A valve-controlled hydraulic mechanical leg active compliance control method based on self-disturbance rejection control

Abstract

This invention discloses an active compliant control method for a valve-controlled hydraulic mechanical leg based on active disturbance rejection control (ADRC). This method combines an inner-loop ADRC controller and an outer-loop admittance controller, designing an active compliant controller that balances position control accuracy and compliance. To address the nonlinearity and uncertainty of the valve-controlled hydraulic mechanical leg, an extended state observer is designed to estimate the dynamic coupling terms of the leg, which are then compensated for in the ADRC using a feedforward approach, resulting in better tracking performance. The external force is calculated based on the mathematical model of the valve-controlled hydraulic mechanical leg and the signals acquired by the force sensor. This force is then passed through the admittance controller to compensate for the desired trajectory of the ADRC, thus achieving active compliant control of the valve-controlled hydraulic mechanical leg.

Description

Technical Field

[0001] This invention belongs to the field of hydraulic mechanical leg servo control technology, specifically relating to an active compliant control method for valve-controlled hydraulic mechanical legs based on active disturbance rejection control. Background Technology

[0002] Compared to wheeled and tracked robots, legged robots are more adaptable to unknown environments. Quadruped robots offer better stability than bipedal robots and a simpler structure than hexaped robots. Common actuation methods for quadruped robot leg joints include electric motors, hydraulic systems, and pneumatic systems. Hydraulic actuation, due to its strong load-bearing and explosive capabilities, is widely used in quadruped robots. Currently, hydraulic drive units are widely used in hydraulic quadruped robots. These units integrate displacement sensors, force sensors, and servo valves onto the hydraulic cylinder, simplifying the structure and improving control performance.

[0003] The control strategy of a robot is the most critical factor affecting its adaptability. Robots replace humans in dangerous tasks such as disaster relief and military operations. Different loads and road conditions impose varying impact forces on their feet, causing instability and structural damage. Therefore, simple position control strategies cannot meet the control requirements of robots, while active compliant control can make the robot's movement exhibit compliance, thereby reducing external impacts. Force-position hybrid control, impedance control, and admittance control are commonly used active compliant control methods. Admittance control considers the dynamic relationship between force and position of the controlled system, involving both force and position control. It ensures robot motion accuracy while avoiding excessive contact forces. Due to its advantages, admittance control has been applied in various fields.

[0004] Position-based admittance control offers higher control accuracy, and the most critical factor affecting this accuracy is the position control strategy. Due to the strong nonlinearity and uncertainty inherent in hydraulic quadruped robots, traditional PID control cannot meet the high-dynamic control requirements of the robotic legs. Han Jingqing's proposed active disturbance rejection control (ADRC) employs an extended state observer to observe unmodeled disturbances in the system. It exhibits good dynamic tracking performance for systems with high uncertainty and high nonlinearity, and boasts advantages such as simple structure, convenient parameter adjustment, and no need for precise modeling. Gao Zhiqiang's proposed bandwidth method can be used to determine the gain parameters of the extended state observer, enhancing the practicality of ADRC. Summary of the Invention

[0005] The purpose of this invention is to provide an active compliant control method for valve-controlled hydraulic mechanical legs based on active disturbance rejection control, which can ensure both the control accuracy of the mechanical legs and the compliant response of the mechanical legs to external forces.

[0006] The technical solution to achieve the purpose of this invention is: an active compliance control method for valve-controlled hydraulic mechanical legs based on active disturbance rejection control, comprising the following steps:

[0007] Step 1: Establish the mathematical model of the valve-controlled hydraulic mechanical leg system, then proceed to Step 2.

[0008] Step 2: Based on the mathematical model of the valve-controlled hydraulic mechanical leg system, design an active compliance controller for the valve-controlled hydraulic mechanical leg based on active disturbance rejection control, and proceed to Step 3.

[0009] Step 3: Using Lyapunov stability theory, the stability of the active compliance controller for valve-controlled hydraulic mechanical legs based on active disturbance rejection control is proved, and the results show that both the system observation error and the tracking error are bounded.

[0010] Compared with the prior art, the significant advantages of this invention are: (1) Position control is used as the inner loop and admittance control is used as the outer loop, which ensures the control accuracy of the mechanical leg while making the mechanical leg respond compliantly when subjected to external force; (2) The inner loop of position control adopts active disturbance rejection control, which has a simple structure, does not require precise modeling, is easy to implement, and has good control performance. Attached Figure Description

[0011] Figure 1 This is a model diagram of the valve-controlled hydraulic mechanical leg of the present invention.

[0012] Figure 2 This is a schematic diagram of the valve-controlled hydraulic mechanical leg structure of the present invention. The shaded part in the right figure represents the same component.

[0013] Figure 3 This is a diagram showing the interaction between the hydraulic mechanical leg of this invention and external forces during movement.

[0014] Figure 4 Under the controller of this invention, the desired trajectory of the three joints of the mechanical leg foot end when subjected to external force.

[0015] Figure 5 It's a mechanical leg. Figure 4 Comparison of tracking errors of the three joints of active disturbance rejection control and PI control under the trajectory.

[0016] Figure 6 It is the control input of the three joints under the action of the active compliance controller of the valve-controlled hydraulic mechanical leg based on self-disturbance rejection control designed in this invention. Detailed Implementation

[0017] Combination Figure 1 and Figure 2 The present invention discloses an active compliance control method for valve-controlled hydraulic mechanical legs based on active disturbance rejection control, comprising the following steps:

[0018] Step 1: Establish a mathematical model of the hydraulic mechanical leg system, which is a coupling of a mechanical system and a hydraulic system, as detailed below:

[0019] According to the Lagrange method, the mechanical dynamics model of the joint space of a valve-controlled hydraulic mechanical leg is described as follows:

[0020]

[0021] Where θ is the angle of the mechanical leg joint. For the angular velocity of the mechanical leg joint, Let ω be the angular acceleration of the mechanical leg joint, τ be the control torque of the mechanical leg joint, and M, C, and G be the inertia matrix, centrifugal force and Coriolis force matrix, and gravitational torque vector in the mechanical leg joint space, respectively.

[0022] Define the actuator extension displacement as x p Then the angular velocity of the mechanical leg joint and actuator extension speed The following relationship exists:

[0023]

[0024] Where J is the Jacobian matrix.

[0025] From equations (1) and (2), we obtain the mechanical dynamics model expression for the actuator space of the mechanical leg:

[0026]

[0027] Where F is the output force of the actuator, and M p C p G p These represent the inertia matrix, centrifugal force and Coriolis force matrices, and gravitational torque vector in the actuator space of the robotic leg, respectively. The actuator extends with acceleration.

[0028] The output force of the actuator is related to the pressure in both chambers and the working area of ​​the actuator as follows:

[0029]

[0030] Where P1 is the pressure of the oil inlet chamber, P2 is the pressure of the oil outlet chamber, A1 is the effective area of ​​the oil inlet chamber, and A2 is the effective area of ​​the oil outlet chamber.

[0031] The dynamic equation for the pressure of the actuator is:

[0032]

[0033] Where, β e V is the elastic modulus of hydraulic oil. 01V is the initial volume of the oil inlet chamber. 02 C is the initial volume of the oil drain chamber. t Where Q1 is the internal leakage coefficient, Q2 is the inlet oil flow rate, and Q2 is the outlet oil flow rate. Let P1 be the first derivative with respect to time. It is the first derivative of P2 with respect to time.

[0034] Since the bandwidth of the servo valve is much higher than the system bandwidth, the valve spool displacement of the servo valve is considered to be proportional to the control input. Therefore, the hydraulic oil flow rate of the two chambers is expressed as:

[0035]

[0036] Where, k t It is the control input gain, u is the control input, P s It is the system oil supply pressure, P r This is the system return oil pressure, where sign is the sign function, represented as:

[0037]

[0038] Define the system's state variables as x = [x1, x2, x3, x4] T , where the state variable x1 = [x p1 ,x p2 ,x p3 ] T State variables State variable x3 = [P 11 ,P 21 ,P 31 ] T State variable x4 = [P 12 ,P 22 ,P 32 ] T x p1 x p2 x p3 These represent the extension displacements of the three actuators. The extension speeds of the three actuators are P and P, respectively. 11 P 21 P 31 , and represent the inlet chamber pressures of the three actuators, respectively. 12 P 22 P 32 , , are the oil discharge chamber pressures of the three actuators, respectively, and T represents transposition.

[0039] The nonlinear model of the system can then be written in the following state-space form:

[0040]

[0041] in, This represents the first derivative of x1 with respect to time. This represents the first derivative of x² with respect to time. This represents the first derivative of x3 with respect to time. This represents the first derivative of x⁴ with respect to time. M represents P The inverse of , where y represents an intermediate variable.

[0042] Step 2: Based on the mathematical model of the valve-controlled hydraulic mechanical leg system, design an active compliance controller for the valve-controlled hydraulic mechanical leg based on active disturbance rejection control, as detailed below:

[0043] Step 2-1: Design a valve-controlled hydraulic robotic leg self-disturbance rejection controller to achieve joint position control of the robotic leg. The specific steps are as follows:

[0044] Let variable z1 = x1, variable z2 = x2, variable Equation (8) can then be rewritten as:

[0045]

[0046] in, Let z1 be the first derivative with respect to time. Let z2 be the first derivative with respect to time. Let f be the first derivative of z3 with respect to time, and let E be an intermediate variable.

[0047]

[0048] for The first derivative with respect to time, C p The first derivative with respect to time, For G p The first derivative with respect to time.

[0049] Extend f to a new system state z4, and the first derivative of z4 with respect to time If w(t) is a time-dependent function, then the system is expanded into a new linear control system:

[0050]

[0051] The corresponding extended state observer is designed as follows:

[0052]

[0053] Where, β 01 ,β 02 ,β 03 ,β 04All are observer gains, and the tracking error ε1 = x1 - x 1d x 1d Let η1 be the expected trajectory, and η1 be the estimation error. For the estimate of z1, For the estimate of z2, For the estimate of z3, For the estimate of z4, for The first derivative with respect to time, for The first derivative with respect to time, for The first derivative with respect to time, for The first derivative with respect to time, the choice of observer gain should be such that its characteristic equation s 4 +β 01 s 3 +β 02 s 2 +β 03 s+β 04 Satisfying the Hurwitz condition, where s represents a complex variable; using the bandwidth method, the observer gain is β. 01 =4ω0, Adjusting the observer gain ω0 allows for the selection of observer parameters.

[0054] The tracking error is defined as:

[0055]

[0056] Where ε1, ε2, and ε3 are all tracking errors, y d It is the desired trajectory, the virtual control law. Virtual control law It is y d The first derivative with respect to time, It is the first derivative of α1 with respect to time, K1,K2∈R 3×3 , is the controller gain, R 3×3 This represents a 3×3 real matrix.

[0057] Based on the estimated state of the robotic leg system from the extended state observer, high-precision control of the robotic leg system is achieved. Therefore, after replacing the system state with its corresponding estimated value, the tracking error of the system is defined as:

[0058]

[0059] in, Both are tracking errors based on system state estimates, and are estimates of the virtual control law. Estimation of virtual control law yes The estimate.

[0060] The control input u is designed as follows:

[0061]

[0062] Among them, E -1 It is the inverse of E, K3∈R 3×3 , is the controller gain.

[0063] Step 2-2: Design an admittance controller to compensate for the desired trajectory of the active disturbance rejection control, thereby achieving active compliant control of the robotic leg. The specific steps are as follows:

[0064] Admittance control takes the desired trajectory as input and calculates the output force F of the hydraulic actuator based on the mechanical dynamics model. When the mechanical leg is subjected to an external force, the calculated actuator output force F and the force feedback F from the force sensor are compared. b The difference between the two is the external force F acting on the mechanical leg. L :

[0065] F L =FF b (17)

[0066] The desired trajectories of the three joints of the robotic leg are compensated by admittance control, causing it to exhibit the characteristics of a mass-spring-damped system; then, under external force F, the robotic leg... L Under the influence of the expected trajectory compensation y z Described as:

[0067]

[0068] in, Indicates y z The first derivative with respect to time, Indicates y z The second derivative with respect to time;

[0069] Since the range of motion of the robotic leg's joints is limited, a saturation function is introduced to ensure that the final desired trajectory lies within the robotic leg's motion space. The resulting desired trajectory is:

[0070]

[0071] Wherein, the constant γ=(1-β)ω c The constant β satisfies 0 < β < 1, and the constant ω c It is the limit angle of the joint, and the expected trajectory after compensation.

[0072] Finally, through the active disturbance rejection controller, the robotic leg follows the final desired trajectory y with high precision. dz The final controller design consists of two parts: an inner loop of active disturbance rejection control that enables the robotic leg to move along the desired trajectory, and an outer loop of admittance control that compensates for the desired trajectory of the robotic leg, making it compliant when subjected to external forces.

[0073] Step 3: Using Lyapunov stability theory, the stability of the active compliance controller for the valve-controlled hydraulic mechanical leg based on active disturbance rejection control is proven, yielding results showing that both the system observation error and tracking error are bounded, as detailed below:

[0074] The Lyapunov function is defined as follows:

[0075]

[0076] Where V1, V2, and V3 are all Lyapunov functions, and their derivatives with respect to V1, V2, and V3 are respectively obtained as follows:

[0077]

[0078] in, It is the first derivative of V1 with respect to time. It is the first derivative of V2 with respect to time. It is the first derivative of V3 with respect to time. Substituting the controller (16) into the equation... get:

[0079]

[0080] also,

[0081]

[0082] Where I is a unit vector, and σ1, σ2, σ3, and σ4 are all constants. Substituting equation (23) into equation (22) yields:

[0083]

[0084] Where H is a constant:

[0085]

[0086] Where max is the maximum value function, which can be obtained according to Young's inequality:

[0087]

[0088] Where, the intermediate variable ψ=2min{λ min {K1},λ min {K2},λ min{K3-I / 2}},λ min {K1} is the smallest eigenvalue of K1, λ min {K2} is the smallest eigenvalue of K2, λ min {K3-I / 2} is the minimum eigenvalue of K3-I / 2, min is the minimum function, and ζ = 1 / 2H 2 Since it is a positive definite constant, we can conclude that V3 is bounded.

[0089] V3≤V3(0)e -ψt +ζ / ψ (27)

[0090] Where e is the natural constant, t is time, and the tracking error ε = [ε1ε2ε3] T The region of convergence is defined as:

[0091]

[0092] Where Λ represents the region of convergence of the tracking error.

[0093] Example

[0094] To verify the performance of the designed controller, the physical parameters of the valve-controlled hydraulic mechanical leg in the simulation are shown in Table 1.

[0095] Table 1 System Physical Parameters

[0096] physical parameters numerical values physical parameters numerical values <![CDATA[k t1 (m 3 / s / V / Pa 1 / 2 )]]> <![CDATA[1.5×10 -8 ]]> <![CDATA[P s (Well)]]> <![CDATA[21×10 6 ]]> <![CDATA[k t2 (m 3 / s / V / Pa 1 / 2 )]]> <![CDATA[1.5×10 -8 ]]> <![CDATA[P r (Well)]]> 0 <![CDATA[k t3 (m 3 / s / V / Pa 1 / 2 )]]> <![CDATA[1.4×10 -8 ]]> <![CDATA[C t (m 5 / (N·s))]]> <![CDATA[2.38×10 -13 ]]> <![CDATA[β e (Well)]]> <![CDATA[8×10 8 ]]>

[0097] Wherein, the control input gain k t =[k t1 ,k t2 ,k t3 ], k t1 ,k t2 ,k t3 These represent the control input gains for each joint of the robotic leg. To verify the effectiveness of compliant control, external forces are applied to the foot of the robotic leg. The lateral swing hip joint primarily resists lateral impacts, while the longitudinal swing hip and knee joints primarily resist vertical impacts. Therefore, vertical and horizontal forces are applied to the foot, such as... Figure 3 As shown. The law governing the change of force magnitude with time t is designed as follows:

[0098]

[0099] Where F1 represents the vertical force, F2 represents the horizontal force, t represents time, and N represents the unit of force, Newton.

[0100] Depend on Figure 4 It can be seen that under admittance control, when the foot of the robotic leg is subjected to an external force, the joint angle of the robotic leg exhibits a compliant response. The inner loop's active disturbance rejection control controls the robotic leg to track the desired trajectory.

[0101] To verify the effectiveness of the active disturbance rejection control in this invention, the inner-loop position controller was compared with traditional PI control. The parameters for the PI control were set as K... P =[2000,3,4]、K I =[5000,50,40]. In active disturbance rejection control, the observer gain of the three joints is ω0 = [180,200,220], and the controller gain of active disturbance rejection control is K1 = [800,900,800], K2 = [600,800,700], K3 = [300,600,600].

[0102] Depend on Figure 5 Therefore, under the same desired trajectory, the maximum error and steady-state error of the three-joint active disturbance rejection control are both smaller than those of the traditional PI control, resulting in higher control accuracy. Figure 6 This is the control input of the controller of the present invention. As can be seen from the figure, the control input is a continuous signal and can be used in a practical controller.

Claims

1. A method for active compliant control of a valve-controlled hydraulic mechanical leg based on active disturbance rejection control, characterized in that, Includes the following steps: Step 1: Establish the mathematical model of the valve-controlled hydraulic mechanical leg system. The nonlinear model of the system is written in the following state-space form: Wherein, the system's state variables are x = [x1, x2, x3, x4]. T x1, x2, x3, and x4 are all state variables. This represents the first derivative of x1 with respect to time. This represents the first derivative of x² with respect to time. This represents the first derivative of x3 with respect to time. M represents the first derivative of x⁴ with respect to time. p C p G p These represent the inertia matrix, centrifugal force and Coriolis force matrices, and gravitational torque vector in the actuator space of the robotic leg, respectively. M represents P The inverse of , y represents an intermediate variable, A1 is the effective area of ​​the oil inlet chamber, A2 is the effective area of ​​the oil outlet chamber, P1 is the pressure of the oil inlet chamber, P2 is the pressure of the oil outlet chamber, β e C is the elastic modulus of hydraulic oil. t V is the internal leakage coefficient, Q1 is the inlet oil flow rate, Q2 is the outlet oil flow rate, and V is the outlet oil flow rate. 01 V is the initial volume of the oil inlet chamber. 02 Let y represent the initial volume of the oil discharge chamber, and y represent an intermediate variable. Proceed to step 2; Step 2: Based on the mathematical model of the valve-controlled hydraulic mechanical leg system, design an active compliance controller for the valve-controlled hydraulic mechanical leg based on active disturbance rejection control: Step 2-1: Design a valve-controlled hydraulic robotic leg self-disturbance rejection controller to achieve joint position control of the robotic leg. The specific steps are as follows: Let variable z1 = x1, variable z2 = x2, variable Equation (8) can then be rewritten as: in, Let z1 be the first derivative with respect to time. Let z2 be the first derivative with respect to time. Let f be the first derivative of z3 with respect to time, E be the intermediate variable, and u be the control input. in, for The first derivative with respect to time, C p The first derivative with respect to time, For G p The first derivative with respect to time; k t P represents the control input gain. s It is the system oil supply pressure, P r It is the system return oil pressure; Extend f to a new system state z4, and the first derivative of z4 with respect to time If w(t) is a time-dependent function, then the system is expanded into a new linear control system: The corresponding extended state observer is designed as follows: Where, β 01 ,β 02 ,β 03 ,β 04 All are observer gains, and the tracking error ε1 = x1 - x 1d x 1d Let η1 be the expected trajectory, and η1 be the estimation error. For the estimate of z1, For the estimate of z2, For the estimate of z3, For the estimate of z4, for The first derivative with respect to time, for The first derivative with respect to time, for The first derivative with respect to time, for The first derivative with respect to time; The choice of observer gain should be such that its characteristic equation s 4 +β 01 s 3 +β 02 s 2 +β 03 s+β 04 Satisfying the Hurwitz condition, where s represents a complex variable; using the bandwidth method, the observer gain is β. 01 =4ω0, Adjusting the observer gain ω0 allows for the selection of observer parameters; The tracking error is defined as: Where ε1, ε2, and ε3 are all tracking errors, y d It is the desired trajectory, the virtual control law. Virtual control law It is y d The first derivative with respect to time, It is the first derivative of α1 with respect to time, and the controller gain K1,K2∈R 3×3 R 3×3 Represents a 3×3 real matrix; Based on the estimated state of the robotic leg system from the extended state observer, control of the robotic leg system is achieved. Therefore, after replacing the system state with its corresponding estimated value, the tracking error of the system is defined as: in, Both are tracking errors based on system state estimates, and are estimates of the virtual control law. Estimation of virtual control law yes The estimate; The control input u is designed as follows: Among them, E -1 It is the inverse of E, and the controller gain K3∈R 3×3 ; Step 2-2: Design an admittance controller to compensate for the desired trajectory of active disturbance rejection control and realize active compliant control of the robotic leg; Proceed to step 3; Step 3: Using Lyapunov stability theory, the stability of the active compliance controller for valve-controlled hydraulic mechanical legs based on active disturbance rejection control is proved, and the results show that both the system observation error and the tracking error are bounded.

2. The active compliant control method for valve-controlled hydraulic mechanical legs based on active disturbance rejection control according to claim 1, characterized in that, In step 1, a mathematical model of the valve-controlled hydraulic mechanical leg system is established, as follows: According to the Lagrange method, the mechanical dynamics model of the joint space of a valve-controlled hydraulic mechanical leg is described as follows: Where θ is the angle of the mechanical leg joint. For the angular velocity of the mechanical leg joint, Let ω be the angular acceleration of the mechanical leg joint, τ be the control torque of the mechanical leg joint, and M, C, and G be the inertia matrix, centrifugal force and Coriolis force matrix, and gravitational torque vector in the mechanical leg joint space, respectively. Define the actuator extension displacement as x p Then the angular velocity of the mechanical leg joint and actuator extension speed The following relationship exists: Where J is the Jacobian matrix; From equations (1) and (2), we obtain the mechanical dynamics model expression for the actuator space of the mechanical leg: Where F is the output force of the actuator, and M p C p G p These represent the inertia matrix, centrifugal force and Coriolis force matrices, and gravitational torque vector in the actuator space of the robotic leg, respectively. To extend the actuator with acceleration; The output force of the actuator is related to the pressure in both chambers and the working area of ​​the actuator as follows: Where P1 is the oil inlet chamber pressure, P2 is the oil outlet chamber pressure, A1 is the oil inlet chamber area, and A2 is the oil outlet chamber area. The dynamic equation for the pressure of the actuator is: Where, β e V is the elastic modulus of hydraulic oil. 01 V is the initial volume of the oil inlet chamber. 02 C is the initial volume of the oil drain chamber. t Where Q1 is the internal leakage coefficient, Q2 is the inlet oil flow rate, and Q2 is the outlet oil flow rate. Let P1 be the first derivative with respect to time. This is the first derivative of P2 with respect to time; Since the bandwidth of the servo valve is much higher than the system bandwidth, the valve spool displacement of the servo valve is considered to be proportional to the control input. Therefore, the hydraulic oil flow rate of the two chambers is expressed as: Where, k t It is the control input gain, u is the control input, P s It is the system oil supply pressure, P r This is the system return oil pressure, where sign is the sign function, expressed as: Define the system's state variables as x = [x1, x2, x3, x4] T , where the state variable x1 = [x p1 ,x p2 ,x p3 ] T State variables State variable x3 = [P 11 ,P 21 ,P 31 ] T State variable x4 = [P 12 ,P 22 ,P 32 ] T x p1 x p2 x p3 These represent the extension displacements of the three actuators. The extension speeds of the three actuators are P and P, respectively. 11 P 21 P 31 , and represent the inlet chamber pressures of the three actuators, respectively. 12 P 22 P 32 and represent the oil discharge chamber pressures of the three actuators, respectively, and T indicates transposition; The nonlinear model of the system can then be written in the following state-space form: in, This represents the first derivative of x1 with respect to time. This represents the first derivative of x² with respect to time. This represents the first derivative of x3 with respect to time. This represents the first derivative of x⁴ with respect to time. M represents P The inverse of , where y represents an intermediate variable.

3. The active compliant control method for valve-controlled hydraulic mechanical legs based on active disturbance rejection control according to claim 1, characterized in that, In step 2-2, an admittance controller is designed to compensate for the desired trajectory of the active disturbance rejection control, thereby achieving active compliant control of the robotic leg. The specific steps are as follows: The admittance controller takes the desired trajectory as input and calculates the output force F of the hydraulic actuator based on the mechanical dynamics model. When the mechanical leg is subjected to an external force, the calculated actuator output force F and the force feedback F from the force sensor are compared. b The difference between the two is the external force F acting on the mechanical leg. L : F L =F-F b (17) The desired trajectories of the three joints of the robotic leg are compensated by admittance control, causing it to exhibit the characteristics of a mass-spring-damped system; then, under external force F, the robotic leg... L Under the influence of the expected trajectory compensation y z Described as: in, Indicates y z The first derivative with respect to time, Indicates y z The second derivative with respect to time; Since the range of motion of the robotic leg's joints is limited, a saturation function is introduced to ensure that the final desired trajectory lies within the robotic leg's motion space. The resulting desired trajectory is: Wherein, the constant γ=(1-β)ω c The constant β satisfies 0 < β < 1, and the constant ω c It is the limit angle of the joint, and the expected trajectory after compensation. Finally, through the active disturbance rejection controller, the robotic leg follows the final desired trajectory y. dz The final controller design consists of two parts: an inner loop of active disturbance rejection control that enables the robotic leg to move along the desired trajectory, and an outer loop of admittance control that compensates for the desired trajectory of the robotic leg, making it compliant when subjected to external forces.

4. The active compliant control method for valve-controlled hydraulic mechanical legs based on active disturbance rejection control according to claim 3, characterized in that, In step 3, the stability of the active compliance controller for the valve-controlled hydraulic mechanical leg based on active disturbance rejection control is proved using Lyapunov stability theory. The results show that both the system observation error and tracking error are bounded, as detailed below: The Lyapunov function is defined as follows: Among them, V1, V2, and V3 are all Lyapunov functions; The stability was proven using Lyapunov stability theory, and the results showed that the observation error and tracking error of the system are bounded.

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