Joint partial failure fault space robot dynamics dexterity analysis method

Abstract

The embodiment of the application provides a joint partial failure fault space mechanical arm motion capability analysis method, comprising: establishing a mapping relationship between joint expected torque output and end acceleration of a joint partial failure fault space mechanical arm according to a joint partial failure fault space mechanical arm kinematics and dynamics model; constructing a joint partial failure fault space mechanical arm dynamics dexterity representation index according to the mapping relationship between the joint expected torque output and the end acceleration of the joint partial failure fault space mechanical arm, and quantitatively representing dynamics dexterity of the joint partial failure fault space mechanical arm; and analyzing influences of a failure joint position and a partial failure fault degree on the dynamics dexterity of the space mechanical arm and dynamics dexterity of the joint partial failure fault space mechanical arm in a task execution process according to the joint partial failure fault space mechanical arm dynamics dexterity representation index.

Description

Technical Field

[0001] This invention relates to a method for analyzing the dexterity of a spatial robotic arm in the event of joint failure, belonging to the technical field of robotic arm motion capability analysis. Background Technology

[0002] Space robotic arms, due to their large span, flexible operation, and high load capacity, are widely used in aerospace engineering to assist or replace astronauts in performing on-orbit operations such as space debris cleanup, on-orbit spacecraft deployment, assembly, and maintenance. With the development of aerospace engineering in countries including my country, the importance of space robotic arms has become increasingly prominent. Due to the microgravity, strong radiation, and large temperature differences of the space environment, space robotic arms may experience joint failures during their on-orbit service, including joint locking failures, joint free swing failures, and partial joint failures. Joint locking failures and partial joint failures refer to two extreme cases: complete loss of velocity output capability and complete loss of torque output capability, respectively. Compared to joint locking failures and joint free swing failures, partial joint failures are more representative of the general forms of space robotic arm joint failures. Partial joint failures cause the velocity or torque output of the faulty joint to perturb below the expected value, leading to deviations from the expected trajectory and motion capability perturbations. Both deviations from the expected trajectory and failure to meet the requirements of on-orbit operation missions result in mission failure. Therefore, in order to ensure that the space robot arm with joint failure can successfully perform on-orbit operations, it is necessary to conduct research on the motion capability analysis of the space robot arm with joint failure, so as to lay the foundation for subsequent trajectory planning and fault-tolerant control.

[0003] Dexterity is crucial in the motion capabilities required for space robotic arms in on-orbit operations. Dexterity can be divided into kinematic dexterity and dynamic dexterity, referring to the ability of the space robotic arm to transmit joint velocity output to the end effector and joint torque output to the end effector, respectively. Existing research on the dexterity of space robotic arms with joint partial failure faults all rely on constructing dexterity characterization indices based on the generalized Jacobian, characterizing the dexterity of the space robotic arm from the kinematic dexterity level. However, kinematic dexterity only reflects the impact of joint velocity partial failure faults on the dexterity of the space robotic arm, not the impact of joint torque partial failure faults; while dynamic dexterity can reflect the impact of joint torque partial failure faults on the dexterity of the space robotic arm. Therefore, conducting research on the dynamic dexterity of space robotic arms with joint torque partial failure faults has significant theoretical research value. Summary of the Invention

[0004] In view of this, the present invention provides a method for analyzing the dynamic dexterity of a space manipulator with joint failure, so as to analyze the influence of the location and degree of failure of the failed joint on the dynamic dexterity of the space manipulator, as well as the dynamic dexterity of the space manipulator with joint failure during the task execution process.

[0005] This invention provides a method for analyzing the dexterity of a space manipulator in the event of joint failure, including:

[0006] Based on the kinematic and dynamic model of the space manipulator with joint failure, a mapping relationship between the expected torque output of the joint and the end-effector acceleration of the space manipulator with joint failure is established.

[0007] Based on the mapping relationship between the expected torque output of the joints and the end-effector acceleration of the space manipulator with joint failure, the minimum singularity, dynamic maneuverability and dynamic condition number of the space manipulator with joint failure are constructed to quantitatively characterize the dynamic dexterity of the space manipulator with joint failure.

[0008] Based on the minimum singularity, dynamic maneuverability, and dynamic condition number indices of the space manipulator with joint partial failure, the influence of the faulty joint location and the degree of partial failure on the dynamic dexterity of the space manipulator, as well as the dynamic dexterity of the space manipulator during task execution.

[0009] Among them, the dynamic dexterity of the aforementioned joint failure fault space manipulator is reflected by three indicators: dynamic minimum singularity, dynamic operability, and dynamic condition number.

[0010] In the above method, establishing the mapping relationship between the expected torque output of the joints and the end-effector acceleration of the space manipulator with joint failure based on the kinematic and dynamic model of the space manipulator with joint failure includes:

[0011] The mapping relationship between the joint angular velocity and the end effector velocity of a manipulator in a fault-prone space is as follows:

[0012]

[0013] In the formula, This is the end-effector pose. For the terminal velocity, For the angular velocities of healthy and faulty joints, For generalized Jacobian matrix, To represent the mapping relationship between healthy joint velocity and end-effector velocity, This represents the mapping relationship between the velocity of the faulty joint and the velocity of the end effector, where m is the dimension of the workspace and n is the number of degrees of freedom of the spatial manipulator.

[0014] The dynamic model of the manipulator in the space of joint failure is as follows:

[0015]

[0016] In the formula, For the base mass matrix, and The coupling mass matrix between the healthy joint and the base; and This represents the coupling mass matrix between the faulty joint and the base. and The coupling quality matrix between healthy and faulty joints. The mass matrix characterizing the coupling relationship between healthy joint angular acceleration and healthy joint torque. The mass matrix characterizing the coupling relationship between the angular acceleration and torque of the faulty joint. These are the nonlinear terms in the dynamic model corresponding to the base, healthy joint, and faulty joint, respectively. and Torque outputs for healthy and faulty joints, respectively. These are the base acceleration, healthy joint angular acceleration, and faulty joint angular acceleration, respectively.

[0017] Based on the first row of the above equation, the mapping relationship between the base acceleration and the angular acceleration of healthy and faulty joints can be obtained as follows:

[0018]

[0019] Substituting the above equation into the second and third rows of the dynamic model of the manipulator in the joint failure space, we obtain the mapping relationship between the acceleration of healthy and faulty joints and the torque of each joint as follows:

[0020]

[0021] In the formula, The coupling matrix between the torque output and angular acceleration of healthy and faulty joints. The nonlinear term represents the mapping relationship between the torque output of healthy and faulty joints and their angular accelerations. Substituting the above equation into the mapping relationship between base acceleration and the angular accelerations of healthy and faulty joints, we obtain the mapping relationship between base acceleration and the torques of healthy and faulty joints as follows:

[0022]

[0023] In the formula, This is the coupling matrix between joint torque output and base acceleration. This is a nonlinear term representing the mapping relationship between joint torque output and base acceleration.

[0024] Differentiating the expression relating joint angular velocity and end-effector velocity yields the end-effector acceleration. The mapping relationship between the angular accelerations of each joint and the angular accelerations of each joint is as follows:

[0025]

[0026] Substituting the mapping relationship between the acceleration of healthy and faulty joints and the torques of each joint into the above equation, we can obtain the mapping relationship between the end-effector acceleration and the torques of each joint, as follows:

[0027]

[0028] In the formula, This is the coupling matrix between the torque output of each joint and the end-effector acceleration. This is a nonlinear term representing the coupling relationship between the torque output of each joint and the end-effector acceleration.

[0029] When a faulty joint experiences partial speed failure, the actual torque output of the faulty joint does not deviate from the expected value, and the actual speed output of the faulty joint becomes... , For multiplicative fault factors, Let be the additive fault factor; Indicates the degree of failure of the speed component of the faulty joint. Indicating the degree of failure in the acceleration component, the actual angular acceleration of the faulty joint is:

[0030]

[0031] In the formula, This represents the expected value of the angular acceleration of the faulty joint.

[0032] Clearly, after a partial failure of the joint velocity occurs, the acceleration of the faulty joint is only affected by the multiplicative fault factor, and not by the additive fault. Substituting the above equation into the mapping relationship between end-effector acceleration and the angular acceleration of each joint, the acceleration mapping relationship from the joint to the end-effector can be expressed as:

[0033]

[0034] In the formula, and The sum of these two items is zero, resulting in additive fault parameters. Since it cannot affect terms containing joint angular acceleration, the expression for the acceleration mapping relationship between the joint and its distal end can be rewritten as follows in the case of joint velocity partial failure:

[0035]

[0036] In the formula, This is the nonlinear term mapping joint angular acceleration to end-effector acceleration;

[0037] Substituting the actual angular acceleration of the faulty joint under the condition of partial velocity failure into the mapping relationship expression between the acceleration of the healthy joint and the faulty joint and the torque of each joint, we can obtain:

[0038]

[0039] Substituting the above equation into the expression for the acceleration mapping relationship between the joint and its distal end in the case of partial joint velocity failure, we can obtain the following mapping relationship between the joint torque output and the distal end acceleration in the case of partial joint velocity failure:

[0040]

[0041] In the formula, This refers to the coupling matrix between joint torque output and end-effector acceleration after a joint velocity failure. It is a nonlinear term;

[0042] When a faulty joint experiences a partial torque failure, the actual torque output of the faulty joint is: The desired torque output is ,make Substituting this into the expression for the mapping relationship between the end-effector acceleration and the torques of each joint, we get:

[0043]

[0044] In the formula, This is the coupling matrix between the expected torque output of the joint and the end-effector acceleration after a partial failure of the joint torque. Characterizes the degree of failure of the torque component of the faulty joint. When the joint is in free swing fault space, the above formula represents the mapping relationship between the joint torque output and the end effector acceleration of the robotic arm.

[0045] The above analysis shows that when a joint velocity component fails, the impact of the failure on the mapping relationship between joint torque and end-effector acceleration is reflected in the nonlinear term. The above will not affect the coupling matrix between joint torque and end-effector acceleration. When a joint torque component fails, Change to The column elements corresponding to the faulty joint are affected by the fault, resulting in an inertial term in the mapping relationship between the joint's expected torque output and end-effector acceleration. Affected.

[0046] In the above method, based on the mapping relationship between the expected torque output and end-effector acceleration of the spatial mechanical arm with joint failure, the minimum singularity, dynamic maneuverability, and dynamic condition number indices of the spatial mechanical arm with joint failure are constructed to quantitatively characterize the dynamic dexterity of the spatial mechanical arm with joint failure, including:

[0047] Based on the singular value decomposition theorem, the coupling matrix between the desired joint torque output and the end-effector acceleration is analyzed. Perform singular value decomposition to obtain for Singularity, These are the maximum and minimum singular values, respectively; based on the coupling matrix between the joint desired torque output and the end-effector acceleration. The singular values ​​can be used to construct the minimum singular values ​​of the joint fault space of the robotic arm. Dynamic operability and dynamic condition number The index is used to quantitatively characterize the dynamic dexterity of a faulty spatial manipulator. The index is defined as follows:

[0048]

[0049]

[0050]

[0051] Among the above indicators, the minimum singular value of the dynamics This characterizes the degree of similarity between the current configuration and the dynamic singular configuration of the fault-space manipulator, as well as the worst-case dynamic dexterity of the manipulator's end effector in a certain direction. A larger minimum dynamic singularity value indicates higher dynamic dexterity of the fault-space manipulator. If this occurs, the robotic arm is in a dynamic singularity state, and the joint torque output cannot be transmitted to the end effector acceleration; dynamic maneuverability... Dynamic dexterity is a comprehensive measure of the dynamic dexterity of the end effector in all directions within a fault-tolerant space. Greater dynamic dexterity indicates stronger dynamic dexterity in all directions, and higher dynamic dexterity in a fault-tolerant space. If the dynamic condition number is not specified, the robotic arm is in a dynamic singular state, at which point its dynamic dexterity is at its worst; Characterizing the degree of approximation of the dynamic dexterity of the robotic arm's end effector in various directions, when At this time, the dynamic dexterity of the end effector of the fault-space manipulator is the same in all directions, and the manipulator exhibits isotropic characteristics, at which point the manipulator's dynamic dexterity is at its best; the aforementioned minimum singular value of dynamics Dynamic operability and dynamic condition number The dynamic dexterity of the manipulator in the fault space was described from different perspectives, and a quantitative characterization of the dynamic dexterity of the manipulator in the fault space was achieved.

[0052] The above method analyzes the influence of the location of the faulty joint and the degree of partial failure on the dynamic dexterity of the space manipulator based on the minimum singularity, dynamic maneuverability, and dynamic condition number indices of the space manipulator with partial joint failure, as well as the dynamic dexterity of the space manipulator during task execution, including:

[0053] Regarding the analysis of the impact of the location and severity of the faulty joint on the dynamic dexterity of the space manipulator, based on the previous analysis of the coupling relationship between the expected torque output and the end effector acceleration under partial joint velocity failure and partial joint torque failure, it can be seen that partial joint torque failure will affect the coupling matrix between the joint torque output and the end effector acceleration. , to make it become Joint velocity partial failure will not affect the coupling matrix. Since the aforementioned dynamic dexterity performance indicators are all constructed based on the coupling matrix between the expected joint torque output and the end effector acceleration, the analysis required is to examine the impact of joint torque partial failure on the dynamic dexterity of the space manipulator. The space manipulator is placed in a given configuration, and different joints are subjected to torque partial failure. Characterizing the degree of multiplicative faults in the faulty joint, in Characterizing the degree of additive fault in the faulty joint, due to ,make exist Within the range exist Within the range, traverse all possible fault levels and calculate the minimum mechanical singularity for each fault level. Dynamic operability and dynamic condition number By obtaining numerical values ​​and plotting three-dimensional surface diagrams, the influence of different faulty joint locations and different joint torque partial failure degrees on the dynamic dexterity of the space manipulator can be analyzed.

[0054] For the dynamic dexterity analysis of a space robot arm during task execution due to joint failure, the degree of failure can be determined first based on the extent of the failure of the torque component of the faulty joint. Numerical values ​​are then used to calculate the coupling matrix between the expected joint torque output and the end effector acceleration at each moment during the execution of the robotic arm's task in the fault space. And solve for the minimum singular value of the dynamics. Dynamic operability and dynamic condition number The numerical values, through the changes in the above-mentioned indicator values, can characterize the changes in the dynamic dexterity of the space robot arm during the task execution process due to joint failure, thus realizing dynamic dexterity analysis.

[0055] The technical solutions of the embodiments of the present invention have the following beneficial effects:

[0056] (1) Based on the kinematic and dynamic model of the space manipulator with joint partial failure fault, this invention establishes the mapping relationship between the expected torque output of the joint and the end acceleration, and analyzes the influence of joint velocity partial failure fault and joint torque partial failure fault on this mapping relationship;

[0057] (2) Based on the mapping relationship between the expected torque output of the joint and the end-effector acceleration of the space manipulator with joint failure, this invention constructs a dynamic dexterity characterization index for the space manipulator with joint failure. Based on the constructed characterization index, it realizes the influence analysis of the fault joint position and the degree of torque failure on the dynamic dexterity of the manipulator, as well as the dynamic dexterity analysis of the space manipulator with joint failure during task execution. Attached Figure Description

[0058] To more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without any creative effort or labor.

[0059] Figure 1 This is a flowchart illustrating the method for analyzing the dynamics of a spatial robotic arm in the event of joint failure, as provided in an embodiment of the present invention.

[0060] Figure 2 This is a schematic diagram illustrating how the minimum singular value of the mechanical arm dynamics in the fault space of the joint failure in this embodiment of the invention is affected by the location and degree of the faulty joint;

[0061] Figure 3 This is a schematic diagram illustrating how the dynamic operability of the manipulator in the fault space is affected by the location and severity of the faulty joint in an embodiment of the present invention.

[0062] Figure 4 This is a schematic diagram illustrating how the dynamic condition number of the spatial robotic arm in the joint failure fault is affected by the location and severity of the fault joint in an embodiment of the present invention.

[0063] Figure 5 This is a schematic diagram illustrating the changes in dynamic dexterity, joint angles, angular velocities, angular accelerations, joint torques, end-effector velocity and acceleration, and end-effector inertial terms during the execution of a task by a space manipulator with joint failure in an embodiment of the present invention. Specific Implementation

[0064] To better understand the technical solution of the present invention, the embodiments of the present invention will be described in detail below with reference to the accompanying drawings.

[0065] It should be understood that the described embodiments are merely some, not all, of the embodiments of the present invention. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without inventive effort are within the scope of protection of the present invention.

[0066] This invention provides a method for dynamic analysis of joint failure in a spatial robotic arm. Please refer to [the relevant documentation]. Figure 1 This is a flowchart illustrating the method for analyzing the dynamics of a spatial robotic arm in the event of joint failure, as provided in an embodiment of the present invention.

[0067] Based on the joint failure fault dynamic analysis method of the spatial manipulator given in the embodiments of the present invention, a simulation of the method was carried out with a seven-degree-of-freedom spatial manipulator as the research object.

[0068] 1. Simulation of the impact of faulty joint location and fault severity on dynamic dexterity

[0069] Assuming the space robotic arm is in The configuration exhibits joint moment failure. The multiplicative failure factor is calculated at intervals of 0.01 at the joints with multiplicative failures. The set of multiplicative fault degrees is obtained by iterating through the range of values. On the other hand, this section uses... As a characterization of the degree of additive fault. Due to , with intervals of 0.01 Range of values The set of additive fault degrees is obtained by traversing this set. Combining the additive and multiplicative fault sets yields the set of partial torque failure faults. The minimum singular value of the dynamics for each element in the partial failure fault set is then calculated using the described method. Dynamic operability kinetic condition number Indicator values. The degree of failure is multiplicative, depending on the type of joint failure. The X-axis represents the degree of additive fault. Using the Y-axis as the basis, and taking the minimum singular value of the dynamics as the basis, respectively Dynamic operability kinetic condition number Using the Z-axis as the index, the variation of the robotic arm's dexterity index in the fault space with the fault location and fault severity can be obtained as follows: Figure 2 , 3 As shown in Figure 4. Figure 2It is known that any torque failure in any joint of a space robotic arm will lead to a decrease in dynamic dexterity and a decrease in the minimum singular value of the dynamics. Furthermore, the magnitude of the decrease in the minimum singular value of the dynamics increases with the severity of the failure. When the actual torque output of the failed joint drops to zero, the minimum singular value of the dynamics decreases to [specific values ​​to be filled in]. , , , , , as well as .Depend on Figure 3 It is known that any torque failure in any joint of a space robotic arm will lead to a decrease in dynamic dexterity and maneuverability, and the greater the severity of the failure, the greater the reduction in maneuverability. When the actual torque output of the failed joint is zero, the maneuverability is significantly reduced compared to when the failure was not present. , respectively reduced to , , , , , , .Depend on Figure 4 It is known that any joint failure in the torque portion of a space robotic arm will lead to an increase in the dynamic condition number and a decrease in dynamic dexterity. Furthermore, the increase in the dynamic condition number is greater as the severity of the failure increases. When the torque output of the failed joint is zero, the dynamic condition number increases to 113206, 42348, 69778, 140774, and 939150, respectively. and The simulation results above show that any joint torque failure in any joint of the space robot arm will lead to a decrease in dynamic dexterity, and the decrease in dynamic dexterity of the space robot arm gradually increases with the severity of the failure.

[0070] 2. Simulation Analysis of the Dexterity and Dynamics of a Spatial Robotic Arm in Response to Joint Failure

[0071] Let the initial joint angle of the robotic arm be The end target pose is The terminal attitude is represented by ZYX Euler angles, and the terminal velocity is planned using a fifth-order polynomial interpolation method. The total mission time is... Step length The faulty joint in the robotic arm is joint 1, and the degree of fault is... During mission execution, the maneuverability, condition number, minimum singularity, joint angles, angular velocity, angular acceleration, torque output, end effector velocity, end effector acceleration, and end effector velocity inertia terms of the space robotic arm are as follows: Figure 5 As shown. By Figure 5 As shown in (a), (b), and (c), the changing trends of the various dynamic dexterity characterization indicators of the space manipulator are as follows: the dynamic operability decreases slightly in the first 5 seconds, then decreases sharply from 5 seconds onwards until the mission ends; the dynamic condition number shows no significant change in the first 5 seconds, gradually increases from 5 to 20 seconds, and decreases somewhat after 20 seconds; the dynamic minimum singularity shows no significant change in the first 5 seconds, gradually decreases from 5 to 20 seconds, and recovers somewhat after 20 seconds. The overall trend of the space manipulator's dynamic dexterity during mission execution is similar to that of the dynamic operability, showing a gradual decrease. The changes in dynamic dexterity, dynamic condition number, and dynamic minimum singularity are compared with the expected results. Figure 5 In (e)(f)(g)(j)(k), the fault-space manipulator at 15s and 35s has end-effector acceleration and joint torque close to their peak values, and the dynamic dexterity at 15s is significantly higher than at 35s. However, according to Figure 5 In the (l)(m)(n)(o)(p) values, the X and Z axis components of the linear acceleration inertia term and the angular acceleration inertia term of the end effector of the space manipulator are significantly higher at 15s than at 35s. This indicates that the contribution of the joint torque to the end effector acceleration is significantly higher at 15s than at 35s. This further proves that the occurrence of this phenomenon is not contradictory to the theoretical part. The constructed dynamic dexterity characterization index is reasonable and can effectively reflect the dynamic dexterity of the space manipulator in the event of joint failure.

[0072] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

[0073] The contents not described in detail in this specification are common knowledge to those skilled in the art.

Claims

1. A method for analyzing the dexterity of a spatial robotic arm in the event of joint failure, characterized in that, The method includes: (1) Based on the kinematic and dynamic model of the space manipulator with joint failure, establish the mapping relationship between the expected torque output of the joint and the end-effector acceleration of the space manipulator with joint failure. (2) Based on the mapping relationship between the expected torque output of the joint and the end-effector acceleration of the space manipulator with joint failure, a dynamic dexterity characterization index for the space manipulator with joint failure is constructed, including the dynamic minimum singular value, dynamic operability, and dynamic condition number index; based on the matrix singular value decomposition theorem, the coupling matrix between the expected torque output of the joint and the end-effector acceleration is... Perform singular value decomposition to obtain , These are the maximum and minimum singular values, respectively; based on the coupling matrix between the joint desired torque output and the end-effector acceleration. The singular values ​​of the joint fault space are used to construct the minimum singular values ​​of the dynamics of the robotic arm. Dynamic operability and dynamic condition number The indicator is defined as follows: (3) Based on the joint failure failure space manipulator dynamic dexterity characterization index, analyze the influence of the fault joint position and the degree of partial failure on the dynamic dexterity of the space manipulator, as well as the dynamic dexterity of the joint failure space manipulator during task execution.

2. The method according to claim 1, characterized in that, Based on the kinematic and dynamic model of the space manipulator with joint failure, a mapping relationship between the expected torque output of the joints and the end-effector acceleration of the space manipulator with joint failure is established, including: The mapping relationship between the joint angular velocity and the end effector velocity of a manipulator in a fault-prone space is as follows: In the formula, This is the end-effector pose. For the terminal velocity, For the angular velocities of healthy and faulty joints, For generalized Jacobian matrix, To represent the mapping relationship between healthy joint velocity and end-effector velocity, This represents the mapping relationship between the velocity of the faulty joint and the velocity of the end effector, where n is the number of degrees of freedom of the spatial manipulator. The dynamic model of the manipulator in the space of joint failure is as follows: In the formula, For the base mass matrix, and The coupling mass matrix between the healthy joint and the base; and This represents the coupling mass matrix between the faulty joint and the base. and The coupling quality matrix between healthy and faulty joints. The mass matrix characterizing the coupling relationship between healthy joint angular acceleration and healthy joint torque. The mass matrix characterizing the coupling relationship between the angular acceleration and torque of the faulty joint. These are the nonlinear terms corresponding to the base, healthy joint, and faulty joint in the dynamic model, respectively. and Torque outputs for healthy and faulty joints, respectively. These are the base acceleration, healthy joint angular acceleration, and faulty joint angular acceleration, respectively. Based on the first row of the above equation, the mapping relationship between the base acceleration and the angular acceleration of healthy and faulty joints can be obtained as follows: Substituting the above equation into the second and third rows of the dynamic model of the manipulator in the joint failure space, we obtain the mapping relationship between the angular acceleration of healthy and faulty joints and the torque of each joint as follows: In the formula, The coupling matrix between the torque output and angular acceleration of healthy and faulty joints. The nonlinear term represents the mapping relationship between the torque output of healthy and faulty joints and their angular accelerations. Substituting the above equation into the mapping relationship between base acceleration and the angular accelerations of healthy and faulty joints, we obtain the mapping relationship between base acceleration and the torques of healthy and faulty joints as follows: In the formula, This is the coupling matrix between joint torque output and base acceleration. This is a nonlinear term representing the mapping relationship between joint torque output and base acceleration. Differentiating the expression relating joint angular velocity and end-effector velocity yields the end-effector acceleration. The mapping relationship between the angular accelerations of each joint and the angular accelerations of each joint is as follows: Substituting the mapping relationship between the angular acceleration of healthy and faulty joints and the torques of each joint into the above equation, we can obtain the mapping relationship between the terminal acceleration and the torques of each joint, as follows: In the formula, This is the coupling matrix between the torque output of each joint and the end-effector acceleration. This is a nonlinear term representing the coupling relationship between the torque output of each joint and the end-effector acceleration. When a faulty joint experiences partial speed failure, the actual torque output of the faulty joint does not deviate from the expected value, and the actual speed output of the faulty joint becomes... , For multiplicative fault factors, Let be the additive fault factor; Indicates the degree of failure of the speed component of the faulty joint. Indicating the degree of failure in the acceleration component, the actual angular acceleration of the faulty joint is: In the formula, This represents the expected value of the angular acceleration of the faulty joint. Clearly, after a joint velocity partial failure occurs, the angular acceleration of the failed joint is only affected by the multiplicative fault factor, not by the additive fault. Substituting the above equation into the mapping relationship between end-effector acceleration and the angular acceleration of each joint, the acceleration mapping relationship from the joint to the end-effector can be expressed as: In the formula, and The sum of these two items is zero, resulting in additive fault parameters. Since it cannot affect terms containing joint angular acceleration, the expression for the acceleration mapping relationship between the joint and its distal end can be rewritten as follows in the case of joint velocity partial failure: In the formula, This is the nonlinear term mapping joint angular acceleration to end-effector acceleration; Substituting the actual angular acceleration of the faulty joint under the condition of partial velocity failure into the mapping relationship expression between the angular acceleration of the healthy and faulty joints and the torques of each joint, we can obtain: Substituting the above equation into the expression for the acceleration mapping relationship between the joint and its distal end in the case of partial joint velocity failure, we can obtain the following mapping relationship between the joint torque output and the distal end acceleration in the case of partial joint velocity failure: In the formula, This refers to the coupling matrix between joint torque output and end-effector acceleration after a joint velocity failure. It is a nonlinear term; When a faulty joint experiences a partial torque failure, the actual torque output of the faulty joint is: The desired torque output is ,make Substituting this into the expression for the mapping relationship between the end-effector acceleration and the torques of each joint, we get: In the formula, This is the coupling matrix between the expected torque output of the joint and the end-effector acceleration after a partial failure of the joint torque. Characterizes the degree of failure of the torque component of the faulty joint. When the joint is in free swing fault space, the above formula represents the mapping relationship between the joint torque output and the end effector acceleration of the robotic arm.

3. The method according to claim 2, characterized in that, Based on the mapping relationship between the expected torque output and end-effector acceleration of the space manipulator with joint failure, a dynamic dexterity characterization index for the space manipulator with joint failure is constructed, including the dynamic minimum singularity, dynamic maneuverability, and dynamic condition number indices, including: Minimum singularity of dynamics This characterizes the degree of similarity between the current configuration and the dynamic singular configuration of the fault-space manipulator, as well as the worst-case dynamic dexterity of the manipulator's end effector in a certain direction. A larger minimum dynamic singularity value indicates higher dynamic dexterity of the fault-space manipulator. If this occurs, the robotic arm is in a dynamic singularity state, and the joint torque output cannot be transmitted to the end effector acceleration; dynamic maneuverability... Dynamic dexterity is a comprehensive measure of the dynamic dexterity of the end effector in all directions within a fault-tolerant space. Greater dynamic dexterity indicates stronger dynamic dexterity in all directions, and higher dynamic dexterity in a fault-tolerant space. If the dynamic condition number is not specified, the robotic arm is in a dynamic singular state, at which point its dynamic dexterity is at its worst; Characterizing the degree of approximation of the dynamic dexterity of the robotic arm's end effector in various directions, when At this time, the dynamic dexterity of the end effector of the fault-space manipulator is the same in all directions, and the manipulator exhibits isotropic characteristics, at which point the manipulator's dynamic dexterity is at its best; the aforementioned minimum singular value of dynamics Dynamic operability and dynamic condition number The dynamic dexterity of the joint-fault space manipulator is described from different perspectives.

4. The method according to claim 2, characterized in that, Based on the aforementioned joint partial failure failure dynamic dexterity characterization index for space manipulators, the influence of the faulty joint location and the degree of partial failure on the dynamic dexterity of the space manipulator, as well as the dynamic dexterity during task execution of space manipulators with joint partial failure failure, are analyzed, including: For the analysis of the impact of the location and severity of the faulty joint on the dynamic dexterity of the space manipulator, the failure of the joint torque portion affects the coupling matrix between the joint torque output and the end effector acceleration. , to make it become Joint velocity partial failure will not affect the coupling matrix, and the constructed dynamic dexterity characterization indexes are all based on the coupling matrix between the joint expected torque output and the end effector acceleration. Therefore, the analysis required is on the impact of joint torque partial failure on the dynamic dexterity of the space manipulator. The space manipulator is placed in a given configuration, and different joints are subjected to torque partial failure. Characterizing the degree of multiplicative faults in the faulty joint, in Characterizing the degree of additive fault in the faulty joint, due to ,make exist Within the range exist The system iterates through all possible fault levels within the range and calculates the minimum singular value of the dynamics for each fault level. Dynamic operability and dynamic condition number By obtaining numerical values ​​and plotting three-dimensional surface diagrams, the influence of different faulty joint locations and different joint torque partial failure degrees on the dynamic dexterity of the space manipulator can be analyzed. For the dynamic dexterity analysis of a space robot arm during task execution due to joint failure, the degree of failure can be determined first based on the extent of the failure of the torque component of the faulty joint. Numerical values ​​are then used to calculate the coupling matrix between the expected joint torque output and the end effector acceleration at each moment during the execution of the robotic arm's task in the fault space. And solve for the minimum singular value of the dynamics. Dynamic operability and dynamic condition number The numerical values, through the changes in the above-mentioned indicator values, can characterize the changes in the dynamic dexterity of the space robot arm during the task execution process due to joint failure, thus realizing dynamic dexterity analysis.

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