Force distribution optimization-based synchronous steering control method for walking excavator

Abstract

The invention discloses a synchronous steering control method of a walking excavator based on force distribution optimization, which is used for solving the problems of poor synchronism and tire wear caused by non-uniform force distribution in the steering process. The method comprises the following steps: S1, establishing a complete machine kinematics model and a dynamical model; s2, estimating the joint speed and the joint external force by adopting a strong tracking Kalman filtering algorithm; s3, minimizing the weighted sum of the supporting force of each supporting leg as a target function, solving the optimal expected joint torque through optimization based on mechanical balance constraint and joint force constraint, and calculating the current magnitude of a pitching joint based on a force controller; s4, acquiring an expected angle of the swinging support leg according to the synchronous steering track plan, and calculating the magnitude of current of the swinging support leg based on a feed-forward compensation PID algorithm; and S5, force distribution adjusting current is applied to the pitching joint of the supporting leg, and steering adjusting current is applied to the swinging supporting leg. According to the method, the steering synchronization performance of the walking excavator can be remarkably improved, and tire abrasion is relieved.

Description

Technical Field

[0001] This invention relates to the field of robot automatic control technology, and in particular to a synchronous steering control method for a walking excavator based on force distribution optimization. Background Technology

[0002] Walking excavators are wheel-leg hybrid excavators suitable for all terrains and various operational scenarios, widely used in emergency rescue missions in unstructured environments such as earthquakes and geological disasters. Two-wheel-drive walking excavators typically use two front outriggers for articulated steering. To ensure overall stability, when the two outriggers are not parallel, each outrigger must be independently controlled for oscillation. However, uneven force distribution between the outriggers can lead to decreased synchronization performance and accelerated tire wear. Traditional synchronization control methods (such as cross-coupling control) primarily focus on improving synchronization accuracy by adjusting control parameters. For wheel-leg hybrid walking excavators, there is currently a lack of effective solutions to improve synchronization performance through force distribution optimization. Regarding the position control of hydraulic outriggers, existing methods such as backstepping and sliding mode control can address system nonlinearity and uncertainty to some extent, but their algorithmic structures are complex and heavily reliant on accurate system models, requiring tedious system identification in practical applications. Furthermore, hydraulic system parameters are susceptible to time-varying characteristics due to oil temperature and load, leading to decreased adaptability of model-based control strategies and difficulty in maintaining stable control performance. On the other hand, conventional model-independent control algorithms (such as PID control), although simple in structure and easy to implement, often struggle to achieve high-precision trajectory tracking control when dealing with highly nonlinear and strongly coupled hydraulic robotic arm systems, and their dynamic response performance and robustness are both insufficient. Summary of the Invention

[0003] The purpose of this invention is to provide a synchronous steering control method for walking excavators based on force distribution optimization, which can dynamically adjust the force distribution of the pitching outriggers while realizing the swing outrigger movement, thereby effectively improving the synchronous steering accuracy and reducing tire wear.

[0004] A synchronous steering control method for a walking excavator based on force distribution optimization, applied to a walking excavator including a robotic arm and multiple outriggers, characterized by comprising the following steps: S1. Establish the kinematic and dynamic models of the whole machine; S2. The strong tracking Kalman filter algorithm is used to estimate the joint velocity and joint external force; S3. Taking the minimization of the weighted sum of the supporting forces of each leg as the objective function, based on mechanical balance constraints and joint force constraints, the optimal desired joint torque is solved by an optimization algorithm, and the pitch joint current is calculated based on the force controller. S4. Obtain the desired angle of the swing outrigger based on the synchronous steering trajectory planning, and calculate the current of the swing outrigger based on the feedforward compensation PID algorithm. S5. Apply force distribution adjustment current to the pitch joint of the outrigger and apply steering adjustment current to the swing outrigger.

[0005] Furthermore, the implementation method of step S1 is as follows: The outriggers of the walking excavator are divided into front outriggers and rear outriggers. The front outriggers have swing and pitch degrees of freedom, while the rear outriggers have swing, pitch, and wheel drive degrees of freedom. The overall machine posture is acquired by an IMU unit installed on the chassis. The cylinder displacement is collected by displacement sensors built into the cylinders, and the cylinder displacement is converted into the corresponding joint angle based on the geometric mapping relationship between the cylinder displacement and the joint angle. The joint torque is measured by pressure sensors installed in the cylinders and then converted into the joint space. The N-degree-of-freedom dynamic model is established as follows: (1) Among them, state variables These are the joint angle, angular velocity, and hydraulic cylinder driving force, respectively. Represents the inertial force matrix. Represents the vectors of the Coriolis force and the centrifugal force. Represents the gravity vector. Let the joint friction force vector be... To centralize interference, For modeling error, This represents the torque vector mapped from the external force to the joint space. This is the transpose of the joint Jacobian matrix. The number of grounding outriggers, As an external force of the environment, , representing the velocity Jacobian matrix between the cylinder and the joint. , representing the Jacobian matrix between cylinder force and joint torque, with the right subscript . Corresponding to hydraulic robotic arms or hydraulic outriggers Joints, diagonal matrix and The element is defined as: , , , , It is the bulk modulus of hydraulic oil. It is the coefficient of the proportional valve. This indicates the effective area of ​​the two cavities. , This indicates the volume of the two cavities. This represents the initial volume of the two cavities. This indicates the amount of change in the cylinder's displacement. To control the input current vector, It is the square root of the pressure difference across the proportional valve.

[0006] Furthermore, step S2 is implemented as follows: The kinematic model established in step S1 is used to calculate the system's geometric relationships and Jacobian matrix, while the dynamic model is used to construct the state equations. Since joint angles can be directly measured while angular velocities are not, the measurable joint angles are selected as the observables. Meanwhile, considering system model errors and external measurement noise, the following state-space equations are derived from the dynamic model shown in formula (1): (2) definition: ,in , It is the output force of the hydraulic cylinder; definition: , The state-space model of the whole nonlinear system in formula (2) is further expressed as: (3) in, , The noise consists of process noise and measurement noise, both of which are Gaussian white noise and are independent of each other. The distance from the walk distance is taken as... Discretize the state equations: (4) Among them, the subscript in the lower right corner Indicates the first Each sampling time, and In respectively , Perform a first-order Taylor expansion at this point: (5) in, , It is the Jacobian matrix at the expansion point. Relative higher-order infinitesimals; Calculate the prior state based on the state prediction equation. : (6) Introducing a fading factor The error covariance prediction equation calculates the prior error covariance. : (7) in, It is the process noise in formula (3) The covariance matrix is ​​used to introduce a fading factor to correct the prediction error covariance matrix in real time, thereby adjusting the Kalman gain to ensure that the filter can effectively track parameter changes. The fading factor matrix... It can be obtained through algorithmic iteration: (8) in, This is the residual sequence, i.e., the estimation error; For undetermined factors, A positive coefficient; Represents finding a matrix traces, Represents finding a matrix traces, The error variance matrix is... express Measure noise at all times The covariance matrix, As a weakening factor, Forgetting factor; Update Kalman gain : (9) Update the state estimate filtering equation and calculate the posterior state. : (10) Calculate the error covariance update equation and posterior error covariance. : (11) in, It is an identity matrix.

[0007] Furthermore, the implementation method of step S3 is as follows: The optimization method employs a quadratic programming (QP) algorithm, with the objective function set to minimize the weighted sum of the supporting forces of each outrigger. Given that the overall machine's center of gravity deviates from the geometric center, weighting coefficients are introduced to set the force distribution weights for different outriggers. Constraints include the system's force balance equations and limitations on the force range of the outriggers. The mathematical expression of this optimization model is as follows: (12) Wherein, the objective function is , Let the expected support force of the four outriggers be the optimization variable. It is a symmetric positive definite weight matrix used to adjust the supporting force weights of each outrigger. These represent the minimum and maximum constraints of the supporting force, respectively, and the equality constraint. Represented as: (13) in, Represents the distance from the center of mass of the entire machine to the inertial coordinate system. Axial distance, Represents the distance from the center of mass of the entire machine to the inertial coordinate system. Axial distance, This indicates the mass of each link. This indicates that the center of mass of each link is in the inertial coordinate system. , The position of the axis These represent the virtual forces in the vertical direction, the roll angle direction, and the pitch angle direction, respectively. The calculation of the virtual forces is expressed as follows: (14) in, It is the virtual force coefficient in the vertical direction. These are the actual height and the expected height in the vehicle's base coordinate system, respectively. These are the actual vertical velocity and the desired vertical velocity in the vehicle's base coordinate system. These are the coefficients of the virtual force in the roll direction. These are the actual angle and the expected angle in the roll direction, respectively. These are the actual angular velocity and the desired angular velocity in the roll direction, respectively. These are the coefficients of the virtual force in the pitch direction. These are the actual angle and the desired angle of the pitch direction, respectively. These are the actual angular velocity and the expected angular velocity in the pitch direction, respectively. The drive current of the pitch legs is expressed as: (15) in, It is the derivative of the expectation force. It is a diagonal positive definite gain matrix. This represents the error between expected force and actual force. This represents the joint velocity estimated by the strong tracking Kalman filter in step 2.

[0008] Furthermore, step S4 is implemented as follows: The trajectory of the swinging outriggers is planned. If the two outriggers are not initially parallel, independent swing adjustment of a single outrigger is performed first. Once they reach a parallel state, synchronous swing control of both outriggers is initiated. The position control of the swinging outriggers is implemented using a PID control algorithm based on feedforward compensation. (16) in, It is a diagonal positive definite gain matrix. These are the desired angle and angular velocity of the swinging outrigger. These are the actual angles and angular velocities of the swinging outriggers. It is the nominal current vector; nominal current vector Specifically, this is achieved through pre-calibration. A data table mapping the relationship between cylinder movement speed, joint force, and drive current is established through experimental calibration. During actual control, based on the specified outrigger swing speed and the joint force estimated in step S2, the corresponding nominal current value can be obtained by consulting this calibration data table. .

[0009] Furthermore, the implementation method of step S5 is as follows: the force adjustment current calculated by the force distribution controller is sent to the pitch outrigger proportional valve, and the swing outrigger current calculated by the synchronous rotation controller is sent to the swing outrigger, so as to realize the support force distribution adjustment while swinging.

[0010] Compared with the prior art, the present invention has the following beneficial effects: (1) In view of the problems of decreased synchronization performance and increased tire wear caused by uneven force during the synchronous steering process of articulated walking excavators, a synchronous steering control method based on force distribution optimization is proposed. This method achieves optimized distribution of outrigger force by introducing weight coefficients, so that each swinging outrigger distributes force according to the weight coefficients during the steering process, thereby significantly improving the synchronization performance of the system and the overall steering stability of the machine.

[0011] (2) To address the issue of poor tracking accuracy in the sway outrigger position control and pitch outrigger force control during synchronous steering of articulated walking excavators due to disturbances, a strong tracking Kalman filter algorithm is proposed to estimate joint speed and external load force in real time, and the estimated values ​​are applied to the control algorithm design. For force control, a model-based control method is adopted to improve the system's response to load dynamics. For position control, a mapping relationship between current and output force is established by calibrating the hydraulic outriggers' speed-joint external force-current, and a PID position control algorithm based on current feedforward compensation is constructed on this basis. This effectively enhances the system's robustness to parameter changes and external disturbances, and improves position tracking accuracy. Attached Figure Description

[0012] To more clearly illustrate the technical solutions in the embodiments of this application, the accompanying drawings used in the description of the embodiments will be briefly introduced below. Obviously, the accompanying drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0013] Figure 1This is a flowchart illustrating the method implementation of an embodiment of the present invention;

[0014] Figure 2 This is a schematic diagram of the control algorithm in an embodiment of the present invention;

[0015] Figure 3 The diagram below shows a hinged synchronous steering system in an embodiment of the present invention: the left diagram shows a synchronous left turn, and the right diagram shows a synchronous right turn. Detailed Implementation

[0016] The present invention will be further described below with reference to the accompanying drawings and embodiments.

[0017] It should be noted that the following detailed descriptions are exemplary and intended to provide further explanation of this application. Unless otherwise specified, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this application pertains.

[0018] The purpose of this invention is to provide a synchronous steering control method for walking excavators based on force distribution optimization, which can adjust the pitch outriggers during synchronous steering of the swing outriggers, improve the force distribution of the swing outriggers, improve the accuracy of synchronous steering, and reduce tire wear.

[0019] To achieve the above-mentioned invention, the technical solution adopted by this invention is: a synchronous steering control method for a walking excavator based on force distribution optimization, comprising the following steps: S1. Establish the kinematic and dynamic models of the whole machine; S2. The strong tracking Kalman filter algorithm is used to estimate the joint velocity and joint external force; S3. Taking the minimization of the weighted sum of the supporting forces of each leg as the objective function, based on mechanical balance constraints and joint force constraints, the optimal desired joint torque is solved by an optimization algorithm, and the pitch joint current is calculated based on the force controller. S4. Obtain the desired angle of the swing outrigger based on the synchronous steering trajectory planning, and calculate the current of the swing outrigger based on the feedforward compensation PID algorithm. S5. Apply force distribution adjustment current to the pitch joint of the outrigger and apply steering adjustment current to the swing outrigger.

[0020] Based on the method proposed in this embodiment, the implementation principle of synchronous steering control for articulated walking excavators is as follows: Figure 2As shown, the specific steps are as follows: First, the controller collects cylinder displacement, cylinder pressure, and chassis attitude data provided by the body sensors of the walking excavator; through geometric transformation, the cylinder displacement and cylinder force are converted into joint angle and joint torque; then, the strong tracking Kalman filter method is used to estimate the joint angular velocity and joint external force; according to the force optimization objective function and its constraints, the desired pitch joint force is obtained; based on the difference between the desired joint force and the actual joint force, force control is implemented on the pitch joint; simultaneously, the desired angle of the swing joint is calculated according to the synchronous swing trajectory planning, and combined with the actual joint angle, the position control of the swing joint is performed; finally, the current signal obtained from the force control and position control calculations is output to the proportional valve group to achieve precise control of the actuator and complete the entire synchronous steering process.

[0021] In step S1, the implementation methods for state acquisition and model building are as follows: The outriggers of the walking excavator are divided into front outriggers and rear outriggers. The front outriggers have swing and pitch degrees of freedom, while the rear outriggers have swing, pitch, and wheel drive degrees of freedom. The overall machine posture is acquired by an IMU unit installed on the chassis. The cylinder displacement is collected by displacement sensors built into the cylinders, and the cylinder displacement is converted into the corresponding joint angle based on the geometric mapping relationship between the cylinder displacement and the joint angle. The joint torque is measured by pressure sensors installed in the cylinders and then converted into the joint space. The N-degree-of-freedom dynamic model is established as follows: (1) Among them, state variables These are the joint angle, angular velocity, and hydraulic cylinder driving force, respectively. Represents the inertial force matrix. Represents the vectors of the Coriolis force and the centrifugal force. Represents the gravity vector. Let the joint friction force vector be... To centralize interference, For modeling error, This represents the torque vector mapped from the external force to the joint space. This is the transpose of the joint Jacobian matrix. The number of grounding outriggers, As an external force of the environment, , representing the velocity Jacobian matrix between the cylinder and the joint. , representing the Jacobian matrix between cylinder force and joint torque, with the right subscript . Corresponding to hydraulic robotic arms or hydraulic outriggers Joints, diagonal matrix and The element is defined as: , , , , It is the bulk modulus of hydraulic oil. It is the coefficient of the proportional valve. This indicates the effective area of ​​the two cavities. , This indicates the volume of the two cavities. This represents the initial volume of the two cavities. This indicates the amount of change in the cylinder's displacement. To control the input current vector, It is the square root of the pressure difference across the proportional valve.

[0022] In step S2, the method for estimating angular velocity and joint external force based on strong tracking Kalman filtering is as follows: The kinematic model established in step S1 is used to calculate the system's geometric relationships and Jacobian matrix, while the dynamic model is used to construct the state equations. Since joint angles can be directly measured while angular velocities are not, the measurable joint angles are selected as the observables. Meanwhile, considering system model errors and external measurement noise, the following state-space equations are derived from the dynamic model shown in formula (1): (2) definition: ,in , It is the output force of the hydraulic cylinder; definition: , The state-space model of the whole nonlinear system in formula (2) is further expressed as: (3) in, , The noise consists of process noise and measurement noise, both of which are Gaussian white noise and are independent of each other. The distance from the walk distance is taken as... Discretize the state equations: (4) Among them, the subscript in the lower right corner Indicates the first Each sampling time, and In respectively , Perform a first-order Taylor expansion at this point: (5) in, , It is the Jacobian matrix at the expansion point. Relative higher-order infinitesimals; Calculate the prior state based on the state prediction equation. : (6) Introducing a fading factor The error covariance prediction equation calculates the prior error covariance. : (7) in, It is the process noise in formula (3) The covariance matrix is ​​used to introduce a fading factor to correct the prediction error covariance matrix in real time, thereby adjusting the Kalman gain to ensure that the filter can effectively track parameter changes. The fading factor matrix... It can be obtained through algorithmic iteration: (8) in, This is the residual sequence, i.e., the estimation error; For undetermined factors, A positive coefficient; Represents finding a matrix traces, Represents finding a matrix traces, The error variance matrix is... express Measure noise at all times The covariance matrix, As a weakening factor, Forgetting factor; Update Kalman gain : (9) Update the state estimate filtering equation and calculate the posterior state. : (10) Calculate the error covariance update equation and posterior error covariance. : (11) in, It is an identity matrix.

[0023] In step S3, the method for implementing force planning and current calculation of the pitching outriggers based on force distribution is as follows: The optimization method employs a quadratic programming (QP) algorithm, with the objective function set to minimize the weighted sum of the supporting forces of each outrigger. Given that the overall machine's center of gravity deviates from the geometric center, weighting coefficients are introduced to set the force distribution weights for different outriggers. Constraints include the system's force balance equations and limitations on the force range of the outriggers. The mathematical expression of this optimization model is as follows: (12) Wherein, the objective function is , Let the expected support force of the four outriggers be the optimization variable. It is a symmetric positive definite weight matrix used to adjust the supporting force weights of each outrigger. These represent the minimum and maximum constraints of the supporting force, respectively, and the equality constraint. Represented as: (13) in, Represents the distance from the center of mass of the entire machine to the inertial coordinate system. Axial distance, Represents the distance from the center of mass of the entire machine to the inertial coordinate system. Axial distance, This indicates the mass of each link. This indicates that the center of mass of each link is in the inertial coordinate system. , The position of the axis These represent the virtual forces in the vertical direction, the roll angle direction, and the pitch angle direction, respectively. The calculation of the virtual forces is expressed as follows: (14) in, It is the virtual force coefficient in the vertical direction. These are the actual height and the expected height in the vehicle's base coordinate system, respectively. These are the actual vertical velocity and the desired vertical velocity in the vehicle's base coordinate system. These are the coefficients of the virtual force in the roll direction. These are the actual angle and the expected angle in the roll direction, respectively. These are the actual angular velocity and the desired angular velocity in the roll direction, respectively. These are the coefficients of the virtual force in the pitch direction. These are the actual angle and the desired angle of the pitch direction, respectively. These are the actual angular velocity and the expected angular velocity in the pitch direction, respectively. The drive current of the pitch legs is expressed as: (15) in, It is the derivative of the expectation force. It is a diagonal positive definite gain matrix. This represents the error between expected force and actual force. This represents the joint velocity estimated by the strong tracking Kalman filter in step 2.

[0024] In step S4, the method for calculating the current of the swing outrigger during the synchronous rotation process is as follows: The trajectory of the swinging outriggers is planned. If the two outriggers are not initially parallel, independent swing adjustment of a single outrigger is performed first. Once they reach a parallel state, synchronous swing control of both outriggers is initiated. The position control of the swinging outriggers is implemented using a PID control algorithm based on feedforward compensation. (16) in, It is a diagonal positive definite gain matrix. These are the desired angle and angular velocity of the swinging outrigger. These are the actual angles and angular velocities of the swinging outriggers. It is the nominal current vector; nominal current vector Specifically, this is achieved through pre-calibration. A data table mapping the relationship between cylinder movement speed, joint force, and drive current is established through experimental calibration. During actual control, based on the specified outrigger swing speed and the joint force estimated in step S2, the corresponding nominal current value can be obtained by consulting this calibration data table. .

[0025] In step S5, the implementation method is as follows: the force adjustment current calculated by the force distribution controller is sent to the pitch outrigger proportional valve, and the swing outrigger current calculated by the synchronous rotation controller is sent to the swing outrigger, so as to realize the support force distribution adjustment while swinging.

Claims

1. A synchronous steering control method for a walking excavator based on force distribution optimization, applied to a walking excavator, the walking excavator comprising a robotic arm and multiple outriggers, characterized in that, Includes the following steps: S1. Establish the kinematic and dynamic models of the whole machine; S2. The strong tracking Kalman filter algorithm is used to estimate the joint velocity and joint external force; S3. Taking the minimization of the weighted sum of the supporting forces of each leg as the objective function, based on mechanical balance constraints and joint force constraints, the optimal desired joint torque is solved by an optimization algorithm, and the pitch joint current is calculated based on the force controller. S4. Obtain the desired angle of the swing outrigger based on the synchronous steering trajectory planning, and calculate the current of the swing outrigger based on the feedforward compensation PID algorithm. S5. Apply force distribution adjustment current to the pitch joint of the outrigger and apply steering adjustment current to the swing outrigger.

2. The synchronous steering control method for a walking excavator based on force distribution optimization according to claim 1, characterized in that: In step S1, the established dynamic model of the proportional valve-cylinder-robotic arm linkage is as follows: The outriggers of the walking excavator are divided into front outriggers and rear outriggers. The front outriggers have swing and pitch degrees of freedom, while the rear outriggers have swing, pitch, and wheel drive degrees of freedom. The overall machine posture is acquired by an IMU unit installed on the chassis. The cylinder displacement is collected by displacement sensors built into the cylinders, and the cylinder displacement is converted into the corresponding joint angle based on the geometric mapping relationship between the cylinder displacement and the joint angle. The joint torque is measured by pressure sensors installed in the cylinders and then converted into the joint space. The N-degree-of-freedom dynamic model is established as follows: （1） Among them, state variables These are the joint angle, angular velocity, and hydraulic cylinder driving force, respectively. Represents the inertial force matrix. Represents the vectors of the Coriolis force and the centrifugal force. Represents the gravity vector. Let the joint friction force vector be... To centralize interference, For modeling error, This represents the torque vector mapped from the external force to the joint space. This is the transpose of the joint Jacobian matrix. The number of grounding outriggers, As an external force of the environment, , representing the velocity Jacobian matrix between the cylinder and the joint. , representing the Jacobian matrix between cylinder force and joint torque, with the right subscript . Corresponding to hydraulic robotic arms or hydraulic outriggers Joints, diagonal matrix and The element is defined as: , , , , It is the bulk modulus of hydraulic oil. It is the coefficient of the proportional valve. This indicates the effective area of ​​the two cavities. , Indicates the volume of the two cavities. This represents the initial volume of the two cavities. This indicates the amount of change in the cylinder's displacement. To control the input current vector, It is the square root of the pressure difference across the proportional valve.

3. The synchronous steering control method for a walking excavator based on force distribution optimization according to claim 1, characterized in that: In step S2, the method for estimating joint angular velocity and joint external force using strong tracking Kalman filtering is as follows: The kinematic model established in step S1 is used to calculate the system's geometric relationships and Jacobian matrix, while the dynamic model is used to construct the state equations. Since joint angles can be directly measured while angular velocities are not, the measurable joint angles are selected as the observables. Meanwhile, considering system model errors and external measurement noise, the following state-space equations are derived from the dynamic model shown in formula (1): （2） definition: ,in , It is the output force of the hydraulic cylinder; definition: , The state-space model of the whole nonlinear system in formula (2) is further expressed as: （3） in, , The noise consists of process noise and measurement noise, both of which are Gaussian white noise and are independent of each other. The distance from the walk distance is taken as... Discretize the state equations: （4） The subscript in the lower right corner Indicates the first Each sampling time, and In respectively , Perform a first-order Taylor expansion at this point: （5） in, , It is the Jacobian matrix at the expansion point. Relative higher-order infinitesimals; Calculate the prior state based on the state prediction equation. : （6） Introducing a fading factor The error covariance prediction equation calculates the prior error covariance. : （7） in, It is the process noise in formula (3) The covariance matrix is ​​used to introduce a fading factor to correct the prediction error covariance matrix in real time, thereby adjusting the Kalman gain to ensure that the filter can effectively track parameter changes. The fading factor matrix... It can be obtained through algorithmic iteration: （8） in, This is the residual sequence, i.e., the estimation error; For undetermined factors, A positive coefficient; Represents finding a matrix traces, Represents finding a matrix traces, The error variance matrix is... express Measure noise at all times The covariance matrix, As a weakening factor, Forgetting factor; Update Kalman gain : （9） Update the state estimate filtering equation and calculate the posterior state. : （10） Calculate the error covariance update equation and posterior error covariance. : （11） in, It is an identity matrix.

4. The synchronous steering control method for a walking excavator based on force distribution optimization according to claim 1, characterized in that: In step S3, the method for calculating the pitch leg control current based on force optimization allocation is as follows: The optimization method employs a quadratic programming (QP) algorithm, with the objective function set to minimize the weighted sum of the supporting forces of each outrigger. Given that the overall machine's center of gravity deviates from the geometric center, weighting coefficients are introduced to set the force distribution weights for different outriggers. Constraints include the system's force balance equations and limitations on the force range of the outriggers. The mathematical expression of this optimization model is as follows: （12） Wherein, the objective function is , Let the expected support force of the four outriggers be the optimization variable. It is a symmetric positive definite weight matrix used to adjust the supporting force weights of each outrigger. These represent the minimum and maximum constraints of the supporting force, respectively, and the equality constraint. Represented as: （13） in, Represents the distance from the center of mass of the entire machine to the inertial coordinate system. Axial distance, Represents the distance from the center of mass of the entire machine to the inertial coordinate system. Axial distance, This indicates the mass of each link. This indicates that the center of mass of each link is in the inertial coordinate system. , The position of the axis These represent the virtual forces in the vertical direction, the roll angle direction, and the pitch angle direction, respectively. The calculation of the virtual forces is expressed as follows: （14） in, It is the virtual force coefficient in the vertical direction. These are the actual height and the expected height in the vehicle's base coordinate system, respectively. These are the actual vertical velocity and the desired vertical velocity in the vehicle's base coordinate system. These are the coefficients of the virtual force in the roll direction. These are the actual angle and the expected angle in the roll direction, respectively. These are the actual angular velocity and the desired angular velocity in the roll direction, respectively. These are the coefficients of the virtual force in the pitch direction. These are the actual angle and the desired angle of the pitch direction, respectively. These are the actual angular velocity and the expected angular velocity in the pitch direction, respectively. The drive current of the pitch outriggers is expressed as: （15） in, It is the derivative of the expectation force. It is a diagonal positive definite gain matrix. This represents the error between expected force and actual force. This represents the joint velocity estimated by the strong tracking Kalman filter in step 2.

5. The synchronous steering control method for a walking excavator based on force distribution optimization according to claim 1, characterized in that: In step S4, the method for controlling the position of the synchronously swinging outrigger is as follows: The trajectory of the swinging outriggers is planned. If the two outriggers are not initially parallel, independent swing adjustment of a single outrigger is performed first. Once they reach a parallel state, synchronous swing control of both outriggers is initiated. The position control of the swinging outriggers is implemented using a PID control algorithm based on feedforward compensation. （16） in, It is a diagonal positive definite gain matrix. These are the desired angle and angular velocity of the swinging outriggers. These are the actual angles and angular velocities of the swinging outriggers. It is the nominal current vector; nominal current vector Specifically, this is achieved through pre-calibration. A data table mapping the relationship between cylinder movement speed, joint force, and drive current is established through experimental calibration. During actual control, based on the specified outrigger swing speed and the joint force estimated in step S2, the corresponding nominal current value can be obtained by consulting this calibration data table. .

6. The synchronous steering control method for a walking excavator based on force distribution optimization according to claim 1, characterized in that, The implementation method for step S5 is as follows: The estimation results of joint velocity and joint load external force are obtained based on the strong tracking Kalman filter method; through force optimization distribution and synchronous steering trajectory planning, the expected planning force of the pitch joint and the expected angle of the swing joint are obtained respectively. Based on the calculation results of the drive current of the swing outrigger and the pitch outrigger, the corresponding current values ​​are input to the corresponding proportional valves, thereby realizing the dynamic adjustment of the outrigger force during synchronous steering, and finally achieving precise and stable articulated synchronous steering.

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