A method for optimizing the stability of an in-pulling mobile machining robot

Abstract

The application discloses an inner support type mobile machining robot stability optimization method, and belongs to the technical field of robot machining.The method optimizes stability by actively regulating and controlling support force.Firstly, the contact between the roller and the inner wall of the pipe is analyzed to form force constraint conditions of the contact interface.Secondly, the force balance relationship of the whole mobile machining robot is established through dynamic and static analysis.Next, potential disturbance characterization and dynamic machining force discretization are carried out, and a high-anti-interference support force distribution model is constructed in combination with the established constraint conditions and force balance relationship, support force output constraints.Finally, the numerical value of each support force is obtained through linear optimization calculation.The robot always maintains stability in the work task under the support force, and the anti-interference ability is significantly enhanced.The application solves the overturning and sliding risk of the mobile robot in the pipe machining through the support force regulation method, and effectively guarantees the stability of the robot.

Description

Technical Field

[0001] This invention belongs to the field of robotic processing technology and relates to a stability optimization method for an internally supported mobile processing robot, which is used to ensure high-quality and reliable in-tube processing by the mobile robot. Background Technology

[0002] Mobile machining robots, as crucial equipment for in-situ machining, have been widely applied in shipbuilding, aerospace, and nuclear industries. With increasing engineering demands, the number of internal machining tasks targeting narrow and confined structures such as pipes and containers is growing, and their application scenarios are gradually expanding to more complex and demanding environments such as small diameter and deep cavities. Unlike traditional fixed machining equipment, mobile machining robots lack a stable external base; their operational stability primarily relies on the force-torque balance established between the robot and its environment. During actual machining, the combined effects of cutting forces, inertial forces, and external environmental disturbances can easily disrupt the original force balance, leading to instability phenomena such as robot tipping or slippage. This results in decreased machining accuracy, job failure, and even workpiece damage, severely impacting the reliability and safety of the machining process. For complex working conditions such as cylindrical or conical structures, varying pipe diameters, and local geometric deformations within pipe environments, mobile machining robots typically employ internally supported structures with variable diameter capabilities. However, these highly compliant structures further exacerbate stability issues under machining loads. Therefore, it is urgent to carry out stability modeling and optimization research on internally supported mobile processing robots to improve their safety and operational reliability under complex tube processing conditions.

[0003] In recent years, research has been conducted on the stability issues of mobile robot processing. Patent CN118444565A discloses a stability criterion method for quadruped robots based on critical stability margin, used for robot stability assessment, but it is only applicable to robots based on planar support. Patent CN114839878A discloses an optimization method for bipedal robot walking stability based on an improved PPO algorithm, achieving walking stability. However, the use of neural networks is costly, has poor generalization ability, and is difficult to apply to industrial environments and other robot configurations. Neither of these methods is applicable to internally supported mobile processing robots. Patent CN120619943A discloses a robot and method for local grinding of municipal drainage pipes, with hydraulic push rods installed on the upper part of the robot. During processing, the robot pushes the pipe wall to resist processing forces and torques. This method can be applied to internally supported mobile processing robots, but this stability enhancement method is non-task-oriented, making it difficult to specifically enhance stability based on the specific processing task and potential instability direction. Therefore, in practical applications, relatively conservative processing parameters must be used, limiting the robot's processing performance. Summary of the Invention

[0004] The purpose of this invention is to solve the problem of processing stability of internally supported mobile processing robots operating in pipelines and containers. It provides a method for optimizing the stability of internally supported mobile processing robots. This method rationally distributes the support force according to the actual working conditions of the mobile processing robot, ensuring that the robot remains stable and enhancing its resistance to potential disturbances.

[0005] This invention employs an internally supported mobile processing robot with controllable support force, comprising a measurement and processing unit, a support unit, a motion unit, and a main shell. The measurement and processing unit is mounted at the front end of the main shell and carries a measurement and processing device. It is driven by a three-degree-of-freedom (rotational, radial, and axial) series motion mechanism to complete the processing tasks of the inner wall features of the cylinder. The support unit is installed inside the main shell and consists of cylinders. Six support units are evenly distributed circumferentially in two rows, spaced 120° apart. Each cylinder in the support unit is independently controlled, extending to adapt to the inner diameter of the tube, and the output support force can be precisely adjusted by changing the input air pressure. The motion unit is equipped with two pairs of rollers, at least one pair of which is driven by a motor, while the remaining wheels are passive. The motion unit is connected to the support unit by a hinge, possessing rotational freedom and adapting to the taper of the inner wall of the tube, ensuring that the rollers fit snugly against the inner wall.

[0006] The technical solution of the present invention is as follows:

[0007] A stability optimization method for an internally supported mobile machining robot is proposed, which optimizes stability by actively controlling the support force. First, the contact between the roller and the inner wall of the tube is analyzed to establish force constraints at the contact interface. Second, through dynamic and static analyses, the force balance relationship of the entire mobile machining robot is established. Next, potential disturbances are characterized and dynamic machining forces are discretized. Combining the established constraints, force balance relationships, and support force output constraints, a highly disturbance-resistant support force distribution model is constructed. Finally, the numerical values ​​of each support force are obtained through linear optimization calculations. The specific steps are as follows:

[0008] Step 1: Establish contact interface constraints

[0009] First, establish the contact constraints between a single roller and the inner wall of the pipe. Under quasi-static conditions, the contact force between the roller and the inner wall of the pipe conforms to the form of a friction cone. To avoid the complexity of nonlinear solutions, the friction cone is approximated as a rectangular pyramid, thereby establishing the contact force relationship of a single roller:

[0010] (1)

[0011] in, This is the component of the friction coefficient; Represents the rolling resistance coefficient; i Indicates the index of the support unit and the motion unit; kIndicates the index of the wheel within the motion unit; and They represent the contact force along the x Xianghe y Tangential component of the direction; This represents the normal component of the contact force along the z-direction; This is the operator for taking the norm of a vector; and They represent the roller edges x Xianghe y The drag coefficient of the direction.

[0012] Next, the equivalent contact constraints of the motion unit are established. Equivalent contact points are established, determined by equivalent contact forces. The relationship between the rollers is used to represent the contact action of each roller, which facilitates subsequent modeling and analysis.

[0013] (2)

[0014] in, , and They represent along x , y , z The three components are denoted as ; and respectively the roller edge x Xianghe y The relationship between the drag coefficient and the equivalent constraint of the motion unit is mapped from the single contact constraint. This refers to the contact interface constraint conditions.

[0015] Step 2: Establish a stable equilibrium relationship for the robot

[0016] First, a dynamic analysis of the machining mechanism is performed. Inertial forces are established. Cutting force The force exerted on the robot body is called the machining force. .

[0017] (3)

[0018] in, This relates to the dynamics of the machining mechanism.

[0019] Next, we will perform overall mechanical modeling of the robot. We will establish the overall force balance relationships under stable conditions:

[0020] (4)

[0021] in, For the forces acting on the robot body, The supporting forces for each motion are intermediate quantities used to represent force transmission. For the weight of the robot itself, From the coordinate system of the motion support branch { c i Transform to robot coordinate system { r The kinematic transformation relation matrix of} For the coordinate system of the machining mechanism { a 0 Transform to robot coordinate system { r The kinematic transformation relation matrix of} n The maximum index value of the support unit and the motion unit, i.e. .

[0022] Establish the internal force relationships of each motion support chain:

[0023] (5)

[0024] in, The main force applied to each motion support chain; and These are the static relationships of the forces within the branch.

[0025] The overall force balance relationship of the robot, represented by gravity, processing force, active support force, and contact force, is obtained and expressed as:

[0026] (6)

[0027] The relationship between the active support force and the contact force within the branch is as follows:

[0028] (7)

[0029] in, This represents the mechanical relationship between the contact force and the active support force within the branch chain. and This refers to the stable equilibrium relationship of the robot.

[0030] Step 3: Establish a highly disturbance-resistant support force distribution model

[0031] The first step is dynamic processing force discretization. The forces generated during the continuous dynamic processing are discretized into... N The processing forces are combined to form a processing force vector. The corresponding contact force vector is , is represented as:

[0032] (8)

[0033] Accordingly, the force balance relationship of the robot under dynamic processing force is based on Can be expanded to :

[0034] (9)

[0035] in, ; ; Represents a length of N A column vector, where all elements are equal to 1; and Then it represents a N An identity matrix of dimension 1.

[0036] Next, potential disturbances are characterized. Based on the disturbance source, the potential disturbance direction vectors acting on the robot are determined; this set of disturbance direction vectors is denoted as... ,in, , j =1~ m The amplitude of the disturbance force that the robot can resist is expressed as... The disturbance forces in each direction can be denoted as: Introduced into the force balance relationship, that is, in Expanding on the basis to :

[0037] (10)

[0038] Next, we establish the drive output force constraint. Considering that the actual force drive device has an upper limit on the output force, denoted as [missing information]. Therefore, the constraint relationship on the active support force is increased:

[0039] (11)

[0040] The constraints and equilibrium relationships formed through the above steps , , , The support force distribution model that constitutes high disturbance resistance is expressed as:

[0041] (12)

[0042] in, For each branch The set, denoted as .

[0043] Step 4: Linear Optimization Calculation

[0044] Using the linear programming method, the calculation formula is:

[0045] (13)

[0046] The distribution of active support force that ensures the stability of the mobile processing robot and has the best disturbance resistance can be obtained through calculation, thereby achieving robot stability optimization.

[0047] The beneficial effects of this invention are as follows: This invention proposes a stability optimization method for an internally supported mobile machining robot to address the risks of overturning and slippage that easily occur during in-tube machining. Through systematic analysis of constraints and balance relationships, accurate and analytical modeling of the robot's stable mechanical interaction relationships under multi-contact conditions with the circumferential pipe wall is achieved. Based on this, a highly disturbance-resistant support force allocation model is established, which can effectively characterize the influence of dynamic machining forces and external disturbances on the robot's force balance. The support force allocated using a linear programming algorithm allows the robot to be specifically reinforced according to the specific machining task and potential instability direction, significantly improving the robot's resistance to disturbances while ensuring stability. This method is applicable to different working conditions and machining tasks, and can effectively improve the machining reliability and engineering applicability of internally supported mobile machining robots. Attached Figure Description

[0048] Figure 1 A schematic diagram is established for the structure and coordinate system of the internally supported mobile processing robot. Wherein, Ⅰ—measurement and processing unit; Ⅱ—support unit; Ⅲ—motion unit; Ⅳ—main body shell; { t}—Tool coordinate system; { a 0}—Coordinate system of the machining mechanism; { r}—Robot coordinate system; { c i}—Motion support chain coordinate system; { p i}—Cylinder piston rod coordinate system; { b i}—Vehicle coordinate system; { m i,k}—Coordinate system of wheel contact point.

[0049] Figure 2 This is a flowchart of a method for optimizing the stability of an internally supported mobile processing robot.

[0050] Figure 3 A schematic diagram is created to illustrate the contact interface constraints.

[0051] Figure 4 A schematic diagram is provided to establish the stable balance relationship of the robot.

[0052] Figure 5 This is a schematic diagram of a circumferential weld seam grinding process using an internally supported mobile machining robot.

[0053] Figure 6 This diagram illustrates the cutting force that a robot can withstand under different support forces; where (a) represents the support force. (a) Characterization of the cutting force that the robot can withstand; (b) Support force The robot can withstand cutting force; (c) represents the supporting force. The cutting force that the robot can withstand is characterized. —Minimum amplitude of cutting force that can withstand in the direction of potential disturbance; —Area of ​​the cutting force domain that can withstand. Detailed Implementation

[0054] The specific embodiments of the present invention will be described in detail with reference to the accompanying drawings and technical solutions.

[0055] A type of internally supported mobile processing robot with controllable support force, its structure is as follows: Figure 1 As shown, the internally supported mobile processing robot consists of a measurement and processing unit I, a support unit II, a motion unit III, and a main shell IV. The measurement and processing unit I is installed at the front end of the main shell IV, carrying a measurement and processing device. It is driven by a three-degree-of-freedom (rotational, radial, and axial) series motion mechanism to complete the processing tasks of the inner wall features of the cylinder. The support unit II is installed inside the main shell IV, with cylinders as its main body. Six sets of support units II are evenly distributed circumferentially in two rows, spaced 120° apart. Each cylinder of the support unit II is independently controlled, capable of extending to adapt to the inner diameter of the tube and precisely adjusting the output support force by changing the input air pressure. The motion unit III is equipped with two pairs of rollers, at least one pair of which is driven by a motor, while the remaining wheels are passive. It is connected to the support unit II via hinges, has a degree of rotational freedom, and can adapt to the taper of the inner wall of the tube, ensuring that the rollers fit snugly against the inner wall.

[0056] Taking the welding seam grinding process of this robot as an example, this paper introduces the implementation process and effect of stability optimization for an internally supported mobile processing robot. The process is as follows: Figure 2 As shown.

[0057] Step 1: Establish contact interface constraints

[0058] like Figure 3 As shown, firstly, the contact constraints between a single roller and the inner wall of the pipe are established. Under quasi-static conditions, the contact force between the roller and the inner wall of the pipe conforms to the form of a friction cone. To avoid the complexity of nonlinear solutions, the friction cone is approximated as a rectangular pyramid, thereby establishing the contact force relationship of a single roller:

[0059] (14)

[0060] in, This is the component of the friction coefficient; Represents the rolling resistance coefficient; iIndicates the index of support unit II and motion unit III; k Indicates the index of the wheel within motion unit III; and These represent the tangential components of the contact force along the x and y directions, respectively. This represents the normal component of the contact force along the z-direction; This is the operator for taking the norm of a vector; and These represent the resistance coefficients of the roller along the x and y directions, respectively.

[0061] Next, the equivalent contact constraints for motion unit III are established. An equivalent contact point coordinate system is established. m i In the vehicle coordinate system { b i} Position, coordinate system direction and { b i Consistent, among which, Indicates the radius of the roller. Indicates the distance from the center of the roller axis in the z-axis to the coordinate system { b i The distance. The motion unit III contains four wheels. k =1,2…,4, therefore the equivalent contact force is expressed as:

[0062] (15)

[0063] in, Represents the coordinate system of each single contact point { m i,k} Relative to the equivalent contact point coordinate system { m i The rotation angle about the x-axis is related to the curvature of the cylinder. This represents a zero matrix with 3 rows and 1 column.

[0064] Based on the asymmetric load relationships of symmetrical structures and the Minkowski inequality, the following two relationships can be obtained:

[0065] (16)

[0066] (17)

[0067] Combining formulas (14), (15), (16), and (17), the following relationship is obtained:

[0068] (18)

[0069] in, Indicates the edge of rollers numbered 1 and 2 xTowards drag coefficient, Indicates the edge of rollers numbered 3 and 4 x Drag coefficient.

[0070] Since the equivalent contact point location is established, the rotational torque is 0. Therefore, formula (18) can be simplified to:

[0071] (19)

[0072] in, This indicates the coordinate system of rollers numbered 1 and 2 along the x-axis to the vehicle platform. b i}distance, This indicates the coordinate system of rollers numbered 3 and 4 along the x-axis to the vehicle platform. b i}distance.

[0073] U1 This refers to the contact interface constraint conditions.

[0074] Step 2: Establish a stable equilibrium relationship for the robot

[0075] like Figure 4 As shown, firstly, a dynamic analysis of the machining mechanism is performed. Inertial forces are established. Cutting force The force exerted on the robot body is called the machining force. .

[0076] (20)

[0077] in, h 1 The dynamic relationship of the machining mechanism is established using the Newton-Euler method.

[0078] Next, we will perform overall mechanical modeling of the robot. We will establish the overall force balance relationships under stable conditions:

[0079] (twenty one)

[0080] in, For the forces acting on the robot body, The supporting forces for each motion are intermediate quantities used to represent force transmission. For the weight of the robot itself, From the coordinate system of the motion support branch { c i Transform to robot coordinate system { r The kinematic transformation relation matrix of} For the coordinate system of the machining mechanism { a 0Transform to robot coordinate system { r The kinematic transformation relationship matrix of} shows that the maximum index value of support unit II and motion unit III is 6, therefore... .

[0081] Establish the internal force relationships of each motion support chain:

[0082] (twenty two)

[0083] in, The main force applied to each motion support chain, To start from the equivalent contact point coordinate system { m i Transform to the coordinate system of the motion support chain { c i The kinematic transformation relation matrix of} and The cancellation operator represents the deletion of the nth element in the matrix / vector. i row and number j List. and These are extraction operators, representing the extraction of the first element from a matrix / vector. i row and number j List( A (This is an example matrix and has no meaning.)

[0084] The overall force balance relationship of the robot, represented by gravity, processing force, active support force, and contact force, is obtained and expressed as follows:

[0085] (twenty three)

[0086] The relationship between the active support force and the contact force within the branch is as follows:

[0087] (twenty four)

[0088] and This refers to the stable equilibrium relationship of the robot.

[0089] Step 3: Establish a highly disturbance-resistant support force distribution model

[0090] The first step is dynamic processing force discretization. The forces generated during the continuous dynamic processing are discretized into... N The processing forces are combined to form a processing force vector. The corresponding contact force vector is , is represented as:

[0091] (25)

[0092] Accordingly, the force balance relationship of the robot under dynamic processing force is based on Can be expanded to :

[0093] (26)

[0094] in, ;

[0095] ; Represents a length of N A column vector, where all elements are equal to 1; and Then it represents a N An identity matrix of dimension 1.

[0096] Next, potential disturbances are characterized. Based on the disturbance source, the potential disturbance direction vectors acting on the robot are determined; this set of disturbance direction vectors is denoted as... ,in, , j =1~ m The amplitude of the disturbance force that the robot can resist is expressed as... The disturbance forces in each direction can be denoted as: Introduced into the force balance relationship, that is, in Expanding on the basis to :

[0097] (27)

[0098] Next, we establish the drive output force constraint. Considering that the actual force drive device has an upper limit on the output force, denoted as [missing information]. Therefore, the constraint relationship on the active support force is increased:

[0099] (28)

[0100] The constraints and equilibrium relationships formed through the above steps , , , The support force distribution model that constitutes high disturbance resistance is expressed as:

[0101] (29)

[0102] in, For each branch The set, denoted as .

[0103] In a scenario involving the grinding of circumferential weld seams using an internally supported mobile machining robot, such as... Figure 5As shown, the robot grinds the weld seam along its circumference. The wheel friction coefficient and rolling resistance coefficient are preset to [value missing]. and Considering the impact of vibration on friction reduction, a safety factor of 0.7 is applied, multiplying the friction and rolling resistance coefficients. Maximum cylinder force. Restricted to 1870 N In the grinding process design, the unit vector of the cutting force is set to (0, -0.9487, -0.3162, 0, 0, 0), and the maximum preset cutting force for conventional welds is (0, -150). N 50 N ,0,0,0). Regions prone to weld beads in the circumferential direction are considered potential disturbance directions, distributed within (-120°, -60°), and the cutting force vector disturbance direction is mapped to { r In the coordinate system, the resulting set of perturbation direction vectors is denoted as:

[0104] (30)

[0105] Step 4: Linear Optimization Calculation

[0106] Using the linear programming method, the calculation formula is:

[0107] (31)

[0108] The active support force required to ensure the stability of the mobile processing robot and provide optimal disturbance resistance under this working condition can be calculated. .

[0109] To demonstrate the effectiveness of robot stability optimization in this scenario, in addition to the support force distribution method proposed in this invention... Two support force control groups were also generated based on gravity balance distribution and distribution that satisfies the stability of a certain processing position. The support forces are denoted as follows: and ;in, Indicates the proposed method, This indicates the method of gravity balance distribution. This represents a distribution method that ensures stability at a certain processing position. The three sets of processing force values ​​are shown in formula (32), with units of: N .

[0110] (32)

[0111] The range of cutting forces that the robot can withstand at various angular positions along its circumference, based on the three sets of supporting forces, is as follows: Figure 6 As shown, Figure 6 As can be seen in (c), the following is adopted: The range of cutting forces that the robot can withstand in a stable state does not cover the basic cutting forces preset by the process, indicating that the stability of the robot in the entire machining area cannot be guaranteed when only a single machining position is considered. Figure 6 (a) and Figure 6 (b) indicates the adoption of and With proper support, the robot can maintain stability under the pre-set basic cutting force. In comparison, support force The minimum amplitude of the cutting force that the robot can withstand in the potential disturbance direction (-120°, -60°) is as follows. It improved by 28.7%, while also increasing the area of ​​the cutting force domain that can withstand. S The larger magnitude indicates that the support force obtained by the method involved in this invention improves the robot's resistance to disturbances while ensuring overall stability. This confirms the effectiveness of the stability optimization method for an internally supported mobile processing robot involved in this invention.

[0112] The present invention provides a stability optimization method for an internally supported mobile processing robot, which effectively ensures the stability of the robot in its internal operation tasks, significantly enhances its anti-interference ability, and guarantees the safety and reliability of processing.

Claims

1. A method for optimizing the stability of an internally supported mobile processing robot, characterized in that, First, the contact between the roller and the inner wall of the tube is analyzed to form the force constraint conditions of the contact interface. Second, through dynamic and static analysis, the force balance relationship of the entire mobile processing robot is established. Next, potential disturbances are characterized and dynamic processing forces are discretized. Combining the established constraints and force balance relationships with the support force output constraints, a highly disturbance-resistant support force distribution model is constructed. Finally, the numerical values ​​of each support force are obtained through linear optimization calculation. The specific steps are as follows: Step 1: Establish contact interface constraints First, establish the contact constraints between a single roller and the inner wall of the pipe; under quasi-static conditions, the contact force between the roller and the inner wall of the pipe conforms to the form of a friction cone; to avoid the complexity of nonlinear solutions, the friction cone is approximated as a rectangular pyramid, thereby establishing the contact force relationship of a single roller: (1) in, This is the component of the friction coefficient; Represents the rolling resistance coefficient; i Indicates the index of the support unit and the motion unit; k Indicates the index of the wheel within the motion unit; and These represent the contact forces along the x-direction and... y Tangential component of the direction; Indicates contact force along z The normal component of the direction; This is the operator for taking the norm of a vector; and They represent the roller edges x Xianghe y The drag coefficient in the direction; Next, establish the equivalent contact constraints for the motion unit; establish the equivalent contact points, determined by the equivalent contact forces. The relationship is used to represent the contact action of each roller; (2) in, , and They represent along x , y , z The three components are denoted as ; and respectively the roller edge x Xianghe y The relationship between the drag coefficient and the equivalent constraint of the motion unit is mapped from the single contact constraint. This refers to the contact interface constraints; Step 2: Establish a stable equilibrium relationship for the robot First, a dynamic analysis of the machining mechanism is performed; inertial forces are established. Cutting force The force exerted on the robot body is called the machining force. ; (3) in, The dynamic relationship of the machining mechanism; Next, we will perform overall mechanical modeling of the robot; and establish the overall force balance relationship of the robot in a stable state: (4) in, For the forces acting on the robot body, The supporting forces for each motion are intermediate quantities used to represent force transmission. For the weight of the robot itself, From the coordinate system of the motion support branch { c i Transform to robot coordinate system { r The kinematic transformation relation matrix of} For the coordinate system of the machining mechanism { a 0 Transform to robot coordinate system { r The kinematic transformation relation matrix of} n The maximum index value of the support unit and the motion unit, i.e. ; Establish the internal force relationships of each motion support chain: (5) in, The main force applied to each motion support chain; and These are the static relationships of the forces within the branch; The overall force balance relationship of the robot, represented by gravity, processing force, active support force, and contact force, is obtained and expressed as: (6) The relationship between the active support force and the contact force within the branch is as follows: (7) in, This represents the mechanical relationship between the contact force and the active support force within the branch chain. and This refers to the stable equilibrium relationship of the robot; Step 3: Establish a highly disturbance-resistant support force distribution model First, dynamic processing force discretization; the force generated during the continuous dynamic processing is discretized into... N The processing forces are combined to form a processing force vector. The corresponding contact force vector is , represented as: (8) Accordingly, the force balance relationship of the robot under dynamic processing force is based on Expand to : (9) in, ; ; Represents a length of N A column vector, where all elements are equal to 1; and Then it represents a N An identity matrix of 3D; Next, potential disturbances are characterized; based on the disturbance source, the potential disturbance direction vectors acting on the robot are determined, and the set of these disturbance direction vectors is denoted as... ,in, , j =1~ m The amplitude of the disturbance force that the robot can resist is expressed as: The disturbance forces in each direction can be denoted as: Introduced into the force balance relationship, that is, in Expanding on the basis to : (10) Next, we establish the drive output force constraint; considering that the actual force drive device has an upper limit on the output force, denoted as . Therefore, the constraint relationship on the active support force is increased: (11) The constraints and equilibrium relationships formed through the above steps , , , The support force distribution model that constitutes high disturbance resistance is expressed as: (12) in, For each branch The set, denoted as ; Step 4: Linear Optimization Calculation Using the linear programming method, the calculation formula is: (13) The active support force distribution that ensures the stability of the mobile processing robot and has the best disturbance resistance can be obtained through calculation, thereby achieving robot stability optimization.

2. The stability optimization method for an internally supported mobile processing robot according to claim 1, characterized in that, The controllable support force internal support mobile processing robot consists of a measurement and processing unit, a support unit, a motion unit, and a main shell. The measurement and processing unit is installed at the front end of the main shell and is equipped with a measurement and processing device. It is driven by a three-degree-of-freedom (rotational, radial, and axial) series motion mechanism to complete the processing tasks of the inner wall features of the cylinder. The support unit is installed inside the main shell and is based on a cylinder. Six support units are evenly distributed in two rows at 120° intervals around the perimeter. Each cylinder of the support unit is independently controlled and can extend to adapt to the inner diameter of the tube. The output support force can be adjusted by changing the input air pressure. The motion unit is equipped with two pairs of rollers, at least one pair of which is driven by a motor, and the remaining wheels are passive wheels. The motion unit and the support unit are connected by a hinge and have rotational freedom. It adapts to the taper of the inner wall of the tube to ensure that the rollers fit the inner wall.

Images