Method for planning singularity-avoiding trajectory of free floating space mechanical arm

Abstract

The invention discloses a singularity-avoiding trajectory planning method for a free floating space mechanical arm, and belongs to the technical field of robot trajectory planning. The method comprises the steps that the expected whole-course tail end position track and posture track of the mechanical arm are obtained; setting a control period and circularly executing; at each control moment, a generalized Jacobian matrix and system singularity measurement are calculated, and whether the system is close to singularity or not is judged; traversing all the possible values of the base postures if the base postures are close to singularity, calculating joint angle states and corresponding singularity measurement which do not change the tail end postures, and searching a system configuration corresponding to the maximum singularity measurement; then, the state of the mechanical arm is reconstructed, and the mechanical arm is made to move to the maximum singularity measurement configuration to be separated from singularity; and calculating the inverse of the generalized Jacobian matrix to obtain velocity inverse kinematics, and further calculating the joint angular velocity and the joint angle at the next moment. According to the method, an accurate trajectory planning effect without introducing any theoretical error is realized while the singularity avoidance capability is ensured.

Description

Technical Field

[0001] This invention belongs to the field of robot trajectory planning technology, specifically relating to a method for planning singular trajectories for a free-floating spatial robotic arm. Background Technology

[0002] The application of space robotic arms in on-orbit servicing such as on-orbit assembly and refueling is increasing. Trajectory planning, a method for calculating the robotic arm's end effector to approach the target with a desired path and attitude, is a crucial technology for on-orbit servicing. When the joints of a robotic arm are in certain specific states, its end effector will lose some translational or rotational degrees of freedom, falling into a singular state. How to avoid singularities and restore motion capability is the challenge of robotic arm trajectory planning. Conventional robotic arms are generally fixed-base, and their singular states are only related to kinematic parameters such as position and attitude. However, the base position and attitude of a free-floating space robotic arm are not actively controlled, and it is in a free-floating state in space. The system is subject to the constraint of non-integrable angular momentum conservation. Its singular state is related not only to kinematic parameters but also to dynamic parameters such as mass and inertia. Therefore, its singularity is called dynamic singularity, and avoiding dynamic singularities is a more complex and difficult problem than conventional kinematic singularities.

[0003] Chinese patent application CN118544352A proposes a singularity avoidance method based on operability optimization for redundant driven robotic arms. This method optimizes the operability metric of the motion trajectory to ensure that the robotic arm always has the highest operability during movement, thus avoiding singularities. However, this method is only applicable to systems with redundant degrees of freedom and is not suitable for planning non-redundant systems such as planar three-degree-of-freedom pose and spatial six-degree-of-freedom pose.

[0004] The journal article "Xu Wenfu, Liang Bin, Liu Yu, et al., A Novel Singularity Avoidance Algorithm for PUMA-Type Robots [J]. Acta Automatica Sinica, 2008, 34(6): 670-675" and Chinese patent application CN119704189A propose singularity avoidance methods based on the inverse of damping and improved approximation of the inverse of damping for non-redundant robotic arms. These methods first analyze the conditions that generate singularities, separate the parameters that cause singularities, and then replace the original ordinary inverse with the inverse of damping or the improved approximation of the inverse of damping to achieve the purpose of avoiding singularities. However, these methods have disadvantages such as complex calculation of singularity parameters, incompatibility with fixed-base robotic arms with irregular configurations and free-floating space robotic arms, and the need to sacrifice end-effector tracking accuracy to varying degrees to avoid singularities.

[0005] Chinese patent application CN114905519A proposes a method combining damped pseudo-inverse and feedback compensation for singularity avoidance trajectory planning in free-floating space robots. This method first uses damped pseudo-inverse to avoid dynamic singularities, and then uses feedback compensation after escaping the singularity region to reduce the trajectory tracking error caused by the damped pseudo-inverse. This method can reduce the tracking error caused by singularity handling to a certain extent, but it lacks a post-compensation opportunity for scenarios where the terminal state is close to a singularity, resulting in a relatively large trajectory tracking error. Summary of the Invention

[0006] To address the aforementioned technical problems, this invention provides a trajectory planning method for free-floating spatial robotic arms without redundant degrees of freedom. This method fully utilizes the nonholonomic characteristics of the free-floating robotic arm subject to the constraint of non-integrable angular momentum conservation, and achieves not only singularity avoidance but also no loss of process tracking accuracy during trajectory planning.

[0007] The present invention adopts the following technical solution:

[0008] A method for planning singular trajectory avoidance for a free-floating space robotic arm includes the following steps:

[0009] Step S110: Obtain the desired end-effector position trajectory and attitude trajectory of the robotic arm, and calculate the corresponding end-effector velocity and angular velocity;

[0010] Step S120: Set the control cycle, denoted as ;

[0011] Step S130: Calculate the generalized Jacobian matrix based on the joint angles at the current moment, and calculate the system singularity metric based on the generalized Jacobian matrix; determine whether the free-floating space robotic arm system is close to singularity at the current moment based on the singularity metric at the current moment: if it is close to singularity, proceed to step S140; if it is not close to singularity, proceed to step S170 to perform the joint motion calculation for the next cycle.

[0012] Step S140: Traverse all possible base pose values, calculate the joint angle states without changing the end effector pose, calculate the corresponding singularity metric based on the obtained joint angles, search for the maximum singularity metric from the set of singularities, and denote the system configuration composed of the base pose and joint angles as follows: ;

[0013] Step S150: Reconstruct the state of the robotic arm so that it moves from the current configuration to the configuration with the maximum singularity metric, thereby escaping the singularity;

[0014] Step S160: Calculate the inverse of the generalized Jacobian matrix to obtain the inverse velocity kinematics, and calculate the joint angular velocity of the robotic arm based on the inverse velocity kinematics;

[0015] Step S170: Calculate the joint angle at the next moment based on the angular velocity;

[0016] Step S180: Repeat steps S130 to S170 until the desired motion trajectory is completed.

[0017] A computing device includes: at least one processor and a memory storing program instructions; when the program instructions are read and executed by the processor, the computing device performs the method.

[0018] A readable storage medium storing program instructions that, when read and executed by a computing device, cause the computing device to perform the method.

[0019] Beneficial effects:

[0020] This invention discloses a method for planning singularity avoidance trajectories for a free-floating space robotic arm. It proposes a design concept that decouples non-singular state trajectory planning and singular configuration escape functions, as well as a singular configuration escape method that does not change the end-effector pose state. This achieves accurate trajectory planning without introducing any theoretical errors while ensuring singularity avoidance capabilities. Attached Figure Description

[0021] The specific embodiments of the present invention will be further described in detail below with reference to the accompanying drawings, wherein:

[0022] Figure 1 This is a flowchart of a method for planning singular trajectories for a free-floating space robotic arm according to an embodiment of the present invention;

[0023] Figure 2 This is a schematic diagram of a planar three-degree-of-freedom free-floating robotic arm model.

[0024] Figure 3 This is a schematic diagram of a planar three-degree-of-freedom free-floating robotic arm VM model;

[0025] Figure 4 A schematic diagram of the kinematic geometry of a planar three-degree-of-freedom free-floating robotic arm VM model;

[0026] Figure 5 To avoid constructing a singularity metric curve;

[0027] Figure 6 To avoid singularity metric curves;

[0028] Figure 7 To avoid singular trajectories, plan the end-effector pose curve;

[0029] Figure 8 To avoid singular trajectories, a terminal pose error curve is planned. Detailed Implementation

[0030] Exemplary embodiments of the present disclosure will now be described in more detail with reference to the accompanying drawings. While exemplary embodiments of the present disclosure are shown in the drawings, it should be understood that the present disclosure may be implemented in various forms and should not be limited to the embodiments set forth herein. Rather, these embodiments are provided so that this disclosure will be thorough and complete, and will fully convey the scope of the disclosure to those skilled in the art.

[0031] Figure 1 This is a flowchart illustrating a method for planning singular trajectories for a free-floating space robotic arm, as described in an embodiment of the present invention. Figure 1 As shown, the method includes the following steps:

[0032] Step S110: Obtain the desired end-effector position trajectory and attitude trajectory of the robotic arm throughout its entire stroke, and calculate the corresponding end-effector velocity and angular velocity. Taking a planar three-degree-of-freedom robotic arm as an example, refer to... Figure 2 In the picture , ( ( ) are the base center of mass and the boom, respectively. ( The center of mass is as follows:

[0033] Let the desired end-effector pose trajectory function of the robotic arm be:

[0034] ;

[0035] in, Indicates the desired position at the end. This indicates the desired attitude at the end point.

[0036] The terminal velocity and angular velocity obtained by differentiation are:

[0037] ;

[0038] in, This represents the expected pose at the end of the entire process; This represents the desired end-effector pose velocity throughout the entire process. Indicates the desired linear velocity at the terminal. This represents the desired angular velocity at the end point.

[0039] Step S120: Set the control cycle, denoted as Starting from the initial moment, for each control moment, trajectory planning is performed according to the following steps.

[0040] Step S130: Calculate the generalized Jacobian matrix based on the joint angles at the current moment; calculate the system singularity metric based on the generalized Jacobian matrix; determine whether the free-floating space robotic arm system is close to singularity at the current moment based on the singularity metric: if close to singularity, proceed to step S140; if not close to singularity, proceed to step S170 to calculate the joint motion for the next cycle. Details are as follows:

[0041] Step S130-1: Derive the pose and velocity of the robotic arm's end effector based on kinematic modeling. With joint angular velocity The motion relationship between them, whose coefficient matrix is ​​the generalized Jacobian matrix, is denoted as . ,Right now:

[0042] ;

[0043] in, Represents the joint angle vector. , , These represent the joint angles of the three joints, in sequence. The three joints refer to the three rotary joints on the robotic arm body (i.e., the joints connecting the three arm links). Singularity metric Defined as a generalized Jacobian matrix The absolute value of the determinant:

[0044] ;

[0045] This represents the determinant of the matrix. The singularity metric for the current moment is calculated using the above formula based on the current joint angle, and is denoted as... , Indicates the current time;

[0046] Step S130-2: Set the singularity metric threshold to Determine the singularity measure at the current moment. and The relative size between them: if If the system is close to singular, proceed to step S140; otherwise, proceed to step S170.

[0047] Step S140: Traverse all possible base pose values, calculate the joint angle states without changing the end effector pose, calculate the corresponding singularity metric based on the obtained joint angles, search for the maximum singularity metric from the set of singularities, and denote the system configuration composed of the base pose and joint angles as follows: The details are as follows:

[0048] Step S140-1: In base posture Establish a singularity measure for the independent variable. about Functional model Specifically, follow steps S140-2 to S140-5. Based on the non-holonomic characteristics of a free-floating robotic arm, it is known that when the joint angle... At a certain time, the posture of the base can be adjusted by methods such as periodic closed-loop motion of the joint angles. Reach any position, targeting Figure 2 A planar three-degree-of-freedom robotic arm, namely The reachable domain is All postures within.

[0049] Step S140-2: Establish a kinematically equivalent virtual robotic arm (VM) model, see [link / reference]. Figure 3 In the picture ( () is the connecting joint between the three arms and the base or rod. , ( ( ) are the base center of mass and the boom, respectively. ( Center of mass, It is from the base center of mass to the joint The length between, , ( ( ) are respectively booms At its own center of mass The lengths of the front and back parts, This is the system centroid of the virtual robotic arm model. The specific parameters of the VM model are as follows: defining the virtual arm length. and virtual boom vector ( )for:

[0050] ;

[0051] ;

[0052] in, The total mass of the robotic arm system, For components ( The mass of ) represents the mass of the base and the three booms, respectively; ( ( ) is the boom Self-center of mass Length of the front and back parts , the sum of , These are the normalized lengths of the two parts, respectively, satisfying... , , ( )yes , The corresponding virtual lever arm vector; in particular, according to the latter equation, we have When the desired attitude at the end Given, It is certain.

[0053] The end-effector kinematics based on the virtual arm is as follows:

[0054] ;

[0055] in, The position vector of the centroid of the robotic arm system; For virtual base vectors, , Center of mass of the base Pointing joint vector, It is the connecting joint between the base and the first arm.

[0056] Step S140-3: Draw a geometric diagram of the kinematics of the VM model.

[0057] See Figure 4 ,in, For the planar system reference coordinate system, With the origin as the point, , Let VG be the center of mass of the virtual robotic arm system, and VG be the two planar coordinate axes. It is a virtual joint between the base and the first arm. It is a virtual joint between the first arm and the second arm. It is a virtual joint between the third arm and the end effector, circular. It is a virtual base vector end With the posture of the base The set of all possible locations that can be reached due to different factors. and It is the center of mass VG and virtual joints Connecting lines and circles The intersections are located at points far from and near VG, respectively. One end is a virtual joint. The two extreme state positions; Given the end effector of the robotic arm, its pose is given as follows: According to the above virtual boom vector expression, we know that ,when Given Yes, therefore virtual joints The location is also fixed.

[0058] Step S140-4: Calculate the virtual joints based on the geometric schematic diagram of the VM model. lie in Joint angle combination on the right side and the corresponding singularity metric .in, It is a virtual joint that connects the first and second arms.

[0059] exist According to the Law of Cosines, we can solve for:

[0060] ;

[0061] in: Given the desired end position; Desired posture at a given end It was determined at that time; As for the position of the center of mass of the robotic arm system, since the freely floating robotic arm system is not subject to external forces, it is constant according to the momentum theorem; only the base vector remains. It concerns the attitude of the base. The function. Therefore, combining all parameters, we can know that, It only concerns the posture of the base. The function.

[0062] Based on the calculation relationship of the virtual boom vector We can solve for:

[0063] ;

[0064] in, , ; , For virtual joints Location coordinates, ; , For virtual joints Location coordinates, According to this expression, It only concerns the posture of the base. The function.

[0065] The third joint angle is:

[0066] ;

[0067] Combination , As a result, it can be seen that It only concerns the posture of the base. The function.

[0068] The desired joint angle combination is obtained by combining the above results. Calculate the singularity measure of this joint angle combination. ,because , , All of these pertain only to the attitude of the base. The function, therefore It only concerns the base posture. The function can be written as .

[0069] Step S140-5: Calculate the virtual joints based on the geometric schematic of the VM model. lie in Joint angle combination when connecting the left side and the corresponding singularity metric .

[0070] exist According to the Law of Cosines, we can solve for:

[0071] ;

[0072] , , , The calculation process and expression are the same as in step S140-4.

[0073] Step S140-6: Search for the system configuration with the largest singularity metric The details are as follows:

[0074] In base posture All reachable domains Above, the singular metrics established in steps S140-2 to S140-5. about Functional model The search for the maximum singularity metric can be performed using various extremum optimization algorithms. One recommended algorithm is based on the base attitude. The reachable region is divided into grids, and local maxima are calculated within each grid. Finally, the extreme values ​​of all grids are compared to obtain the global maximum singularity metric. The corresponding system configuration is denoted as ,in The base pose corresponding to the maximum singularity metric. The joint angle corresponding to the maximum singularity metric.

[0075] Step S150: Reconstruct the state of the robotic arm, moving it from the current configuration to the configuration with the maximum singularity metric. This allows us to escape the singularity. The problem is then transformed into an optimal control problem for solution, as follows:

[0076] The system configuration state variables are The control quantity is Based on the kinematic modeling of the robotic arm, the state equations of the system configuration can be obtained:

[0077] ;

[0078] in, It is the state matrix of the system configuration motion.

[0079] The initial time of the specified base attitude adjustment segment is... Terminal time is , The set base attitude adjustment period duration, the initial state and expected terminal state boundary conditions that the reconfiguration planning must satisfy are:

[0080] ;

[0081] ;

[0082] Under the above state equations and boundary condition constraints, find the input. , To minimize the following performance indicators, any optimal control algorithm can be used to solve the problem:

[0083] ,

[0084] in, This represents the joint angular velocity.

[0085] Step S160: Calculate the inverse of the generalized Jacobian matrix to obtain the inverse velocity kinematics. Calculate the joint angular velocities of the robotic arm based on the inverse velocity kinematics, as follows:

[0086] Generalized Jacobian matrix The inverse is:

[0087] ;

[0088] Based on this, the angular velocity of the robotic arm joints is:

[0089] .

[0090] in, It is the expected end-point trajectory throughout the entire process.

[0091] Step S170: Calculate the joint angle at the next moment based on the angular velocity, as follows:

[0092] .

[0093] Step S180: Repeat steps S130 to S170 until the desired end-effector trajectory is achieved. .

[0094] The following example illustrates the above method for planning the avoidance of singular trajectories by a free-floating robotic arm.

[0095] System model reference Figure 2 This is a planar three-degree-of-freedom robotic arm, with two degrees of freedom in-plane translation and rotation about the plane normal. The system model parameters are shown in Table 1. Furthermore, the center-of-mass position parameters are... ( ).

[0096] Table 1. Parameters of the planar three-degree-of-freedom robotic arm model

[0097] The specific steps are as follows:

[0098] Step S110: Obtain the desired end-effector position trajectory and attitude trajectory of the robotic arm, and calculate the corresponding end-effector velocity and angular velocity.

[0099] Taking a planar three-degree-of-freedom robotic arm as an example, see [link / reference]. Figure 2 The desired end-effector pose trajectory is as follows, where The unit of the calculation result inside the function is The total motion time was 12.1 seconds.

[0100] ;

[0101] in, It is the desired position at the end. The X component, It is the desired position at the end. The Y component.

[0102] The initial base attitude of the system is The initial joint angle is .

[0103] Based on the above motion trajectory, the expected end pose for the entire journey is:

[0104] ;

[0105] The expected end-effector pose velocity for the entire process is:

[0106] .

[0107] Step S120: Set the control period. Starting from the initial time, for each control time, perform trajectory planning according to the following steps. In this embodiment, the control period is set to 0.01s.

[0108] Step S130: Calculate the generalized Jacobian matrix based on the joint angles at the current moment; calculate the system singularity metric based on the generalized Jacobian matrix; determine whether the free-floating space robotic arm system is close to singularity based on the singularity metric at the current moment: if close to singularity, proceed to step S140; if not close to singularity, proceed to step S170 to perform the joint motion calculation for the next cycle. As an example, in this embodiment, the singularity metric threshold is set to... =0.06, the singularity metric calculated at the initial time is 0.058, which falls within the threshold. Therefore, the next step is to proceed to step S140 to reconstruct the joint angles. Furthermore, if no singularity avoidance is performed throughout the entire process, refer to the singularity metric curve for details. Figure 5 It can be observed that there are a large number of time periods where the singularity measure is less than the threshold. This indicates that the system frequently falls into near-singular states.

[0109] Step S140: Traverse all possible base pose values, calculate the joint angle states without changing the end effector pose, calculate the corresponding singularity metric based on the obtained joint angles, search for the maximum singularity metric from the set of singularities, and denote the system configuration composed of the base pose and joint angles as follows: In this embodiment, for the singular state at the initial moment, its end-effector pose is: The base posture reachable domain The system is divided into 18 intervals at 20° intervals. While maintaining the end-effector pose, the fminbnd function in Matlab is used to search within each interval. Minimum value, corresponding The maximum value is represented by the search results for the 18 intervals shown in the table below:

[0110] Table 2 Search results for maximum singularity metric for each interval

[0111] Comparing the optimization results for all the intervals above, the maximum singular metric on the interval [0, 20] is the global maximum singular metric, and the result is: =0.133, corresponding to the base attitude of the configuration is The joint angle combination is .

[0112] Step S150: Reconstruct the state of the robotic arm, moving it from the current configuration to the configuration with the maximum singularity metric. This avoids the singularity. In this example, the initial state and desired terminal state boundary conditions that the reconfigurable planning must satisfy are:

[0113] , ;

[0114] The proposed optimal control problem is solved using the direct shooting method, yielding the control function. As follows, the system can complete the expected reconfiguration under this control:

[0115] ;

[0116] Step S160: Calculate the inverse of the generalized Jacobian matrix to obtain the inverse velocity kinematics, and calculate the joint angular velocity of the robotic arm based on the inverse velocity kinematics.

[0117] Step S170: Calculate the joint angle at the next moment based on the angular velocity.

[0118] Step S180: Repeat steps S130 to S170 until the desired motion trajectory is completed. .

[0119] In this embodiment, the singularity metric curve obtained after planning is referred to. Figure 6 This shows that a singularity avoidance and reconstruction motion was performed only once at the initial moment, and the singularity metric was always greater than the threshold of 0.06 at other times, indicating that the singularity was avoided; the end pose throughout the entire process is shown in the figure. Figure 7 For end-effector pose error, please refer to [reference]. Figure 8 As can be seen, the end-effector pose error remains approximately zero outside the reconstructed time period, with the small non-zero error introduced by the integral calculation during the planning process. Therefore, in summary, the trajectory planning method provided by this invention not only achieves singularity avoidance but also maintains the accuracy of process tracking.

[0120] Numerous specific details are set forth in the specification provided herein. However, it will be understood that embodiments of the invention may be practiced without these specific details. In some instances, well-known methods, structures, and techniques have not been shown in detail so as not to obscure the understanding of this specification.

[0121] Although the invention has been described with respect to a limited number of embodiments, those skilled in the art will understand from the foregoing description that other embodiments are conceivable within the scope of the invention described herein. Furthermore, it should be noted that the language used in this specification has been chosen primarily for readability and instructional purposes, and not for the purpose of explaining or limiting the subject matter of the invention.

Claims

1. A method for planning singular trajectories for a free-floating spatial robotic arm, characterized in that, include: Step S110: Obtain the desired end-effector position trajectory and attitude trajectory of the robotic arm, and calculate the corresponding end-effector velocity and angular velocity; Step S120: Set the control cycle, denoted as ; Step S130: Calculate the generalized Jacobian matrix based on the joint angle at the current moment, and calculate the system singularity metric based on the generalized Jacobian matrix; determine whether the free-floating space robotic arm system is close to singularity at the current moment based on the singularity metric at the current moment: if it is close to singularity, proceed to step S140. If the problem is not approaching a singularity, proceed to step S170 to perform joint motion calculations for the next cycle. Step S140: Traverse all possible base pose values, calculate the joint angle states without changing the end effector pose, calculate the corresponding singularity metric based on the obtained joint angles, search for the maximum singularity metric from the set of singularities, and denote the system configuration composed of the base pose and joint angles as follows: ; Step S150: Reconstruct the state of the robotic arm so that it moves from the current configuration to the configuration with the maximum singularity metric, thereby escaping the singularity; Step S160: Calculate the inverse of the generalized Jacobian matrix to obtain the inverse velocity kinematics, and calculate the joint angular velocity of the robotic arm based on the inverse velocity kinematics; Step S170: Calculate the joint angle at the next moment based on the angular velocity; Step S180: Repeat steps S130 to S170 until the desired motion trajectory is completed.

2. The method for planning a singular trajectory avoidance for a free-floating space robotic arm according to claim 1, characterized in that, Step S110 includes: Let the desired end-effector pose trajectory function of the robotic arm be: ； in, Indicates the desired position at the end. Indicates the desired terminal attitude; The terminal velocity and angular velocity obtained by differentiation are: ； in, This represents the expected pose at the end of the entire process; This represents the desired end-effector pose velocity throughout the entire process. Indicates the desired linear velocity at the terminal. This represents the desired angular velocity at the end point.

3. The method for planning a singular trajectory avoidance for a free-floating space robotic arm according to claim 2, characterized in that, Step S130 includes: Step S130-1: Derive the pose and velocity of the robotic arm's end effector based on kinematic modeling. With joint angular velocity The motion relationship between them, whose coefficient matrix is ​​the generalized Jacobian matrix, is denoted as . ,Right now: ； in, Represents the joint angle vector. , , The joint angles of the three joints are represented sequentially; the three joints refer to the three rotary joints on the robotic arm body; singularity metric. Defined as a generalized Jacobian matrix The absolute value of the determinant: ； Let represent the determinant of the matrix; the singularity metric at the current moment is calculated using the above formula based on the current joint angle, denoted as . , Indicates the current time; Step S130-2: Set the singularity metric threshold to Determine the singularity measure at the current moment. and The relative size between them: if If the system is close to singular, proceed to step S140; otherwise, proceed to step S170.

4. The method for planning a singular trajectory avoidance for a free-floating space robotic arm according to claim 3, characterized in that, Step S140 includes: Step S140-1: In base posture Establish a singularity measure for the independent variable. about Functional model ; Step S140-2: Establish a kinematically equivalent virtual robotic arm (VM) model: Define the virtual arm length. and virtual boom vector for: ， ； in, , The total mass of the robotic arm system, For components The masses represent the masses of the base and the three booms, respectively. ; For boom Self-center of mass Length of the front and back parts , The sum of , These are the normalized lengths of the two parts, respectively, satisfying... According to the latter equation, we have When the desired attitude at the end Given, It is certain; The end-effector kinematics based on the virtual arm is as follows: ； in, The position vector of the centroid of the robotic arm system; For virtual base vectors, , Center of mass of the base Pointing joint vector, It is the connecting joint between the base and the first arm; Step S140-3: Draw a geometric schematic diagram of the kinematics of the VM model; Step S140-4: Calculate the virtual joints based on the geometric schematic diagram of the VM model. lie in Joint angle vector on the right side and the corresponding singularity metric ;in, It is a virtual joint connecting the first and second arms; in According to the cosine theorem, we can obtain: ； Based on the calculation relationship of the virtual boom vector Solving for: ； in, , ; , For virtual joints Location coordinates, ; , For virtual joints Location coordinates, ; The third joint angle is: ； Obtain the desired joint angle vector Calculate the singularity metric of the joint angle vector. ; Step S140-5: Calculate the virtual joints based on the geometric schematic of the VM model. lie in Joint angle vector when connecting the left side and the corresponding singularity metric ; exist According to the cosine theorem, we can obtain: ； , , , The calculation process and expression are the same as in step S140-4; Step S140-6: Search for the system configuration with the largest singularity metric The details are as follows: In base posture All reachable domains The above is the singular metric established in steps S140-2 to S140-5. about Functional model Search for the maximum singularity metric The corresponding system configuration is denoted as ,in The base pose corresponding to the maximum singularity metric. The joint angle corresponding to the maximum singularity metric.

5. The method for planning a singular trajectory avoidance for a free-floating space robotic arm according to claim 4, characterized in that, Step S140-6 includes: adjusting the base attitude. The reachable region is divided into grids, and local maxima are calculated within each grid. Finally, the extreme values ​​of all grids are compared to obtain the global maximum singularity metric. .

6. The method for planning a singular trajectory avoidance for a free-floating space robotic arm according to claim 5, characterized in that, Step S150 includes: The system configuration state variables are The control quantity is Based on the kinematic modeling of the robotic arm, the state equations of the system configuration are obtained as follows: ,in, It is the state matrix of the system configuration motion; The initial time of the specified base attitude adjustment segment is... Terminal time is , The set base attitude adjustment period duration, the initial state and expected terminal state boundary conditions that the reconfiguration planning must satisfy are: ； ； Under the above state equations and boundary condition constraints, find the input. , Minimize the following performance metrics: ， in, This represents the joint angular velocity.

7. The method for planning a singular trajectory avoidance for a free-floating space robotic arm according to claim 6, characterized in that, Step S160 includes: Generalized Jacobian matrix The inverse is: ； Based on this, the angular velocity of the robotic arm joints is: ， in, It is the expected end-point trajectory throughout the entire process.

8. The method for planning a singular trajectory avoidance for a free-floating space robotic arm according to claim 7, characterized in that, Step S170 includes: calculating the joint angle at the next moment as follows: .

9. A computing device, characterized in that, include: At least one processor and a memory storing program instructions; When the program instructions are read and executed by the processor, the computing device performs the method as described in any one of claims 1-8.

10. A readable storage medium storing program instructions, characterized in that, When the program instructions are read and executed by the computing device, the computing device performs the method as described in any one of claims 1-8.

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