Singularity prediction and motion control method of under-freedom manipulator and robot

Abstract

The present invention discloses a singularity prediction and motion control method for a robot with less degrees of freedom. The method includes: establishing a virtual axis for the robot with less degrees of freedom to transform it into a 6-axis robot with virtual joints; the joint control amount of the robot with less degrees of freedom and the virtual joint control amount constitute the 6 control amounts of the 6-axis robot in the joint space; performing initial value positive solution pre-calculation on the 6-axis robot, pre-storing the corresponding relationship between some positive solution control amounts and posture; when seeking an inverse solution, using the above initial values ​​for screening and traversing the iterative method to seek a convergent solution; solving the Jacobian matrix of the 6-axis robot to calculate the singularity of the robot to obtain a singular point solution set; during the motion process, according to the target posture, combined with the singular point solution set, planning the optimal path point of the robot, then seeking the inverse solution control amount according to the path point, and finally issuing the control amount of each axis in sequence to complete the motion control of the robot with less degrees of freedom. The present invention can complete the singularity prediction and motion control of the robot with less degrees of freedom.

Description

Technical Field

[0001] The present invention belongs to the field of mechanical arms, and in particular relates to a singularity prediction and motion control method for a mechanical arm with less degrees of freedom and a robot. Background Art

[0002] A less-freedom robotic arm refers to a mechanical system in which the control input dimension is less than the system's degree of freedom. Due to the reduction of driving devices and the presence of passive joints or free joints, the robotic arm has the advantages of light weight and low power consumption, and has broad application prospects in special operation scenarios.

[0003] Due to the lack of one or several driving devices, the acceleration of the passive joints of the under-freedom manipulator is only subject to the dynamic constraints from other joints, and it is impossible to express any spatial position and posture. It can only move to the desired position and posture limited by fewer joints. It is necessary to use the dynamic coupling of the active-passive joints and complete the task through appropriate control strategies, which greatly increases the difficulty of developing and debugging the manipulator control algorithm and singularity evaluation related algorithms. At the same time, the under-freedom robot has many singular points, and it is difficult to complete some posture control when approaching the singular point. Summary of the invention

[0004] The present invention provides a singularity prediction and motion control method for a robotic arm with less degrees of freedom and a robot, which solve the singularity evaluation and control problems of the robotic arm with less degrees of freedom.

[0005] The present invention adopts the following technical solution:

[0006] A method for singularity prediction and motion control of a low-degree-of-freedom manipulator comprises the following steps:

[0007] S1. Establish a virtual axis for the linkage model of the under-freedom robot arm to transform it into a 6-axis robot arm with virtual joints. The original under-freedom robot arm joint control quantity and the added virtual joint control quantity together form the 6 control quantities θ1, θ2, θ3, θ4, θ5, and θ6 of the 6-axis robot arm in the joint space. When the joint type is a translation joint, θ i The value is the translation distance. When the joint type is a rotational joint, θ i The value is the rotation angle, where i = 1, 2, 3.., 6;

[0008] S2, 6-axis robot arm joint space control quantity θ1, θ2, θ3, θ4, θ5, θ6 and 6-axis robot arm position X, Y, Z and posture There are the following corresponding relationships:

[0009]

[0010] According to the above formula, the initial value of the 6-axis robot arm is pre-solved, and some of the positive solution control quantities and posture correspondences are pre-stored as initial value inputs for subsequent inverse solution. When the inverse solution is obtained, the above initial values ​​are used for screening and the convergent solution is obtained by traversing the iteration method. The convergent solution is brought into the positive solution verification. If the positive solution verification passes, the inverse solution is successfully obtained.

[0011] S3. Solve the Jacobian matrix J(θ) of the 6-axis robot arm. The Jacobian matrix J(θ) and its transposed matrix J T (θ) Calculate the singularity of the robot The singularity of the points in the reachable range of the under-freedom manipulator is estimated by this formula to obtain the singular point solution set;

[0012] S4. During the motion process, according to the target position of the under-freedom manipulator and the singular point solution set, the optimal path points of the under-freedom manipulator are planned, and then the inverse solution control quantity is calculated according to the path points. Finally, the control quantity of each axis is issued in turn to complete the motion control of the under-freedom manipulator.

[0013] Furthermore, the virtual joint in S1 is added to the starting joint, joint connection or end of the existing joint of the N-axis robot arm with insufficient degrees of freedom; wherein N<6.

[0014] Furthermore, the virtual joint is a translational joint or a rotational joint.

[0015] Furthermore, in S2, the forward solution pre-calculation and inverse solution calculation include the following steps:

[0016] S21. Obtain the corresponding single-axis angle limit θ based on the actual N-axis and actual safe working range of the under-freedom manipulator. min ,θ max , for each single axis within the safe working range, the step angle θ step , perform N-layer nested traversal kinematics forward solution calculation to obtain the N-axis angle f Angle (θ1,θ2…θ N ) and the robot arm posture The mapping relationship is:

[0017]

[0018] Build the mapping set:

[0019]

[0020] Among them, θ i Represents the angle of the i-th axis, taking θ min to θ max , step length θ step ;

[0021] S22, according to the target posture With mapping set Compare and extract f that satisfies the following spatial position Map value:

[0022] |X ArmPose -X Map |≤L

[0023] |Y ArmPose -Y Map |≤L

[0024] |Z ArmPose -Z Map |≤L

[0025] That is, the extraction position is located around the target posture, and the mapping relationship within the grid with a side length of L is used as the initial screening f Map result;

[0026] S23, in the initial screening f Map In the equation, find and Position X, Y, Z difference and attitude Difference:

[0027] ΔX=|X ArmPose -X Map |

[0028] ΔY=|Y ArmPose -Y Map |

[0029] ΔZ=|Z ArmPose -Z Map |

[0030]

[0031] And superimpose a weighted value k on the posture to find the initial screening f Map With f AmPose The weighted sum Δf of the pose differences:

[0032]

[0033] Take the smallest m values ​​in the weighted sum of all pose differences to obtain the finely screened initial mapping relationship:

[0034]

[0035] S24, the m initial mapping relationships θ1, θ2…θ N Perform the iterative method to calculate the inverse solution:

[0036]

[0037] For the obtained inverse solution values, perform forward and reverse calculations respectively:

[0038]

[0039] When the positive solution is consistent with the target pose, it is confirmed that the correct inverse solution is obtained:

[0040] f 逆解 (θ1,θ2…θ N ).

[0041] Furthermore, in S3, the Jacobian matrix of the robot arm is solved by the vector product method, which specifically includes:

[0042] The Jacobian matrix is ​​calculated column by column. If joint i is a moving joint, the i-th column of the Jacobian matrix is:

[0043]

[0044] If joint i is a rotational joint, the i-th column of the Jacobian matrix is:

[0045]

[0046] Where: Ji represents the i-th column of the Jacobian matrix, × represents the vector product symbol, The position vector of the origin of the end effector relative to the coordinate system {i} in the base coordinate system {0}, Z i represents the z-axis unit vector of coordinate system {i} expressed in base coordinate system {0}, Represents the rotation transformation matrix of coordinate system {i} relative to base coordinate system {0};

[0047] The m*n order Jacobian matrix is ​​obtained from all the columns obtained:

[0048]

[0049] Furthermore, in S3, the steps for obtaining the singular point solution set are as follows:

[0050] S31, according to the actual N-axis and the actual safe working range of the under-freedom robot arm, the corresponding angle limit of each single axis is obtained, and each single axis is stepped at an angle θ within the safe working range. step , perform N-layer nested traversal reachability calculation, i.e. singularity estimation, and obtain the angles of N axes (θ1, θ2…θ N ) and the mapping relationship between reachability ω:

[0051] f Map (ω,θ1,θ2…θ N )

[0052] S32. Find the largest ω value ω in the mapping relationship during traversalmax , then all f Map (ω,θ1,θ2…θ N ) is used to represent the value of ω Replace, get the angles of N axes (θ1, θ2…θ N ) and accessibility coefficient The mapping relationship is:

[0053]

[0054] S33. Define a critical accessibility coefficient extract All mapping relationships that are not greater than the critical accessibility coefficient are recorded as singular points, and the angle values ​​in the mapping relationships are extracted and each is represented by θ step The range of / 2 is diffused into a point cloud, and the set of all singular points and their diffused point clouds is recorded as the singular point solution set. The expression of the singular point solution set is as follows:

[0055] f Singularity (θ1,θ2…θ N ).

[0056] Furthermore, the critical accessibility coefficient The value range is 1% to 3%.

[0057] Furthermore, the optimal path point of the manipulator in S4 is obtained by interpolation based on the target posture of the manipulator and the singular point solution set.

[0058] A robot has a less-freedom robotic arm, wherein the less-freedom robotic arm adopts the above-mentioned singularity prediction and motion control method of the less-freedom robotic arm.

[0059] Compared with the prior art, the present invention has the following advantages and beneficial effects:

[0060] There is a solvability problem for robots with less degrees of freedom. The difficulty of the inverse solution algorithm of the robot with less degrees of freedom can be reduced by establishing a virtual control axis and applying the inverse solution method of the standard 6-axis robot. At the same time, the common methods of the standard 6-axis robot (such as the vector product method) can be applied to solve the Jacobian matrix of the robot arm, and then complete the real-time singularity evaluation. The singularity results can be integrated into the motion control process to avoid moving to the singularity point and achieve a smooth motion control effect. BRIEF DESCRIPTION OF THE DRAWINGS

[0061] Figure 1 It is a flow chart of the singularity estimation and motion control method of the under-freedom manipulator;

[0062] Figure 2 This is a schematic diagram of adding virtual joints to a robotic arm with less degrees of freedom;

[0063] Figure 3 It is a flowchart of pre-solution and inverse solution;

[0064] Figure 4 It is a flow chart for solving the singular point solution set;

[0065] Figure 5 It is a motion control flow chart.

[0066] In the figure: 1-joint, 2-link, 3-virtual joint. DETAILED DESCRIPTION

[0067] In order to make the purpose, technical solutions and advantages of the present invention more clearly understood, the present invention is further described in detail below in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not intended to limit the present invention. In addition, the technical features involved in the various embodiments of the present invention described below can be combined with each other as long as they do not conflict with each other.

[0068] The present invention proposes a general singularity prediction and motion control method for a robot with less degrees of freedom, such as Figure 1 As shown, it mainly includes the following steps:

[0069] S1. According to the robot model with less degrees of freedom, a virtual axis is established to transform the robot into a standard 6-axis robot. The original joint control amount of the robot arm with less degrees of freedom and the added virtual joint control amount together constitute the 6 joint control amounts θ1, θ2, θ3, θ4, θ5, θ6 (θ i , i=1, 2, 3.., 6); when the joint type is a translation joint, θ i The value is the translation distance. When the joint type is a rotational joint, θ i The value is the rotation angle.

[0070] S2. The general six-axis robot forward solution model is:

[0071]

[0072] The inverse solution model of the general six-axis robot is:

[0073]

[0074] Before solving the inverse solution, the robot is pre-solved for the initial value forward solution, and the corresponding relationship between some forward solution control quantities and terminal postures is pre-stored as the appropriate initial value input for subsequent inverse solution. When solving the inverse solution, the above initial values ​​are used for screening and the iterative method is used to find the convergent solution. All convergent solutions need to be brought into the forward solution verification. If the forward solution verification passes, the inverse solution is successfully found.

[0075] S3. Use the vector product method to solve the robot Jacobian matrix J(θ):

[0076] J(θ)=(θ1, θ2, θ3, θ4, θ5, θ6) T

[0077] The following singularity formula is used to complete the quantitative calculation and evaluation of the robot singularity:

[0078]

[0079] According to the singularity formula, the singularity of the points in the reachable range is quantitatively calculated and evaluated offline. In the subsequent actual motion control process, the robot is simply judged whether it is in or close to a singular state based on the special state of each axis corresponding to the calculated singularity quantitative evaluation result, which serves as the basis for path selection during real-time motion control.

[0080] S4. During the motion process, it is usually necessary to directly control the robot's posture. After determining the target posture, first combine the singularity state of step S3 to plan the optimal path point, then use step S2 to obtain the inverse solution control quantity, and finally send the control quantity of each axis in turn to complete the real-time motion control of the robot.

[0081] The singularity prediction and motion control method of a low-degree-of-freedom manipulator according to an embodiment of the present invention comprises the following steps:

[0082] Step 1: For the linkage model of the under-freedom robot arm, establish a virtual control axis to transform it into a standard 6-axis full-freedom robot arm.

[0083] The robot arm is a collection of many links 2 connected by joints 1. Figure 2 As shown, for an N (N<6)-axis robotic arm with insufficient degrees of freedom, a virtual joint 3 is added at the starting joint, joint connection or end of its existing joints. The virtual joint can be a rotational joint or a translational joint, so that the robotic arm with insufficient degrees of freedom is transformed into a new robotic arm with 6 axes and full degrees of freedom having virtual joints.

[0084] The original joint control amount of the under-freedom robot arm and the added virtual joint control amount together constitute the six joint control amounts θ1, θ2, θ3, θ4, θ5, θ6 (θ i , i=1,2,3..,6); when the joint type is a translation joint, θ i The value is the translation distance. When the joint type is a rotational joint, θ i The value is the rotation angle.

[0085] The six-axis robot arm joint space control quantities θ1, θ2, θ3, θ4, θ5, θ6 and the rectangular coordinate system space position and posture X, Y, Z, There are the following function correspondences:

[0086]

[0087] The “virtual joint” controls the joint control variable θ i The translation distance and rotation angle of the virtual joint are determined according to the virtual joint type.

[0088] Step 2: Perform a pre-calculation of the initial value forward solution for the robot, and pre-store the corresponding relationship between the kinematic forward solution angle and the terminal posture, which will be used as the initial value input for the subsequent kinematic inverse solution. When the inverse solution is obtained, the above initial values ​​are used for screening and the iterative method is used for solution. All converged solutions need to be brought into the forward solution verification. If the forward solution verification passes, the inverse solution is successfully solved.

[0089] The pre-calculation and inverse solution process is as follows Figure 3 As shown, the following steps are included:

[0090] 1. According to the actual N axes (N<6) and the actual safe working range, the corresponding single-axis angle limit θ is obtained min ,θ max , for each single axis within the safety range with a fixed step angle θ step , perform N-layer nested traversal kinematics forward solution calculation to obtain the N-axis angles (θ1, θ2…θ N ) and 6 degrees of freedom at the end of the robot The mapping relationship is:

[0091]

[0092] Among them, θ i Represents the angle of the i-th axis, taking θ min to θ max , step length θ step

[0093] 2. When iterative method is needed to calculate the inverse kinematic solution, according to the known terminal target position Same as in step 1 Compare and extract f that satisfies the following spatial position Map value:

[0094] |X ArmPose -X Map |≤L

[0095] |Y ArmPose -Y Map |≤L

[0096] |Z ArmPose -Z Map |≤L

[0097] That is, the extraction position is located in the grid with a side length of L around the target posture, and is used as the initial screening fMap result.

[0098] 3. In the initial screening of f Map In the equation, find and Position X, Y, Z difference and attitude Difference:

[0099] ΔX=|X ArmPose -X Map |

[0100] ΔY=|Y ArmPose -Y Map |

[0101] ΔZ=|Z ArmPose -Z Map |

[0102]

[0103] And superimpose a weighted value k on the posture to find the initial screening f Map With f ArmPose The weighted sum Δf of the pose differences:

[0104]

[0105] The smallest m values ​​are taken from the weighted sum of all pose differences to obtain a finely screened initial mapping relationship.

[0106]

[0107] (i=1,2…m,satisfying Δf i =minΔf i )

[0108] 4. The θ1, θ2…θ in the initial mapping relationship of the fine screening N Perform the iterative method to calculate the inverse solution:

[0109]

[0110] For the inverse solution values ​​obtained by Newton's iteration method, perform forward and reverse calculations respectively:

[0111]

[0112] When the correct solution is completely consistent with the known end target pose, it can be confirmed that the correct inverse solution is obtained:

[0113] f 逆解 (θ1,θ2…θ N ).

[0114] Step 3: Calculate the Jacobian matrix by column. If joint i is a moving joint, the i-th column of the Jacobian matrix is:

[0115]

[0116] If joint i is a rotational joint, the i-th column of the Jacobian matrix is:

[0117]

[0118] Where:

[0119] J i ——the i-th column of the Jacobian matrix;

[0120] × ——vector product symbol;

[0121] ——The position vector of the end effector coordinate origin relative to the coordinate system {i} in the base coordinate system {0}, that is:

[0122]

[0123] In the formula, i P n represents the position vector of coordinate system {n} relative to coordinate system {i};

[0124] Z i ——the z-axis unit vector of coordinate system {i} (expressed in base coordinate system {0});

[0125] ——The rotation transformation matrix of coordinate system {i} relative to the base coordinate system {0}.

[0126] From all the columns obtained, we can get the m*n order Jacobian matrix:

[0127]

[0128] The Jacobian matrix J(θ) and its transpose J T (θ) can be used to obtain the robot singularity index ω:

[0129]

[0130] Where det is the determinant value. The singularity ω is the reachability.

[0131] The process of calculating the singular solution set is as follows Figure 4 As shown, the following steps are included:

[0132] 1. According to the reachability calculation formula, the corresponding single-axis angle limit can be obtained in advance according to the actual N axes (N < 6) and the actual safe working range, and the appropriate step angle θ can be selected for each single axis within the safe range. step , perform N-layer nested traversal reachability calculations and obtain the angles of N axes (θ1, θ2…θ N ) and the mapping relationship between reachability ω:

[0133] f Map (ω,θ1,θ2…θ N )

[0134] 2. Find the largest ω value ω in the mapping relationship during traversal max , then all f Map (ω,θ1,θ2…θ N ) is used to represent the value of ω By replacing, we can get the angles of N axes (θ1, θ2…θ N ) and accessibility coefficient The mapping relationship is:

[0135]

[0136] 3. Define a critical accessibility coefficient ( Usually 1% to 3%), extract All the coefficients not greater than the critical accessibility coefficient (i.e. satisfying ) is recorded as a singular point, and the angle value in the mapping relationship is extracted and each is expressed as θ step / 2 is diffused into a point cloud, and the set of all singular points and their diffused point clouds is recorded as the singular point solution set. The expression of the singular point solution set is:

[0137] f Singularity (θ1,θ2…θ N ).

[0138] Step 4: Motion control. Figure 1 This is a motion control flow chart. As shown in the figure, the motion control steps are as follows:

[0139] 1. During motion control, according to the external target posture command given to the robot, combined with the singular point solution set f Singularity (θ1,θ2…θ N ), interpolate to find the optimal path point

[0140] 2. Obtain the path points using the inverse solution method of step 2 The angle f that each axis needs to reach 逆解 (θ1,θ2…θ N), and send the target positions to the robot in turn to complete motion control.

[0141] The present invention also provides a robot having a less-freedom robotic arm, and the less-freedom robotic arm adopts the above-mentioned singularity prediction and motion control method of the less-freedom robotic arm.

[0142] It will be easily understood by those skilled in the art that the above are only preferred embodiments of the present invention and are not intended to limit the present invention. Any modifications, equivalent substitutions and improvements made within the spirit and principles of the present invention should be included in the protection scope of the present invention.

Claims

1. A method for singularity prediction and motion control of a robot arm with less degrees of freedom, characterized in that: The following steps are involved: S1. Establish a virtual axis for the linkage model of the under-freedom robot arm to transform it into a 6-axis robot arm with virtual joints. The original under-freedom robot arm joint control quantity and the added virtual joint control quantity together form the 6 control quantities θ1, θ2, θ3, θ4, θ5, and θ6 of the 6-axis robot arm in the joint space. When the joint type is a translation joint, θ i The value is the translation distance. When the joint type is a rotational joint, θ i The value is the rotation angle, where i = 1, 2, 3.., 6; S2, 6-axis robot arm joint space control quantity θ1, θ2, θ3, θ4, θ5, θ6 and 6-axis robot arm position X, Y, Z and posture There are the following corresponding relationships: According to the above formula, the initial value of the 6-axis robot arm is pre-solved, and some of the positive solution control quantities and posture correspondences are pre-stored as initial value inputs for subsequent inverse solution. When the inverse solution is obtained, the above initial values ​​are used for screening and the convergent solution is obtained by traversing the iteration method. The convergent solution is brought into the positive solution verification. If the positive solution verification passes, the inverse solution is successfully obtained. S3. Solve the Jacobian matrix J(θ) of the 6-axis robot arm. The Jacobian matrix J(θ) and its transposed matrix J T (θ) Calculate the singularity of the robot The singularity of the points in the reachable range of the under-freedom manipulator is estimated by this formula to obtain the singular point solution set; S4. During the motion process, according to the target position of the under-freedom manipulator and the singular point solution set, the optimal path points of the under-freedom manipulator are planned, and then the inverse solution control quantity is calculated according to the path points. Finally, the control quantity of each axis is issued in turn to complete the motion control of the under-freedom manipulator.

2. The singularity prediction and motion control method of a low-degree-of-freedom manipulator according to claim 1, characterized in that: The virtual joint in S1 is added at the starting joint, joint connection or end of the existing joint of the N-axis robot arm with insufficient degrees of freedom; wherein N<6.

3. The singularity prediction and motion control method of a low-degree-of-freedom manipulator according to claim 2, characterized in that: The virtual joint is a translation joint or a rotation joint.

4. The singularity prediction and motion control method of a low-degree-of-freedom manipulator according to claim 1, characterized in that: In S2, the forward solution pre-calculation and inverse solution calculation include the following steps: S21. Obtain the corresponding single-axis angle limit θ based on the actual N-axis and actual safe working range of the under-freedom manipulator. min ,θ max , for each single axis within the safe working range, the step angle θ step , perform N-layer nested traversal kinematics forward solution calculation to obtain the N-axis angle f Angle (θ1,θ2…θ N ) and the robot arm posture The mapping relationship is: Build the mapping set: Among them, θ i Represents the angle of the i-th axis, taking θ min to θ max , step length θ step ; S22, according to the target posture With mapping set Compare and extract f that satisfies the following spatial position Map value: |X ArmPose -X Map |≤L |And ArmPose -AND Map |≤L |From ArmPose -WITH Map |≤L That is, the extraction position is located around the target posture, and the mapping relationship within the grid with a side length of L is used as the initial screening f Map result; S23, in the initial screening f Map In the equation, find and Position X, Y, Z difference and attitude Difference: ΔX=|X ArmPose -X Map | ΔY=|Y ArmPose -Y Map | ΔZ=|Z ArmPose -Z Map | And superimpose a weighted value k on the posture to find the initial screening f Map With f ArmPose The weighted sum Δf of the pose differences: Take the smallest m values ​​in the weighted sum of all pose differences to obtain the finely screened initial mapping relationship: S24, the m initial mapping relationships θ1, θ2…θ N Perform the iterative method to calculate the inverse solution: For the obtained inverse solution values, perform forward and reverse calculations respectively: When the positive solution is consistent with the target pose, it is confirmed that the correct inverse solution is obtained: f 逆解 (θ1,θ2…θ N )。 5. The singularity prediction and motion control method of a low-degree-of-freedom manipulator according to claim 1, characterized in that: In S3, the Jacobian matrix of the robot arm is solved by the vector product method, which specifically includes: The Jacobian matrix is ​​calculated column by column. If joint i is a moving joint, the i-th column of the Jacobian matrix is: If joint i is a rotational joint, the i-th column of the Jacobian matrix is: Where: Ji represents the i-th column of the Jacobian matrix, × represents the vector product symbol, The position vector of the origin of the end effector relative to the coordinate system {i} in the base coordinate system {0}, Z i represents the z-axis unit vector of coordinate system {i} expressed in base coordinate system {0}, Represents the rotation transformation matrix of coordinate system {i} relative to base coordinate system {0}; The m*n order Jacobian matrix is ​​obtained from all the columns obtained:

6. The singularity prediction and motion control method of a low-degree-of-freedom manipulator according to claim 1, characterized in that: In S3, the steps for obtaining the singular point solution set are as follows: S31, according to the actual N-axis and the actual safe working range of the under-freedom robot arm, the corresponding angle limit of each single axis is obtained, and each single axis is stepped at an angle θ within the safe working range. step , perform N-layer nested traversal reachability calculation, i.e. singularity estimation, and obtain the angles of N axes (θ1, θ2…θ N ) and the mapping relationship between reachability ω: f Map (ω,θ1,θ2…θ N ) S32. Find the largest ω value ω in the mapping relationship during traversal max , then all f Map (ω,θ1,θ2…θ N ) is used to represent the value of ω Replace, get the angles of N axes (θ1, θ2…θ N ) and accessibility coefficient The mapping relationship is: S33. Define a critical accessibility coefficient extract All mapping relationships that are not greater than the critical accessibility coefficient are recorded as singular points, and the angle values ​​in the mapping relationships are extracted and each is represented by θ step The range of / 2 is diffused into a point cloud, and the set of all singular points and their diffused point clouds is recorded as the singular point solution set. The expression of the singular point solution set is as follows: f Singularity (θ1,θ2…θ N )。 7. The singularity prediction and motion control method of a low-degree-of-freedom manipulator according to claim 1, characterized in that: Critical accessibility coefficient The value range is 1% to 3%.

8. The singularity prediction and motion control method of a low-degree-of-freedom manipulator according to claim 1, characterized in that: The optimal path point of the manipulator in S4 is obtained by interpolation based on the target posture of the manipulator and the singular point solution set.

9. A robot, characterized in that: The robot has a less-freedom robotic arm, and the less-freedom robotic arm adopts the singularity prediction and motion control method of the less-freedom robotic arm described in any one of claims 1 to 8.

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