A method for anti-overturning control of a Mecanum wheel mobile operation platform

Abstract

The application relates to a roll-over prevention control method of a Mecanum wheel mobile operation platform, which comprises the following steps: establishing a roll-over model of the Mecanum wheel mobile operation platform in a world coordinate system; introducing a virtual force and torque of a mass center, establishing a force distribution model of the mass center-Mecanum wheel by statics analysis and in combination with the roll-over model in step one, which is used for the conversion of the virtual force and torque of the mass center to the force borne by the Mecanum wheel; designing a quadratic programming-based optimization algorithm to optimize and solve the force distribution model, so that the optimal ground friction force required by the Mecanum wheel is obtained; through the dynamics analysis of the Mecanum wheel, a mapping relationship between the driving motor of the Mecanum wheel and the ground friction force borne is established, so that the actual motor torque for driving the Mecanum wheel to move is obtained, and the steady-state control of the Mecanum wheel mobile operation platform under collision impact is realized.

Description

Technical Field

[0001] This invention belongs to the field of mobile robot technology and relates to an anti-tipping control method for a Mecanum wheel mobile operation platform. Background Technology

[0002] Compared to stationary robots, mobile robots offer greater range of motion, flexibility, and maneuverability. Omnidirectional mobile robots, exemplified by Mecanum wheels, can move in any direction without altering their orientation, making them even more agile. However, Mecanum wheel mobile robots are limited to planar omnidirectional motion. To expand their applications, researchers have integrated robotic arms into Mecanum wheel mobile robots, creating Mecanum wheel mobile manipulation platforms. The multi-degree-of-freedom robotic arms address the limitation of planar omnidirectional motion, while the platforms themselves enhance the arm's flexibility. This allows the Mecanum wheel mobile manipulation platforms to operate in complex and varied environments, significantly broadening their application scope. However, considering that the robotic arm inevitably comes into contact with or collides with external elements during task execution, excessive contact or impact, such as a large shock, can cause the Mecanum wheel mobile manipulation platform to tip over. This not only affects normal task execution but also poses a significant safety hazard.

[0003] Currently, many scholars have studied the anti-tipping problem of Mecanum wheel mobile operating platforms and proposed many feasible control methods. Some scholars have tried to avoid or reduce the impact of collisions by planning the platform's motion in advance, thereby improving the platform's overturning stability. Many others treat collisions as disturbances and use state observers to compensate for them when designing controllers. These methods handle general contact collisions well, but they have certain shortcomings when collisions are random and high-speed, such as impact shocks. First, random, high-speed impacts are difficult to detect and plan platform motion in advance, making them unavoidable. Second, when a Mecanum wheel mobile operating platform is subjected to an impact shock, it will inevitably overturn. This changes the mathematical model of the entire platform system, requiring a re-analysis of its kinematics and dynamics. However, most existing control methods treat collisions as disturbances and do not consider this, making it difficult for controllers designed to guarantee the anti-tipping effect of the Mecanum wheel mobile operating platform under impact shocks. Summary of the Invention

[0004] To overcome the shortcomings of existing technologies, this invention provides an anti-tipping control method for a Mecanum wheel-based mobile operating platform under collision impact. Considering that collision impact is unavoidable, this invention establishes a tilting model of the Mecanum wheel-based mobile operating platform based on the tilting situation. Then, it introduces virtual forces and torques at the center of mass to establish a force distribution model between the center of mass and the Mecanum wheel. To solve this model, an optimization algorithm based on quadratic programming is proposed, which minimizes the output force while ensuring the steady-state error and convergence speed of the Mecanum wheel-based mobile operating platform. Finally, through the dynamic model of the Mecanum wheel, the solution obtained by the optimization algorithm is transformed into motor torque for practical control. The technical solution of this invention is as follows:

[0005] A method for preventing overturning of a Mecanum wheel mobile operating platform includes the following steps:

[0006] Step 1: Establish the overturning model of the Mecanum wheel moving operation platform in the world coordinate system;

[0007] Step 2: Introduce virtual forces and moments at the center of mass. Through static analysis and in conjunction with the overturning model in Step 1, establish a force distribution model between the center of mass and the wheel, which is used to transform the virtual forces and moments at the center of mass into forces on the wheel.

[0008] Step 3: Design an optimization algorithm based on quadratic programming to optimize and solve the force distribution model in Step 2, and obtain the optimal ground friction force required by the wheat wheel;

[0009] Step 4: Through dynamic analysis of the Mecanum wheel, establish the mapping relationship between the drive motor of the Mecanum wheel and the ground friction force it experiences, obtain the motor torque that actually drives the Mecanum wheel, and realize steady-state control of the Mecanum wheel moving operation platform under collision impact.

[0010] Furthermore, assuming the mobile operating platform has three rotary joints and two robotic arms, the method for step one is as follows: number its four reels as follows: The first wheel defines the world coordinate system, the base coordinate system, the three rotational joint coordinate systems, and the four corner point coordinate systems:

[0011] World coordinate system is defined as The base coordinate system is defined as The three rotational joint coordinate systems are defined as follows: The coordinate systems of the four corner points are defined as follows: ;in These are the four contact points between the Mecanum wheel mobile platform and the ground. yes The centroid and corner points of the quadrilateral are always aligned with the three axes of the world coordinate system.

[0012] In the base coordinate system Next, determine the centroid coordinates of the Mecanum wheel moving platform. as follows:

[0013] (1)

[0014] in, The masses of the Mecanum wheel moving platform, the first robotic arm, and the second robotic arm are respectively. For the quality of the entire Mecanum wheel-moving operating platform; These are the lengths of the first and second segments of the robotic arm, respectively. These are the rotation angles of the three joints; h The height of the Mecanum wheel moving platform;

[0015] With the center of gravity of the Mecanum wheel mobile operating platform system As the apex, the contact points of the four Mecanum wheel mobile platform with the ground. Using corner points as references, connect each corner point sequentially to form four sides, thus constructing a square pyramid. The process of the Mecanum wheel moving platform overturning due to collision and impact is considered as the rotational motion of the pyramid around any one corner point. This rotational motion is described by tilt, pitch, and yaw. Under collision and impact, the pyramid sequentially rotates around a certain corner point. Axis tilt Corner, around Axis pitch Corner, around Axis deflection Angle; combining equation (1), the coordinates of the corner point are obtained through coordinate transformation. Down The position of the center of gravity of the Mecanum wheeled mobile operating platform after it overturned. As shown below:

[0016] (2)

[0017] in The homogeneous transformation matrix is ​​expressed as follows:

[0018] (3)

[0019] In equation (3), around the corner point During rotation, ; around the corner point During rotation, ; around the corner point During rotation, ; around the corner point During rotation, ; ; aand l These represent the length and width of the Mecanum wheel moving platform, respectively.

[0020] It can be obtained in world coordinates Below, the coordinates of the center of mass of the Mecanum wheeled mobile operating platform after it overturned. As shown below:

[0021] (4)

[0022] Equation (4) is the overturning model of the Knum wheel mobile operating platform, where Corner points In the world coordinate system The lower position, .

[0023] Furthermore, the method for step two is as follows: The forces acting on the entire Mecanum wheel-mounted mobile operating platform system—the ground reaction force... and gravity Concentrated at the center of mass, forming virtual force and virtual torque After decomposition in the world coordinate system, virtual forces in three directions are obtained. And virtual torques in three directions The displacement of the center of mass in the three directions in world coordinates. and attitude angles around the three axes The required virtual force and torque are generated using a PID controller, with the following control law:

[0024] (5)

[0025] in, ; ; The desired center of mass pose; These are proportional gain, integral gain, and derivative gain, respectively.

[0026] Based on the number of Mecanum wheel liftoffs, the overturning of the Mecanum wheel mobile operating platform under collision impact is divided into the following three categories: one Mecanum wheel liftoff, two Mecanum wheels liftoffs, and three Mecanum wheels liftoffs. Next, corresponding center of mass-Mecanum wheel force distribution models will be established for these three cases respectively.

[0027] (1) In the case of one wheel leaving the ground, the corresponding center of mass-McMoRan force distribution model is established as follows:

[0028] (6)

[0029] In the formula These represent the ground reaction forces acting on the three wheat wheels that are not lifted off the ground in the world coordinate system; These represent the position vectors of the three contact points between the wheat wheel and the ground, which are not off the ground, relative to the center of mass.

[0030] (2) When both wheels are off the ground, the corresponding center of mass-wheel force distribution model is as follows:

[0031] (7)

[0032] In the formula These represent the ground reaction forces experienced by the two wheat wheels that are not lifted off the ground in the world coordinate system. These represent the position vectors of the two contact points between the wheat wheel and the ground relative to the center of mass;

[0033] (3) When all three wheels are off the ground, the corresponding center of gravity-wheel force distribution model is as follows:

[0034] (8)

[0035] In the formula This represents the ground reaction force experienced by the wheat sheave that is not lifted off the ground in the world coordinate system; This represents the position vector of the point of contact between the wheat sheave that is not off the ground and the ground, relative to the center of mass.

[0036] Furthermore, the method for step three is as follows:

[0037] The centroid-McLean force distribution model expressed by equations (6), (7), and (8) can be written as a unified expression: The difference between each case is only the matrix. There are differences; in order to solve At the same time, it also guarantees To minimize the value of in order to reduce the output force, the objective function is established as follows:

[0038] (9)

[0039] in, The weighting matrix for the virtual force and torque at the center of mass is used. It is a positive definite diagonal matrix; To minimize the weight matrix that satisfies the optimization requirement for the output force, It is also a positive definite diagonal matrix with order and They have the same order;

[0040] Ignoring the fourth term, the force distribution problem is transformed into solving a constrained quadratic programming problem:

[0041] (10)

[0042] Equation (10) is transformed into a QP optimization problem, in the following form:

[0043] (11)

[0044] in,

[0045] (12)

[0046] Let the coefficient of friction of the ground be... Then the constraint condition for friction is shown in equation (13):

[0047] (13)

[0048] (14)

[0049] In equation (14) This represents the acceleration of the center of mass of the moving platform along the Z-axis in the world coordinate system using the Mecanum wheel. For ground-based Mecanum wheeled mobile operating platform along Total support force in the direction .

[0050] Furthermore, the method for step four is as follows:

[0051] The mapping relationship between the drive motors of wheat wheels 1 and 3 and the ground friction force they experience is as follows:

[0052] (15)

[0053] The mapping relationship between the drive motors of the No. 2 and No. 4 wheat wheels and the ground friction force they experience is as follows:

[0054] (16)

[0055] in , It is the radius of the wheat wheel. This refers to the output torque of the motor in the Mailun wheel. and It is the acceleration of the point of contact between the wheat wheel and the ground in the world coordinate system;

[0056] Achieve steady-state control of the Mecanum wheel-driven operating platform under collision impact. Attached Figure Description

[0057] Figure 1 Schematic diagram of the Mecanum wheel moving operation platform.

[0058] Figure 2 : Overturning model of Mecanum wheel mobile operating platform.

[0059] Figure 3 Overall control block diagram.

[0060] Figure 4 Schematic diagram of force distribution model of Mecanum wheel moving operation platform under the condition of one wheel leaving the ground.

[0061] Figure 5 Schematic diagram of wheat wheel dynamics analysis.

[0062] Figure 6 : Comparison curves of two attitude angles of the Mecanum wheel moving operation platform after being subjected to a collision impact, with and without the control method of this invention. Detailed Implementation

[0063] The present invention will now be further described in conjunction with the accompanying drawings and embodiments.

[0064] Step 1: Overturning model of the Mecanum wheel moving operation platform

[0065] This invention assumes that the mass distribution of the Mecanum wheel moving operation platform is uniform, and its four Mecanum wheels are numbered as follows: The number wheel provides the definitions of each coordinate system, as follows: Figure 1 As shown. The world coordinate system is defined as follows. The base coordinate system is defined as The three rotational joint coordinate systems are defined as follows: The coordinate systems of the four corner points are defined as follows: .in These are the four contact points between the Mecanum wheel mobile platform and the ground. yes The centroid and corner points of the quadrilateral are always aligned with the three axes of the world coordinate system.

[0066] First, in the base coordinate system Next, determine the centroid coordinates of the Mecanum wheel moving platform. as follows:

[0067] (1)

[0068] in, The masses of the Mecanum wheel moving platform, the first robotic arm, and the second robotic arm are respectively. For the quality of the entire Mecanum wheel-moving operating platform; These are the lengths of the first and second segments of the robotic arm, respectively. These are the rotation angles of the three joints; These are the length, width, and height of the Mecanum wheeled mobile platform, respectively.

[0069] Next, considering that the Mecanum wheel-driven operating platform would overturn after a collision, in order to determine the location of the center of gravity, such as... Figure 2 As shown, the center of mass of the Mecanum wheel mobile operating platform system is... As the apex, the contact points of the four Mecanum wheel mobile platform with the ground. Using corner points as references, four edges are sequentially connected to form a quadrangular pyramid. This constructs the quadrangular pyramid, allowing the collision and overturning process of the Mecanum wheel-driven platform to be viewed as the pyramid rotating around any one of its corner points (edges). This rotational motion can be described by tilting, pitching, and yaw. For ease of modeling the overturning, it is stipulated that under collision impact, the quadrangular pyramid rotates around a certain corner point sequentially. Axis tilt Corner, around Axis pitch Corner, around Axis deflection Angle. When Angle or When the angle is zero, the square pyramid becomes a rotation about one of its sides. Therefore, rotation about a side is a special case of rotation about a corner point. Combining equation (1), we can obtain the coordinates of the corner point in the coordinate system through coordinate transformation. Down The position of the center of gravity of the Mecanum wheeled mobile operating platform after it overturned. As shown below:

[0070] (2)

[0071] in The homogeneous transformation matrix is ​​expressed as follows:

[0072] (3)

[0073] In the above formula, around the corner point During rotation, ; around the corner point During rotation, ; around the corner point During rotation, ; around the corner point During rotation, . .

[0074] Ultimately, the world coordinates can be obtained. Below, the coordinates of the center of mass of the Mecanum wheeled mobile operating platform after it overturned. As shown below:

[0075] (4)

[0076] The above formula is the overturning model of the Mecanum wheel moving operation platform, where Rotation corner points In the world coordinate system At the lower position, because the rotation corner point is always in contact with the ground, therefore .

[0077] Step 2: Introduce virtual forces and moments at the center of mass. Through static analysis and combining the overturning model from Step 1, establish a force distribution model between the center of mass and the wheat wheel.

[0078] First, this invention addresses the forces acting on the entire Mecanum wheel mobile operating platform system—the ground reaction force. and gravity All concentrated at the center of mass, forming a virtual force. and virtual torque After decomposition in the world coordinate system, virtual forces in three directions are obtained. And virtual torques in three directions This corresponds exactly to the displacement of the center of mass in the three directions in world coordinates. and attitude angles around the three axes Here, a pure PID controller is used directly to generate the required virtual force and torque, with the control law as follows:

[0079] (5)

[0080] in, ; ; The desired center of mass pose; These are proportional gain, integral gain, and derivative gain, respectively.

[0081] Based on the number of Mecanum wheel liftoffs, this invention categorizes the overturning of the Mecanum wheel mobile operating platform under collision impact into three types: one Mecanum wheel liftoff, two Mecanum wheels liftoffs, and three Mecanum wheels liftoffs. Next, corresponding center-of-mass-Mecanum wheel force distribution models are established for each of these three scenarios.

[0082] (1) The case where one round leaves the ground. For example... Figure 4 As shown, the corresponding centroid-McLummus force distribution model is established as follows:

[0083] (6)

[0084] In the formula These represent the ground reaction forces acting on the three wheat wheels that are not lifted off the ground in the world coordinate system; These represent the position vectors of the three contact points between the still-grounded wheat wheel and the ground relative to the center of mass.

[0085] (2) The case where both wheels are off the ground. The corresponding center of gravity-wheel force distribution model is as follows:

[0086] (7)

[0087] In the formula These represent the ground reaction forces experienced by the two wheat wheels that are not lifted off the ground in the world coordinate system. These represent the position vectors of the two contact points between the wheat wheel and the ground relative to the center of mass.

[0088] (3) The case where all three wheels are off the ground. The corresponding center of gravity-wheel force distribution model is as follows:

[0089] (8)

[0090] In the formula This represents the ground reaction force experienced by the wheat sheave that is not lifted off the ground in the world coordinate system; This represents the position vector of the point of contact between the wheat sheave that is not off the ground and the ground, relative to the center of mass.

[0091] Step 3: Design an optimization algorithm based on quadratic programming to optimize and solve the force distribution model in Step 2.

[0092] Although the centroid-McLean force distribution models expressed in equations (6), (7), and (8) differ in form, they can all be written as a unified expression: The only difference is the matrix. They are different. To solve... At the same time, it also guarantees To minimize the value of in order to reduce the output force, the objective function is established as follows:

[0093] (9)

[0094] in, The weighting matrix for the virtual force and torque at the center of mass is used. It is a positive definite diagonal matrix; To minimize the weight matrix that satisfies the optimization requirement for the output force, It is also a positive definite diagonal matrix with order and They have the same order.

[0095] Based on the preceding analysis, we need to find the minimum value of the objective function. Since the fourth term in equation (9) is a constant term, it can be ignored when solving the extremum problem. Therefore, the force distribution problem is transformed into solving a constrained quadratic programming problem:

[0096] (10)

[0097] To utilize existing function libraries in computer solving, accelerate computation, and ensure real-time optimization, the above equation is further transformed into a standard QP optimization problem, as follows:

[0098] (11)

[0099] in,

[0100] (12)

[0101] Assuming the ground friction coefficient is The constraint condition for friction is shown in equation (13). Due to the supporting force of the ground on the wheat wheel... It belongs to passive force, which is objectively determined by the motion state of the system, as shown in equation (14). It cannot be actively controlled, so in quadratic programming we first solve for it. Then, it is added as a known force to the constraints, only for controllable frictional forces. Perform a quadratic programming approach to find the optimal solution.

[0102] (13)

[0103] (14)

[0104] In equation (14) This represents the acceleration of the center of mass of the moving platform along the Z-axis in the world coordinate system using the Mecanum wheel. For ground-based Mecanum wheeled mobile operating platform along Total support force in the direction Because the platform's attitude and center of gravity don't change much after one liftoff, and the remaining two wheels are roughly symmetrically distributed on either side of the center of gravity after two liftoffs, we can approximate the total support force... Apply evenly to each wheat wheel.

[0105] Step 4: Through dynamic analysis of the Mecanum wheel, establish the mapping relationship between the drive motor of the Mecanum wheel and the ground friction force it experiences.

[0106] like Figure 5 As shown, the mapping relationship between the drive motors of wheat wheels 1 and 3 and the ground friction force they experience is as follows:

[0107] (15)

[0108] The mapping relationship between the drive motors of the No. 2 and No. 4 wheat wheels and the ground friction force they experience is as follows:

[0109] (16)

[0110] in , It is the radius of the wheat wheel. This refers to the output torque of the motor in the Mailun wheel. and It is the acceleration of the point of contact between the wheat wheel and the ground in the world coordinate system.

[0111] Thus, by introducing virtual force and torque at the center of mass and combining it with the overturning model, we established a force distribution model between the center of mass and the Mecanum wheel. Using an optimization method based on quadratic programming, we derived the optimal force on the Mecanum wheel. Finally, by mapping the ground friction force to the torque of the Mecanum wheel drive motor, we obtained the control torque of the motor, thereby achieving steady-state control of the Mecanum wheel moving operation platform under collision impact.

[0112] To verify the effectiveness and feasibility of the anti-tipping control method for the Mecanum wheel mobile operating platform provided in this invention, a simulation experiment was conducted using MATLAB software to test the control algorithm designed in this invention. The control objective is to control two attitude angles related to tipping when the Mecanum wheel mobile operating platform is subjected to a collision impact— and It can approach zero as quickly as possible.

[0113] The mass of the Mecanum wheel moving platform used in this simulation experiment is... ,long ,Width ,high The mass of the first robotic arm ,long The second segment of the robotic arm's mass ,long The magnitude of the impact force is The duration of action is The point of action is the end of the second segment of the robotic arm.

[0114] from Figure 6 It can be seen that after a collision, the Mecanum wheel-operated mobile platform will overturn significantly without control, approximately... about, The angle was reached. This indicates that the platform has completely overturned and fallen to the ground. After using the control method proposed in this invention, it can be... The maximum overshoot of the angle is controlled within Within, and only A stable state can be reached by moving left and right, while simultaneously... The maximum overshoot of the angle is controlled within Within, and only less than This allows the platform to reach a stable state. Therefore, the Mecanum wheel mobile operation platform anti-tipping control method proposed in this invention can effectively adjust the platform's attitude angle under collision impact, effectively preventing platform tipping, and has excellent transient performance.

Claims

1. A method for preventing overturning of a Mecanum wheel-operated platform, comprising the following steps: Step 1: In the world coordinate system, establish the overturning model of the Mecanum wheel mobile operating platform. Assume the mobile operating platform has three rotary joints and two robotic arms, as follows: The four Mecanum wheels are numbered as The wheel number, the world coordinate system, the base coordinate system, the three rotary joint coordinate systems, and the four corner point coordinate systems are defined. The world coordinate system is defined as , the base coordinate system is defined as , three rotary joint coordinate systems are defined as , four corner point coordinate systems are defined as ; wherein are four contact points of the Mecanum wheel mobile operation platform with the ground, is the center of the quadrilateral composed of , the directions of the three axes of the corner point coordinate system are always the same as the directions of the three axes of the world coordinate system; In the base coordinate system Next, determine the centroid coordinates of the Mecanum wheel moving platform. as follows: (1) in, The masses of the Mecanum wheel moving operation platform, the first robotic arm, and the second robotic arm are respectively. For the quality of the entire Mecanum wheel-moving operating platform; These are the lengths of the first and second segments of the robotic arm, respectively. These are the rotation angles of the three joints; h The height of the Mecanum wheel-driven operating platform; With the center of gravity of the Mecanum wheel mobile operating platform system As the apex, the contact points between the four Mecanum wheels of the Mecanum wheel moving operation platform and the ground. Using corner points as references, connect each corner point sequentially to form four sides, thus constructing a square pyramid. The process of the Mecanum wheel moving platform overturning due to collision and impact is considered as the rotational motion of the pyramid around any one corner point. This rotational motion is described by tilt, pitch, and yaw. Under collision and impact, the pyramid sequentially rotates around a certain corner point. Axis tilt Corner, around Axis pitch Corner, around Axis deflection Angle; combining equation (1), the coordinates of the corner point are obtained through coordinate transformation. Down The position of the center of gravity of the Mecanum wheeled mobile operating platform after it overturned. As shown below: （2） in The homogeneous transformation matrix is ​​expressed as follows: （3） In equation (3), around the corner point During rotation, ; around the corner point During rotation, ; around the corner point During rotation, ; around the corner point During rotation, ; ; a and l These represent the length and width of the Mecanum wheel-driven operating platform, respectively. In the world coordinate system Below, the coordinates of the center of mass of the Mecanum wheeled mobile operating platform after it overturned. As shown below: （4） Equation (4) is the overturning model of the Mecanum wheel mobile operating platform, where Corner points In the world coordinate system The lower position, ; Step Two: Introduce virtual forces and moments at the center of mass. Through static analysis and combining the overturning model from Step One, establish a force distribution model between the center of mass and the Mecanum wheel. This model is used to transform the virtual forces and moments at the center of mass into forces acting on the Mecanum wheel. The method is as follows: The forces acting on the entire Mecanum wheel mobile operating platform system—the ground reaction force and gravity Concentrated at the center of mass, forming virtual force and virtual torque After decomposition in the world coordinate system, virtual forces in three directions are obtained. And virtual torques in three directions The displacement of the center of mass in the three directions in the world coordinate system. and attitude angles around the three axes The required virtual force and torque are generated using a PID controller, with the control law as follows: （5） in, ; ; The desired center of mass pose; These are proportional gain, integral gain, and derivative gain, respectively. Based on the number of Mecanum wheels that are off the ground, the overturning of the Mecanum wheel mobile operating platform under collision impact is divided into the following three categories: one Mecanum wheel off the ground, two Mecanum wheels off the ground, and three Mecanum wheels off the ground; next, corresponding center of mass-Mecanum wheel force distribution models are established for these three cases respectively. (1) In the case where one wheel is off the ground, the corresponding center of mass-Mecanum wheel force distribution model is established as follows: （6） In the formula These represent the ground reaction forces acting on the three Mecanum wheels that are not off the ground in the world coordinate system; These represent the position vectors of the three contact points between the Mecanum wheel (which is not off the ground) and the ground relative to the center of mass; (2) When both wheels are off the ground, the corresponding center of gravity-Mecanum wheel force distribution model is as follows: （7） In the formula These represent the ground reaction forces acting on the two Mecanum wheels that are not off the ground in the world coordinate system. These represent the position vectors of the two contact points between the Mecanum wheel (which is not off the ground) and the ground, relative to the center of mass. (3) When all three wheels are off the ground, the corresponding center of gravity-Mecanum wheel force distribution model is as follows: （8） In the formula This represents the ground reaction force experienced by the Mecanum wheel that is not lifted off the ground in the world coordinate system; This represents the position vector of the point of contact between the Mecanum wheel that is not off the ground and the ground, relative to the center of mass.

2. The anti-overturning control method according to claim 1, characterized in that, The method for step three is as follows: The center-of-mass-Mecanum wheel force distribution model expressed by equations (6), (7), and (8) can be written as a unified expression: The difference between each case is only the matrix. There are differences; in order to solve At the same time, it also guarantees To minimize the value of in order to reduce the output force, the objective function is established as follows: (9) in, The weighting matrix for the virtual force and torque at the center of mass is used. It is a positive definite diagonal matrix; To minimize the weight matrix that satisfies the optimization requirement for the output force, It is also a positive definite diagonal matrix with order and They have the same order; Ignoring the fourth term, the force distribution problem is transformed into solving a constrained quadratic programming problem: （10） Equation (10) is transformed into a QP optimization problem, in the following form: （11） in, （12） Let the coefficient of friction of the ground be... Then the constraint condition for friction is shown in equation (13): （13） （14） In equation (14) This represents the acceleration of the center of mass of the moving platform along the Z-axis in the world coordinate system using the Mecanum wheel. For ground-based Mecanum wheeled mobile operating platform along Total support force in the direction ; Step 3: Design an optimization algorithm based on quadratic programming to optimize and solve the force distribution model in Step 2, and obtain the optimal ground friction force required by the Mecanum wheel; Step 4: Through dynamic analysis of the Mecanum wheel, establish the mapping relationship between the drive motor of the Mecanum wheel and the ground friction force it experiences, obtain the motor torque that actually drives the Mecanum wheel, and realize steady-state control of the Mecanum wheel moving operation platform under collision impact.

3. The anti-overturning control method according to claim 1, characterized in that, The method for step four is as follows: The mapping relationship between the drive motors of Mecanum wheels 1 and 3 and the ground friction forces they experience is as follows: （15） The mapping relationship between the drive motors of Mecanum wheels 2 and 4 and the ground friction forces they experience is as follows: （16） in , It is the radius of the Mecanum wheel. The motor output torque for the Mecanum wheel; and It is the acceleration of the point of contact between the Mecanum wheel and the ground in the world coordinate system; Achieve steady-state control of the Mecanum wheel-driven operating platform under collision impact.

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