the mathematical model of the joint torque of the robotic arm under the action of gravity environment and gravity compensation system.

[0309] The specific process of step C4 is as follows:

[0310] For any arm type θ, the combined effects of the arm's gravity, the weight of the suspended fixture, and the suspension force exert a torque τ on the rotary joint j. j for:

[0311]

[0312] The magnitudes of the joint torques are represented as row vectors:

[0313] τ=[τ1 τ2…τ j …τ n ]

[0314] The magnitudes of each suspension force are represented as row vectors:

[0315] F = [F1 F2…F] k …F q ]

[0316] Under gravity, when the mass parameters of the robotic arm, the installation parameters of the suspension fixture, and the mass parameters are determined, for any set of arm shapes θ, the joint torque τ generated by the suspension force F can be expressed as a function:

[0317] τ = f1(F,θ).

[0318] Step D: Select several typical task configurations of the robotic arm, such as Figure 5 As shown.

[0319] Several arm configurations were selected from the robotic arm's ground testing process as typical mission configurations, consisting of w arm configuration angles θ. i Composition, a typical task configuration Θ can be represented as:

[0320]

[0321] In this embodiment, w=6, and six arm types are selected as typical task configurations for the robotic arm. The arm type angle sequence is shown in Table 4:

[0322] Table 4. Arm Angle Sequences Corresponding to Typical Task Configurations of Robotic Arms

[0323] Arm angle (°) <![CDATA[θ1]]> <![CDATA[θ2]]> <![CDATA[θ3]]> <![CDATA[θ4]]> <![CDATA[θ5]]> <![CDATA[θ6]]> <![CDATA[θ7]]> S1 180 90 90 0 -30 -90 -90 S2 90 90 90 0 -30 -90 -90 S3 0 90 90 0 -30 -90 -90 S4 0 90 90 -65.02 -30 -90 -90 S5 0 90 0 -65.02 -30 -90 -90 S6 60 66.82 -48.81 -65.02 -30 -90 -90

[0324] Step E: Based on the mathematical model of the joint torque of the robotic arm and the typical task configuration of the robotic arm, design the objective function and use mathematical optimization methods to determine the hanging force of the gravity compensation system.

[0325] For a typical mission configuration Θ, the joint moment matrix τs generated by the suspension force F is:

[0326]

[0327] Where τ j It is the sequence of torques acting on joint j in a typical mission configuration Θ under the action of the suspension force F, and is a column vector of w×1.

[0328] Extract the joint torque τ in the j-th column of τs j The maximum value τ jmax and minimum value τ jminDesign the objective function:

[0329]

[0330] objective function τ f The effect of the hanging force F on the gravity compensation of the robotic arm during the test was measured.

[0331] Assuming the maximum range of the spring scale and force sensor in the gravity compensation system's suspension device is 400N, within the range of 200N to 400N, the three suspension forces are discretized with a step size of 10N. Using an enumeration method, 21×21×21 combinations of suspension forces are constructed, and the objective function value under each group of suspension forces is calculated. The objective function values ​​are arranged in ascending order, and the suspension force parameters corresponding to the first 10 groups are shown in Figure 0. The suspension force with the smallest objective function value is selected as the design input for the suspension force of the gravity compensation system, i.e., the optimal suspension force F. best =[370250360].

[0332] Table 5. Hanging force parameters for the first 10 groups

[0333] Hanging force (N) <![CDATA[F1]]> <![CDATA[F2]]> <![CDATA[F3 <!-- 16 -->]]> 1 370 250 360 2 330 300 330 3 360 280 340 4 390 220 380 5 350 270 350 6 380 260 350 7 320 290 340 8 400 230 370 9 360 240 370 10 370 240 370

[0334] If a ground test of the space robotic arm is conducted directly without using a gravity compensation system, the joint moments corresponding to a typical mission configuration under the gravity of each link are shown in Table 6 below:

[0335] Table 6. Joint torques for typical task configurations of the robotic arm (without using a gravity compensation system).

[0336]

[0337] As shown in Table 6, when the gravity compensation system is not used, the maximum joint torque corresponding to the typical mission configuration is greater than 1500 Nm, which far exceeds the bearing capacity of the space robotic arm and will cause joint damage.

[0338] Ground tests of a space robotic arm were conducted using a gravity compensation system, and the suspension force parameter F was set. best = [370 250360], the joint moments corresponding to typical task configurations are shown in Table 7 below:

[0339] Table 7. Joint torques corresponding to typical task configurations of robotic arms.

[0340]

[0341]

[0342] The joint angle curves during the ground testing of this robotic arm are planned as follows: Figure 6As shown, this includes all six arm angles corresponding to the typical mission configurations in Table 4. The joint moments during this ground test were calculated, and the joint moment curves are shown below. Figure 7 As shown in Table 8, the range of joint torques is as follows:

[0343] Table 8. Joint torque range of the robotic arm during ground testing.

[0344]

[0345] As shown in Table 8, the hanging force parameter of the gravity compensation system is F. best = [370 250 360]. During the ground test of the robotic arm, the torque of joint 5 was the largest, about 11.89 Nm, which is within the bearing capacity of the space robotic arm and can ensure the safety of the robotic arm.

[0346] As can be seen from the above examples, by using the method provided by this invention, suitable hanging force parameters can be designed through mathematical modeling and optimization, which can be used as the force input of the gravity compensation system for the ground test of the space robotic arm. This ensures that the rotating joints of the robotic arm do not bear excessive bending moment and torque during typical tasks. The method is easy to implement and has significant effects.

[0347] Although the present invention has been disclosed above with reference to preferred embodiments, it is not intended to limit the present invention. Any person skilled in the art can make possible changes and modifications to the technical solutions of the present invention by utilizing the methods and techniques disclosed above without departing from the spirit and scope of the present invention. Therefore, any simple modifications, equivalent changes and alterations made to the above embodiments based on the technical essence of the present invention without departing from the content of the technical solutions of the present invention shall fall within the protection scope of the technical solutions of the present invention.

[0348] The contents not described in detail in this specification are common knowledge to those skilled in the art.

Claims

1. A method for designing the suspension force for gravity compensation in ground testing of a space robotic arm, characterized in that... include: Determine the kinematic and dynamic parameters of the robotic arm structure; Determine the installation and mass parameters of the gravity compensation system suspension fixture; Considering the gravitational environment, a mathematical model of the joint torque of the robotic arm is derived to calculate the torque of each rotating joint of the robotic arm under any set of hanging forces and with any arm shape. Determine the typical task configuration of the robotic arm, and based on the obtained mathematical model of the joint torque of the robotic arm, calculate the joint torque matrix of the robotic arm under any set of hanging forces for the typical task configuration; Using the joint moment matrix of a typical task configuration of a robotic arm as input, an objective function is designed. After discretization optimization by enumeration method, the optimal hanging force of the gravity compensation system is calculated. The specific steps for deriving the mathematical model are as follows: Based on the kinematic and dynamic parameters of the robotic arm structure, calculate the torque exerted by the gravity of each link on each rotary joint of the robotic arm in any arm configuration. Based on the installation and mass parameters of the gravity compensation system hanging fixtures, calculate the torque exerted by the gravity of each hanging fixture on each rotating joint of the robotic arm in any arm configuration; Based on the installation parameters and hanging force parameters of the gravity compensation system hanging fixture, calculate the torque of each hanging force on each rotating joint of the robotic arm in any arm shape; By superimposing all the calculated torques, a mathematical model of the joint torques of the robotic arm under the action of gravity environment and gravity compensation system is determined; The method for determining the optimal hanging force of the gravity compensation system's hanging fixture is as follows: Determine typical task configurations medium hanging force The generated joint moment matrix for: In the formula, It is the hanging force Under the influence of the action, typical task configuration Middle joint The sequence of torques is Column vectors; Extracting the joint moment matrix The Middle Joint torque maximum value and minimum value Design the objective function, specifically: Through the objective function Evaluate a set of hanging forces The effect of gravity compensation on the robotic arm; The hanging forces are discretized using an enumeration method to construct different combinations of hanging forces. The objective function value of each group of hanging forces is calculated, and the values ​​are arranged in ascending order from smallest to largest. The group of hanging forces with the smallest objective function value is selected as the optimal hanging force for the gravity compensation system. .

2. The hanging force design method for gravity compensation in ground testing of a space robotic arm according to claim 1, characterized in that: The robotic arm structure is mounted on an external base, which is set on a simulated wall or an air-floating platform.

3. The hanging force design method for gravity compensation in ground testing of a space robotic arm according to claim 1, characterized in that: The kinematic parameters of the robotic arm are DH coordinates, and the dynamic parameters of the robotic arm are the mass and center of mass position of each link of the robotic arm.

4. The hanging force design method for gravity compensation in ground testing of a space robotic arm according to claim 1, characterized in that: The specific steps for calculating the torque exerted by the weight of each link of the robotic arm on each rotary joint when the robotic arm is in any arm configuration are as follows: For a degree of freedom Serial robotic arms, including There are several links, specifically link 0, link 1, ..., link 2. The DH coordinate system represents the coordinate system of adjacent links. and The pose relationship between them is as follows: In the formula, For adjacent link coordinate systems and The homogeneous transformation matrix between them , , and Link Improved DH coordinates; For any homogeneous transformation matrix The included attitude transformation matrix and position vector Specifically: when When the two coordinate systems being described have the same direction, , express The identity matrix; For any type of robotic arm Joint variables via DH coordinates Represented as: Calculate the link coordinate system Relative to the base coordinate system The homogeneous transformation matrix is: Define a global coordinate system according to actual needs. The direction and the base coordinate system are determined. Relative to global coordinate system The attitude transformation matrix is ; When the direction of gravity is along the global coordinate system of When the axis is in the direction of gravity, the gravitational acceleration vector in the global coordinate system is determined as follows: ; Determine the link In the global coordinate system The gravity vector in is: in, Link The quality; Determine the link centroid coordinate system Relative to the link coordinate system The homogeneous transformation matrix is: in, Link centroid coordinate system Relative to the link coordinate system Position vector; Calculate the link centroid coordinate system Relative to the base coordinate system The homogeneous transformation matrix is: Calculate the link centroid coordinate system Relative to the other link Link coordinate system The homogeneous transformation matrix is: Determine the link Gravity vector transformation to base coordinate system The expression in the text is as follows: Determine the link Gravity vector transformation to link coordinate system The expression in the text is as follows: Rotation joint Represented as a link coordinate system Determine the link centroid coordinate system Gravity at the rotation joint torque for: Define a calculation factor as: For any arm type Determine the effect of gravity on the rotational joints of each link of the robotic arm. torque for: 。 5. The hanging force design method for gravity compensation in ground testing of a space robotic arm according to claim 1, characterized in that: The specific steps for calculating the torque exerted by the weight of each hanging fixture on each rotary joint of the robotic arm in any arm configuration are as follows: Determine the quantity of hoisting fixtures as follows Hanging fixtures With connecting rod The connection will The sequence of the connecting rods of the hoisting fixture is denoted as follows: ; Hanging force With connecting rod The intersection point is called the lifting point. The location of the lifting points is consistent with the installation parameters of the lifting fixture; the lifting fixture The center of mass is located at the suspension force On the axis, the hanging fixture Gravity and hanging force Collinear in opposite directions, with all points of application in the hoisting point coordinate system. ; Determine the hoisting fixture In the global coordinate system The gravity vector in is: in, For hanging fixtures The quality; Determine the coordinate system of the lifting point Relative to the link coordinate system The homogeneous transformation matrix is: in, For the lifting point coordinate system Relative to the link coordinate system Position vector; Calculate the coordinate system of the lifting point Relative to the base coordinate system The homogeneous transformation matrix is: Calculate the coordinate system of the lifting point Relative to the link coordinate system The homogeneous transformation matrix is: Hanging fixtures Gravity vector transformation to base coordinate system Specifically: Hanging fixtures Gravity vector transformation to link coordinate system Specifically: Determine the hoisting fixture In the lifting point coordinate system Gravity at the rotation joint torque for: Define a calculation factor as: For any arm type Determine the effect of the gravity of each hoisting fixture on the rotary joint. torque for: 。 6. The hanging force design method for gravity compensation in ground testing of a space robotic arm according to claim 1, characterized in that: The specific steps for calculating the torque exerted by each hanging force on each rotary joint of the robotic arm in any arm configuration are as follows: Determine the hanging force The size is Determine the global coordinate system Hanging force in The vector is: Determine the hanging force Vector transformation to base coordinate system The vector in is: Determine the hanging force Vector transformation to link coordinate system The vector in is: Determine the coordinate system of the lifting point Hanging force at the location For rotational joints torque for: For any arm type Determine the effect of each suspension force on the rotating joint. torque for: 。 7. The hanging force design method for gravity compensation in ground testing of a space robotic arm according to claim 1, characterized in that: For any arm type Determine the weight of each link of the robotic arm, the weight of each hanging fixture, and the effect of each hanging force on the rotational joints of the robotic arm. torque for: The magnitudes of the joint torques are represented as row vectors: The magnitudes of each suspension force are represented as row vectors: Determine any set of arm shapes When the mass parameters of the robotic arm, the installation parameters of the hoisting fixture, and the mass parameters are determined, the hoisting force... Developed joint torque The mathematical model is as follows: 。 8. The hanging force design method for gravity compensation in ground testing of a space robotic arm according to claim 1, characterized in that: The typical task configuration of the robotic arm consists of individual arm-shaped angle Composition, specifically described as follows: In the formula, the robotic arm can be of any shape. for The row vector, For the degrees of freedom of the robotic arm.

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