Anti-rod-falling device based on inertia detection and dynamic balance algorithm

Abstract

The invention discloses an anti-rod-falling device based on inertia detection and a dynamic balance algorithm, and relates to the technical field of automatic control. The device comprises an anti-falling rod body, a sensor system and a control system, the sensor system is used for acquiring inertial state parameters of the rod body of the anti-falling rod in real time and constructing inertial state parameter vectors; the control system is used for analyzing the real-time energy-momentum coupling state of the rod body of the anti-falling rod based on the obtained inertial state parameters so as to obtain the real-time total energy of the rod body of the anti-falling rod, and then calculating the stability tensor of the rod body of the anti-falling rod on the differential manifold; calculating the maximum Lyapunov index by combining the inertial state parameter vector, and predicting the instability prediction time of the rod body of the anti-falling rod; and according to the instability prediction time, the optimal compensation force needed for preventing the anti-falling rod body from falling is calculated, and the motion of the anti-falling rod body is controlled. The method has higher accuracy, adaptivity and reliability.

Description

Technical Field

[0001] This application relates to the field of automatic control technology, and particularly to a falling prevention rod device based on inertial detection and dynamic balance algorithm. Background Art

[0002] In construction, traffic facilities, industrial equipment, and other high-risk working environments, the falling prevention rod device, as an important safety protection equipment, is widely used to prevent people or equipment from falling due to accidental instability. Currently, there are various types of falling prevention rod systems on the market, including mechanical fixed support structures, elastic support structures, damping vibration reduction devices, etc. These existing technologies provide a certain degree of fall protection, but there are still many limitations, making their stability and adaptability in complex environments challenged. Especially in high-dynamic environments, such as aerial work platforms under strong wind or support structures during earthquakes, traditional falling prevention rod systems often struggle to achieve intelligent and stable control, resulting in the equipment being greatly affected by external disturbances and thus reducing safety. Therefore, aiming at the deficiencies of the existing technologies, a falling prevention rod device based on inertial detection and dynamic balance algorithm is proposed, which can effectively monitor the movement state of the rod, predict possible instability trends, and apply optimal compensation forces to ensure that the rod always remains within the stable range, improving safety performance and service life.

[0003] The falling prevention rod technologies on the current market are mainly divided into several categories. The most common one is the fixed falling prevention rod. This type of falling prevention rod usually adopts a rigid support structure and directly fixes the rod to the installation point, such as the temporary safety guardrails at construction sites and the limit rods of industrial equipment. Although such structures can provide a certain degree of protection, they lack active adjustment capabilities. When subjected to external forces such as strong wind, earthquake, and mechanical shock, they are prone to support failure, resulting in the rod falling off or deforming. In addition, such devices generally cannot adapt to different usage environments and are difficult to adjust according to actual working conditions after fixed installation, having relatively large limitations. Another relatively common technology is the elastic support falling prevention rod, which mainly relies on springs, dampers, or flexible materials to provide a certain degree of buffering effect to reduce the risk of instability caused by external impacts. Such devices can improve the anti-impact ability to a certain extent, but due to the lack of precise dynamic adjustment capabilities, they still cannot provide efficient stability control in complex environments. For example, in a high-altitude environment with strong wind speed, the swing amplitude of the rod may exceed the recovery ability of the elastic support, resulting in equipment damage or falling. In addition, the damping parameters of elastic support devices are usually fixed and difficult to adaptively adjust according to different environmental conditions. Therefore, fatigue failure may occur during strong impacts or long-term use, affecting safety. Summary of the Invention

[0004] The embodiment of the present application provides a falling prevention rod device based on inertial detection and dynamic balance algorithm, which realizes accurate evaluation of the stability of the rod body and early prediction of the instability time. Compared with the traditional falling prevention rod technology, the present invention can not only analyze the dynamic evolution trend of the rod body in real time, but also calculate the optimal compensation force before the rod body is about to become unstable, and actively adjust the stability of the rod body through an intelligent control strategy. The device has higher accuracy, self - adaptability and reliability, is applicable to various complex environments, effectively improves the safety performance of the falling prevention rod, and reduces the falling risk.

[0005] The embodiment of the present application provides a falling prevention rod device based on inertial detection and dynamic balance algorithm. The device includes: a falling prevention rod body, a sensor system and a control system; the sensor system is used to obtain the inertial state parameters of the falling prevention rod body in real time and construct an inertial state parameter vector; the control system is used to analyze the real - time energy - momentum coupling state of the falling prevention rod body based on the obtained inertial state parameters to obtain the real - time total energy of the falling prevention rod body, then calculate the stability tensor of the falling prevention rod body on the micro - differential manifold; construct the state evolution function of the falling prevention rod body, calculate the maximum Lyapunov exponent in combination with the inertial state parameter vector, and predict the instability prediction time of the falling prevention rod body according to the maximum Lyapunov exponent; calculate the optimal compensation force required to prevent the falling prevention rod body from falling according to the instability prediction time, and control the movement of the falling prevention rod body according to the optimal compensation force.

[0006] Further, the sensor system includes: a three - dimensional velocity sensor, a three - dimensional acceleration sensor, a three - axis angular displacement sensor, a three - axis angular velocity sensor and a three - axis angular acceleration sensor; the inertial state parameter vector is where t is time; r(t) is the three - dimensional position coordinate of the centroid of the falling prevention rod body; v(t) is the three - dimensional velocity of the centroid of the falling prevention rod body; a(t) is the three - dimensional acceleration of the centroid of the falling prevention rod body; θ(t) is the angular displacement of the falling prevention rod body on three axes; w(t) is the angular velocity of the falling prevention rod body on three axes; α(t) is the angular acceleration of the falling prevention rod body on three axes.

[0007] Further, the real - time energy - momentum coupling state of the falling prevention rod body is analyzed through the following formula to obtain the real - time total energy of the falling prevention rod body:

[0008]

[0009] where E total (t) is the real - time total energy; g is the gravitational acceleration; m is the main body mass of the falling prevention rod body; α is the non - linear gravitational field correction coefficient, and the value range is from 0.2 to 0.5; h(t) is the centroid height function of the falling prevention rod body; z(t) is the Z - axis component of the three - dimensional position coordinate r(t) of the centroid of the falling prevention rod body; I x 、I yand I z are the principal moments of inertia of the anti - falling rod body about the X - axis, Y - axis, and Z - axis respectively, which are fixed values; ω x (t), ω y (t), and ω z (t) are the components of ω(t) about the X - axis, Y - axis, and Z - axis respectively; z is the integration variable.

[0010] Furthermore, the centroid height function of the anti - falling rod body is expressed by the following formula:

[0011]

[0012] where θ x (t) and θ y (t) are the components of θ(t) about the X - axis and Y - axis respectively; L is the distance from the centroid of the anti - falling rod body to the fulcrum.

[0013] Furthermore, the stability tensor of the anti - falling rod body is calculated on the differential manifold by the following formula:

[0014]

[0015] where ∑ stability (t) is the stability tensor; T E (t) is the energy contribution tensor; T θ (t) is the angular displacement contribution tensor; T ω (t) is the angular velocity contribution tensor;

[0016]

[0017] where E ref is the reference energy value, which is a set value; σ E is the energy sensitivity parameter, which is a set value; I3 is the 3×3 identity matrix;

[0018]

[0019] where is the tensor product; θ critical is the critical inclination angle;

[0020]

[0021] where ω ref is the reference angular velocity; R ω (t) is the rotation matrix about the axis; ω ref is the reference angular velocity.

[0022] Furthermore, the maximum Lyapunov exponent λ max (t) is calculated by the following formula:

[0023]

[0024] Among them, Δt is the time step; f(S(t)) is the state evolution function of the anti-falling rod body; ||·||2 is the L2 norm.

[0025] Furthermore, the state evolution function of the anti-falling rod body is expressed by the following formula:

[0026]

[0027] Among them, T is the Jacobian matrix from angular velocity to angular displacement; S is the inertia tensor of the anti-falling rod body.

[0028] Furthermore, through the following formula, predict the instability prediction time T of the anti-falling rod body failure (t):

[0029]

[0030] Among them, ||·|| F is the F norm; ||·|| is the L1 norm; tr(·) represents calculating the trace of the matrix; ρ critical is the critical stability threshold, which is a set value.

[0031] Furthermore, through the following formula, calculate the optimal compensation force required to prevent the anti-falling rod body from falling according to the instability prediction time:

[0032]

[0033] Among them, F comp (t) is the optimal compensation force.

[0034] A falling prevention rod device based on inertial detection and dynamic balance algorithm provided by the present application has the following beneficial effects: The present invention adopts a stability calculation method based on energy-momentum coupling analysis, fundamentally improving the stability evaluation ability of the falling prevention rod system. Most of the existing technologies adopt simple feedback control of angular displacement or angular velocity, failing to consider the influence of the change of the overall energy of the rod on stability. The present invention accurately describes the stability state of the system by calculating the total energy of the falling prevention rod and combining various factors such as potential energy, kinetic energy, and rotational energy. The system can identify the distribution of energy in different directions, thereby judging whether the falling prevention rod is in a stable state and calculating the stability tensor of the system accordingly. The calculation method of the stability tensor can comprehensively depict the stability change trend of the falling prevention rod, enabling the system to not only identify the current stable state but also predict possible instability situations. Compared with the traditional single-variable analysis method, the energy-momentum coupling analysis method of the present invention can more comprehensively reflect the true state of the system and improve the accuracy of stability evaluation. The present invention introduces the calculation method of the maximum Lyapunov exponent to evaluate the sensitivity of the system to initial small perturbations. Traditional methods usually rely on fixed angle or speed thresholds to judge whether the system enters the unstable state, but this method has large misjudgment and hysteresis. The present invention can predict the instability time of the rod in real time by calculating the Jacobian matrix of the system state evolution function and using the Lyapunov exponent to evaluate the amplification trend of the perturbation. This prediction method based on nonlinear dynamics analysis enables the system to early warn the unstable region that the rod may enter and provides a time window for subsequent control strategies. Compared with the traditional hysteresis control method, the instability prediction method of the present invention can not only improve the response speed of the falling prevention rod but also reduce false alarms and false triggers, improving the reliability of the system. For the compensation control of the falling prevention rod, the present invention provides an optimal compensation force calculation method to ensure that the system can apply accurate correction torque at the appropriate time to restore the stability of the rod. The existing falling prevention rod control systems usually adopt fixed torque or simple elastic support methods for restoration, but these methods are difficult to adapt to complex environmental changes and are prone to problems such as insufficient compensation or over-compensation. The compensation force calculation method of the present invention is based on multiple factors such as the instability prediction time, the total energy of the system, and the angular momentum, and calculates the direction and magnitude of the optimal compensation force through optimization. When the system is close to the unstable state, it can dynamically adjust the compensation force according to the real-time calculation results, making the compensation process more accurate and efficient. This intelligent compensation control method enables the falling prevention rod not only to passively respond to the instability situation but also to actively adjust the control strategy to achieve the maximum stability restoration with the minimum energy consumption. BRIEF DESCRIPTION OF THE DRAWINGS

[0035] The following will make the technical solutions and other beneficial effects of the present application obvious by describing the specific embodiments of the present application in detail in conjunction with the drawings.

[0036] Figure 1 This is a schematic structural diagram of a falling prevention rod device based on inertial detection and dynamic balance algorithm provided by an embodiment of the present invention. Specific embodiments

[0037] Next, the technical solutions in the embodiments of the present application will be clearly and completely described in conjunction with the accompanying drawings in the embodiments of the present application. Obviously, the described embodiments are only a part of the embodiments of the present application, rather than all the embodiments. Based on the embodiments in the present application, all other embodiments obtained by those skilled in the art without creative efforts belong to the scope of protection of the present application.

[0038] Embodiment 1: Refer to Figure 1 , a falling prevention rod device based on inertial detection and dynamic balance algorithm, the device includes: a falling prevention rod body, a sensor system, and a control system; the sensor system is used to obtain the inertial state parameters of the falling prevention rod body in real time and construct an inertial state parameter vector; the control system is used to analyze the real-time energy-momentum coupling state of the falling prevention rod body based on the obtained inertial state parameters to obtain the real-time total energy of the falling prevention rod body, and then calculate the stability tensor of the falling prevention rod body on the microdifferential manifold; construct the state evolution function of the falling prevention rod body, calculate the maximum Lyapunov exponent in combination with the inertial state parameter vector, and predict the instability prediction time of the falling prevention rod body according to the maximum Lyapunov exponent; calculate the optimal compensation force required to prevent the falling prevention rod body from falling according to the instability prediction time, and control the movement of the falling prevention rod body according to the optimal compensation force.

[0039] Specifically, the control system first obtains the inertial state parameters of the anti-falling rod from the inertial measurement unit. These parameters include key variables such as the acceleration, angular velocity, and angular displacement of the anti-falling rod. The inertial measurement unit is usually composed of high-precision accelerometers and gyroscopes, and combines the Kalman filtering algorithm for data fusion to eliminate noise and improve the accuracy of the data. The obtained inertial state parameters are constructed into an inertial state parameter vector, which contains the position information, velocity information, and attitude information of the anti-falling rod, and becomes the basic data for subsequent energy calculation and stability analysis. After obtaining the inertial state parameters, the system needs to analyze the energy-momentum coupling state of the anti-falling rod. The movement of the anti-falling rod is a complex non-linear dynamic system, affected by various factors such as gravity, inertial force, and constraint force. Therefore, it is difficult to effectively predict its state evolution trend solely by linear analysis. To accurately describe its state, the control system calculates the total energy of the anti-falling rod, which includes kinetic energy and potential energy. The kinetic energy is jointly determined by the translational motion and rotational motion of the anti-falling rod, while the potential energy depends on the height change of the anti-falling rod. Through the law of conservation of energy, the system can dynamically calculate the energy distribution of the anti-falling rod in different states, thereby determining its motion trend. In addition, the system also analyzes the conservation relationship of momentum, calculates the changes in angular momentum and linear momentum of the anti-falling rod at different time points, and these variables reflect the motion stability of the anti-falling rod and are used for further stability analysis.

[0040] After obtaining the real-time energy of the anti-falling rod, the system needs to calculate its stability tensor to evaluate the stability in the current state. The stability tensor is a mathematical quantity constructed based on the theory of differential manifolds, which describes the stability distribution of the anti-falling rod in the phase space. Since the movement trajectory of the anti-falling rod can be regarded as a dynamic system on a differential manifold, the stability of the system can be judged by calculating the stability tensor. The calculation of the stability tensor involves solving the second-order partial derivatives of the energy function, that is, analyzing the local curvature characteristics of the energy function. If all the eigenvalues of the stability tensor are positive, it means that the system is in a locally stable state; if negative eigenvalues appear, it indicates that the system may enter an unstable state, and thus control measures need to be taken for compensation. After determining the stability of the anti-falling rod, the control system further calculates its maximum Lyapunov exponent to predict the time of instability. The Lyapunov exponent is an index to measure the sensitivity of the system to initial perturbations, which can characterize the chaos and stability of the system. By calculating the maximum Lyapunov exponent, the system can determine whether the anti-falling rod is in a stable region and predict the time range in which it may become unstable. Specifically, if the maximum Lyapunov exponent is negative, it means that the anti-falling rod can naturally return to a stable state; if the exponent is positive, it indicates that the anti-falling rod has a tendency of exponential divergence and will become unstable within a certain time. The system calculates the instability prediction time based on the calculated Lyapunov exponent, that is, the time point when the anti-falling rod is about to become unstable, so as to provide a decision-making basis for the control system.

[0041] After determining the instability time of the anti-falling rod, the system needs to calculate the optimal compensation force required to prevent its fall. The calculation of the compensation force of the anti-falling rod relies on nonlinear control theory. The system calculates the required compensation force based on the differential geometry method, enabling the anti-falling rod to return to a stable state on the optimal control path. The calculation of the compensation force mainly considers the potential energy gradient of the anti-falling rod and the motion damping term. The potential energy gradient determines the tendency of the anti-falling rod to deviate from the equilibrium position, while the motion damping term is used to reduce excessive oscillations and improve the stability of the system. The system calculates the magnitude and direction of the optimal compensation force by solving the control equation and adjusts the control torque of the anti-falling rod in real time to make its motion tend to be stable. Finally, the control system adjusts the motion state of the anti-falling rod according to the calculated optimal compensation force to ensure that it does not fall. This process requires the combination of high-precision actuators, such as servo motors and intelligent shock-absorbing devices, so as to be able to quickly respond to the instructions of the control system. The actuator adjusts the supporting force or rotational torque of the anti-falling rod in real time according to the compensation force calculated by the system to make it return to a stable state. To improve the control accuracy, the system adopts an adaptive control algorithm, which continuously adjusts the control parameters according to the real-time motion state of the anti-falling rod to cope with the influence of external disturbances. Compared with traditional anti-falling rod technologies, the control system of the present invention has significant advantages. First, traditional anti-falling rod devices mainly rely on mechanical limit or fixed support methods to prevent falls, while the present invention adopts intelligent dynamic monitoring technology, which can obtain the motion state of the anti-falling rod in real time and analyze its stability through a high-order mathematical model. This method improves the adaptability of the system to complex motion states. Second, traditional anti-falling rod devices usually adopt simple static control strategies, such as setting a fixed supporting force or mechanical locking, while the present invention adopts a dynamic balance algorithm. By calculating the energy-momentum coupling relationship and Lyapunov exponents, active prediction and intervention are realized, and optimal compensation measures can be taken before instability occurs, thereby improving the safety and reliability of the system. In addition, the control accuracy of traditional anti-falling rod devices is relatively low, and it is often difficult to cope with complex external environmental changes, while the present invention adopts an adaptive control strategy, which can dynamically adjust the control parameters according to real-time data, enabling the system to have stronger environmental adaptability.

[0042] Embodiment 2: The sensor system includes: a three-dimensional velocity sensor, a three-dimensional acceleration sensor, a three-axis angular displacement sensor, a three-axis angular velocity sensor, and a three-axis angular acceleration sensor; the inertial state parameter vector is where t is time; r(t) is the three-dimensional position coordinates of the centroid of the anti-falling rod body; v(t) is the three-dimensional velocity of the centroid of the anti-falling rod body; a(t) is the three-dimensional acceleration of the centroid of the anti-falling rod body; θ(t) is the angular displacement of the anti-falling rod body on three axes; ω(t) is the angular velocity of the anti-falling rod body on three axes; α(t) is the angular acceleration of the anti-falling rod body on three axes.

[0043] Specifically, in the mathematical description of the inertial state parameter vector, S(t), as a function of time t, contains six sets of key variables that characterize the complete motion characteristics of the anti-falling rod in three-dimensional space. First, r(t) represents the three-dimensional position coordinates of the centroid of the anti-falling rod body, which is obtained from three-dimensional velocity sensors and integrated acceleration data and can reflect the absolute position of the rod body in space. Second, v(t) is the three-dimensional velocity of the centroid of the anti-falling rod body, indicating the instantaneous motion rate of the rod body. Its data is sourced from three-dimensional velocity sensors and can be corrected by integrating the acceleration signal. Further, a(t) represents the three-dimensional acceleration of the centroid of the anti-falling rod body, which is directly from three-dimensional acceleration sensors and can be used to analyze the external forces and inertial changes acting on the rod body. In the angular motion part, θ(t) represents the angular displacement of the anti-falling rod body on three axes, that is, its rotation angle relative to the inertial reference frame. This parameter is usually measured by a three-axis angular displacement sensor and can provide the attitude information of the anti-falling rod. The related ω(t) represents the angular velocity of the anti-falling rod on three axes. This data is mainly obtained by gyroscopes and can be used to describe the rotational dynamic characteristics of the rod body. And α(t) is the angular acceleration of the anti-falling rod body on three axes, usually calculated by differentiating the angular velocity data or directly measured by an angular acceleration sensor. It is used to measure the change trend of the rod body's rotation rate and is crucial for stability analysis.

[0044] The construction of this inertial state parameter vector lays a data foundation for the intelligent control of the anti-falling rod. Traditional anti-falling rod devices mainly rely on simple inclination sensors or single acceleration sensors, often unable to comprehensively capture the motion state of the rod body, resulting in relatively crude control strategies and difficulty in adapting to complex dynamic environments. Through multi-sensor fusion, this invention accurately obtains the linear and rotational motion states of the rod body, enabling the system to make more precise decisions based on complete dynamic information. Especially when the rod body is about to become unstable, its angular velocity and angular acceleration often show a non-linear growth trend. The high-precision inertial measurement unit of this system can detect this change in real time and input the data into the control system to calculate the stability tensor and maximum Lyapunov exponent of the anti-falling rod, predicting the likelihood and time of instability. Through this sensor system, the control system of the anti-falling rod can accurately sense its inertial state and, combined with dynamic modeling and intelligent prediction algorithms, achieve precise control of the motion trend of the rod body. This comprehensive inertial measurement method enables the anti-falling rod to maintain a high degree of stability in complex environments and can actively adjust its motion trajectory at the moment approaching instability, thus effectively preventing falls. Compared with traditional static control methods, the sensor system of this invention provides more accurate real-time data input, making the control strategy of the anti-falling rod more intelligent and precise, providing a solid foundation for achieving efficient and stable control of the anti-falling rod.

[0045] Embodiment 3: Analyze the real-time energy-momentum coupling state of the anti-falling rod body through the following formula to obtain the real-time total energy of the anti-falling rod body:

[0046]

[0047] where E total (t) is the real-time total energy; g is the acceleration due to gravity; m is the mass of the main body of the anti-falling rod body; α is the non-linear gravitational field correction coefficient, and its value range is from 0.2 to 0.5; h(t) is the function of the centroid height of the anti-falling rod body; z(t) is the Z-axis component of the three-dimensional position coordinate r(t) of the centroid of the anti-falling rod body; I x 、I y and I z are the principal moments of inertia of the anti-falling rod body about the X-axis, Y-axis, and Z-axis respectively, and are fixed values; ω x (t), ω y (t), and ω z (t) are the components of ω(t) along the X-axis, Y-axis, and Z-axis respectively; z is the integration variable.

[0048] Specifically, the translational energy of the anti-falling rod reflects the linear motion state of its centroid. This part of the energy is determined by the centroid velocity v(t), and its mathematical expression includes where the mass m represents the inertial property of the rod body, and v(t) is the instantaneous velocity vector of the centroid of the anti-falling rod in three-dimensional space. Since the anti-falling rod may be affected by external forces in actual application scenarios, such as wind loads, ground vibrations, or structural deformations, its velocity state is not stable but will be dynamically adjusted with changes in external conditions. By measuring the change of v(t) in real time through an inertial sensor and calculating the value of the translational energy, the system can determine in real time whether the anti-falling rod is in a normal operating state. If the energy value shows abnormal fluctuations, it indicates that the rod body may be experiencing external impacts or deviating from the equilibrium position due to inertia, which provides a prerequisite for the intervention of the control system. In addition to the translational energy, the rotational energy of the anti-falling rod also plays a crucial role in dynamic balance control. In the formula, the rotational energy part is represented by where I x , I y , I z are the principal moments of inertia of the anti-falling rod body about the X, Y, and Z axes respectively, and ω x (t), ω y (t), ω z(t) is the angular velocity component of the rod body in the corresponding axial direction. This part of the energy reflects the rotational motion characteristics of the anti-falling rod. With the support of the inertial detection system, the angular velocity data can be measured in real time by the gyroscope and used to calculate the rotational kinetic energy of the rod body around different axes. During the operation of the anti-falling rod, its attitude stability is directly related to the rotational kinetic energy. For example, when the angular velocity of the rod body changes drastically, it means that the system may be experiencing a large attitude deviation. If the increase in rotational kinetic energy exceeds a certain threshold, it indicates that the rod body may enter an unstable state. Therefore, by calculating the real-time rotational energy, the control system can predict the attitude trend of the rod body and apply a compensatory force when necessary to offset the excess rotational inertia and maintain overall stability. Among the three major components of energy calculation, the change in potential energy has a particularly significant impact on the stability of the anti-falling rod. Traditional methods for calculating potential energy usually assume a linear gravitational field, that is, the potential energy has a monotonic linear relationship with height. However, in the anti-falling rod system of the present invention, a non-linear correction is introduced into the potential energy calculation to make it more consistent with the characteristics of gravitational forces in the real physical environment. The potential energy term in the formula is given in integral form and expressed as where g represents the acceleration due to gravity, h(t) is the height of the centroid of the anti-falling rod, and α is the non-linear gravitational field correction coefficient. The sine-squared function in the correction term plays a role in adjusting the potential energy gradient, so that in different height regions, the rate of change of potential energy is not fixed but is regulated by height dependence. When the height of the rod body increases or decreases, the increase or decrease in potential energy is no longer a linear change but shows a certain non-linear trend. This characteristic can more realistically simulate the influence of the external environment on gravitational potential energy and provide more accurate instability prediction information. The non-linear correction of potential energy is of great significance for predicting the stability of the anti-falling rod. In traditional analysis methods, due to the linearization assumption of potential energy, the system often cannot accurately describe the gravitational influence of the rod body under different height changes, resulting in the control system being unable to provide accurate compensatory force calculations when approaching instability. In the present invention, by introducing a correction term, the value of potential energy is closer to the actual force situation, thereby improving the prediction accuracy of the control system. For example, when the anti-falling rod undergoes a small swing due to external actions, the corrected potential energy gradient can reflect the potential energy increment brought about by a small angular change, enabling the system to anticipate in advance whether the rod body has a tendency to develop towards an unstable state and calculate the corresponding compensatory strategy when necessary. This method not only improves the overall response ability of the anti-falling rod but also enables the system to adapt to more complex environmental conditions and ensure that the rod body remains stable under different external disturbances.

[0049] Embodiment 4: The centroid height function of the anti-falling rod body is expressed using the following formula:

[0050]

[0051] where, θ x (t) and θy (t) are the components of θ(t) on the X-axis and Y-axis respectively; L is the distance from the centroid of the anti-falling rod body to the fulcrum.

[0052] Specifically, the basic idea of this formula is that the centroid height of the anti-falling rod is not only affected by its vertical coordinate but also restricted by the tilt angle. When the anti-falling rod tilts in the X-axis or Y-axis direction, its centroid is no longer at the static reference height but will fluctuate up and down with the change of the tilt angle. Therefore, a mathematical expression needs to be established to directly map the tilt angles θ x (t) and θ y (t) to the change in centroid height. The change in centroid height is closely related to the geometric structure of the rod body. In particular, the distance L from the centroid of the rod body to the fulcrum directly affects the offset amplitude of the centroid position during tilting. In this formula, this term is used to correct the coupling effect of multi-axis tilt on height. Generally, if only single-axis tilt is considered, the centroid height can be calculated by a simple cosine function. However, in practical applications, the anti-falling rod often offsets simultaneously in multiple directions, resulting in a non-linear characteristic of height change. This correction term, in the form of a square root function, introduces the product between sin 2 θ x (t) and sin 2 θ y (t), so that when the rod body undergoes biaxial tilt, the decrease amplitude of the centroid height can more conform to the real physical law. This correction method ensures the accuracy of the calculation results under different tilt combinations and avoids the error accumulation problem of the traditional single-axis model in complex motion scenarios.

[0053] In addition, the roles of the cosine and arctangent functions in this formula are to describe the relative influence between different inclined axes. Since the inclination angle of the anti-falling rod generally does not change strictly along a certain coordinate axis, but shows a certain cross-inclination trend, it is necessary to use the arctangent function arctan to calculate the inclination ratio in two directions and adjust the amplitude through the cosine function. This calculation method can ensure that even in the case of asymmetric inclination, the system can still accurately estimate the centroid height and avoid calculation errors caused by simple linear approximation. For example, when the anti-falling rod is mainly inclined along the X-axis direction and the inclination in the Y-axis direction is small, this formula can automatically adjust the calculation weight, making the inclination contribution of the X-axis larger, and not overcorrecting the centroid height due to the slight deviation of the Y-axis. Similarly, when the inclination degrees of the X-axis and Y-axis are similar, this formula can ensure that the calculated centroid height will not be amplified or reduced due to the influence of a certain axis, but accurately reflects the real spatial motion state. A significant advantage of this centroid height calculation method is its strong adaptability, which can effectively cope with different structural sizes and fulcrum constraint conditions. Since the change of the centroid height is directly related to L, by adjusting this parameter, it can be applied to anti-falling rod systems of different specifications. In the design of the control strategy, this formula provides the basis for height dynamic adjustment, enabling the system to predict its potential instability trend based on real-time monitoring of the rod body attitude. For example, when the centroid height rapidly decreases due to the increase of the inclination angle, the system can identify that the rod body may enter the unstable state, and combine energy analysis and Lyapunov exponent calculation to take compensation measures in advance to prevent the rod body from swinging violently or falling. Compared with the traditional fixed-threshold monitoring method, this centroid height model based on non-linear geometric calculation can more accurately reflect the actual motion trend of the rod body, thus improving the prediction accuracy and response speed of the system. In the application of the dynamic balance algorithm, the calculation result of this formula can also be used to optimize the compensation force control strategy. When the anti-falling rod inclines in a certain direction, the reduction of its centroid height will cause a change in potential energy, and the change in potential energy directly affects the energy distribution and stability state of the system. By calculating h(t) in real time, the system can deduce the potential energy gradient and calculate the direction and magnitude of the optimal compensation force accordingly. For example, when the decrease amplitude of the centroid height exceeds a certain threshold, the system can calculate the correction torque to be applied according to the change rate of the inclination angle to offset the influence of unstable factors. In addition, this formula can also combine the data provided by the inertial measurement unit (IMU) to further optimize the control strategy, making the application of the compensation force more accurate and efficient. This control method based on real-time calculation of the centroid height enables the anti-falling rod device to achieve adaptive adjustment under different working conditions, thereby improving its anti-interference ability and long-term stability.

[0054] Example 5: Calculate the stability tensor of the anti-falling rod body on the microdifferential manifold through the following formula:

[0055]

[0056] Among them, ∑ stability (t) is the stability tensor; T E (t) is the energy contribution tensor; T θ (t) is the angular displacement contribution tensor; T ω (t) is the angular velocity contribution tensor;

[0057]

[0058] Among them, E ref is the reference energy value, which is a set value; σ E is the energy sensitivity parameter, which is a set value; I3 is the 3×3 identity matrix;

[0059]

[0060] Among them, is the tensor product; θ critical is the critical inclination angle;

[0061]

[0062] Among them, ω ref is the reference angular velocity; R ω (t) is the rotation matrix about axis; ω ref is the reference angular velocity.

[0063] Specifically, the calculation of the stability tensor is based on the interaction of three core tensors, namely, the energy contribution tensor, the angular displacement contribution tensor, and the angular velocity contribution tensor. First, the energy contribution tensor T E (t) reflects the degree of deviation of the total energy of the system from the reference energy and is modeled using a Gaussian decay function. This Gaussian function form ensures that when the energy level of the anti-falling rod approaches the set reference value E ref , the value of this tensor approaches the identity matrix I3, indicating that the system is in a stable state. However, when the total energy of the rod significantly deviates from the reference value, the value of this tensor will show an exponential decrease, reflecting the possibility that the system enters the unstable region. The energy level is crucial for the stability of the anti-falling rod because the kinetic and potential energies of the system directly determine the movement trend of the rod, and energy mutation is often the key signal for the system to transition from a stable state to an unstable state. Therefore, through the calculation of the energy contribution tensor, the system can identify whether the anti-falling rod has abnormal energy due to external interference, providing necessary prior information for instability prediction. In addition to the energy state, the influence of angular displacement on the stability of the rod cannot be ignored. Therefore, the second component of the stability tensor T θ(t) adopts the form of sine function correction to accurately depict the influence of angular displacement on stability. In this expression, sin 2 function is used to adjust the contribution weights within different angular ranges, such that when the angular displacement is small, the value of this tensor approaches the identity matrix, indicating that the system is still in a stable state. While when the angular displacement increases to a certain range, the value of this tensor gradually deviates from the identity matrix, meaning that the system stability is declining. The change of angular displacement reflects the adjustment of the anti-falling rod's attitude. Especially when disturbed by an external torque, the angular displacement of the rod body often undergoes a sudden change, and this sudden change may cause the rod body to enter the instability boundary. Therefore, the angular displacement contribution tensor is not only used to evaluate the influence of the rod body's angular change on stability in real time, but also can further judge whether the system is about to enter an unstable state by combining the change trend of the energy contribution tensor. Due to the non-linear characteristic of the angular displacement variable θ(t) itself, the method of sine function correction can more accurately describe the stability change within different angular ranges, enabling the system to maintain a high stability when the angle is small, and being able to issue an instability warning in time when the angle approaches the critical value θ critical .

[0064] In addition, the influence of angular velocity on system stability is also crucial in dynamic balance control. Therefore, the angular velocity contribution tensor T ω (t) adopts the method combining exponential decay and rotation matrix to ensure that it can accurately reflect the effect of the rod body's rotational motion on stability. When the angular velocity is small, the main contribution of this tensor comes from the exponential decay term At this time, the tensor value approaches the identity matrix, indicating that the rotational motion of the system is still within the controllable range. However, when the angular velocity increases to approach the reference angular velocity ω ref , this exponential term decays rapidly, making the main contribution of the tensor determined by the rotation matrix R ω (t), indicating that the system enters a high-speed rotation state and may be about to enter the instability region. The advantage of this modeling method is that it can consider both the magnitude and direction of the angular velocity, and describe the influence of the rod body's rotational motion on stability through the rotation matrix. Especially when the rod body undergoes violent rotation, the system can use the angular velocity contribution tensor to predict the change trend of the moment of inertia, and combine with other tensors to calculate the instability time, so as to apply the optimal compensation force in advance to prevent the rod body from entering an irreversible unstable state. Finally, the stability tensor ∑ stability(t) is calculated through the tensor product of three sub-tensors. This calculation method ensures that the system can comprehensively consider the impacts of energy, angular displacement, and angular velocity on stability, and conduct a global analysis of the stability of the anti-falling rod within the framework of differential manifolds. The application of the tensor product enables the coupling calculation of the impacts of various variables in different directions, ensuring the accuracy of the stability analysis when different physical variables interact with each other. For example, when the total energy of the rod body changes little, but the angular displacement and angular velocity reach relatively high levels simultaneously, the stability tensor can still reflect that the stability of the system is decreasing, and prompt the control system to take corresponding compensation measures. This calculation method avoids the local distortion problems that may occur in traditional linear stability assessment methods and can adapt to more complex dynamic environments, enabling the anti-falling rod device to remain stable under the influence of various uncertain factors. In practical applications, this stability tensor can not only serve as the core tool for stability analysis but also be used to optimize control strategies. The system can adjust the compensation force of the anti-falling rod in real-time according to the calculation result of ∑ stability (t), and predict the time window for the system to enter the unstable state in combination with the Lyapunov exponent. When the value of the stability tensor is lower than the set threshold, the system can calculate the optimal compensation strategy in advance and, through precise control of the torque and direction, enable the anti-falling rod to return to the stable region before instability. In addition, the generality of this calculation method enables it to be applicable to anti-falling rod devices with different structures and specifications. By simply adjusting parameters such as the energy reference value and the angular velocity reference value, it can be applied to different engineering environments.

[0065] Example 6: Calculate the maximum Lyapunov exponent λ max (t) through the following formula:

[0066]

[0067] where Δt is the time step; f(S(t)) is the state evolution function of the anti-falling rod body; ||·||2 is the L2 norm.

[0068] Specifically, the calculation of the maximum Lyapunov exponent depends on the state evolution function f(S(t)) of the system, which describes the state changes of the anti-falling rod at different time points. Since the movement of the anti-falling rod is affected by various factors, including inertia, gravity, external disturbances, etc., the state vector S(t) needs to comprehensively consider information such as the centroid position, velocity, acceleration, angular displacement, angular velocity, and angular acceleration of the rod body. Specifically, S(t) consists of multiple physical variables, such as the centroid coordinate r(t), centroid velocity v(t), angular displacement θ(t), and angular velocity ω(t). The changes of these variables are constrained by the state evolution function f(S(t)), which describes how the anti-falling rod evolves over time under given initial conditions. When the system is in a stable state, the change rate of f(S(t)) is small, that is, the response of the state variables to small perturbations is weak; while when the system tends to become unstable, the change rate of this function will increase rapidly, indicating that the system's response to the initial perturbation becomes extremely sensitive and may even enter a chaotic state. To quantify this state change trend, the calculation of the maximum Lyapunov exponent uses the Jacobian matrix of the state evolution function to calculate the L2 norm and then divide by the time step Δt after taking the logarithm. The physical meaning of this calculation method is that the Jacobian matrix characterizes the local geometric properties of the system in the phase space and can describe the amplification or attenuation of small perturbations during the time evolution process. By calculating the L2 norm of this matrix, the sensitivity of the system state to perturbations can be obtained, and dividing by Δt after taking the logarithm can normalize this change rate to eliminate the influence of the time scale on the calculation result. When the maximum Lyapunov exponent λ max (t) is negative, it means that the state evolution of the system tends to converge, that is, small perturbations will not be amplified, and the anti-falling rod is still in the stable region; when λ max (t) approaches zero, the system enters the critical stable state, indicating that the rod body may start to enter the unstable region; while when λ max (t) becomes positive, the movement of the system will show an exponential divergence trend, indicating that the anti-falling rod has entered the unstable state and may even enter the chaotic dynamics region. At this time, the system is extremely sensitive to the initial conditions, and small perturbations may cause the rod body to quickly deviate from the equilibrium position and eventually fall.

[0069] An important feature of this calculation method is that it can not only be used to evaluate the stability of the current state but also to predict the instability time of the system. Through the trend analysis of λ max (t), the system can infer when the rod body may enter the unstable region and calculate the time window before the instability occurs. For example, if λ max(t) remaining close to zero or becoming positive over a period of time indicates that the system is about to enter the instability region. The control system can apply a compensatory force in advance based on this to prevent irreversible attitude deviation of the rod. This predictive ability has important application value in the dynamic balance control of the anti-falling rod, enabling the system to take proactive control measures before instability occurs rather than responding passively, thus greatly enhancing the safety and stability of the system. In addition, this calculation method can also adapt to different types of anti-falling rod structures and different environmental conditions. Since the calculation of the maximum Lyapunov exponent only depends on the state evolution function f(S(t)) and its Jacobian matrix, this method can be applied to different anti-falling rod design schemes regardless of the specific dynamic equations of the system. For example, in the presence of additional elastic supports or air damping effects, only by adjusting the expression form of f(S(t)), λ max (t) can be recalculated to ensure the generality of this method. This high adaptability enables the anti-falling rod device of the present invention to remain stable under different application scenarios and dynamically adjust the control strategy according to the real-time calculation results to optimize the anti-falling performance of the anti-falling rod. Compared with traditional stability assessment methods, the calculation method based on the maximum Lyapunov exponent has higher sensitivity and predictive ability. Traditional methods usually adopt a threshold monitoring strategy, such as setting fixed critical values for angular displacement or angular velocity and triggering compensatory control when the threshold is exceeded. However, the disadvantage of this method is that it can often only respond after the system has entered the unstable state and cannot predict the instability trend in advance. The Lyapunov exponent calculation method adopted by the present invention can identify the dynamic change characteristics of the system before instability occurs and predict the time of instability based on this, enabling the system to take intervention measures in advance to avoid the anti-falling rod entering an uncontrollable unstable state. In addition, since this method is directly based on the time evolution of state variables, it can more comprehensively reflect the true dynamic behavior of the system rather than simply monitoring based on a single variable, which enables this method to still maintain high calculation accuracy and stability under complex working conditions. In the actual application of the anti-falling rod control system, this method can be combined with the stability tensor calculation method to provide more accurate stability assessment. The stability tensor is mainly used to describe the overall stability of the system under different energy levels, angular displacements, and angular velocity conditions, while the maximum Lyapunov exponent is used to predict the future state evolution trend of the system. By combining these two methods, the system can calculate the change trend of λ max (t) when detecting changes in the stability tensor to further confirm whether the system is about to enter the instability region and adjust the compensatory control strategy according to the calculation results. This multi-level stability analysis method enables the anti-falling rod device not only to respond quickly after instability occurs but also to take proactive intervention before instability occurs, thus improving the overall stability and safety of the system.

[0070] Example 7: The state evolution function of the anti-falling rod body is represented by the following formula:

[0071]

[0072] where T is the Jacobian matrix from angular velocity to angular displacement; S is the inertia tensor of the anti-falling rod body.

[0073] Specifically, in this formula, the state vector S(t) includes multiple dynamic parameters of the anti-falling rod body, including variables such as the centroid position, linear velocity, linear acceleration, angular velocity, angular acceleration, and inertia tensor. The first part v(t) of the state evolution function directly represents the instantaneous velocity of the rod body, which is obtained by integrating the velocity and acceleration at the previous moment and reflects the translational dynamics characteristics of the rod body. And a(t) represents the instantaneous acceleration of the rod body, which is usually determined by external forces, inertial forces, and fulcrum constraint conditions and is one of the core variables in system dynamics calculations. By obtaining acceleration data in real time through an inertial measurement unit (IMU), the system can continuously track the acceleration changes of the rod body and thus calculate the movement trend of the centroid. In the angular motion part of the state evolution equation, this term describes the coupling relationship between angular velocity and angular acceleration. Since the rotation state of the anti-falling rod in space is affected by the moment of inertia and the fulcrum moment, the calculation of angular acceleration needs to consider the contribution relationship of angular velocity to angular displacement. Here, T represents the Jacobian matrix from angular velocity to angular displacement, which is used to describe the local linear relationship of rigid body rotational motion. When the angular velocity of the rod body changes, the inverse transformation T -1 (ω(t)) can be used to calculate the influence of angular velocity on angular displacement, and the partial derivative term further considers the contribution of angular velocity changes to angular acceleration, making the calculation result more accurate. This calculation method can ensure that even in complex rotational motion states, the system can still accurately predict the rotation trend of the rod body and adjust the control strategy accordingly to improve the stability and response speed of the system.

[0074] In addition, the term S -1 (t)[-ω(t)×Sω(t)] describes the influence of angular velocity on the inertia tensor. In rigid body dynamics, the inertia tensor S determines the angular momentum distribution of the rod body, and the angular velocity ω(t) reflects the change trend of angular momentum at different time steps through the cross product operation -ω(t)×Sω(t). The inverse matrix S of the inertia tensor -1(t) is further used to calculate the evolution of angular momentum, enabling the system to transform between different inertial coordinate systems and ensuring the stability of the calculation. This part of the calculation is crucial for the rotational control of the anti-falling rod because, in the state of high angular velocity motion, the change in angular momentum may significantly affect the stability of the rod body. Based on the changing trend of the inertia tensor calculated by this formula, the system can predict the rotational stability of the rod body and take appropriate compensation measures. Finally, This part further describes the influence of the change of the inertia tensor over time on the angular acceleration. This term reflects the dynamic adjustment of the system's inertial parameters when there are external disturbances or slight changes in the structural parameters of the rod body through the calculation of the time derivative of the inertia tensor. This calculation method enables the system to adapt to different working environments and adjust the control strategy of the anti-falling rod in real time according to the changes in the inertial parameters, thereby improving the intelligence level and adaptive ability of the system. The state evolution function of the present invention has stronger adaptability and accuracy compared with the traditional rigid body dynamics equation. Traditional methods usually adopt a simplified Euler dynamics model, only considering the simple relationship between angular velocity and angular acceleration, while ignoring the dynamic change of the inertia tensor and the non-linear influence of angular velocity on angular acceleration. The state evolution function of the present invention makes the calculation result more in line with the actual rigid body dynamics characteristics and can maintain a high calculation accuracy in a more complex dynamic environment by introducing the inverse transformation of the Jacobian matrix, the time derivative of the inertia tensor, and the angular velocity cross product term. In addition, since this formula adopts a matrix form of representation, it can be easily extended to different types of anti-falling rod structures. Whether it is a fixed fulcrum mode, an elastic fulcrum mode, or a multi-degree-of-freedom mode, this formula can be applied to different system configurations, enabling the anti-falling rod device to maintain high stability in different engineering scenarios. In the practical application of the control system, this state evolution equation can be used to predict the motion trend of the rod body in real time and calculate the instability time in combination with the maximum Lyapunov exponent. By numerically integrating the time evolution of S(t), the system can judge in advance whether the rod body enters a high-risk area and apply the optimal compensation force after detecting the instability trend. For example, when the angular velocity contribution tensor T ω (t) shows that the rotational energy of the rod body increases sharply and the state evolution equation predicts that the angular velocity will continue to increase in a short period of time, the system can analyze the time window of instability occurrence in combination with the Lyapunov exponent and adjust the support torque or apply a damping force in advance to prevent the anti-falling rod from entering an uncontrollable high-speed rotation state.

[0075] Example 8: Predict the instability prediction time T failure (t) of the anti-falling rod body through the following formula:

[0076]

[0077] Among them, ||·|| F is the Frobenius norm; ||·|| is the L1 norm; tr(·) represents calculating the trace of a matrix; σ critical is the critical stability threshold, which is a set value.

[0078] Specifically, the first part in the formula is mainly used to estimate the time window for the system to enter the unstable state starting from the current time t. The stability tensor Σ stability (t) is a mathematical quantity reflecting the real-time stability of the system, and its Frobenius norm ||Σ stability (t)|| F represents the overall scale of this tensor. By calculating the ratio with the set critical stability threshold σ critical and taking the logarithm, the relative distance between the current state and the instability boundary can be measured. Subsequently, this ratio is further divided by the maximum Lyapunov exponent λ max (t), thereby indicating the time required for the system to enter the unstable state from the current state. If λ max (t) is positive, it means the system is in an exponentially divergent state, and small perturbations will be amplified rapidly, making the instability time T failure (t) become smaller. If λ max (t) is still negative, it indicates that the system is still in a stable state, the instability time is far away, and the system still has sufficient adjustment space. The second part of the formula further corrects the calculation accuracy of the instability time. Here, tr(∑ stability (t) T ∑ stability (t)) calculates the trace of the stability tensor, that is, the sum of the diagonal elements of the matrix. This value can effectively characterize the change trend of the overall stability of the system. The square root operation of the trace is used to normalize the influence of the stability tensor to ensure that its numerical magnitude will not cause a large deviation to the final calculation result. In addition, the denominator of this part contains the maximum Lyapunov exponent λ max (t) and the state vector norm

[0079] ||S(t)||, where the former is used to measure the time scale of system instability, while the latter is used to measure the current state strength of the system, so as to fully consider the influence of the absolute value of state variables when calculating the instability time. The state vector S(t) includes physical quantities such as the displacement, velocity, and angular velocity of the anti-falling rod body. Its L1 norm ||S(t)|| measures the deviation degree of the overall system state through summation operation, making the finally calculated instability time not only depend on the change of the stability tensor, but also be affected by the current state variables of the system. The advantage of this calculation method is that it can dynamically adjust the instability prediction time, enabling the system to respond more flexibly to different environmental changes. In traditional anti-falling rod control systems, a fixed critical angle or angular velocity is usually used as the basis for instability judgment. The defect of this method is the lack of consideration of the global state, which may lead to misjudgment in the case of low energy but high angular velocity, or wrong judgment in the case of high energy but low angular velocity. However, the present invention combines the stability tensor, trace operation, and maximum Lyapunov exponent, enabling the system to automatically adjust the instability time prediction according to the actual state, thereby improving the prediction accuracy and reducing the risk of false alarms or missed alarms. In the practical application of the anti-falling rod control strategy, this calculation formula can be used in combination with the active compensation control system. When the T failure (t) calculated by the system enters a dangerous threshold, for example, less than the set safety time window T safe when, the system can apply a compensation force in advance to delay or prevent the occurrence of instability. This control method can effectively improve the stability of the anti-falling rod and ensure that even under the action of external disturbances, the system can still avoid the rod body from falling by adjusting the strategy in advance. For example, in an actual application scenario, when the wind speed suddenly changes or ground vibration causes the energy level of the rod body to rise, the system can calculate the change of the F norm through the stability tensor and the change trend of the Lyapunov exponent, judge the instability time in advance, and adjust the supporting moment of the anti-falling rod accordingly, so that the rod body can return to the stable state before instability occurs. In addition, this instability prediction time calculation method also has strong adaptability and versatility. Since the formula uses matrix norm, trace operation, and nonlinear logarithmic correction, it can be applied to different types of anti-falling rod systems, including rigid rods, multi-degree-of-freedom rods, and flexible rods and other structural forms. By adjusting the calculation method of the stability tensor and the parameters of the state evolution function, the system can optimize the instability time prediction model for different environmental conditions, enabling the present invention to achieve accurate instability prediction and active control in a variety of application scenarios.

[0080] Example 9: According to the following formula, calculate the optimal compensation force required to prevent the anti-falling rod body from falling according to the instability prediction time:

[0081]

[0082] where, F comp(t) is the optimal compensation force.

[0083] Specifically, the first part of the formula mainly describes the restoring force caused by gravitational potential energy and the influence of the instability time on the intensity of the applied compensation force. The numerator part mg·(1 - reflects the change in potential energy due to the inclination of the rod, where θ x (t) and θ y (t) respectively represent the angular displacements of the rod in the X-axis and Y-axis directions. When the inclination angle of the rod is small, the cosine function approaches 1, making this term approach 0, indicating that the system is still within the stable range and no compensation force needs to be applied; but when the inclination angle increases, this term gradually increases, meaning that the potential energy of the system has changed significantly relative to the equilibrium state, and an additional compensation force is needed to counteract the unstable trend caused by gravity. The denominator part is used to adjust the intensity of the applied compensation force so that when the instability time T failure (t) approaches the current time t, the denominator tends to zero, thereby causing the compensation force to increase significantly. This design ensures that when the rod approaches the instability critical point, the system can quickly apply a large correction force to prevent the rod from entering the irrecoverable instability region. The second part of the formula further corrects the calculation of the compensation force to ensure that its application method conforms to the energy distribution state of the system. Here, E total (t) represents the total energy of the system, and r(t) represents the position vector of the center of mass of the rod. This term calculates the gradient change rate of the energy along the direction of the rod's motion and is normalized in combination with the standard deviation σ stability (t) of the stability tensor to ensure that the calculation result of the compensation force will not deviate too much due to drastic fluctuations in the energy state. Physically, the role of this term is to balance the application of the compensation force so that it can effectively counteract the unstable trend of the system without causing excessive oscillation of the rod due to the application of too large a correction force, thereby affecting the control accuracy. The last part of the formula It is mainly used to correct the angular momentum effect of the rod body to ensure that the compensation force can effectively offset the influence of rotational inertia on the system stability. Since the rotational motion of the anti-falling rod will cause changes in angular momentum, the angular velocity ω(t) and the inertia tensor S need to be introduced in the compensation force calculation to adjust the direction and magnitude of the force. This calculation is for the rotational inertia force generated by the cross product of the angular velocity of the rod body and the inertia tensor, and is normalized by its modulus length to ensure that the calculated correction torque is physically reasonable. Its function is that when the angular velocity of the rod body is relatively large, this item can automatically increase the compensation force to offset the unstable factors caused by rotational inertia, thereby improving the anti-rotation interference ability of the system. The advantage of this compensation force calculation method is that it not only considers the attitude change of the anti-falling rod, but also combines the energy state, instability time prediction and angular momentum correction, making the application method of the compensation force more accurate and intelligent. Compared with the traditional fixed torque compensation method, the calculation method of the present invention can automatically adjust the magnitude and direction of the compensation force according to the real-time state of the system, so as to ensure that the system can maintain high stability in different external environments. For example, in the case of small external disturbances, the value of the compensation force is relatively small to avoid energy loss caused by excessive control; when the rod body enters a high-risk area, the compensation force will automatically increase to ensure that the system can quickly return to a stable state. This adaptive adjustment mechanism enables the system to more efficiently resist various uncertain factors and improve the overall safety of the anti-falling rod. In addition, this calculation method can also be used in combination with other control strategies, such as combining with the maximum Lyapunov exponent prediction and stability tensor calculation to further improve the accuracy of the compensation force. When the calculated instability time of the system is short and the stability tensor shows that the system is in a high-risk state, the compensation force calculation can give priority to a larger correction force to ensure that the system quickly returns to stability; when the system is still in a relatively stable state, the compensation force calculation can aim at minimizing energy loss to improve the energy efficiency ratio of the system. This multi-level calculation method enables the anti-falling rod device to maintain high stability in various complex environments and take active compensation measures before instability occurs, thus avoiding the risk of falling.

[0084] The embodiments of the present invention have been described in detail above. Specific examples are used in this article to elaborate on the principle and implementation manner of the present invention. The description of the above embodiments is only used to help understand the method and its core idea of the present invention; at the same time, for those skilled in the art, according to the idea of the present invention, there will be changes in the specific implementation manner and application scope. In summary, the content of this specification should not be construed as a limitation to the present invention.

Claims

1. An anti-drop rod device based on inertia detection and dynamic balance algorithm, characterized in that: The device comprises: an anti-drop rod body, a sensor system and a control system; the sensor system is used for acquiring the inertial state parameters of the anti-drop rod body in real time and constructing an inertial state parameter vector; the control system is used for analyzing the real-time energy-momentum coupling state of the anti-drop rod body based on the acquired inertial state parameters to obtain the real-time total energy of the anti-drop rod body, and then calculating the stability tensor of the anti-drop rod body on the differential manifold; constructing the state evolution function of the anti-drop rod body, calculating the maximum Lyapunov exponent in combination with the inertial state parameter vector, and predicting the instability prediction time of the anti-drop rod body according to the maximum Lyapunov exponent; calculating the optimal compensation force required to prevent the anti-drop rod body from falling according to the instability prediction time, and controlling the movement of the anti-drop rod body according to the optimal compensation force.

2. The anti-drop pole device based on inertia detection and dynamic balance algorithm as claimed in claim 1, characterized in that: The sensor system includes: a three-dimensional velocity sensor, a three-dimensional acceleration sensor, a three-axis angular displacement sensor, a three-axis angular velocity sensor and a three-axis angular acceleration sensor; the inertial state parameter vector is Wherein, t is time; r(t) is the three-dimensional position coordinate of the center of mass of the anti-drop rod body; v(t) is the three-dimensional velocity of the center of mass of the anti-drop rod body; a(t) is the three-dimensional acceleration of the center of mass of the anti-drop rod body; θ(t) is the angular displacement of the anti-drop rod body on the three axes; ω(t) is the angular velocity of the anti-drop rod body on the three axes; α(t) is the angular acceleration of the anti-drop rod body on the three axes.

3. The anti-drop pole device based on inertia detection and dynamic balance algorithm as claimed in claim 2, characterized in that: The real-time energy-momentum coupling state of the anti-drop rod body is analyzed by the following formula to obtain the real-time total energy of the anti-drop rod body: Among them, E total (t) is the real-time total energy; g is the gravitational acceleration; m is the main mass of the anti-drop rod body; α is the nonlinear gravity field correction coefficient, ranging from 0.2 to 0.5; h(t) is the height function of the center of mass of the anti-drop rod body; z(t) is the Z-axis component of the three-dimensional position coordinate r(t) of the center of mass of the anti-drop rod body; I x ,I y and I z are the principal moments of inertia of the anti-drop rod body on the X-axis, Y-axis and Z-axis, which are fixed values; ω x (t),ω y (t) and ω z (t) are the components of ω(t) on the X-axis, Y-axis and Z-axis respectively; z is the integral variable.

4. The anti-drop pole device based on inertia detection and dynamic balance algorithm as claimed in claim 3, characterized in that: The center of mass height function of the anti-drop rod body is expressed using the following formula: Among them, θ x (t) and θ y (t) are the components of θ(t) on the X-axis and Y-axis respectively; L is the distance from the center of mass of the anti-drop rod to the fulcrum.

5. The anti-drop pole device based on inertia detection and dynamic balance algorithm as claimed in claim 4, characterized in that: The stability tensor of the anti-drop rod body is calculated on the differential manifold using the following formula: Among them, ∑ stability (t) is the stability tensor; T E (t) is the energy contribution tensor; T θ (t) is the angular displacement contribution tensor; T ω (t) is the angular velocity contribution tensor; Among them, E ref is the reference energy value, is the set value; σ E is the energy sensitivity parameter, is the set value; I3 is the 3×3 unit matrix; in, is the tensor product; θ critical is the critical inclination angle; Among them, ω ref is the reference angular velocity; R ω (t) is around The rotation matrix of the axis; ω ref is the reference angular velocity.

6. The anti-drop pole device based on inertia detection and dynamic balance algorithm as claimed in claim 5, characterized in that: The maximum Lyapunov exponent λ is calculated by the following formula: max (t): Wherein, Δt is the time step; f(S(t)) is the state evolution function of the anti-drop rod body; ||·||2 is the L2 norm.

7. The anti-drop pole device based on inertia detection and dynamic balance algorithm as claimed in claim 6, characterized in that: The state evolution function of the anti-drop rod body is expressed by the following formula: Wherein, T is the Jacobian matrix from angular velocity to angular displacement; S is the inertia tensor of the anti-drop rod.

8. The anti-drop pole device based on inertia detection and dynamic balance algorithm as claimed in claim 7, characterized in that: The instability prediction time T of the anti-drop rod body is predicted by the following formula failure (t): Among them, ||·|| F is the F norm; ||·|| is the L1 norm; tr(·) represents the trace of the calculation matrix; σ critical is the critical stability threshold, and is the set value.

9. The anti-drop pole device based on inertia detection and dynamic balance algorithm as claimed in claim 8, characterized in that: The optimal compensation force required to prevent the anti-drop rod from falling is calculated according to the predicted instability time using the following formula: Among them, F comp (t) is the optimal compensation force.

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