A method for determining the joint travel of a robot arm using a Monte Carlo method

Abstract

The application relates to a method for determining the joint stroke of a mechanical arm by using a Monte Carlo method, comprising the following steps: step 1, determining the pose constraint of the mechanical arm, wherein the pose constraint comprises the activity range and the pointing range of the end position of the mechanical arm; step 2, constructing the inverse kinematics equation of the mechanical arm according to the configuration parameters of the mechanical arm, wherein the configuration parameters comprise the included angle between the rotation axes of each adjacent joint of the mechanical arm; and step 3, taking a certain state of the mechanical arm containing different joint angle information as a Monte Carlo sample point, and calculating the joint angle information set in different Monte Carlo sample points according to the pose constraint of the mechanical arm and the inverse kinematics equation, wherein the joint angle information set comprises the stroke envelope of different joints in the mechanical arm. The application can determine the stroke envelope of the joint unit of the mechanical arm in the case that the configuration of the mechanical arm is known and a certain specified probability is determined, so as to guide the fine design of the envelope formed by the joints of the mechanical arm.

Description

Technical Field

[0001] This invention relates to a method for determining the joint stroke of a robotic arm using the Monte Carlo method. Background Technology

[0002] The integrated attitude and orbit control of satellites employing a robotic arm and thrusters offers several advantages by leveraging the robotic arm's ability to actively adjust its end effector position and orientation. These advantages include: fewer thrusters are required due to the active adjustment of both thruster position and azimuth; theoretically, only one thruster is needed for integrated attitude and orbit control; the robotic arm's end effector position and orientation adjustments can be integrated to achieve the desired thrust in any direction, maximizing satellite fuel utilization; and for satellites requiring attitude maneuvers or attitude offsets, the robotic arm's active attitude control can compensate for the satellite's attitude in real time, allowing the satellite to perform its intended integrated attitude and orbit control tasks normally during these maneuvers or offsets.

[0003] Based on the structural parameters of the robotic arm (such as the length of the arm components), when designing the control rate of the robotic arm, if the stroke constraint is too tight, it will affect the normal performance of the robotic arm; if the stroke constraint is too loose, there may be a safety risk of the robotic arm colliding with a celestial body. Therefore, in order to improve the safety of robotic arm control without affecting the normal execution of the robotic arm's tasks, it is necessary to evaluate the joint stroke of the robotic arm and impose appropriate constraints.

[0004] However, for a robotic arm system with n joints (4 ≤ n ≤ 6; if n < 4, the robotic arm is insufficient for simultaneous pose control; if n > 6, the robotic arm joints have multiple solutions and cannot be used to evaluate the joint range of motion), the process of calculating joint parameters based on the end-effector pose state is essentially a process of solving an n-variable transcendental equation, which can be solved using a multi-parameter gradient optimization algorithm. Therefore, there is no explicit analytical solution for calculating the joint angles of the robotic arm, the calculation process is quite lengthy, and the formation envelope of the robotic arm joints cannot be obtained based on normal analysis methods. Summary of the Invention

[0005] To address the aforementioned problems, a method for determining the joint stroke of a robotic arm using the Monte Carlo method is proposed. The Monte Carlo method, also known as the statistical simulation method, is a crucial numerical calculation method guided by probability and statistics theory. It emerged in the mid-1940s due to advancements in science and technology and the invention of electronic computers. Based on probability and statistics theory and the law of large numbers (using the sample mean to approximate the population mean), it utilizes electronic computer digital simulation technology to solve complex problems that are difficult to solve directly using mathematical operations or cannot be solved by other methods.

[0006] This patent addresses the problem of determining the stroke envelope of the robotic arm joint units with a specified probability based on task requirements, given a known robotic arm configuration, in order to guide the refined design of the robotic arm joint envelope formation.

[0007] This invention provides a method for determining the joint stroke of a robotic arm using the Monte Carlo method, comprising the following steps:

[0008] Step 1: Determine the pose constraints of the robotic arm. The pose constraints include the range of motion and pointing range of the robotic arm's end effector.

[0009] Step 2: Construct the inverse motion equation of the robotic arm based on the robotic arm configuration parameters, which include the angles between the rotation axes of each adjacent joint of the robotic arm;

[0010] Step 3: Take a certain state of the robotic arm containing different joint angle information as a Monte Carlo sample point. Based on the pose constraints of the robotic arm and the inverse motion equation, calculate the set of joint angle information in different Monte Carlo sample points. This set of joint angle information contains the travel envelope of different joints in the robotic arm.

[0011] Preferably, in step 1, probabilistic modeling is performed based on the range of motion and pointing range of the robotic arm's end effector.

[0012] Preferably, the probability modeling includes:

[0013] The robotic arm's pose limit state is determined by the satellite's rolling attitude and the thruster installed at the end of the robotic arm;

[0014] Among them, the distance L0 from the satellite's center of mass to the end effector of the robotic arm under nominal conditions, and the satellite yaw range include: the satellite's X-axis rotation attitude range is (-phi_1, phi_1), the satellite's Z-axis rotation attitude range is (-psi_1, psi_1); the range of the robotic arm's end effector thruster's yaw angle towards the ±X-axis is (-psi_2, psi_2); and the range of the thruster's yaw angle towards the ±Z-axis is (-phi_2, phi_2).

[0015] The limiting angle of deviation of the mechanical end from the satellite's X-axis is phi = phi_1 + phi_2;

[0016] The limit angle of deviation of the robotic arm end effector from the satellite's Z-axis is psi = psi_1 + psi_2;

[0017] The semi-major axis of the elliptical envelope at the end of the robotic arm is Apx = R + L0 × sin(phi);

[0018] The semi-major axis of the elliptical envelope at the end of the robotic arm is Apz = R + L0 × sin(psi);

[0019] The angle between the end effector of the robotic arm and the semi-major axis of the ellipse in the X direction is Avx = phi + alpha;

[0020] The angle of the semi-major axis of the ellipse at the end of the robotic arm is Avz = psi + alpha; for the nth sample point, the expression for the end-effector position is:

[0021] X(n)=Apx×rand(-1,1)×cos(rand(-1,1)×2×π);

[0022] Z(n)=Apz×rand(-1,1)×sin(rand(-1,1)×2×π);

[0023] The robotic arm pointing expression is:

[0024] Vx(n)=Avx×rand(-1,1)×cos(rand(-1,1)×2×π);

[0025] Vz(n)=Avz×rand(-1,1)×sin(rand(-1,1)×2×π);

[0026] rand(-1,1) generates uniformly distributed random numbers ranging from -1 to 1.

[0027] Preferably, the probabilistic modeling further includes: for the constraint on the distance between the end of the robotic arm and the center of mass of the satellite, the constraint is added as: Y(n) = rand(y0, y1), where: y0 is the closest distance between the end of the robotic arm and the center of mass of the satellite; y1 is the farthest distance between the end of the robotic arm and the center of mass of the satellite.

[0028] Preferably, the probabilistic modeling further includes: for the constraint of the end effector thruster of the robotic arm along the axial direction, adding the constraint: Vy(n)=rand(vy0,vy1), where: vy0 is the minimum value of the y-axis rotation angle of the robotic arm coordinate system; vy1 is the maximum value of the y-axis rotation angle of the robotic arm coordinate system.

[0029] Preferably, the robotic arm has 6 joints, and the pose transfer matrix from the (i-1)th joint coordinate system to the ith joint coordinate system is:

[0030]

[0031] Where, θ i Let α be the angle of the i-th joint of the robotic arm, representing the information from the i-th joint to the (i+1)-th joint, and its value ranges from the travel distance of the i-th joint of the robotic arm; i-1 Let x be the angle from the (i-1)th joint of the robotic arm to the ith joint, representing information from the (i-1)th joint to the ith joint, and denoted as a configuration parameter of the robotic arm; i ,yi ,z i Let be the position vector of the origin of the i-th joint coordinate system in the (i-1)-th joint coordinate system; specifically, the pose transfer matrix from the satellite centroid body coordinate system to the first joint coordinate system is:

[0032]

[0033] Among them, C 0b The attitude transfer matrix from the satellite's center-of-mass coordinate system to the base coordinate system; x b ,y b ,z b This is the position vector of the base in the coordinate system of the satellite's center of mass. The base is located at the connection between the robotic arm and the satellite.

[0034] For a 6-joint robotic arm, the pose transformation matrix from the satellite's center of mass body coordinate system to the robotic arm's end effector coordinate system is... b T6 is: b T6 = b T1 1 T2 2 T3 3 T4 4 T5 5 T6, b T6 represents the positive motion of the robotic arm's pose; b T6 is defined as:

[0035]

[0036] For the nth sample, the state equation of the robotic arm's end effector pose satisfies:

[0037] X(n)=T 14

[0038] Y(n) = T 24

[0039] Z(n) = T 34

[0040] Vx(n)=T 12

[0041] Vy(n)=T 22

[0042] Vz(n)=T 32 .

[0043] Preferably, for each Monte Carlo sample point, all joint angles are calculated using the Newton gradient method, and the envelope formed by the set of sample points for each joint is the travel envelope of that joint angle.

[0044] For the nth sample, the state equation for the pose of the robotic arm's end effector can be formally written as:

[0045] f x (θ1,θ2,θ3,θ4,θ5,θ6)=0

[0046] f y (θ1,θ2,θ3,θ4,θ5,θ6)=0

[0047] f z (θ1,θ2,θ3,θ4,θ5,θ6)=0

[0048] f vx (θ1,θ2,θ3,θ4,θ5,θ6)=0

[0049] f vy (θ1,θ2,θ3,θ4,θ5,θ6)=0

[0050] f vz (θ1,θ2,θ3,θ4,θ5,θ6)=0

[0051] Where f x f y f z f vx f vy f vz To represent the state at each component of the robotic arm's end effector, we take the partial differentials of each joint angle for the above system of equations, and obtain the Jacobian matrix:

[0052]

[0053] Initial joint angle: X0 = [θ] 1_0 θ 2_0 θ 3_0 θ 4_0 θ 5_0 θ 6_0 ] T The joint angle X is adjusted by iterating through the matrix DX_i. i Perform iterative processing;

[0054]

[0055] when In this case, j represents the number of joints, and err represents the accuracy of the iterative solution.

[0056] X i+1 =X i +DX_i

[0057] Otherwise, when This indicates that the required precision has been met, so the iteration stops, and the last calculated X... iThis refers to the joint angle corresponding to the sample, DX_i is the error between two iterations, and dt_i is the arithmetic square root of the difference between the joint angles obtained from two adjacent iterations.

[0058] This invention can determine the stroke envelope of the robotic arm joint units with a specified probability according to the task requirements, given a known robotic arm configuration, thereby guiding the refined design of the robotic arm joint envelope formation. Attached Figure Description

[0059] Figure 1 This is a flowchart illustrating the process of determining the joint formation envelope of the robotic arm according to the present invention.

[0060] Figure 2 This is a schematic diagram of the pose envelope of the robotic arm;

[0061] Figure 3 The ellipse represents the pose envelope of the robotic arm. Detailed Implementation

[0062] The method for determining the joint stroke of a robotic arm using the Monte Carlo method, as proposed in this invention, will be further described in detail below with reference to the accompanying drawings and specific embodiments. The advantages and features of this invention will become clearer from the following description.

[0063] like Figure 1 As shown, the present invention includes the following steps:

[0064] Step 1: Determine the pose constraints of the robotic arm. The pose constraints include the range of motion and pointing range of the robotic arm's end effector.

[0065] Step 2: Construct the inverse motion equation of the robotic arm based on the robotic arm configuration parameters, which include the angles between the rotation axes of each adjacent joint of the robotic arm;

[0066] Step 3: Take a certain state of the robotic arm containing different joint angle information as a Monte Carlo sample point. Based on the pose constraints of the robotic arm and the inverse motion equation, calculate the set of joint angle information in different Monte Carlo sample points. This set of joint angle information contains the travel envelope of different joints in the robotic arm.

[0067] Based on the robot arm pose constraints in step 1 and the robot arm inverse motion equations in step 2, the inverse motion equations can be solved using the Newton-Raphson iteration method. These inverse motion equations are a set of transcendental equations, and the joint angle information of the corresponding sample points can be obtained by solving this set of transcendental equations.

[0068] Preferably, the pose constraint of the robotic arm in step 1 is probabilistically modeled. It is assumed that the nominal state of the robotic arm is pointing towards the satellite +Y axis, and the line connecting the satellite's center of mass to the end of the robotic arm coincides with the satellite +Y axis. That is, the thrust of the thruster installed at the end of the robotic arm points towards the +Y axis, and the thrust passes through the satellite's center of mass.

[0069] Assuming normal operation, the satellite's rotational attitude range along the X-axis is (-phi_1, phi_1); and its rotational attitude range along the Z-axis, also known as yaw attitude, is (-psi_1, psi_1). In this example, a robotic arm serves as an attitude derotation (eliminating rotation through a force opposite to the direction of motion) platform to achieve fixed spatial pointing of the satellite. The robotic arm's range of motion must cover the satellite's attitude range of motion. Based on the satellite's attitude range of motion, the specific angle range that the robotic arm may use is determined. This range is part of the robotic arm's movable area to allow for safety limiting of the robotic arm's joint angles. Specifically, the satellite's yaw attitudes phi_1 and psi_1 should not exceed the robotic arm's range of motion.

[0070] When the satellite is in a three-axis zero-attitude state and the robotic arm is in its nominal state, the thruster points towards the satellite's Y-axis and can provide normal thrust. By using the robotic arm to deflect the thruster towards the ±X-axis, tangential thrust can be generated, with the deflection angle range being (-psi_2, psi_2). By using the robotic arm to deflect the thruster towards the ±Z-axis, radial thrust can be generated, with the deflection angle range being (-phi_2, phi_2).

[0071] Based on the fact that the robotic arm thruster also has an angular momentum unloading function, three-axis angular momentum unloading can be achieved by actively adjusting the position and direction of the robotic arm's end effector. Three-axis angular momentum unloading is performed based on the thruster's direction, with the robotic arm's end effector displacement range being R and the robotic arm's direction range being alpha.

[0072] robotic arm pose limit states such as Figure 2 As shown, Figure 2 In the diagram, O represents the satellite's center of mass; X, Y, and Z represent the satellite's three axes, respectively; L0 is the distance (in meters) from the satellite's center of mass to the end of the robotic arm under nominal conditions; psi = psi_1 + psi_2 is the limit angle of the robotic arm's deviation from the satellite's z-axis; and phi = phi_1 + phi_2 is the limit angle of the robotic arm's deviation from the satellite's x-axis.

[0073] Figure 3 The pose envelope of the robotic arm is an ellipse. Figure 3 (a) is the elliptical envelope to which the robotic arm points; Figure 3 (b) is the elliptical envelope to which the robotic arm points.

[0074] according to Figure 2 and Figure 3 It can be seen that the semi-major axis of the elliptical envelope at the end of the robotic arm is (in meters):

[0075] Apx = R + L0 × sin(phi)

[0076] The semi-major axis of the elliptical envelope at the end of the robotic arm is (in meters):

[0077] Apz = R + L0 × sin(psi)

[0078] The semi-major axis of the ellipse, pointing in the X direction from the end of the robotic arm, is (in rad):

[0079] Avx = phi + alpha

[0080] The semi-major axis of the ellipse at the end of the robotic arm is (in rad):

[0081] Avz = psi + alpha

[0082] For the nth sample point:

[0083] The expression for the end effector position (in meters) of the robotic arm is:

[0084] X(n)=Apx×rand(-1,1)×cos(rand(-1,1)×2×π);

[0085] Z(n)=Apz×rand(-1,1)×sin(rand(-1,1)×2×π);

[0086] The expression for the robotic arm pointing (in rad) is:

[0087] Vx(n)=Avx×rand(-1,1)×cos(rand(-1,1)×2×π);

[0088] Vz(n)=Avz×rand(-1,1)×sin(rand(-1,1)×2×π);

[0089] If there is also a requirement for the distance between the end of the robotic arm and the center of mass of the satellite, it can be achieved by adding one joint. The added constraint is: Y(n) = rand(y0,y1), where: y0 is the closest distance between the end of the robotic arm and the center of mass of the satellite; y1 is the farthest distance between the end of the robotic arm and the center of mass of the satellite.

[0090] If there are axial constraints on the end effector of the robotic arm, they can be achieved by adding one joint. The added constraint is: Vy(n) = rand(vy0, vy1), where: vy0 is the minimum y-axis rotation angle of the robotic arm coordinate system; vy1 is the maximum y-axis rotation angle of the robotic arm coordinate system.

[0091] Here, rand(-1,1) represents generating uniformly distributed random numbers ranging from -1 to 1. The set of all samples forms the range of motion and pointing range of the robotic arm's end effector.

[0092] Specifically, in step 2, the inverse motion equation of the robotic arm is constructed based on the configuration parameters of the robotic arm;

[0093] Without loss of generality, assume the robotic arm has 6 joints and possesses 3D position and 3D pose adjustment capabilities. Assume the pose transfer matrix from the (i-1)th joint coordinate system to the ith joint coordinate system is:

[0094]

[0095] Where, θ i Let α be the rotation angle of the i-th joint of the robotic arm, representing the information from the i-th joint to the (i+1)-th joint, in rad. Its value range is the joint travel of the robotic arm, and it is the object of satellite control; i-1 Let be the rotation angle from the (i-1)th joint to the ith joint of the robotic arm, in rad, representing information from the (i-1)th joint to the ith joint; and be a structural parameter of the robotic arm, a constant value; x i ,y i ,z i The position vector of the origin of the i-th joint coordinate system in the (i-1)-th joint coordinate system, in meters;

[0096] Specifically, the pose transfer matrix from the satellite's center of mass coordinate system to the first joint is:

[0097]

[0098] Among them, C 0b x is the attitude transfer matrix from the satellite's intrinsic coordinate system to the base coordinate system; b ,y b ,z b This is the position vector of the base position vector in the satellite's centroid body coordinate system, in meters (m).

[0099] In summary, for a 6-joint robotic arm, the pose transformation matrix from the satellite's own structure to the robotic arm's end effector... b T6 is:

[0100] b T6 = b T1 1 T2 2 T3 3 T4 4 T5 5 T6

[0101] b T6 represents the positive motion of the robotic arm's pose.

[0102] Will b T6 is defined as:

[0103]

[0104] For the nth sample, the state equation of the robotic arm's end effector pose satisfies:

[0105] X(n)=T 14

[0106] Y(n) = T 24

[0107] Z(n) = T 34

[0108] Vx(n)=T 12

[0109] Vy(n)=T 22

[0110] Vz(n)=T 32 .

[0111] Furthermore, in step 3, for each Monte Carlo sample point, the Newton gradient method is used to calculate all corresponding joint angles. The envelope formed by the set of sample points for each joint is the travel envelope of that joint angle.

[0112] For the nth sample, the state equation for the pose of the robotic arm's end effector can be formally written as:

[0113] f x (θ1,θ2,θ3,θ4,θ5,θ6)=0

[0114] f y (θ1,θ2,θ3,θ4,θ5,θ6)=0

[0115] f z (θ1,θ2,θ3,θ4,θ5,θ6)=0

[0116] f vx (θ1,θ2,θ3,θ4,θ5,θ6)=0

[0117] f vy (θ1,θ2,θ3,θ4,θ5,θ6)=0

[0118] f vz (θ1,θ2,θ3,θ4,θ5,θ6)=0

[0119] Where f x f y f z f vx f vy f vz To represent the state at each component of the robotic arm's end effector, we take the partial differentials of each joint angle for the above system of equations, and obtain the Jacobian matrix:

[0120]

[0121] Initial joint angle: X0 = [θ] 1_0 θ 2_0 θ 3_0 θ 4_0 θ 5_0 θ 6_0 ] T Optionally, the joint angle X0 = [0 0 0 0 00] T The sample point is selected as the envelope center point. In this example, the robot arm position envelope center is X = 0, Z = 0; the robot arm pointing envelope center is Vx = 0, Vz = 0. Based on the above method, calculate X that meets the accuracy requirements. i This is the initial value of the joint angle in this paper. By selecting this initial value, the number of iterations required to obtain the joint angle that meets the accuracy requirements can be effectively reduced.

[0122]

[0123] when Performing iterative calculations, we have:

[0124] X i+1 =X i +DX_i;

[0125] Otherwise, when This indicates that the required precision has been met, so the iteration stops, and the last calculated X... i This refers to the joint angle corresponding to the sample, where j represents the number of joints, err is a very small positive number representing the accuracy of the iterative solution, DX_i is the error between two iterations, which gets closer and closer to 0 as the iteration progresses, and dt_i is the arithmetic square root of the difference between the joint angles obtained from two adjacent iterations (which is also the square root of the sum of the squares of the differences between the joint angles obtained from two adjacent iterations).

[0126] This invention can determine the stroke envelope of the robotic arm joint units with a specified probability according to the task requirements, given a known robotic arm configuration, thereby guiding the refined design of the robotic arm joint envelope formation.

[0127] 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.

Claims

1. A method for determining the joint stroke of a robotic arm using the Monte Carlo method, characterized in that, The steps include: Step 1, determining the pose constraints of the robotic arm, which include the range of motion and pointing range of the robotic arm's end effector; Step 2: Construct the inverse motion equation of the robotic arm based on the robotic arm configuration parameters, which include the angles between the rotation axes of each adjacent joint of the robotic arm; Step 3: A certain state of the robotic arm containing different joint angle information is taken as a Monte Carlo sample point. Based on the pose constraints of the robotic arm and the inverse motion equation, the set of joint angle information in different Monte Carlo sample points is calculated. This set of joint angle information contains the travel envelope of different joints in the robotic arm. In step 1, probabilistic modeling is performed based on the range of motion and pointing range of the robotic arm's end effector. The probability modeling includes: The robotic arm's pose limit state is determined by the satellite's rolling attitude and the thruster installed at the end of the robotic arm; The nominal distance L0 from the satellite's center of mass to the end effector of the robotic arm, and the satellite yaw range include: the satellite's X-axis rotation attitude range is (-phi_1, phi_1), the satellite's Z-axis rotation attitude range is (-psi_1, psi_1); the range of the robotic arm's end effector thruster's yaw angle towards the ±X-axis is (-psi_2, psi_2); and the range of the thruster thruster's yaw angle towards the ±Z-axis is (-phi_2, phi_2). The limiting angle of deviation of the mechanical end from the satellite's X-axis is phi = phi_1 + phi_2; The limit angle of deviation of the robotic arm end effector from the satellite's Z-axis is psi = psi_1 + psi_2; The semi-major axis of the elliptical envelope at the end of the robotic arm is Apx = R + L0 × sin(phi); The semi-major axis of the elliptical envelope at the end of the robotic arm is Apz = R + L0 × sin(psi); The angle between the end effector of the robotic arm and the semi-major axis of the ellipse in the X direction is Avx = phi + alpha; The angle of the semi-major axis of the ellipse at the end of the robotic arm is Avz = psi + alpha; For the nth sample point: The expression for the end effector position of the robotic arm is: X(n)= Apx×rand(-1, 1)×cos(rand(-1,1) ×2×π) Z(n)= Apz×rand(-1, 1)×sin(rand(-1,1) ×2×π) The robotic arm pointing expression is: Vx(n)= Avx×rand(-1, 1)×cos(rand(-1,1) ×2×π) Vz(n)= Avz×rand(-1, 1)×sin(rand(-1,1) ×2×π) rand(-1,1) generates uniformly distributed random numbers ranging from -1 to 1; The probabilistic modeling also includes: for the constraint on the distance between the end effector of the robotic arm and the center of mass of the satellite, the constraint is added as: Y(n)=rand(y0,y1), where: y0 is the closest distance between the end effector of the robotic arm and the center of mass of the satellite; y1 is the farthest distance between the end effector of the robotic arm and the center of mass of the satellite; The probabilistic modeling also includes: for the axial constraint of the end effector of the robotic arm, the constraint is added as: Vy(n)=rand(vy0,vy1), where: vy0 is the minimum value of the y-axis rotation angle of the robotic arm coordinate system; vy1 is the maximum value of the y-axis rotation angle of the robotic arm coordinate system.

2. The method for determining the joint stroke of a robotic arm as described in claim 1, characterized in that, The robotic arm has 6 joints. The pose transfer matrix from the (i-1)th joint coordinate system to the ith joint coordinate system is: in, Let be the i-th joint angle of the robotic arm, representing the information from the i-th joint to the (i+1)-th joint, and its value range is the travel distance of the i-th joint of the robotic arm; The angle from the (i-1)th joint to the ith joint of the robotic arm represents the information from the (i-1)th joint to the ith joint, and is a configuration parameter of the robotic arm. Let be the position vector of the origin of the i-th joint coordinate system in the (i-1)-th joint coordinate system; The pose transfer matrix from the satellite's center-of-mass coordinate system to the first joint coordinate system is: in, This is the attitude transfer matrix from the satellite's center-of-mass coordinate system to the base coordinate system; This is the position vector of the base in the coordinate system of the satellite's center of mass. The base is located at the connection between the robotic arm and the satellite. For a 6-joint robotic arm, the pose transformation matrix from the satellite's center of mass body coordinate system to the robotic arm's end effector coordinate system is... for: ; This represents the positive motion of the robotic arm's pose; Will Defined as: For the nth sample, the state equation of the robotic arm's end effector pose satisfies: X(n)=T 14 ; Y(n)=T 24 ; Z(n)= T 34 ; Vx(n)= T 12 ; Vy(n)= T 22 ; Vz(n)= T 32 。 3. The method for determining the joint stroke of a robotic arm as described in claim 2, characterized in that, For each Monte Carlo sample point, Newton's gradient method is used to calculate all joint angles. The envelope formed by the set of sample points for each joint is the travel envelope of that joint angle. For the nth sample, the state equation for the pose of the robotic arm's end effector is formally: in To represent the state at each component of the robotic arm's end effector, we take the partial differentials of each joint angle for the above system of equations, and obtain the Jacobian matrix: Initial joint angle values: ; through the iteration matrix For joint angle Perform iterative processing; when , Represents the accuracy of iterative solutions; ； Otherwise, when This indicates that the required precision has been met, and the iteration stops; this is the last calculation. This refers to the joint angle corresponding to the sample, where DX_i is the error between two iterations. It is the arithmetic square root of the difference between the joint angles obtained from two consecutive iterations.

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