A method and system for measuring the resolution of robot spatial pose adjustment

Abstract

The present invention discloses a method and system for measuring the resolution of robot spatial pose adjustment. By measuring and analyzing the fine motion ability of the robot with the minimum motion instruction, technical indicators such as pose cumulative error, pose backlash, and forward and reverse pose adjustment resolution are included. Among them, the two technical indicators of pose cumulative error and pose backlash can provide important reference bases for engineers to plan the motion trajectory of the robot, so as to plan a more reasonable and efficient pose adjustment path for the robot. The measurement method of forward and reverse pose adjustment resolution solves the problem of measuring the resolution of robot spatial pose adjustment; the results of its measurement and analysis can provide a basis for the selection or type selection of the system detection feedback unit for robot system integration engineers; more importantly, according to the spatial pose adjustment resolution results obtained from the measurement and analysis, it can be evaluated whether the working performance of the robot integration system can meet the task requirements.

Description

Technical Field

[0001] The present invention relates to the technical field of robot detection, and particularly relates to a method and system for measuring the resolution of robot spatial pose adjustment. Background Art

[0002] Robots are essential basic production equipment in high-tech fields such as aviation, aerospace, national defense, and mechanical manufacturing. Robots are commonly used in various occasions such as spatial docking and assembly of large-scale equipment or components, manufacturing and processing of products with complex spatial contours, and adaptive polishing; in the final key steps of the docking and assembly of devices or components or product processing, the robot needs to continuously perform fine adjustment of its spatial pose; aiming at continuously approaching the robot's spatial target pose, the current pose of the robot is continuously iteratively corrected according to the feedback of the measurement module (unit) of the robot system to achieve the final assembly effect of the device or the final processing requirements of the product.

[0003] In actual situations, when the robot is performing spatial docking and assembly of key steps of the device, normal vector alignment of complex curved surface machining, adaptive compliant control assembly, etc., it is necessary to detect and feedback through measurement units such as six-axis force sensors, line laser sensors, and high-resolution vision systems, measure the spatial pose offset between the tool center point at the end of the robot and the target point and feedback it to the robot control system. The control system performs corresponding pose movement adjustment on the tool center point at the end according to the spatial pose offset to reach the target pose point. The robot system continuously performs pose adjustment according to the feedback instructions of the measurement unit to approach the target pose. When the tool center point at the end of the robot is very close to the target pose, when performing the final key step of spatial pose adjustment, the minimum spatial pose adjustment ability that the robot can stably achieve needs to be considered at this time.

[0004] Currently, there is no measurement method for robot pose resolution in relevant national / industry standards related to robots, and there are also no parameters for robot pose adjustment resolution in the product parameters provided by robot manufacturers. Through this method, the pose movement adjustment resolution of the robot within the reachable motion space can be measured. Summary of the Invention

[0005] The technical problem to be solved by the present invention is that there is no measurement method for the pose resolution of robots in current national / industry standards related to robots, and there are no parameters for the pose adjustment resolution of robots in the product parameters provided by robot manufacturers; the purpose of the present invention is to provide a measurement method and system for the spatial pose adjustment resolution of robots, which solves the problem of measuring the spatial pose adjustment resolution of robots. Through this measurement method, the spatial pose adjustment resolution of robots can be intuitively obtained, thereby providing a basis for the selection or type selection of system detection feedback units (six-axis force sensors, line laser sensors, vision systems) for robot system integration engineers; the pose adjustment resolution obtained through the present invention is convenient for evaluating the feasibility of robot systems to complete projects and for selecting types of various detection modules of robot systems; among them, the position cumulative error, attitude cumulative error, position backlash, and attitude backlash can also provide important reference bases for engineers to perform robot trajectory planning.

[0006] The present invention is realized through the following technical solutions:

[0007] This solution provides a measurement method for the spatial pose adjustment resolution of robots, and the measurement method is realized based on a laser tracker; it includes:

[0008] Obtain the position cumulative error L of the robot for position adjustment with the minimum position command in the base coordinate system L and the position backlash B L ; considering the position cumulative error L L and the position backlash B L , measure the position adjustment resolution of the robot for position adjustment with the minimum position command in the base coordinate system.

[0009] Fit a spatial circle in the measurement coordinate system of the laser tracker, and obtain the attitude cumulative error L of the robot for attitude adjustment with the minimum attitude command in the base coordinate system based on the spatial circle Z and the attitude backlash B Z ; considering the attitude cumulative error L Z and the attitude backlash B Z , measure the attitude adjustment resolution of the robot for attitude adjustment with the minimum attitude command in the base coordinate system.

[0010] The working principle of this solution: This solution measures and analyzes six indicators including the position cumulative error L L , attitude cumulative error L Z , position backlash B L , attitude backlash B Z , forward and reverse position adjustment resolutions, and forward and reverse attitude adjustment resolutions of the robot's pose adjustment movement with the minimum movement command. Among them, the position cumulative error L L, Attitude cumulative error L Z , Position backlash B L , Attitude backlash B Z These four indicators can provide important reference for engineers to plan the motion trajectory of the robot, so as to formulate a more reasonable and efficient pose adjustment path for the robot. The measurement methods of the forward and reverse position adjustment resolution and attitude adjustment resolution solve the problem of measuring the spatial pose adjustment resolution of the robot. Through this measurement method, the spatial pose adjustment resolution of the robot can be obtained intuitively, thus providing a basis for the selection or type selection of system detection feedback units (six-axis force sensor, line laser sensor, vision system) for robot system integration engineers. More importantly, based on the spatial pose adjustment resolution results obtained from measurement and analysis, it can be evaluated whether the final working performance of the robot integration system can meet the task requirements.

[0011] A further optimized solution is that it also includes pose adjustment resolution determination, including the process:

[0012] Position adjustment resolution determination: Compare the position adjustment resolution with the position adjustment threshold to determine whether the position adjustment resolution meets the preset threshold;

[0013] Attitude adjustment resolution determination: Compare the attitude adjustment resolution with the attitude adjustment threshold to determine whether the attitude adjustment resolution meets the preset threshold.

[0014] A further optimized solution is that it also includes pose adjustment resolution determination, including the process:

[0015] Position adjustment resolution determination: According to the formula sa = |D i -m|max to calculate the minimum position command error sa; According to the formula to calculate the minimum position command relative error sb; Based on the minimum position command error sa and the minimum position command relative error sb, determine whether the position adjustment resolution meets the preset threshold; where D ｉ represents the actual spatial position value of the i-th minimum position command; m represents the theoretical spatial position value of a minimum position command; |*|max represents taking the maximum absolute value; represents the sum of the actual spatial position values of k consecutive minimum position commands;

[0016] Attitude adjustment resolution determination: According to the formula ωa = |θ i -m θ |max to calculate the minimum attitude command error ωa; According to the formula to calculate the minimum attitude command relative error ωb; Based on the minimum attitude command error ωa and the minimum attitude command relative error ωb, determine whether the attitude adjustment resolution meets the preset threshold; where θ iDenote the actual spatial attitude angle of the i-th smallest attitude command, m θ Denote the theoretical spatial attitude angle of a smallest attitude command; |*|max represents taking the maximum absolute value; Denote the sum of the actual spatial attitude angles of k consecutive smallest attitude commands.

[0017] A further optimization scheme is that the position cumulative error L L The acquisition method includes:

[0018] The robot performs position adjustment movements along each coordinate axis in the base coordinate system with the smallest position command i. The robot collects the spatial position coordinates of the target ball once for each execution of a smallest position command. After the robot executes n smallest position commands, calculate the distance value between two adjacent spatial position coordinates to obtain the actual spatial position values of n smallest position commands;

[0019] If the consistency of the spatial position values from the (j + 1)-th to the n-th smallest position commands is better than the consistency of the spatial position values of the previous j smallest position commands, where j < n, then it is determined that there is a position cumulative error L in the spatial position values of the previous j smallest position commands L , L L = j * i;

[0020] A further optimization scheme is that the position backlash B L The acquisition method includes:

[0021] After the robot executes n smallest position commands, it performs reverse movement at the current position and executes m smallest position commands i. The robot collects the spatial position coordinates once for each execution of a smallest position command. After the robot executes m smallest position commands, calculate the distance between two adjacent spatial position coordinates to obtain the actual spatial position values of m smallest position commands;

[0022] If the spatial position values of the first t smallest position commands during reverse movement are 0 or are continuously unstable position values, and there are continuously stable position values from the (t + 1)-th to the m-th smallest position commands, where t < m, then it is determined that there is a position backlash B in the position values of the first t smallest position commands during reverse position adjustment movement L , B L = t * i;

[0023] A further optimization scheme is that the position adjustment resolution includes forward position adjustment resolution and reverse position adjustment resolution; the measurement method of the position adjustment resolution includes:

[0024] The robot is ordered to perform position adjustment motion along each coordinate axis in the base coordinate system with the minimum position instruction; starting from the hth minimum position instruction, the robot collects the spatial position coordinates of the target ball once after each minimum position instruction is executed, where h≥j+t; j represents the position cumulative error L of the first j minimum position instructions L , t represents the position backlash B of the first t minimum position instructions L ; After executing k minimum position instructions continuously, k+1 spatial position coordinates are obtained, and k continuous spatial position values are calculated to obtain the robot forward position adjustment resolution;

[0025] The robot is ordered to continue to execute e minimum position instructions in this direction, where e ≥ j + t, and then the robot is ordered to move in the opposite direction to execute e minimum position instructions;

[0026] The position coordinates are collected starting from the eth minimum position instruction executed by the robot in the reverse motion. After k minimum position instructions are executed continuously, k+1 spatial position coordinates are obtained. K continuous spatial position values are calculated to obtain the robot reverse position adjustment resolution.

[0027] The further optimization scheme is that the space circle fitting method includes:

[0028] The robot is ordered to perform equal-angle posture adjustments around each tool coordinate axis. The robot collects the spatial position coordinates of the target ball once after each posture adjustment. After measuring the spatial position coordinates of the terminal target ball under multiple postures of the robot, a spatial ball with the origin of the robot tool coordinate system as the ball center and the spatial ball center C are fitted. o (a, b, c) and the radius of the sphere r; a, b, c is the center of the sphere C o The coordinates of

[0029] Fitting a spatial plane based on all coordinate points of the robot rotating around a tool coordinate axis alone;

[0030] Based on the joint equation of the space ball and the space plane, the space circle and the center point C of the space circle that the robot rotates around each tool coordinate axis are solved. a (x a ,y a ,,z a ), where x a ,y a and z a is the coordinate of the center point of the circle in space.

[0031] The further optimization scheme is that the cumulative attitude error J Z include:

[0032] Starting from the current pose, the robot adjusts its pose with the minimum pose command o around the RX (RY, RZ) axis of the tool coordinate. After each execution of a minimum pose command, the robot pauses for several seconds, and the laser tracker collects the current target ball coordinates. After continuously executing N minimum pose commands o, the actual pose angles of the current N minimum command poses o can be calculated. If the pose angles of the first J (J < N) minimum pose commands o have poor consistency and the pose angles of the minimum pose commands o from J + 1 to N have good consistency, it indicates that the pose angles of the first J minimum pose commands o are not consistent due to the cumulative error of the robot's movement; that is, J Z = J * o.

[0033] Pose reverse clearance B Z Includes:

[0034] The robot moves in the reverse pose for M minimum pose commands o, and the actual pose angles of the reverse movement of M minimum pose commands o can be calculated. If the pose angles of the first T (T < M) minimum pose commands o of the reverse movement are 0 or continuous unstable pose angles, and there are continuous stable pose angle values for the minimum pose commands o from T + 1 to M, it indicates that there is a pose reverse clearance B in the pose angles of the first T minimum pose commands during the robot's reverse pose adjustment movement Z , that is, the pose adjustment reverse clearance value B of the robot Z = T * o.

[0035] A further optimization scheme is that the pose adjustment resolution includes forward pose adjustment resolution and reverse pose adjustment resolution; the measurement method of the pose adjustment resolution includes:

[0036] Let the robot adjust its pose around each tool coordinate axis with the minimum pose command. Starting from the Hth minimum pose command, the robot collects the pose coordinates once after each execution of a minimum pose command, where H ≥ T + J, and J represents the pose cumulative error J of the first J minimum pose commands Z , and T represents the pose reverse clearance B of the first T minimum pose commands Z ;

[0037] After continuously executing K minimum pose commands, K + 1 forward pose coordinates Q are obtained Z , and the actual spatial pose angles of the robot continuously executing K minimum pose commands are calculated based on the spatial circle triangle method; the forward pose adjustment resolution of the robot is obtained

[0038] Let the robot continue to execute E minimum pose commands in this direction, E ≥ T + J, and then let the robot move in the reverse direction and execute E minimum pose commands

[0039] Collect the position coordinates starting from the E-th minimum posture instruction executed in the reverse movement of the robot. After continuously executing K minimum posture instructions, obtain K + 1 reverse posture coordinates P Z , and calculate the actual spatial posture angle of the robot continuously executing K minimum posture instructions based on the spatial circle triangle method; obtain the reverse posture adjustment resolution of the robot.

[0040] A further optimization scheme is that the calculation method of the posture adjustment resolution includes:

[0041] The forward posture adjustment space point coordinates Q1(X Q1 ,Y Q1 ,Z Q1 ), Q2(X Q2 ,Y Q2 ,Z Q2 ),..,, Q K (X QK ,Y QK ,Z QK ) and the reverse posture adjustment space points P1(X P1 ,Y P1 ,Z P1 ), P2(X P2 ,Y P2 ,Z P2 ),..,, P K (X PK ,Y PK ,Z PK ) and the spatial center point C a (x a , y a ,, z a ) to obtain multiple radius values RQ1, RQ2... of the spatial circle, RQ K (RP1, RP2...,, RP K ); Calculate the spatial distances (i.e., spatial circle chord lengths) DQ1, DQ2…DQ between adjacent point coordinates Q1, Q2... of the positive (reverse) posture adjustment target ball K (P1, P2...., P K ), DP1, DP2…DP K (DP1, DP2…DP K ). Based on the spatial triangle formed by RQ1, RQ2 (RP1, RP2) and DQ1 (DP1), use the cosine theorem to calculate the actual posture angle of the robot adjusting with the minimum posture instruction; for the K spatial triangles formed by K consecutive minimum posture instructions, the positive and reverse posture adjustment resolutions of the robot around the tool coordinate axis with the minimum posture instruction can be obtained.

[0042] The present solution also provides a measurement system for the resolution of robot spatial pose adjustment, which is used to implement the measurement method for the resolution of robot spatial pose adjustment described in the above solution, and includes:

[0043] A first measurement module, configured to obtain the position cumulative error J of the robot for position adjustment with the minimum position command in the base coordinate system L and the position backlash B L ; Considering the position cumulative error J L and the position backlash B L , measure the position adjustment resolution of the robot for position adjustment with the minimum position command in the base coordinate system;

[0044] A second measurement module, configured to fit a spatial circle in the measurement coordinate system of the laser tracker, and obtain the attitude cumulative error J of the robot for attitude adjustment with the minimum attitude command based on the spatial circle Z and the attitude backlash B Z ; Considering the attitude cumulative error J Z and the attitude backlash B Z , measure the attitude adjustment resolution of the robot for attitude adjustment with the minimum attitude command.

[0045] Compared with the prior art, the present invention has the following advantages and beneficial effects:

[0046] A measurement method and system for the resolution of robot spatial pose adjustment provided by the present invention, by measuring and analyzing the position cumulative error L of the robot's movement with the minimum motion command L , attitude cumulative error L Z , position backlash B L , attitude backlash B Z , forward and reverse position adjustment resolutions, and forward and reverse attitude adjustment resolutions. Among them, the position cumulative error L L , attitude cumulative error L Z , position backlash B L , attitude backlash B Z These four indicators can provide important reference basis for engineers to plan the motion trajectory of the robot, so as to formulate a more reasonable and efficient pose adjustment path for the robot. The measurement methods for the forward and reverse position adjustment resolutions and attitude adjustment resolutions solve the problem of measuring the resolution of robot spatial pose adjustment. Through this measurement method, the resolution of robot spatial pose adjustment can be intuitively obtained, thus providing a basis for the selection or type selection of system detection feedback units (six-axis force sensors, line laser sensors, vision systems) for robot system integration engineers. More importantly, based on the resolution of robot spatial pose adjustment obtained by measurement and analysis, it can be evaluated whether the final working performance of the robot integration system can meet the task requirements. Description of the Drawings

[0047] To more clearly illustrate the technical solutions of the exemplary embodiments of the present invention, the following will briefly introduce the drawings required for the embodiments. It should be understood that the following drawings only show some embodiments of the present invention, and thus should not be regarded as limiting the scope. For those of ordinary skill in the art, without creative efforts, other related drawings can also be obtained based on these drawings. In the drawings:

[0048] Figure 1 It is a schematic diagram of the position arrangement of the robot, laser tracker and target ball;

[0049] Figure 2 It is a schematic diagram of the position adjustment of the robot;

[0050] Figure 3 It is a schematic diagram of the rotation of the robot end around each tool coordinate axis;

[0051] Figure 4 It is a schematic diagram of the spatial attitude adjustment of the robot.

[0052] The reference signs in the drawings and the corresponding names of the components:

[0053] 1 - Robot, 2 - Laser tracker, 3 - Target ball, 4 - Position adjustment trajectory of the robot, 5 - Attitude adjustment trajectory of the robot. Specific embodiments

[0054] To make the objectives, technical solutions and advantages of the present invention clearer and more understandable, the following will further elaborate on the present invention in combination with the embodiments and drawings. The illustrative embodiments of the present invention and their descriptions are only used to explain the present invention and are not intended to limit the present invention.

[0055] Embodiment 1

[0056] This embodiment provides a method for measuring the resolution of robot spatial pose adjustment, which is implemented based on a laser tracker; including:

[0057] Obtain the position cumulative error J L and position backlash B L of the robot during position adjustment with the minimum position command in the base coordinate system; considering the position cumulative error J L and position backlash B L , measure the position adjustment resolution of the robot during position adjustment with the minimum position command in the base coordinate system;

[0058] Judge the position adjustment resolution: The forward position adjustment resolution and the reverse position adjustment resolution can be compared with the position adjustment threshold to determine whether the position adjustment resolution meets the preset threshold; or according to the formula sa = |Di -m|max calculates the minimum position command error sa; according to the formula calculate the minimum position command relative error sb; determine whether the position adjustment resolution meets the preset threshold based on the minimum position command error sa and the minimum position command relative error sb; where D i represents the actual spatial position value of the i-th minimum position command; m represents the theoretical spatial position value of a minimum position command; |*|max represents taking the maximum absolute value; represents the sum of the actual spatial position values of k consecutive minimum position commands;

[0059] Position cumulative error J L The acquisition method includes:

[0060] The robot performs position adjustment movements along each coordinate axis in the base coordinate system with the minimum position command i. The robot collects the spatial position coordinates of the target ball once for each execution of a minimum position command. After the robot executes n minimum position commands, calculate the distance values between adjacent spatial position coordinates to obtain the spatial position values of n minimum position commands;

[0061] If the consistency of the spatial position values from the (j + 1)-th to the n-th minimum position commands is better than the consistency of the spatial position values of the previous j minimum position commands, where j < n, then it is determined that there is a position cumulative error J in the spatial position values of the previous j minimum position commands L , J L = j * i;

[0062] Position backlash B L The acquisition method includes:

[0063] After the robot executes n minimum position commands, it performs reverse movement at the current position to execute m minimum position commands i. The robot collects the spatial position coordinates once for each execution of a minimum position command. After the robot executes m minimum position commands, calculate the distances between adjacent spatial position coordinates to obtain the spatial position values of m minimum position commands;

[0064] If the space of the first t minimum position commands during reverse movement is 0 or is a series of continuously unstable position values, and there are continuous stable spatial position values from the (t + 1)-th to the m-th minimum position commands, where t < m, then it is determined that there is a position backlash B in the spatial position values of the first t minimum position commands during reverse movement L , B L = t * i.

[0065] The position adjustment resolution includes the forward position adjustment resolution and the reverse position adjustment resolution; the measurement method of the position adjustment resolution includes:

[0066] Let the robot perform position adjustment movements along each coordinate axis in the base coordinate system with the minimum position command; starting from the hth minimum position command, the robot collects the position coordinates once after executing each minimum position command, where h ≥ j + t; j represents the position cumulative error L of the first j minimum position commands L , and t represents the position backlash B of the first t minimum position commands L ; After continuously executing k minimum position commands, k + 1 spatial position coordinates are obtained, k consecutive spatial distance values are calculated, and the forward position adjustment resolution of the robot is obtained;

[0067] Let the robot continue to execute e minimum position commands along this direction, where e ≥ j + t, and then let the robot move in the reverse direction and execute e minimum position commands;

[0068] Collect the position coordinates starting from the e-th minimum position command when the robot moves in the reverse direction. After continuously executing k minimum position commands, k + 1 spatial position coordinates are obtained, k consecutive spatial distance values are calculated, and the reverse position adjustment resolution of the robot is obtained;

[0069] Fit a spatial circle in the measurement coordinate system of the laser tracker, and based on the spatial circle, obtain the attitude cumulative error J of the robot's attitude adjustment with the minimum attitude command in the base coordinate system Z and the attitude backlash B Z ; Considering the attitude cumulative error J Z and the attitude backlash B Z , measure the attitude adjustment resolution of the robot's attitude adjustment with the minimum attitude command.

[0070] The spatial circle fitting method includes:

[0071] Let the robot perform equal-angle attitude adjustments around each tool coordinate axis in the base coordinate system. The robot collects the spatial position coordinates of the target ball once after adjusting each attitude angle. After measuring the spatial position coordinates of the end target ball of the robot in multiple postures, fit a spatial sphere with the origin of the robot's tool coordinate system as the center of the sphere, the spatial sphere center C o (a, b, c) and the sphere radius r; where a, b, c are the coordinates of the spatial sphere center C o ;

[0072] Fit a spatial plane based on all the coordinate points of the robot rotating around a single tool coordinate axis;

[0073] Based on the spatial sphere and the spatial plane, solve for the spatial circle and the spatial center point C a (x a , y a , z a ) around each tool coordinate axis of the robot, where x a, y a and z a are the spatial center point coordinates.

[0074] The attitude cumulative error J Z is obtained by the following method:

[0075] Adjust the attitude around the tool coordinate axis with the minimum attitude command o, and collect the spatial position coordinates of the target ball at the end of the robot each time a minimum attitude command o is executed; after continuously executing N minimum attitude commands o, calculate the actual attitude angles of the N minimum command attitudes o.

[0076] If the attitude angle consistency from the (J + 1)-th to the N-th minimum attitude command is better than that of the first J minimum attitude commands, where J < N, then it is determined that there is an attitude cumulative error L in the attitude angles of the first J minimum attitude commands executed by the robot Z , L Z = J * o.

[0077] The attitude backlash B Z is obtained by the following method:

[0078] After the robot executes N minimum attitude commands o, perform a reverse attitude movement of M minimum attitude commands o at the current position, and calculate the actual attitude angles of the reverse attitude movement of M minimum attitude commands o.

[0079] If the attitude angles of the first T minimum attitude commands in the reverse movement are 0 or are continuously unstable attitude angles, and there are continuously stable attitude angles from the (T + 1)-th to the M-th minimum attitude commands, where T < M, then it is determined that there is an attitude backlash B in the attitude angles of the first T minimum attitude commands in the reverse attitude adjustment movement Z , B Z = T * o.

[0080] The attitude adjustment resolution includes a forward attitude adjustment resolution and a reverse attitude adjustment resolution; the acquisition method of the attitude adjustment resolution includes:

[0081] Let the robot perform attitude adjustment movements around each tool coordinate axis in the base coordinate system with the minimum attitude command. Starting from the H-th minimum attitude command, the laser tracker collects the target ball coordinates each time the robot executes a minimum attitude command, where H ≥ T + J, and J represents the attitude cumulative error J of the first J minimum attitude commands Z , T represents the attitude backlash B of the first T minimum attitude commands Z ;

[0082] After continuously executing K minimum attitude commands, obtain K + 1 forward attitude coordinates Q Z, where Z = 0, 1, 2, 3... K; the actual attitude angle of the robot for continuously executing K minimum attitude instructions is calculated based on the spatial circular triangle method; the forward attitude adjustment resolution of the robot is obtained;

[0083] Let the robot continue to execute E minimum attitude instructions in this direction, where E ≥ T + J, and then let the robot move in the reverse direction and execute E minimum attitude instructions;

[0084] Collect the position coordinates starting from the E-th minimum attitude instruction when the robot moves in the reverse direction, and obtain K + 1 reverse attitude coordinates P after continuously executing K minimum attitude instructions Z , where Z = 0, 1, 2, 3... K; the actual attitude angle of the robot for continuously executing K minimum attitude instructions is calculated based on the spatial circular triangle method; the reverse attitude adjustment resolution of the robot is obtained;

[0085] The attitude adjustment resolution calculation method includes:

[0086] Respectively calculate the distances between adjacent attitude target ball coordinates Q Z (P Z ) and the spatial center point C a (x a , y a ,, z a ) to obtain RQ1 (RP1) and RQ2 (RP2); calculate the spatial distance DQ1 (DP1) between adjacent attitude coordinates Q1, Q2 (P1, P2) of the robot. Based on RQ1 (RP1), RQ2 (RP2) and DQ1 (DP1), a spatial triangle is formed, and the actual attitude angle of the robot for adjusting with the minimum attitude instruction is calculated using the cosine theorem; for the K spatial triangles formed by K consecutive minimum attitude instructions, the actual attitude adjustment resolution of the robot can be obtained.

[0087] Judge the attitude adjustment resolution: The forward attitude adjustment resolution and the reverse attitude adjustment resolution can be compared with the attitude adjustment threshold to determine whether the attitude adjustment resolution meets the preset threshold; or according to the formula ωa = |θ i -m θ |max to calculate the minimum attitude instruction error ωa; according to the formula calculate the relative error ωb of the minimum attitude instruction; based on the minimum attitude instruction error ωa and the relative error ωb of the minimum attitude instruction, determine whether the attitude adjustment resolution meets the preset threshold; where θ i represents the actual spatial attitude angle of the i-th minimum attitude instruction, and m θ represents the theoretical spatial attitude angle of a minimum attitude instruction; |*|max represents taking the maximum absolute value; represents the sum of the actual spatial attitude angles of k consecutive minimum attitude instructions.

[0088] Example 2

[0089] This embodiment provides a measurement system for the resolution of robot spatial pose adjustment, which is used to implement the measurement method for the resolution of robot spatial pose adjustment described in the previous embodiment.

[0090] The robot is installed on the base, the target ball is installed on the end effector of the robot, and the laser tracker is installed at a suitable position directly in front of the robot, as Figure 1 shown; the robot 1 performs position adjustment movement with the minimum position command, and the laser tracker 2 collects the coordinates of the target ball 3, as Figure 2 shown. The position adjustment trajectory 4 of the robot is shown in the figure; the tool end of the robot rotates around the tool coordinate axes RX (RY, RZ), as Figure 3 shown; the robot performs spatial pose adjustment with the minimum pose command, and the tracker collects the coordinates of the target ball, as Figure 4 shown. The pose adjustment trajectory 5 of the robot is shown in the figure.

[0091] This measurement system includes:

[0092] A first measurement module, which is used to obtain the position cumulative error J L and the position backlash B L of the robot during position adjustment with the minimum position command in the base coordinate system; considering the position cumulative error J L and the position backlash B L , the position adjustment resolution of the robot during position adjustment with the minimum position command in the base coordinate system is measured.

[0093] At any arbitrary position in space, the target ball is adsorbed at a suitable position on the end effector of the robot. The robot performs position adjustment movement along the X (Y, Z) axis in the base coordinate system with the minimum position command i. After the robot executes each minimum position command i, it pauses for several seconds, and the laser tracker collects the coordinates of the target ball at the current position. After the robot executes n minimum position commands, by calculating the distance value between two adjacent points in space:

[0094] the actual position values of the position adjustment for the first n minimum position commands i can be calculated. If the spatial position values of the first j (j < n) minimum position commands i are poorly consistent, and the spatial position values of the minimum position commands from j + 1 to n are well consistent, it can be determined that the spatial position values of the first j minimum position commands i are poorly consistent due to the spatial position cumulative error of the robot's movement, that is, J L = j * i.

[0095] The robot moves in the reverse direction by m minimum position commands i at the above position. After the robot executes each minimum position command i, it pauses for several seconds. The laser tracker collects the position coordinates of the target ball at the current position. After the robot executes m minimum position commands, by calculating the distance value between two adjacent position coordinates in space:

[0096] The actual position value of moving in the reverse direction by m minimum position commands i is obtained. If the spatial position values of the first t (t < m) minimum position commands i during the reverse movement are 0 or very small (the measurement repeatability accuracy of the laser tracker), and there are continuous position values from the (t + 1)-th to the m-th minimum position commands i, it indicates that the position values of the first t minimum position commands i are due to the reverse clearance of the robot, resulting in no actual movement of the robot. Therefore, the position adjustment reverse clearance value B of the robot can be obtained L , that is, B L = t * i.

[0097] The robot returns to the initial position. The robot performs position adjustment movements along the X (Y, Z) axis in the base coordinate system with the minimum position command. Among them, the first h (h ≥ j + t) points are to eliminate the position cumulative error J L and the position reverse clearance error B L , and the laser tracker does not collect coordinate values; starting from the h-th minimum position command, after the robot executes each minimum position command, it pauses for several seconds. The laser tracker collects the position coordinate values of the current target ball. After continuously executing k minimum position commands, W0(x0, y0, z0), W1(x1, y1, z1), W2(x2, y2, z3),........W k (x k , y k , z k ) are obtained. At this time, the laser tracker stops collecting position coordinate values, then continues to run e (e ≥ j + t) minimum position commands in this direction, and then makes the robot move in the reverse direction by e minimum position commands. Moving in the forward direction by e minimum position commands and moving in the reverse direction by e minimum position commands are to eliminate the position cumulative error (J L ) and the position reverse error (B L ), and the laser tracker does not perform coordinate collection; starting from the e-th minimum position command after the reverse movement, after the robot executes each minimum position command, it pauses for several seconds. The laser tracker collects the position coordinate values of the current target ball. After continuously collecting k minimum position commands, M0(x0, y0, z0), M1(x1, y1, z1), M2(x2, y2, z3),........M k (x k , y k , z k), at this time, the laser tracker stops coordinate acquisition; by calculating the distance value between two adjacent points in space Obtain the actual values of the minimum position command for position adjustment along the positive and negative directions of the X(Y, Z) axes of the robot base coordinate system. According to the above method, the positive and negative position adjustment resolutions of the robot along the X(Y, Z) axes of the base coordinate system can be measured at the front, middle, and end of the stroke.

[0098] Determine whether the position adjustment resolution of the robot along the X(Y, Z) axes under the base coordinate system meets the user's requirements based on the final data;

[0099] It is also possible to evaluate the minimum position command error through sa = |D i -m|max;

[0100] sa---Minimum position command error

[0101] D i ---The actual spatial position value of the i-th minimum position command;

[0102] m---The theoretical spatial position value of a minimum position command.

[0103] Evaluate the relative error of the minimum position command;

[0104] sb---Is the relative error of the minimum position command;

[0105] ---Is the sum of the actual spatial positions of k consecutive minimum position commands.

[0106] The second measurement module is used to fit a spatial circle in the measurement coordinate system of the laser tracker and obtain the attitude cumulative error J Z and attitude backlash B Z of the robot for attitude adjustment around the tool coordinate axis with the minimum attitude command; considering the attitude cumulative error J Z and attitude backlash B Z , measure the attitude adjustment resolution of the robot for attitude adjustment with the minimum attitude command.

[0107] First, perform spatial circle fitting: Install the target at a suitable position on the robot end effector. The robot rotates its end effector at equal angles around the tool RX, RY, and RZ axes respectively. The robot pauses for several seconds after each rotation of an attitude angle. At this time, the laser tracker measures the coordinates of the current target ball a1(x1, y1, z1), a2(x2, y2, z3),........a n (x n , y n , z n) Acquisition: After measuring the coordinates of several points, a spatial sphere of the robot rotating around the tool coordinate axes RX, RY, and RZ is fitted by the least squares method, and the spatial sphere center point C is obtained. o (a, b, c) coordinates and the sphere radius r. The coordinate points collected by rotating around a single RX (RY, RZ) axis of the tool coordinate are fitted to a spatial plane. By solving the spatial sphere and the spatial plane, the spatial circle and the center coordinate C rotating around the RX (RY, RZ) axis of the tool coordinate alone are obtained. a (x a , y a , z a ).

[0108] The spatial sphere equation is as follows: (x - a) 2 +(y - b) 2 +(z - c) 2 =r 2 (1)

[0109] The equation transformation is as follows: 2ax + 2by + 2cz - a 2 -b 2 -c 2 +r 2 =x 2 +y 2 +z 2 (2)

[0110] Let 2a = A, 2b = B, 2c = C, a 2 +b 2 +c 2 -r 2 =D

[0111] The above equation is written in matrix form as follows:

[0112]

[0113] The matrix is transformed as follows:

[0114]

[0115] By solving equation (4), A, B, C, and D are obtained, and substituting a = A / 2, b = B / 2, c = C / 2,

[0116] the sphere center coordinate C o (a, b, c) and the sphere radius r can be obtained.

[0117] Spatial plane fitting

[0118] The spatial plane equation can be expressed as: A1x + B1y + C1z + 1 = 0. The matrix form of the equation is as follows:

[0119]

[0120] The following equation can be obtained through matrix transformation:

[0121]

[0122] Solve for the coefficients A1, B1, and C1 to obtain the spatial plane equation. Combine this spatial plane equation (5) with the sphere equation (1) obtained in the previous step to find the spatial center coordinates C a (x a , y a ,, z a ).

[0123] Let the robot start from the current posture and perform posture adjustment around the tool coordinate RX (RY, RZ) axis with the minimum posture command o. The robot pauses for several seconds after each execution of a minimum posture command, and the laser tracker collects the current target ball coordinates; after continuously executing N minimum posture commands o, the actual posture angles of the current N minimum command postures o can be calculated. If the posture angles of the first J (J < N) minimum posture commands o have poor consistency and the posture angles of the minimum posture commands o from J + 1 to N have good consistency, it can be judged that the posture angles of the first J minimum posture commands o are due to the cumulative error of the robot's movement posture resulting in poor consistency; that is, J Z = J * o.

[0124] Let the robot move in the reverse direction of the above posture by M minimum posture commands o, and the actual posture angles of the reverse movement of M minimum posture commands o can be calculated. If the posture angles of the first T minimum posture commands o of the reverse movement are 0 or very small (the measurement repeatability accuracy of the laser tracker) and there are continuous posture angle values for the minimum posture commands o from T + 1 to M, it indicates that the first T minimum posture commands o are due to the reverse clearance of the robot resulting in no actual movement of the robot. Therefore, the reverse clearance value B of the robot's posture adjustment can be obtained θ = T * o.

[0125] Posture resolution measurement

[0126] The robot returns to the initial position and performs posture adjustment movement around the RX (RY, RZ) axis in the tool coordinate system with the minimum posture command. Among them, the first H (H ≥ J + T) points are to eliminate the cumulative error J of the robot's posture adjustment Z and the reverse clearance error B Z, the laser tracker does not collect coordinate values; starting from the H-th smallest pose command, the robot pauses for a few seconds after executing each smallest pose command, and the laser tracker collects the current target ball coordinates. After executing K smallest pose commands, the laser tracker stops coordinate collection and obtains the point coordinates Q0(x0, y0, z0), Q1(x1, y1, z1), Q2(x2, y2, z3),........Q K (x K , y K , z K ), and then continue to execute E (E≥J+T) smallest pose commands in this direction, and then let the robot execute E smallest pose commands in the reverse direction. Executing E smallest pose commands in the forward direction and E smallest pose commands in the reverse direction is to eliminate the cumulative error J Z and the reverse backlash error B Z , the laser tracker does not perform coordinate collection; starting from the E commands after reversing, the robot pauses for a few seconds after executing each smallest pose command, and the laser tracker collects the current target ball coordinates. After continuously executing K smallest pose commands, the laser tracker stops coordinate collection and obtains the point coordinates P0(x0, y0, z0), P1(x1, y1, z1), P2(x2, y2, z3),........P k (x K , y K , z K ). Calculate the distances RQ0, RQ1, RQ2,....Q K (P0, P1, P2,....P K ) from the spatial points Q0, Q1, Q2,....Q a (x a , y a ,, z a ) to the spatial center point C K (RP0, RP1, RP2,....RP K ). By calculating the distances between adjacent spatial points Q1, Q2,....Q K ,(P1, P2,....P K ), that is, the chord length values DQ1, DQ2…DQ K (DP1, DP2…DP K ) between two points on the spatial circle. The RQ0, RQ1, DQ1 (RP0, RP1, DP1) form a spatial triangle. Using the cosine theorem:

[0127]

[0128] The calculated actual values of the robot's attitude adjustment around the positive and negative directions of the RX (RY, RZ) axis with the minimum attitude command. According to the above method, the robot takes any three spatial positions within the effective space circular travel range, and measures the resolution of the robot's attitude adjustment around the RX (RY, RZ) axis with the minimum attitude command in the positive and negative directions.

[0129] Determine whether the attitude adjustment resolution of the robot under the effective travel meets the user's requirements through the final data.

[0130] It is also possible to use ωa=|θ i -m θ |max to evaluate the minimum attitude command error;

[0131] ωa represents the minimum attitude command error

[0132] θ ｉ represents the actual spatial attitude angle of the i-th minimum attitude command;

[0133] m θ represents the theoretical spatial attitude angle of a minimum attitude command.

[0134] By evaluate the relative error of the minimum attitude command;

[0135] ωb represents the relative error of the minimum attitude command;

[0136] --- The sum of the actual spatial attitude angles of k consecutive minimum attitude commands.

[0137] In summary, the present invention realizes the measurement of the robot's spatial pose adjustment resolution based on the spherical coordinate system of the laser tracker. The robot performs spatial position adjustment movements along the X, Y, and Z axes in the base coordinate system with several minimum position commands. The laser tracker collects several spatial position coordinate points of the robot, calculates the spatial distance between two consecutive points, and the subdivision ability of the robot's spatial position adjustment movement can be obtained. The robot performs spatial attitude adjustment movements around the RX, RY, and RZ axes of the tool coordinate system with several minimum attitude commands. The laser tracker collects several spatial position coordinate points of the robot, and the chord length D is obtained through the calculation of the coordinate values of two consecutive points in space. The connecting lines of adjacent points to the center of the circle are R1 and R2; R1, R2, and D form a spatial triangle. In the spatial triangle, the cosine theorem can be used to obtain the central angle between two adjacent points. By measuring several minimum attitude commands of the robot, several spatial triangles can be obtained, and the central angle of each triangle is the subdivision ability of the robot's spatial attitude movement. The robot runs with the minimum position command to measure the spatial position adjustment resolution of the robot, and the robot runs with the minimum attitude command to measure the spatial attitude adjustment resolution of the robot. Based on the above measurements of the robot's spatial position and spatial attitude respectively, the spatial pose adjustment resolution of the robot can be characterized.

[0138] The specific implementation manners described above further elaborate on the purpose, technical solutions, and beneficial effects of the present invention. It should be understood that the above are only specific implementation manners of the present invention and are not used to limit the protection scope of the present invention. Any modifications, equivalent replacements, improvements, etc. made within the spirit and principles of the present invention shall be included in the protection scope of the present invention.

Claims

1. A method for measuring the resolution of a robot's spatial pose adjustment, characterized in that The measurement method is based on a laser tracker and includes: Obtain the position cumulative error L of the robot for position adjustment with the minimum position command L and the position backlash B L ; Considering the position cumulative error L L and the position backlash B L , collect the position adjustment resolution of the robot for position adjustment with the minimum position command; Fit a spatial circle in the measurement coordinate system of the laser tracker, and obtain the attitude cumulative error L of the robot for attitude adjustment with the minimum attitude command based on the spatial circle Z and the attitude backlash B Z ; Considering the attitude cumulative error L Z and the attitude backlash B Z , collect the attitude adjustment resolution of the robot for attitude adjustment with the minimum attitude command; Position cumulative error L L and attitude cumulative error L Z The acquisition method includes: The robot performs position adjustment movements along the directions of each coordinate axis in the base coordinate system with the minimum position command i. The robot collects the spatial position coordinates of the target ball once for each execution of a minimum position command. After the robot executes n minimum position commands, the distance values between two adjacent spatial position coordinates are calculated to obtain the actual spatial position values of the robot for continuously executing n minimum position commands. If the spatial position value consistency of the smallest position instructions from the (j + 1)-th to the n-th is better than that of the first j smallest position instructions, where j < n, then it is determined that there is a position cumulative error L in the spatial position values of the first j smallest position instructions executed by the robot L , L L = j * i; Based on fitting a spatial circle in the measurement coordinate system of the laser tracker, starting from the current posture, the robot performs posture adjustment around the tool coordinate axis with the minimum posture command o, and collects the spatial position coordinates of the target ball at the end of the robot once for each execution of a minimum posture command. After continuously executing N minimum posture commands o, the actual spatial posture angles of the N minimum command postures o are calculated. If the attitude angle consistency of the attitude commands from the (J + 1)-th to the N-th smallest attitude commands is better than that of the first J smallest attitude commands, where J < N, then it is determined that there is an attitude cumulative error L in the attitude angles of the first J smallest attitude commands executed by the robot Z , L Z = J * o; Position backlash B L and attitude backlash B Z The acquisition method includes: After the robot executes n minimum position commands i, it performs reverse movement at the current position and executes m minimum position commands i. The robot collects the spatial position coordinates once for each execution of a minimum position command. After the robot executes m minimum position commands i, the distance between two adjacent spatial position coordinates is calculated to obtain the actual spatial position values of the m minimum position commands i. If the spatial position values of the first t minimum position commands for reverse movement are 0 or continuous unstable position values, and there are continuous stable position values for the minimum position commands from t + 1 to m, where t < m, then it is determined that there is a position reverse gap B in the position values of the first t minimum position commands during the reverse position adjustment movement L , B L = t * i; After the robot executes N minimum posture commands o, it performs reverse execution of M minimum posture commands o at the current position, and calculates the actual spatial posture angles of the reverse execution of M minimum posture commands o. If the attitude angles of the first T minimum attitude commands for reverse movement are 0 or consecutive unstable attitude angles, and there are consecutive stable attitude angles for the minimum attitude commands from T + 1 to M, where T < M, then it is determined that there is an attitude reverse gap B in the attitude angles of the first T minimum attitude commands during the reverse attitude adjustment movement Z , B Z = T * o; The position adjustment resolution includes forward position adjustment resolution and reverse position adjustment resolution. The measurement method of the position adjustment resolution includes: Let the robot perform position adjustment movements along each coordinate axis in the base coordinate system with the minimum position command; starting from the h-th minimum position command, the robot collects the spatial position coordinates of the target ball once after each execution of a minimum position command, where h ≥ j + t; j represents the position cumulative error L of the first j minimum position commands L , and t represents the position backlash B of the first t minimum position commands L ; after continuously executing k minimum position commands, k + 1 spatial position coordinates are obtained, k consecutive actual spatial position values are calculated, and the forward position adjustment resolution of the robot is obtained; Let the robot continue to execute e minimum position commands in this direction, where e≥j + t, and then let the robot perform reverse movement and execute e minimum position commands. Collect the position coordinates starting from the e-th minimum position command during the reverse movement of the robot. After continuously executing k minimum position commands, k + 1 spatial position coordinates are obtained, and k consecutive actual spatial position values are calculated to obtain the reverse position adjustment resolution of the robot.

2. The measurement method for the resolution of the robot spatial pose adjustment according to claim 1, characterized in that, It also includes pose adjustment resolution determination, including the process: Position adjustment resolution determination: Compare the position adjustment resolution with the position adjustment threshold to determine whether the position adjustment resolution meets the preset threshold. Pose adjustment resolution determination: Compare the pose adjustment resolution with the pose adjustment threshold to determine whether the pose adjustment resolution meets the preset threshold.

3. A method for measuring the resolution of a robot's spatial pose adjustment, according to claim 1, characterized in that It also includes pose adjustment resolution determination, including the process: Position adjustment resolution determination: According to Equation Calculate the minimum position command error sa ; According to Equation Calculate the relative error sb of the minimum position command; Based on the minimum position command error sa And the relative error sb of the minimum position command, determine whether the position adjustment resolution meets the preset threshold; where D i Represents the actual spatial position value of the i-th minimum position command; m represents the theoretical spatial position value of a minimum position command; |*|max represents taking the maximum absolute value; Represents the sum of the actual spatial position values of k consecutive minimum position commands; Attitude adjustment resolution determination: According to the formula Calculate the minimum attitude command error ; According to the formula Calculate the relative error of the minimum attitude command ; Based on the minimum attitude command error And the relative error of the minimum attitude command Determine whether the attitude adjustment resolution meets the preset threshold; where Represents the actual spatial attitude angle of the i-th minimum attitude command, Represents the theoretical spatial attitude angle of a minimum attitude command; |*|max means taking the maximum absolute value; Represents the sum of the actual spatial attitude angles of k consecutive minimum attitude commands.

4. A method for measuring the resolution of a robot's spatial pose adjustment, as described in claim 1, characterized in that, The spatial circle fitting method includes: Let the robot perform equal-angle attitude adjustments around each tool coordinate axis in the base coordinate system. After the robot adjusts each attitude angle, collect the spatial position coordinates of the target ball once. After measuring the spatial position coordinates of the end target ball of the robot in multiple attitudes, fit a spatial sphere with the origin of the robot tool coordinate system as the center of the sphere, the spatial sphere center C o (a, b, c) and the sphere radius r; where a, b, c are the coordinates of the spatial sphere center C o coordinates; Fitting a spatial plane based on all coordinate points where the robot rotates alone around a tool coordinate axis. Solve the spatial circle and the spatial center point C of the robot rotating around each tool coordinate axis based on the spatial sphere and the spatial plane a (x a , y a , z a ), where x a , y a and z a are the coordinates of the spatial center point.

5. A method for measuring the resolution of a robot's spatial pose adjustment, according to claim 4, characterized in that, The pose adjustment resolution includes forward pose adjustment resolution and reverse pose adjustment resolution. The measurement method of the pose adjustment resolution includes: The robot is commanded to perform attitude adjustment movements around each tool coordinate axis with the minimum attitude commands. Starting from the Hth minimum attitude command, the robot collects the spatial position coordinates of the target ball once after executing each minimum attitude command, where H ≥ T + J, J represents the attitude cumulative error L of the first J minimum attitude commands Z , and T represents the attitude backlash B of the first T minimum attitude commands Z ; After continuously executing K minimum attitude commands, the end target ball coordinates Q of the robot's forward attitude adjustment are obtained Z , and the actual spatial attitude angles of the robot continuously executing K minimum attitude commands are calculated based on the spatial circular triangle method; the forward attitude adjustment resolution of the robot is obtained Let the robot continue to execute E minimum pose commands in this direction, E≥T + J, and then let the robot perform reverse movement and execute E minimum pose commands. Collect the spatial position coordinates of the target ball starting from the E-th smallest pose instruction executed during the reverse movement of the robot. After continuously executing K smallest pose instructions, obtain the end target ball coordinates P of K + 1 reverse pose adjustments of the robot. Z , calculate the actual spatial attitude angle of the robot continuously executing K smallest pose instructions based on the spatial circle triangle method; obtain the reverse pose adjustment resolution of the robot.

6. A method for measuring the resolution of a robot's spatial pose adjustment, according to claim 5, characterized in that The calculation method of the pose adjustment resolution includes: Computer robot forward attitude adjustment end target ball coordinate Q Z The spatial distance from the spatial center point C a to obtain the radius RQ Z , and calculate the spatial distance DQ Z between two adjacent coordinate points Q Z of the forward attitude adjustment end target ball, where Z = 0, 1, 2, 3…K; Based on RQ Z-1 , RQ Z , DQ Z constitute a spatial triangle, and the actual attitude angle of the robot adjusted with the minimum attitude command is calculated using the cosine theorem; For the K spatial triangles formed by K consecutive minimum attitude commands, the forward attitude adjustment resolution of the robot around the tool coordinate axis with the minimum attitude command can be obtained; The coordinates P of the end target ball for the reverse attitude adjustment of the robotic arm Z The spatial distance from the spatial center point C a to obtain the radius RP Z , and calculate the spatial distance DP Z between two adjacent coordinate points P of the end target ball in the reverse attitude Z , where Z = 0, 1, 2, 3... K; based on RP Z-1 , RP Z , and DP Z a spatial triangle is formed. Using the cosine theorem, the actual attitude angle of the robot's adjustment with the minimum attitude command is calculated; for the K spatial triangles formed by K consecutive minimum attitude commands, the reverse attitude adjustment resolution of the robot around the tool coordinate axis with the minimum attitude command can be obtained.

7. A measurement system for the resolution of robot spatial pose adjustment, characterized in that, A measurement method for realizing the robot spatial pose adjustment resolution described in any one of claims 1-6 includes: The first measurement module is used to obtain the position cumulative error L of the robot for position adjustment with the minimum position command in the base coordinate system L and the position backlash B L ; Considering the position cumulative error L L and the position backlash B L , measure the position adjustment resolution of the robot for position adjustment with the minimum position command in the base coordinate system; A second measurement module, configured to fit a spatial circle in the measurement coordinate system of the laser tracker, and obtain the attitude cumulative error L of the robot for attitude adjustment with a minimum attitude command based on the spatial circle Z and the attitude backlash B Z ; Considering the attitude cumulative error L Z and the attitude backlash B Z , measure the attitude adjustment resolution of the robot for attitude adjustment with a minimum attitude command.

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