Non-linear analysis-based stability control method for continuous reconstruction motion of metamorphic robot

Abstract

The invention discloses a stability control method for continuous reconstruction motion of a metamorphic robot based on nonlinear analysis, which comprises the following steps of: 1, establishing a continuous reconstruction kinematics model of the metamorphic robot by using a spinor theory so as to obtain homogeneous coordinates of centroids of all motion components; 2, establishing a pitch angle-vertical displacement two-degree-of-freedom nonlinear vibration model for continuous reconstruction of the metamorphic robot, and deducing an improved ZMP criterion containing foot wheel nonlinear vertical stiffness; and 4, converting the complex continuous reconstruction nonlinear dynamic model of the metamorphic robot into a simple linear system model for adjusting a centroid mechanism through a sliding block expected displacement deviation solver, and further converting the motion control of each leg joint with continuous reconstruction stability into the displacement control of a sliding block in the centroid mechanism. Therefore, stability control over the metamorphic robot in the continuous reconstruction process is achieved through the LQR controller optimized based on the artificial bee colony algorithm.

Description

Technical Field

[0001] This invention belongs to the technical field of motion control for variable-cell robots, specifically relating to a nonlinear analysis and stability control method for continuous reconfiguration motion of variable-cell robots. Background Technology

[0002] A morphological robot is a novel type of deformable robot designed based on an automotive structure. It achieves morphological reconstruction through the introduction of morphological mechanisms. When facing a structured surface, it can travel at high speed in its automotive form. When facing an unstructured surface, the folding leg morphological mechanism unfolds, and the horizontal lifting morphological mechanism raises the front of the robot, reconstructing it from an automotive form to a humanoid form. This allows it to walk or climb stairs, exhibiting high mobility. Therefore, morphological robots can be widely used in fields such as home entertainment services, engineering exploration, military reconnaissance, and interstellar exploration. The continuous reconstruction of a morphological robot is based on task requirements or environmental changes (such as needing to continuously traverse obstacles while driving on a flat road). Through the coordinated movement of the morphological mechanisms, it achieves a continuous and uninterrupted reconstruction and inverse reconstruction process between the automotive and humanoid forms. This continuous reconstruction between the automotive and humanoid forms is a global reconstruction with significant structural and shape differences. During continuous reconstruction, the system's center of mass changes significantly, and the support area changes markedly. These factors lead to poor stability during the continuous reconstruction process, making the system prone to tipping and instability. Therefore, it is necessary to conduct nonlinear analysis and stability control studies on continuous reconfiguration motion in order to improve the stability of continuous reconfiguration of the system. Summary of the Invention

[0003] The purpose of this invention is to address the shortcomings of the existing technology and provide a stability control method for the continuous reconfiguration motion of a variable-cell robot based on nonlinear analysis, in order to suppress large-scale changes in the position of the system's centroid during the continuous reconfiguration process, thereby improving the stability of the continuous reconfiguration of the variable-cell robot.

[0004] To solve the above-mentioned technical problems, the present invention provides the following technical solution: This invention discloses a stability control method for the continuous reconfiguration motion of a variable-cell robot based on nonlinear analysis. The variable-cell robot includes a front body, a rear body, a center-of-gravity adjustment mechanism, a horizontal lifting mechanism, and a leg mechanism. The leg mechanism is mounted on the floor of the rear body and includes an ankle, lower leg, thigh, and foot tires. The horizontal lifting mechanism includes a lower lifting rod and an upper lifting rod, and achieves horizontal lifting of the front body via a drive motor and an electric push rod. The center-of-gravity adjustment mechanism is mounted on the rear body and consists of a slider motor, a slide rail, and a battery. The stability control method comprises the following steps: Step 1: Establish a basic coordinate system on the horizontal plane where the sole of the foot is located. ,Will The origin It is positioned in the middle of the two foot plates. The positive direction of the axis is the forward direction of the variable-structure robot, and the basic coordinate system is... The positive direction of the axis is perpendicular to the horizontal plane and upwards, in the basic coordinate system. The positive direction of the axis is perpendicular to shaft and The plane containing the axis points outwards from the vehicle body; Based on spinor theory, a kinematic model for the continuous reconfiguration of the variable-cell robot is established, and the homogeneous coordinates of the centers of mass of each moving component are obtained. | ,in, Indicates the first Homogeneous coordinates of the center of mass of a moving component These respectively represent the ankle, calf, thigh, rear body, lower lift bar, front body, electric push bar, and upper lift bar; Step 2: Establish an electromechanical model relating the displacement y of the slider in the adjustment center of mass mechanism to the input voltage u of the slider motor; Step 3: Equivalently represent the tire on the sole of the foot as a nonlinear stiffness spring, and obtain the first... The elastic force of a nonlinear stiffness spring Therefore, based on A two-degree-of-freedom nonlinear vibration model for the continuous reconstruction of the variable-structure robot was established based on Newton-Euler theory to calculate the ground support force acting on the robot. To obtain the improved ZMP criterion; Step 4: Based on the improved ZMP criterion, calculate the actual zero-moment point position at time t during the continuous reconfiguration process of the morphological robot. ; Step 5: Position of the ideal zero torque point By subtracting the values, we obtain the ZMP deviation at time t. ;like If the value is zero, it indicates that stability control has been achieved; otherwise, proceed to step six. Step Six: Based on the improved ZMP criterion, design a slider expected displacement deviation solver; The input is fed into the slider expected displacement deviation solver, which outputs the expected displacement deviation of the slider at time t. ;Will The actual displacement of the slider at time t Adding them together gives the desired displacement of the slider at time t. ;right and Differentiate to obtain the desired velocity of the slider at time t. and the actual velocity of the slider at time t ; Step 7: Calculation and The first error signal between as well as and The second error signal between And these are input together into the LQR controller for processing, to obtain the slider motor in Input voltage at time ;according to Using an electromechanical model, the slider in the center-of-mass adjustment mechanism is obtained. Actual displacement at time +1 and actual speed ; Step 8, if and If all values ​​are zero, then the actual displacement of the slider at time t+1 will be zero. Input the data into the improved ZMP criterion and output the actual zero-torque point position at time t+1. Otherwise, assign t+1 to t and return to step four for sequential execution.

[0005] The stability control method for continuous reconfiguration motion of a variable-cell robot based on nonlinear analysis described in this invention is characterized in that, in step one, the first step is to calculate the value of the first step according to equation (1). Homogeneous coordinates of the center of mass of each moving component : (1) In equation (1), The first term representing the morphomorphic robot The rotational motion of a moving component The first term representing the morphomorphic robot The joint angles corresponding to each moving component For the first morphobot The rotation index of the motion of a moving component The first before continuous reconstruction of the morphobot Homogeneous coordinates of the centroid of each component; These represent the first and second digits of the variability robot. A moving component in the basic coordinate system Below axis, axis, The coordinates of the axis.

[0006] Furthermore, step two involves establishing the electromechanical model based on equation (2): (2) In equation (2), This is the equivalent rotational inertia of the motor drive system. This is the equivalent damping coefficient of the motor drive system. and These are the current constant and torque constant of the motor, respectively. This represents the transmission ratio of the linear guide rod. This is the input voltage of the motor. To adjust the speed of the slider in the center-of-gravity mechanism, To adjust the acceleration of the slider in the center-of-mass mechanism.

[0007] Furthermore, step three includes: Step 3.1: Calculate the first step according to formula (3). The elastic force of a nonlinear stiffness spring : (3) In equation (3), For tire stiffness, These are nonlinear coefficients. For the corresponding number Deformation of a nonlinear stiffness spring; Step 3.2: Establish a two-degree-of-freedom nonlinear vibration model for continuous reconstruction of the variable-cell robot according to equation (4): (4) In equation (4), It is the total mass of the morphobot. and These are the vertical displacement and vertical acceleration of the morphological robot, respectively. and These are the centers of mass of the cellular robot at... Displacement and acceleration in the axial direction, The center of mass of the cellular robot is in Acceleration in the axial direction, and These are the pitch angle and pitch acceleration of the variable-structure robot, respectively. and These are the distances from the center of mass of the cellular robot to the front and rear wheels, respectively. Let be the rotational inertia of the variable-cell robot; Step 3.3: Combining equations (3) and (4), the ground support force on the variable-structure robot is obtained according to equation (5). : (5) In equation (5), For the first morphobot The mass of each moving component This is the value of gravitational acceleration. The first stage of continuous reconfiguration of the cellular robot A moving component in the basic coordinate system Below Inertial acceleration in the axial direction, , These are the elastic forces of the first and second nonlinear stiffness springs, respectively, equivalent to the tires on the soles of the variable-structure robot during continuous reconstruction. Step 3.4: Combining equation (5), the improved ZMP criterion is obtained according to equation (6): (6) In equation (6), The first stage of continuous reconfiguration of the cellular robot A moving component in the basic coordinate system Below Inertial acceleration in the axial direction, This represents the actual zero-torque point location during the continuous reconfiguration process of the morphological robot.

[0008] Furthermore, step six involves constructing a slider expected displacement deviation solver based on equation (7): (7) In equation (7), This refers to the actual zero-torque point deviation during the continuous reconfiguration process of the variable-cell robot. Let be the desired displacement deviation of the slider.

[0009] Furthermore, the LQR controller in step seven is obtained using equation (8) to determine the slider motor's position. Input voltage at time : (8) In equation (8), K is the optimal feedback gain matrix, E(t) is the error variable at time t, and E(t) = .

[0010] The present invention provides an electronic device, including a memory and a processor, characterized in that the memory is used to store a program supporting the processor in performing the method described therein, and the processor is configured to execute the program stored in the memory.

[0011] The present invention discloses a computer-readable storage medium storing a computer program, characterized in that the computer program is executed by a processor to perform the steps of the method described thereon.

[0012] Compared with existing technologies, the beneficial effects of this invention are reflected in: 1. This invention establishes a kinematic model for the continuous reconfiguration of a variable-cell robot using spinor theory and calculates the homogeneous coordinates of the centers of mass of each moving component. Considering the influence of nonlinear tire stiffness on the stability of the continuous reconfiguration of the variable-cell robot, a two-degree-of-freedom nonlinear vibration model of pitch angle and vertical displacement for continuous reconfiguration of the variable-cell robot is established, and an improved ZMP criterion including the nonlinear vertical stiffness of the foot wheel is derived, thus ensuring the reliability of the stability study from the source. 2. This invention transforms the complex nonlinear dynamic model of continuous reconstruction of a morphological robot into a simple linear system model of a center-of-mass adjustment mechanism by using a slider expected displacement deviation solver. This transforms the motion control of each leg joint, crucial for continuous reconstruction stability, into the displacement control of the slider within the center-of-mass adjustment mechanism. An LQR controller optimized based on an artificial bee colony algorithm is designed, and its control parameters are adjusted in real time to achieve precise tracking of the expected slider displacement and velocity. This ensures that the ZMP value of the morphological robot remains stable at the center of the support region, thereby guaranteeing the stability of the continuous reconstruction process. 3. In order to avoid the impact of a large change in the position of the centroid on the stability during continuous reconstruction of the variable-cell robot, this invention performs nonlinear analysis and stability control on the continuous reconstruction motion of the variable-cell robot, thereby improving the stability of continuous reconstruction of the variable-cell robot and achieving high cost performance. Attached Figure Description

[0013] Figure 1 This is a schematic diagram of the components of the cellular robot involved in this invention; Figure 2 This is a simplified kinematic diagram of the reconfiguration mechanism of the variable-cell robot involved in this invention; Figure 3 This is a two-degree-of-freedom nonlinear vibration model for continuous reconstruction of the variable-cell robot involved in this invention; Figure 4 This is a comparison diagram of the nonlinear analysis of continuous reconfiguration of the variable-cell robot involved in this invention; Figure 5 This is a schematic diagram of the continuous reconfiguration stability control principle of the variable-cell robot involved in this invention; Figure 6 This is a simulation comparison diagram of the stability control of continuous reconfiguration of the morphological robot involved in this invention. Detailed Implementation

[0014] The present invention will be further described below with reference to the accompanying drawings and specific embodiments: The metamorphic robot is a novel type of multi-degree-of-freedom, bilaterally symmetrical ground mobile robot, consisting of five main modules: a front body, a rear body, a center-of-gravity adjustment mechanism, a horizontal lifting mechanism, and a leg mechanism. Figure 1 As shown. Figure 1The illustrated morphological robot in its vehicle mode possesses motion functions such as acceleration, deceleration, steering, and braking. Hub motors are installed on the front and rear wheels, enabling distributed drive-by-wire propulsion. The MacPherson strut independent suspension design at both the front and rear of the vehicle reduces road impacts and the effects of relative wheel bounce. Figure 1 The humanoid form of the illustrated morphological robot possesses mobility functions such as walking and obstacle crossing. The leg mechanism is a hybrid motion mechanism mounted on the rear chassis and includes: ankles, lower legs, thighs, and foot tires. The horizontal lifting mechanism includes lower and upper lifting rods, which achieve horizontal lifting of the front of the robot body via a drive motor and an electric push rod, thereby completing the continuous reconfiguration process of the morphological robot. The center-of-gravity adjustment mechanism, mounted on the rear chassis, consists of a drive motor, slide rails, and a battery, and is a key component for achieving continuous system reconfiguration. Considering increasing space and reducing power consumption, the slider of the center-of-gravity adjustment mechanism is powered by a battery. Figure 1 The illustrated morphological robot can achieve continuous forward and reverse reconstruction between a vehicle state and a humanoid state. During the continuous reconstruction process, when reconstructing from the vehicle state to the humanoid state, the robot first unfolds its folding legs and supports itself on the ground. Then, the folding legs continue to unfold, and simultaneously, a horizontal lifting mechanism raises the front of the robot body until it transforms into the humanoid state. The reverse reconstruction from the humanoid state to the vehicle state is achieved through inverse motion.

[0015] Significant progress has been made in the study of robot motion stability, with ZMP theory being the most widely used approach in this field. In this embodiment, a continuously reconfigurable kinematic model of the variable-cell robot is first established based on spinor theory. Specifically, as follows... Figure 2 As shown. The lifting V-bar consists of rods. and The feet of the metacellular robot are fixed together. calves ,thigh Rear body Front body Electric linear actuator The center of mass of the lifting V-shaped bar is located at the midpoint of the bar's symmetry. Establish a basic coordinate system on the horizontal plane containing the foot. ,Will The origin It is positioned in the middle of the two foot plates. The positive direction of the axis is the forward direction of the variable-structure robot, and the basic coordinate system is... The positive direction of the axis is perpendicular to the horizontal plane and upwards, in the basic coordinate system. The positive direction of the axis is perpendicular to shaft and The plane containing the axis points outwards from the vehicle body. Specifically, the method includes the following steps: Step 1: Based on spinor theory, establish a kinematic model for the continuous reconstruction of the variable-structure robot, and obtain the homogeneous coordinates of the centers of mass of each moving component. | ,in, Indicates the first Homogeneous coordinates of the center of mass of a moving component These respectively represent the ankle, calf, thigh, rear body, lower lift bar, front body, electric push bar, and upper lift bar; Step 1.1: Calculate the first step according to formula (1). Homogeneous coordinates of the center of mass of each moving component : (1) In equation (1), The first term representing the morphomorphic robot The rotational motion of a moving component The first term representing the morphomorphic robot The joint angles corresponding to each moving component For the first morphobot The rotation index of the motion of a moving component The first before continuous reconstruction of the morphobot Homogeneous coordinates of the centroid of each component; These represent the first and second digits of the variability robot. A moving component in the basic coordinate system Below axis, axis, The coordinates of the axis.

[0016] Step 2: Establish an electromechanical model relating the displacement y of the slider in the adjustment center of mass mechanism to the input voltage u of the slider motor; Step 2.1: Establish the electromechanical model according to equation (2): (2) In equation (2), This is the equivalent rotational inertia of the motor drive system. This is the equivalent damping coefficient of the motor drive system. and These are the current constant and torque constant of the motor, respectively. This represents the transmission ratio of the linear guide rod. This is the input voltage of the motor. To adjust the speed of the slider in the center-of-gravity mechanism, To adjust the acceleration of the slider in the center-of-mass mechanism.

[0017] Step 2.2, Definition It is the system's state variable. It controls the input variables. It is a system output variable. It is to adjust the system matrix of the center-of-mass mechanism system. It is the system's input matrix. For the output matrix, Let be the feedforward matrix. Based on the electromechanical dynamics model, the state-space equations are established according to equation (3): (3) In equation (3), , = , = , = , Step 2.3: Calculate the first error signal of the system according to equation (4). Second error signal : (4) In equation (4), and These are respectively adjusting the actual displacement and the desired displacement of the slider in the center-of-mass mechanism. and These are the actual speed and the desired speed of the slider in the center-of-mass mechanism, respectively.

[0018] A continuously reconfigurable morphological robot is a multi-degree-of-freedom variable center-of-mass system. The wheel of the morphological robot exhibits nonlinear elastic characteristics; from a mechanical perspective, it can be equivalent to a spring with nonlinear stiffness. The morphological robot can be simplified as a sprung mass block at its center of mass. Under continuous reconfiguration excitation, the morphological robot generates nonlinear vibrations with two degrees of freedom (pitch and vertical) and a variable center of mass. Based on Newton-Euler theory, and combined with a nonlinear wheel model and a pitch-vertical two-degree-of-freedom vibration model, a nonlinear vibration equation for the pitch angle-vertical displacement two-degree-of-freedom of the continuously reconfigurable morphological robot is established. In summary, the vibration during continuous reconfiguration affects the ZMP position of the system, thus affecting the stability of the system during continuous reconfiguration. However, the traditional ZMP formula is based on rigid support feet and does not consider the influence of the elastic deformation of the wheel on the system stability; therefore, the ZMP formula needs to be improved. Specifically, this method includes the following steps: Step 3: Equivalently represent the tire on the sole of the foot as a nonlinear stiffness spring, and obtain the first... The elastic force of a nonlinear stiffness spring Therefore, based on A two-degree-of-freedom nonlinear vibration model for the continuous reconstruction of the variable-structure robot was established based on Newton-Euler theory to calculate the ground support force acting on the robot. To obtain the improved ZMP criterion.

[0019] Step 3.1: Calculate the first step according to equation (5). The elastic force of a nonlinear stiffness spring : (5) In equation (5), For tire stiffness, These are nonlinear coefficients. For the corresponding number The deformation of a nonlinear stiffness spring.

[0020] Step 3.2: Establish a two-degree-of-freedom nonlinear vibration model for continuous reconstruction of the variable-cell robot according to equation (6): (6) In equation (6), It is the total mass of the morphobot. and These are the vertical displacement and vertical acceleration of the morphological robot, respectively. and These are the centers of mass of the cellular robot at... Displacement and acceleration in the axial direction, The center of mass of the cellular robot is in Acceleration in the axial direction, and These are the pitch angle and pitch acceleration of the variable-structure robot, respectively. and These are the distances from the center of mass of the cellular robot to the front and rear wheels, respectively. Let be the rotational inertia of the morphomorphic robot.

[0021] Step 3.3: Combining equations (5) and (6), the ground support force on the variable-structure robot is obtained according to equation (7). : (7) In equation (7), For the first morphobot The mass of each moving component This is the value of gravitational acceleration. The first stage of continuous reconfiguration of the cellular robot A moving component in the basic coordinate system Below Inertial acceleration in the axial direction, , These represent the elastic forces of the first and second nonlinear stiffness springs, respectively, equivalent to the tires on the soles of the morphological robot during continuous reconstruction.

[0022] Step 3.4: Combining equation (7), the improved ZMP criterion is obtained according to equation (8): (8) In equation (8), The first stage of continuous reconfiguration of the cellular robot A moving component in the basic coordinate system Below Inertial acceleration in the axial direction, This represents the actual zero-torque point location during the continuous reconfiguration process of the morphological robot.

[0023] Comparison curves of ZMP nonlinear analysis during the continuous reconstruction process of the morphological robot are shown below. Figure 4 As shown. By Figure 4 As shown in part (a), when the stiffness is 6000, the waveforms within a single period in the time-domain plot under the same period cannot represent the entire time series, meaning the waveforms cannot be precisely superimposed. This indicates that the continuous reconstruction process of the system is formed by the superposition of incommensurable frequency components, exhibiting quasi-periodic motion characteristics. (T=8s) The curve shows a large amplitude change and is closer to the support domain boundary, indicating a high probability of system instability. When T=16s and T=24s, Although the amplitude of the curve change has decreased, its starting and ending positions are still located in dangerous positions near the boundary of the support domain. Therefore, the variable-cell robot still faces a high risk of instability at this point. Figure 4 Part (b) of the text is related to Figure 4 As shown in part (c), the phase trajectories under different periods all constitute toroidal projections rather than simple closed curves. The corresponding Poincaré map points are not randomly scattered but form a discrete string of points along the vertical direction, exhibiting significant quasi-periodic characteristics. Furthermore, the phase trajectories lack a convergence trend towards a stable equilibrium point, indicating that the system's stability may be affected by multiple factors, suggesting the existence of unstable factors and a high risk of instability. In summary, to ensure the stability of the variable-cell robot during continuous reconfiguration, it is necessary to select an appropriate control strategy for its stability control.

[0024] During continuous reconfiguration, the centroid position of a morphological robot changes significantly, posing a high risk of tipping over and becoming unstable. Therefore, stability control during continuous reconfiguration is necessary. This embodiment presents a stability control method for the continuous reconfiguration motion of a morphological robot, specifically, as follows: Figure 5As shown. In this embodiment, the present invention designs an LQR controller based on an artificial bee colony algorithm optimization. This controller effectively improves the stability of the system during continuous reconstruction by adjusting the slider position of the centroid mechanism. Figure 5 It can be seen that the principle diagram of continuous reconfiguration stability control of the variable-cell robot consists of a ZMP calculation module, a slider expected displacement deviation solver, an LQR controller, and an artificial bee colony algorithm optimization module. Figure 5 The LQR controller is the main component. Through closed-loop feedback control of the slider's displacement and velocity, it achieves dual tracking control of the desired slider displacement and velocity during continuous reconstruction, thus improving the stability of the metamorphic robot during continuous reconstruction. Specifically, the method includes the following steps: Step 4: Based on the improved ZMP criterion, calculate the actual zero-moment point position at time t during the continuous reconfiguration process of the morphological robot. .

[0025] Step 5: Position of the ideal zero torque point By subtracting the values, we obtain the ZMP deviation at time t. ;like If the value is zero, it indicates that stability control has been achieved; otherwise, proceed to step six.

[0026] Step Six: Based on the improved ZMP criterion, design a slider expected displacement deviation solver; The input is fed into the slider expected displacement deviation solver, which outputs the expected displacement deviation of the slider at time t. ;Will The actual displacement of the slider at time t Adding them together gives the desired displacement of the slider at time t. ;right and Differentiate to obtain the desired velocity of the slider at time t. and the actual velocity of the slider at time t ; Construct a slider expected displacement deviation solver based on equation (9): (9) In equation (9), This refers to the actual zero-torque point deviation during the continuous reconfiguration process of the variable-cell robot. Let be the desired displacement deviation of the slider.

[0027] Step 7: Calculation and The first error signal between as well as and The second error signal between And these are input together into the LQR controller for processing, to obtain the slider motor in Input voltage at time ;according to Using an electromechanical model, the slider in the center-of-mass adjustment mechanism is obtained. Actual displacement at time +1 and actual speed ; The slider motor is obtained using equation (10) Input voltage at time : (10) In equation (10), K is the optimal feedback gain matrix, E(t) is the error variable at time t, and E(t) = .

[0028] Step 8, if and If all values ​​are zero, then the actual displacement of the slider at time t+1 will be zero. Input the data into the improved ZMP criterion and output the actual zero-torque point position at time t+1. Otherwise, assign t+1 to t and return to step four for sequential execution.

[0029] LQR control aims to find a control strategy (usually represented by a control function) that enables the system to achieve optimal operating conditions according to a certain performance index under certain constraints. The core objective in constructing an LQR controller is to solve for an optimal feedback gain matrix K, thereby enabling the quadratic cost function to achieve optimal performance. To obtain the minimum value. Quadratic cost function. This represents the accumulated error between the actual output and the desired output of a control system. In the continuous reconfiguration stability control of a variable-structure robot, This indicates the error value between the actual displacement and the desired displacement of the slider in the adjustment center mechanism. The smaller the value, the higher the control quality of the LQR controller. Cost function It can be described by equation (11): = (11) In equation (11), This is a state weighting matrix, used to measure the degree of penalty for each state deviating from the equilibrium point. The control weighting matrix is ​​used to measure the cost of controlling energy consumption. Let be the error variable. The weights are described according to equation (12). matrix, Matrix and Variable : = , , (12) To minimize the quadratic performance index function, the K matrix is ​​obtained by solving the algebraic Riccati equation according to equation (13): (13) In equation (13), P is obtained from the Riccati equation (14): (14) LQR controllers suffer from difficulties in selecting weight matrices Q and R. The artificial bee colony algorithm can automate parameter tuning and obtain the globally optimal solution. Each individual (nectar source location) in the algorithm represents a candidate solution to the optimization problem, i.e., a set of possible weight coefficients (…). At this point, the fitness function can be described as: fitness(e) = J= dt (15) The Artificial Bee Colony Algorithm (APA) is a swarm intelligence optimization algorithm inspired by the foraging behavior of bee colonies. APA possesses excellent global search capabilities. Through the random search mechanism of scout bees and the probability-based selection mechanism of follower bees, the algorithm can extensively explore the entire solution space, effectively avoiding premature entrapment in local optima. Specifically, after optimization by the APA, the control parameters... , and As shown in Table 1: Table 1 LQR Control Parameters

[0030] Simulation comparison curves of stability control performance indicators during continuous reconfiguration of the morphological robot are shown below. Figure 6 As shown. Figure 6 Parts (a), (b), and (c) of the diagram respectively present the continuous reconfiguration process of the variable-cell robot under different control strategies at different periods. The time-domain curves of slider displacement and slider velocity. (From...) Figure 6 As shown in (a), when the system adopts an uncontrolled strategy, its Exhibiting significant unstable motion characteristics: at the initial moment of the reconstruction process Located near the danger zone at the boundary of the upper support domain, then moving towards the center of the support domain ( =0) Migration, after breaking through the equilibrium position, continues to move towards the opposite boundary, eventually stabilizing in the danger zone on the other side. The inverse reconstruction process begins at... Starting from a stable position during the reconfiguration process, the system eventually stabilizes near the danger zone of the upper support domain boundary. This indicates that under uncontrolled conditions, the system exhibits significant nonlinear dynamic instability, and the continuous reconfiguration process carries a high risk of collapse. When using sliding mode control, As the robot continuously approaches the center of the supporting domain, its stability during continuous reconfiguration is improved. However, It is difficult to reach a stable state quickly, resulting in poor real-time performance of the controller. However, under LQR control optimized with the ABC algorithm, the controller exhibits excellent transient regulation capability. At different cycles, Both converged to the center of the support domain in about 1.6 seconds and remained relatively stable, which is 0.3 seconds faster than sliding mode control. =8s, The maximum overshoot is 0.0035m, which is much smaller than the maximum overshoot of 0.0065m under sliding mode control, resulting in better system stability. =16s and =24s, The maximum overshoots were 0.002m and 0.001m, respectively, both smaller than the maximum overshoot under the corresponding sliding mode control, further improving system stability. Figure 6 As shown in (b), during each cycle of motion under different periods, the optimized LQR controller exhibits a significant improvement in trajectory tracking performance compared to sliding mode control. Specifically, the fitting degree between the displacement response curve and the desired displacement trajectory of the optimized system is significantly improved, and the maximum tracking error is significantly reduced. Furthermore, the optimized LQR controller can control the slider to reach the target position in approximately 1.6 seconds, achieving faster tracking of the desired slider displacement compared to sliding mode control, resulting in better real-time performance. Figure 6 As shown in (c), during each cycle of motion under different periods, the optimized LQR controller exhibits significantly better dynamic characteristics: its output speed is consistently higher than that of the sliding mode control for a long period during the continuous reconstruction process, which confirms the effectiveness of the controller in improving the system's response capability. From the curve shape, the optimized trajectory shows a smoother exponential convergence characteristic, which also indicates that the former has stronger anti-interference capability.

Claims

1. A stability control method for continuously reconstructed motion of a variable-cell robot based on nonlinear analysis, wherein the variable-cell robot comprises: The vehicle comprises a front body, a rear body, a center-of-gravity adjustment mechanism, a horizontal lifting mechanism, and a leg mechanism; wherein the leg mechanism is mounted on the floor of the rear body and includes: ankle, lower leg, thigh, and foot tire; the horizontal lifting mechanism includes: a lower lifting rod and an upper lifting rod, and achieves horizontal lifting of the front body through a drive motor and an electric push rod; the center-of-gravity adjustment mechanism is mounted on the rear body and consists of a slider motor, a slide rail, and a battery; characterized in that the stability control method includes the following steps: Step 1: Establish a basic coordinate system on the horizontal plane where the sole of the foot is located. ,Will The origin It is positioned in the middle of the two foot plates. The positive direction of the axis is the forward direction of the variable-structure robot, and the basic coordinate system is... The positive direction of the axis is perpendicular to the horizontal plane and upwards, in the basic coordinate system. The positive direction of the axis is perpendicular to shaft and The plane containing the axis points outwards from the vehicle body; Based on spinor theory, a kinematic model for the continuous reconfiguration of the variable-cell robot is established, and the homogeneous coordinates of the centers of mass of each moving component are obtained. | ,in, Indicates the first Homogeneous coordinates of the center of mass of a moving component These respectively represent the ankle, calf, thigh, rear body, lower lift bar, front body, electric push bar, and upper lift bar; Step 2: Establish an electromechanical model relating the displacement y of the slider in the adjustment center of mass mechanism to the input voltage u of the slider motor; Step 3: Equivalently represent the tire on the sole of the foot as a nonlinear stiffness spring, and obtain the first... The elastic force of a nonlinear stiffness spring Therefore, based on A two-degree-of-freedom nonlinear vibration model for the continuous reconstruction of the variable-structure robot was established based on Newton-Euler theory to calculate the ground support force acting on the robot. To obtain the improved ZMP criterion; Step 4: Based on the improved ZMP criterion, calculate the actual zero-moment point position at time t during the continuous reconfiguration process of the morphological robot. ; Step 5: Position of the ideal zero torque point By subtracting the values, we obtain the ZMP deviation at time t. ;like If the value is zero, it indicates that stability control has been achieved; otherwise, proceed to step six. Step Six: Based on the improved ZMP criterion, design a slider expected displacement deviation solver; The input is fed into the slider expected displacement deviation solver, which outputs the expected displacement deviation of the slider at time t. ;Will The actual displacement of the slider at time t Adding them together gives the desired displacement of the slider at time t. ;right and Differentiate to obtain the desired velocity of the slider at time t. and the actual velocity of the slider at time t ; Step 7: Calculation and The first error signal between as well as and The second error signal between And these are input together into the LQR controller for processing, to obtain the slider motor in Input voltage at time ;according to Using an electromechanical model, the slider in the center-of-mass adjustment mechanism is obtained. Actual displacement at time +1 and actual speed ; Step 8, if and If all values ​​are zero, then the actual displacement of the slider at time t+1 will be zero. Input the data into the improved ZMP criterion and output the actual zero-torque point position at time t+1. Otherwise, assign t+1 to t and return to step four for sequential execution.

2. The stability control method for continuous reconfiguration motion of a variable-cell robot based on nonlinear analysis according to claim 1, characterized in that, In step one, the first step is to calculate the first step according to formula (1). Homogeneous coordinates of the center of mass of each moving component : (1) In equation (1), The first term representing the morphomorphic robot The rotational motion of a moving component The first term representing the morphomorphic robot The joint angles corresponding to each moving component For the first morphobot The rotation index of the motion of a moving component The first before continuous reconstruction of the morphobot Homogeneous coordinates of the centroid of each component; These represent the first and second digits of the variability robot. A moving component in the basic coordinate system Below axis, axis, The coordinates of the axis.

3. The stability control method for continuous reconfiguration motion of a variable-cell robot based on nonlinear analysis according to claim 1, characterized in that, The second step involves establishing the electromechanical model based on equation (2): (2) In equation (2), This is the equivalent rotational inertia of the motor drive system. This is the equivalent damping coefficient of the motor drive system. and These are the current constant and torque constant of the motor, respectively. This represents the transmission ratio of the linear guide rod. This is the input voltage of the motor. To adjust the speed of the slider in the center-of-gravity mechanism, To adjust the acceleration of the slider in the center-of-mass mechanism.

4. The stability control method for continuous reconfiguration motion of a variable-cell robot based on nonlinear analysis according to claim 1, characterized in that, Step three includes: Step 3.1: Calculate the first step according to formula (3). The elastic force of a nonlinear stiffness spring : (3) In equation (3), For tire stiffness, These are nonlinear coefficients. For the corresponding number Deformation of a nonlinear stiffness spring; Step 3.2: Establish a two-degree-of-freedom nonlinear vibration model for continuous reconstruction of the variable-cell robot according to equation (4): (4) In equation (4), It is the total mass of the morphobot. and These are the vertical displacement and vertical acceleration of the morphological robot, respectively. and These are the centers of mass of the cellular robot at... Displacement and acceleration in the axial direction, The center of mass of the cellular robot is in Acceleration in the axial direction, and These are the pitch angle and pitch acceleration of the variable-structure robot, respectively. and These are the distances from the center of mass of the cellular robot to the front and rear wheels, respectively. Let be the rotational inertia of the morphobot; Step 3.3: Combining equations (3) and (4), the ground support force on the variable-structure robot is obtained according to equation (5). : (5) In equation (5), For the first morphobot The mass of each moving component This is the value of gravitational acceleration. The first stage of continuous reconfiguration of the morphobot represents the... A moving component in the basic coordinate system Below Inertial acceleration in the axial direction, , These are the elastic forces of the first and second nonlinear stiffness springs, respectively, equivalent to the tires on the soles of the variator robot during continuous reconstruction. Step 3.4: Combining equation (5), the improved ZMP criterion is obtained according to equation (6): (6) In equation (6), The first stage of continuous reconfiguration of the morphobot represents the... A moving component in the basic coordinate system Below Inertial acceleration in the axial direction, This represents the actual zero-torque point location during the continuous reconfiguration process of the morphological robot.

5. The stability control method for continuous reconfiguration motion of a variable-cell robot based on nonlinear analysis according to claim 1, characterized in that, Step six involves constructing a slider expected displacement deviation solver based on equation (7): (7) In equation (7), This refers to the actual zero-torque point deviation during the continuous reconfiguration process of the variable-cell robot. Let be the desired displacement deviation of the slider.

6. The stability control method for continuous reconfiguration motion of a variable-cell robot based on nonlinear analysis according to claim 1, characterized in that, The LQR controller in step seven is obtained using equation (8) for the slider motor. Input voltage at time : (8) In equation (8), K is the optimal feedback gain matrix, E(t) is the error variable at time t, and E(t) = .

7. An electronic device, comprising a memory and a processor, characterized in that, The memory is used to store a program that supports a processor in executing the method of any one of claims 1-6, the processor being configured to execute the program stored in the memory.

8. A computer-readable storage medium storing a computer program thereon, characterized in that, The computer program is executed by a processor to perform the steps of the method according to any one of claims 1-6.

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