Disturbance observer-based adaptive obstacle function sliding mode control method and device for heavy-duty robot arm

Abstract

The application discloses a heavy-load mechanical arm obstacle function adaptive sliding mode control method and device based on a disturbance observer, the method establishes a dynamic model considering model errors, unmodeled parts, friction and the collective disturbance caused by external loads, converts the estimation problem of the collective disturbance into the state estimation problem of a linear system driven by an unknown input defined by an auxiliary state variable, and designs a sliding mode disturbance observer for estimating and compensating the collective disturbance; for the disturbance estimation error, a bounded adaptive control gain of the controller is designed by using an obstacle function, so that the error is kept within a preset range while control chattering is avoided. Through systematic control architecture design, the application effectively solves the key problem that the high-precision tracking and control smoothness of a shovel in a complex working environment are difficult to be considered simultaneously.

Description

Technical Field

[0001] This invention relates to the field of engineering machinery, and in particular to an adaptive sliding mode control method and device for obstacle function of heavy-duty robotic arms based on a disturbance observer. Background Technology

[0002] Heavy-duty robotic arms, as widely used engineering machinery, play a crucial role in infrastructure construction, emergency rescue, and other fields. To meet the ever-increasing demands for operational precision and efficiency, and to adapt to hazardous and harsh working environments, their intelligent and autonomous development has become an inevitable trend. The control system, as the execution hub of the robotic arm, has always been a research hotspot, encompassing classical PID methods and their extensions and improvements, as well as modern control methods based on state-space or dynamic models. Benefiting from these theoretical developments and their applications in robotic systems, Sliding Mode Control (SMC) has become a solution for the efficient operation of complex systems, including heavy-duty robotic arms. However, the core challenges to its applicability lie in accelerating arrival and sliding speeds and improving the adaptability of SMC to loaded systems to avoid overestimation / underestimation of disturbances. Summary of the Invention

[0003] To address the problems existing in the background technology, this invention proposes an adaptive sliding mode control method for obstacle functions of heavy-duty robotic arms based on a disturbance observer.

[0004] The objective of this invention is achieved through the following technical solution: Firstly, this invention provides an adaptive sliding mode control method for a heavy-duty robotic arm based on a disturbance observer's obstacle function, the method comprising the following steps:

[0005] (1) Dynamic modeling: Establish a dynamic model that considers model errors, unmodeled parts, friction and lumped disturbances caused by external loads;

[0006] (2) Sliding mode disturbance observer design: The problem of estimating lumped disturbances is transformed into the problem of estimating the state of a linear system driven by defined auxiliary state variables and unknown inputs. A sliding mode disturbance observer is designed to estimate and compensate for lumped disturbances.

[0007] (3) Adaptive sliding mode control based on obstacle function: Based on the sliding mode disturbance observer, the bounded adaptive control gain of the controller is designed using the obstacle function for the disturbance estimation error, so as to avoid control jitter and keep the error within the preset range.

[0008] Furthermore, in step (1), the Lagrange method is used to perform dynamic modeling of the heavy-duty robotic arm, and the system input is transformed into the actuator space.

[0009] Furthermore, in step (3), the perturbation estimate obtained by combining the dynamic model of the heavy-duty robotic arm and the sliding mode observer is used to design the control law and the adaptive law based on the system sliding variables, and the adaptive uncertainty term gain matrix is ​​obtained. The elements in the matrix are determined based on the integral gain and the barrier function.

[0010] Furthermore, the lumped disturbance is described by the state of a linear system driven by unknown input. Based on the linear system driven by unknown input, a sliding perturbation observer and observation error are obtained. The gain of the sliding perturbation observer is designed so that the observation error realizes terminal sliding motion in a finite time. Then, the lumped disturbance can be accurately estimated in a finite time.

[0011] Furthermore, in step (3), the designed control law and adaptive law enable the system sliding variables and joint errors to converge and eventually remain in the desired region without disturbing the observation error limits.

[0012] Furthermore, the control law is obtained based on the perturbation estimate obtained by combining a linear sliding function with the dynamic model of the actuator space of the heavy-duty robotic arm and a sliding mode perturbation observer.

[0013] Furthermore, the adaptive rate is the adaptive uncertainty gain in the control law. When the sliding variable is outside the barrier boundary, the adaptive gain can be increased until the sliding variable reaches the preset neighborhood. And when the sliding variable enters the preset neighborhood, the adaptive gain switches to the barrier function form to keep the output variable within the neighborhood.

[0014] Secondly, the present invention provides a heavy-duty robotic arm obstacle function adaptive sliding mode control device based on a disturbance observer, including a memory and one or more processors. The memory stores executable code, and when the processor executes the executable code, it implements the aforementioned heavy-duty robotic arm obstacle function adaptive sliding mode control method based on a disturbance observer.

[0015] Thirdly, the present invention provides a computer-readable storage medium having a program stored thereon, which, when executed by a processor, implements the aforementioned adaptive sliding mode control method for a heavy-duty robotic arm based on a disturbance observer obstacle function.

[0016] Fourthly, the present invention provides a computer program product, including a computer program, which, when executed by a processor, implements the aforementioned adaptive sliding mode control method for a heavy-duty robotic arm based on a disturbance observer obstacle function.

[0017] The beneficial effects of this invention are:

[0018] The excavator safety control method based on kinematic control obstacle function and adaptive sliding mode of obstacle function provided by this invention has the following significant advantages compared with the prior art:

[0019] Through a systematic control architecture design, this method effectively solves the critical problem of balancing high-precision tracking and control smoothness in excavators operating under complex conditions. First, it innovatively defines the control objective as "achieving chatter-free control input while ensuring joint tracking error converges within a predetermined range." This setting better aligns with the engineering reality of excavator hydraulic actuators having weak high-frequency response capabilities, avoiding the inherent flaw of traditional methods that sacrifice control smoothness in pursuit of theoretically precise convergence. Second, by introducing a sliding mode disturbance observer to quickly and accurately estimate lumped disturbances, including unmodeled dynamics and drastically changing external loads, it provides a precise feedforward compensation basis for the controller, reducing the control system's dependence on disturbance upper bound information. Based on this, the adaptive sliding mode controller based on the obstacle function can adjust the control gain in real time and smoothly according to the disturbance estimation error: when the tracking error is large, the gain automatically increases to ensure rapid convergence; when the error enters the preset neighborhood, the gain is dynamically adjusted according to the obstacle function. Thus, without needing to know the upper bound of the disturbance estimation error, it can effectively suppress the high-frequency chatter of the control signal caused by gain overestimation, and ensure continuous disturbance suppression capability. Ultimately, the system achieves a good balance between strong robustness and control smoothness, improving the overall performance of intelligent excavator operation. Attached Figure Description

[0020] Figure 1 This is a schematic diagram of the adaptive uncertainty gain trend based on BF.

[0021] Figure 2 This is a block diagram of an adaptive sliding mode control based on an obstacle function (SMDO).

[0022] Figure 3 This diagram illustrates the tracking errors of each joint and their control inputs for different controllers used in unloaded straight-line trajectories. Specifically, NDO-ASM is a single-increment adaptive sliding mode controller based on a nonlinear disturbance observer; SMDO-APSM is an adaptive piecewise sliding mode controller based on a sliding mode disturbance observer; and SMDO-BFSM is a barrier function adaptive sliding mode controller based on a sliding mode disturbance observer.

[0023] Figure 4 This diagram illustrates the tracking errors of each joint and their control inputs for different controllers used in linear trajectories under load. NDO-ASM: Single-increment adaptive sliding mode controller based on a nonlinear disturbance observer; SMDO-APSM: Adaptive piecewise sliding mode controller based on a sliding mode disturbance observer; SMDO-BFSM: Obstacle function adaptive sliding mode controller based on a sliding mode disturbance observer.

[0024] Figure 5This is a structural diagram of an adaptive sliding mode control device for a heavy-duty robotic arm based on a disturbance observer, according to the present invention. Detailed Implementation

[0025] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described below with reference to the accompanying drawings and examples. It should be understood that the specific examples described herein are merely illustrative and not intended to limit the invention.

[0026] like Figure 1 As shown, the present invention provides an adaptive sliding mode control method for a heavy-duty robotic arm based on a disturbance observer obstacle function, which specifically includes the following steps:

[0027] Step 1: Establish a system dynamic model of the heavy-duty robotic arm. A more accurate dynamic model is a prerequisite for high-precision control. The dynamic modeling of the robotic arm usually adopts the Lagrangian method or the Newton-Euler method. The Lagrangian method can ignore the internal constraint forces between the arms.

[0028] Step 1-1, Dynamic Model:

[0029] (1)

[0030] In the formula, These are the nominal inertia matrix, the Coriolis matrix, and the gravity matrix, respectively. These are joint position, velocity, and acceleration, respectively. For driving torque, This refers to the lumped disturbance caused by model errors, unmodeled parts, friction, and other external loads. Let be the number of degrees of freedom of the robotic arm joints. Transforming the input of the dynamic model into the actuator space, equation (1) is rewritten as:

[0031] (2)

[0032] In the formula, Input the force vector to the actuator. Driving space Jacobian matrix Defined as In the formula, For the displacement of parallel joint actuators (such as hydraulic cylinders). These correspond to the displacements of the four joints, respectively.

[0033] Steps 1-2 analyze the dynamic model of formula (1), which includes the following characteristics:

[0034] Property 1: Inertia Matrix It is symmetric, positive definite, and bounded, satisfying In the formula , Let represent the minimum and maximum eigenvalues ​​of the matrix, respectively. Represents the identity matrix.

[0035] Property 1 can be understood as the existence of positive constants. ,for All have , for The Euclidean norm, when When it is a vector, ,when When it is a matrix, .

[0036] Property 2: It is a skew-symmetric matrix. That is... .

[0037] Property 3: Given bounded ,but Bounded, that is , making .

[0038] Step 2: Design a sliding mode perturbation observer to estimate and compensate for lumped perturbations. And prove its stability.

[0039] Step 2-1, Design the sliding mode perturbation observer:

[0040] Define auxiliary quantity Taking its derivative, we get:

[0041] (3)

[0042] In the formula, Define a new auxiliary state variable:

[0043] (4)

[0044] In the formula, The variables are constants. Establish the state-space form of the auxiliary variables:

[0045] (5)

[0046] For equation (5), the lumped disturbance can be... The estimation problem is transformed into the estimation of new state variables. For state estimation problems involving linear systems driven by unknown inputs, it is necessary to establish the following assumptions:

[0047] Assumption 1: Unknown lumped disturbance It is bounded and differentiable, and its bounding value is Unknown, and can be derived from the time derivative The differentiable function description.

[0048] The bounded assumption makes it necessary that Bounded, otherwise it would lead to Unbounded, we can further assume:

[0049] Assumption 2: There always exists a positive scalar constant. , making .

[0050] definition The following systems exist:

[0051] (6a)

[0052] (6b)

[0053] For the linear system with unknown inputs as shown in equations (6a) and (6b), the sliding mode observer is designed as follows:

[0054] (7a)

[0055] (7b)

[0056] In the formula, ~ This refers to the observer gain. , , State variables The estimated value, , Defined as:

[0057] (8)

[0058] In the formula, , , All are odd constants greater than zero, and , Representing vectors The Each element.

[0059] Step 2-2, prove the stability of the sliding mode perturbation observer and analyze its convergence characteristics: To prove the stability of the observer, define the observation error. Combining equations (6a) and (6b) with equations (7a) and (7b), the error dynamic equation is defined by equations (9a) and (9b):

[0060] (9a)

[0061] (9b)

[0062] Theorem 1: (Uniformly Bounded) Consider a linear system (Equations (6a) and (6b)) satisfying Assumptions 1-2, transformed from the dynamic model of the heavy-duty robotic arm system (Equation (1)). If there is a sliding mode observer (Equations (7a) and (7b)), and its initial state is estimated as... , Then the observation errors of formulas (9a) and (9b) Consistency is ultimately bounded.

[0063] Theorem 2: (Finite-Time Convergence) For the dynamic model of a heavy-duty robotic arm system satisfying Assumptions 1-2 (Equation (1)), its lumped disturbance can be described by the state of a linear system with unknown inputs (Equations (6a) and (6b)). Considering the sliding mode observer SMDO (Equations (7a) and (7b)) and observation error dynamics (Equations (9a) and (9b)) obtained from this linear system, when the observer gain... , , The values ​​of satisfy:

[0064] ,

[0065]

[0066] In the formula, It is a positive scalar;

[0067]

[0068] Then observation error , Can be done in a limited time Internally realize terminal sliding motion, lumped disturbance It can be accurately estimated within a finite time, that is:

[0069]

[0070] In the formula, .

[0071] The proofs of Theorems 1 and 2 can be found in the literature (Reaction wheel fault compensation and disturbance rejection for spacecraft attitude tracking).

[0072] From Assumption 2 and Theorem 2, we know that Bounded makes It must be bounded, and ,Right now , for elements, .

[0073] Step 3: An adaptive sliding mode control method based on the barrier function (BF) is proposed.

[0074] Step 3-1, consider the dynamic system of the heavy-duty robotic arm (Equations (1) and (2)) and the disturbance observer (Equations (7a) and (7b)). Define arbitrarily small positive numbers , Design the control law and adaptive law to make the system sliding variable and joint error It converges and eventually settles in the desired region without perturbing the upper bound of the observation error:

[0075]

[0076] In the formula, For the desired joint angle, To pre-define obstacle boundaries, The gain is the sliding function.

[0077] Consider a linear sliding function:

[0078] (10)

[0079] In the formula, Combining the disturbance estimates obtained from the dynamic system of the heavy-duty robotic arm (Equation (2)) and the observers (Equations (7a) and (7b)), the control law can be designed:

[0080] (11a)

[0081] (11b)

[0082] In the formula, , , , , For the adaptive uncertainty term gain to be designed, , , Let each be the nth element in the corresponding matrix, defined as:

[0083] (12)

[0084] In the formula, For input saturation parameters, This is the integral gain.

[0085] The purpose and advantage of the adaptive rate (Formula (12)) are:

[0086] 1) When the sliding variable When outside the barrier boundary, increase the adaptive gain until the sliding variable reaches the preset neighborhood.

[0087] 2) When When entering a preset neighborhood, the adaptive gain switches to BF mode to keep the output variable within the neighborhood, as shown in the attached diagram. Figure 1 As shown.

[0088] 3) This establishes an upper bound for the switching term gain, preventing oversaturation during adaptive rate switching and when the sliding variable approaches the preset boundary.

[0089] 4) In theory, the proposed strategy does not require a perturbation limit and the switching term gain is not overestimated.

[0090] The inner-loop tracking controller is now proposed as follows:

[0091] Theorem 3: Consider a heavy-duty robotic arm system that satisfies Assumptions 1-2 (Equation (1)). If its motion space control input satisfies the conditions determined by Equations (7a) and (7b), (10)-(12), Then the sliding variable and tracking error It will eventually converge to the zero region. , .

[0092] Step 3-2: Prove Theorem 3 in two parts, using the preset range as the boundary.

[0093] Step 3-2-1, firstly, for the adaptive rate (formula (12)), when the sliding variable is outside the preset boundary at the initial moment or the heavy-duty robot arm is in When the sliding variable is subjected to sudden loads that cause it to cross the preset boundary, , The Lyapunov function is selected as follows:

[0094]

[0095] In the formula, , Let be a constant. Taking the derivative, combining equations (1) and (10)-(12), we have:

[0096]

[0097]

[0098]

[0099]

[0100] (13)

[0101] Combining property 1, we have:

[0102]

[0103]

[0104] (14)

[0105] As can be seen from the literature (Tracking control of a linear motor positioner based on barrier function adaptive sliding mode), there must exist a positive number. Make the upper bound of the adaptive rate (Equation (12)) be ,Right now Therefore, we can conclude that:

[0106] (15)

[0107] definition Therefore, there must exist a condition that satisfies the given conditions. , making ,Right now:

[0108] (16)

[0109] Furthermore, consider the actuator saturation parameter. There exists a time period during which the integral gain is active. Make From this point onward, the sliding variable... Approaching zero Continue to increase until Therefore, it must exist. Make This holds true. That is, regardless of whether the actuator is saturated, the heavy-duty robotic arm system will inevitably move towards [the desired state] under the influence of the control rate (equations (11a) and (11b)) and the adaptive rate (equation (12)). go ahead.

[0110] Step 3-2-2: When the sliding variable enters the preset range under the action of the integral form adaptive rate, Let BF be the initial sliding variable value. At this point, the adaptive gain... In the formula:

[0111] (17)

[0112] At the initial moment of the BF adaptive gain, Choose the Lyapunov function:

[0113]

[0114] Taking the derivative and combining it with equation (13), we get:

[0115] (18)

[0116] Therefore It will asymptotically converge to zero. Neighborhood.

[0117] Further consideration Design auxiliary variables:

[0118] , (19)

[0119] for The i-th element in, then Choose a Lyapunov function:

[0120]

[0121] Differentiate, combining equations (10)-(12) and (13):

[0122]

[0123]

[0124] (20)

[0125] In the formula, .definition:

[0126]

[0127] when Therefore,

[0128] (twenty one)

[0129] Therefore, for any initial state, the sliding variable It will eventually converge to the region .

[0130] Next, we will prove that the tracking error will eventually converge to the neighborhood. Equation (10) can be written as:

[0131] (twenty two)

[0132] make ,because ,but Therefore, Equation (22) maintains the same stability as Equation (10), which means that the tracking error converges to the region. Theorem 3 is proved.

[0133] Theoretically, with compensation from the perturbation observer (Equations (7a) and (7b)), the gain is adaptively estimated. and its boundary value All of these are only related to the disturbance estimation error, which greatly reduces the uncertain gain and avoids controller saturation to a certain extent. When hour, , The input vibration reaches its minimum value. In addition, it can be noted that when the adaptive gain (formula (12)) is switched from integral form to BF, there will always be a discontinuous segment, but from the perspective of error convergence trend, this discontinuity is very short.

[0134] It can be directly understood that the switching item gain It is not overrated because it only requires the output variable to converge to a predefined neighborhood of zero, meaning the control input is continuous and chatter-free.

[0135] From an engineering application perspective, it is necessary to consider not only that the sliding variable value of the heavy-duty robotic arm system at the initial moment is outside the BF (Boundary Factor), but also that it has structural clearances, a long power transmission chain, and drastically abrupt external loads. After entering the preset range for the first time, there is still a possibility of exceeding the preset range. At this time, the adaptive rate (formula (12)) is switched. Judging the value of the adaptive gain by using a time-based method rather than time-based methods can avoid negative or infinite values, which has greater practical engineering significance.

[0136] BF can ensure that the system error of the heavy-duty robotic arm remains within a preset range over a long period of time, and different preset ranges can be selected according to the actual application scenario and safety requirements. For example, in the leveling condition, a preset range that meets engineering requirements can be selected. ; Higher excavation working conditions To make the input smoother; in urban operation scenarios with high safety requirements, a smaller error range is selected to ensure absolute kinematic safety.

[0137] Corresponding to the aforementioned embodiment of an adaptive sliding mode control method for a heavy-duty robotic arm based on a disturbance observer, the present invention also provides an embodiment of an adaptive sliding mode control device for a heavy-duty robotic arm based on a disturbance observer.

[0138] See Figure 5 The present invention provides an adaptive sliding mode control device for obstacle function of heavy-duty robotic arm based on disturbance observer, comprising a memory and one or more processors. The memory stores executable code, and when the processor executes the executable code, it is used to implement an adaptive sliding mode control method for obstacle function of heavy-duty robotic arm based on disturbance observer as described in the above embodiment.

[0139] The embodiment of the obstacle function adaptive sliding mode control device for a heavy-duty robotic arm based on a disturbance observer provided by this invention can be applied to any device with data processing capabilities, such as a computer. The device embodiment can be implemented in software, hardware, or a combination of both. Taking software implementation as an example, as a logical device, it is formed by the processor of any data-processing device loading the corresponding computer program instructions from non-volatile memory into memory for execution. From a hardware perspective, such as... Figure 5 The diagram shown is a hardware structure diagram of any data processing-capable device, including the heavy-duty robotic arm obstacle function adaptive sliding mode control device based on a disturbance observer provided by the present invention. (Except for...) Figure 5 In addition to the processor, memory, network interface, and non-volatile memory shown, any data processing device in the embodiment may also include other hardware depending on the actual function of the data processing device, which will not be described in detail here.

[0140] The specific implementation process of the functions and roles of each unit in the above device can be found in the implementation process of the corresponding steps in the above method, and will not be repeated here.

[0141] For the device embodiments, since they basically correspond to the method embodiments, the relevant parts can be referred to in the description of the method embodiments. The device embodiments described above are merely illustrative. The units described as separate components may or may not be physically separate, and the components shown as units may or may not be physical units, that is, they may be located in one place or distributed across multiple network units. Some or all of the modules can be selected to achieve the purpose of the present invention according to actual needs. Those skilled in the art can understand and implement this without creative effort.

[0142] This invention also provides a computer-readable storage medium storing a program thereon, which, when executed by a processor, implements an adaptive sliding mode control method for a heavy-duty robotic arm obstacle function based on a disturbance observer as described in the above embodiments.

[0143] The computer-readable storage medium can be an internal storage unit of any data processing device described in any of the foregoing embodiments, such as a hard disk or memory. The computer-readable storage medium can also be an external storage device of any data processing device, such as a plug-in hard disk, smart media card (SMC), SD card, flash card, etc., equipped on the device. Furthermore, the computer-readable storage medium can include both internal storage units and external storage devices of any data processing device. The computer-readable storage medium is used to store the computer program and other programs and data required by the data processing device, and can also be used to temporarily store data that has been output or will be output.

[0144] The present invention also provides a computer program product, including a computer program that, when executed by a processor, implements the aforementioned adaptive sliding mode control method for a heavy-duty robotic arm based on a disturbance observer obstacle function.

[0145] The above embodiments are used to explain and illustrate the present invention, but not to limit the present invention. Any modifications and changes made to the present invention within the spirit and scope of the claims shall fall within the protection scope of the present invention.

Claims

1. An adaptive sliding mode control method for obstacle function of a heavy-duty robotic arm based on a disturbance observer, characterized in that, The method includes the following steps: (1) Dynamic modeling: Establish a dynamic model that considers model errors, unmodeled parts, friction and lumped disturbances caused by external loads; (2) Sliding mode disturbance observer design: The problem of estimating lumped disturbances is transformed into the problem of estimating the state of a linear system driven by defined auxiliary state variables and unknown inputs. A sliding mode disturbance observer is designed to estimate and compensate for lumped disturbances. (3) Adaptive sliding mode control based on obstacle function: Based on the sliding mode disturbance observer, for the disturbance estimation error, the obstacle function is used to design the bounded adaptive control gain of the controller to avoid control jitter while keeping the error within the preset range; specifically: combining the dynamic model of the heavy-duty manipulator and the disturbance estimation obtained by the sliding mode observer, the control law and adaptive law are designed based on the system sliding variable to obtain the adaptive uncertainty term gain matrix, the elements of which are determined based on the integral gain and the obstacle function; the designed control law and adaptive law enable the system sliding variable and joint error to converge and eventually stay in the desired region without the need for the disturbance observation error limit; the control law is obtained based on the linear sliding function combined with the dynamic model of the actuator space of the heavy-duty manipulator and the disturbance estimation obtained by the sliding mode disturbance observer, and the adaptive law is the adaptive uncertainty term gain in the control law. When the sliding variable is outside the obstacle boundary, the adaptive gain can be increased until the sliding variable reaches the preset neighborhood; and when the sliding variable enters the preset neighborhood, the adaptive gain is switched to the obstacle function form to keep the output variable within the neighborhood.

2. The adaptive sliding mode control method for obstacle function of a heavy-duty robotic arm based on a disturbance observer according to claim 1, characterized in that, In step (1), the Lagrange method is used to perform dynamic modeling of the heavy-duty robotic arm and the system input is transformed into the actuator space.

3. The adaptive sliding mode control method for obstacle function of a heavy-duty robotic arm based on a disturbance observer according to claim 1, characterized in that, The lumped disturbance is a state description of a linear system driven by unknown input. Based on the linear system driven by unknown input, a sliding perturbation observer and observation error are obtained. The gain of the sliding perturbation observer is designed so that the observation error realizes terminal sliding motion in a finite time. Then the lumped disturbance can be accurately estimated in a finite time.

4. A heavy-duty robotic arm obstacle function adaptive sliding mode control device based on a disturbance observer, comprising a memory and one or more processors, wherein the memory stores executable code, characterized in that, When the processor executes the executable code, it implements an adaptive sliding mode control method for obstacle function of a heavy-duty robotic arm based on a disturbance observer, as described in any one of claims 1-3.

5. A computer-readable storage medium having a program stored thereon, characterized in that, When the program is executed by the processor, it implements the adaptive sliding mode control method for obstacle function of heavy-duty robotic arm based on disturbance observer as described in any one of claims 1-3.

6. A computer program product, comprising a computer program, characterized in that, When the computer program is executed by the processor, it implements the adaptive sliding mode control method for obstacle function of a heavy-duty robotic arm based on a disturbance observer as described in any one of claims 1-3.

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