Caisson tracked robot trajectory tracking method and system

Abstract

The invention provides a caisson tracked robot trajectory tracking method and system, and relates to the technical field of robotics.The caisson tracked robot trajectory tracking method comprises the steps that original control input is processed through a micro-saturable function based on a Gaussian error function, and a smooth saturation control signal is obtained; calculating a difference value between the smooth saturation control signal and original control input to obtain a saturation error compensation signal; using the smooth saturation control signal, the saturation error compensation signal and the initial state to construct a basic framework of a sliding mode surface through a feed-forward function; and introducing a nonlinear feedback function to the basic framework, and performing staged adjustment on the state of the sliding mode surface through the function to inhibit steady-state overshoot so as to obtain a state variable of the sliding mode surface. According to the method, high-precision and fast-convergence trajectory tracking of the caisson tracked robot in a complex underwater environment is realized through micro saturation processing, dynamic sliding mode surface control, a self-adaptive reaching law and online disturbance compensation.

Description

Technical Field

[0001] This invention relates to the field of robotics, and in particular to a method and system for tracking the trajectory of a caisson-mounted tracked robot. Background Technology

[0002] The caisson tracked dredging robot is an important special equipment for the construction and maintenance of underwater infrastructure such as ports, waterways, and reservoirs. During operation, it needs to move precisely along a predetermined trajectory to achieve efficient dredging. However, the uncertainty of the underwater environment, time-varying disturbances (such as water flow impact and bottom sediment changes) and strong nonlinearity pose severe challenges to its trajectory tracking control.

[0003] Sliding mode control is widely used for controlling nonlinear systems due to its robustness to parameter uncertainties and external disturbances. However, traditional sliding mode control has several drawbacks: First, when the actuator input is saturated, it may cause system overshoot and steady-state overshoot, affecting trajectory tracking accuracy. Second, it is not robust enough to handle unknown time-varying disturbances underwater, which may lead to increased tracking errors or even instability. Third, the approaching law has a constant velocity when approaching the sliding surface, which may result in long convergence times and significant chattering, affecting the lifespan of the actuator and the smoothness of control. Fourth, global integral sliding mode or nonlinear integral sliding surface may produce integral saturation effect due to the accumulation of error integrals, reducing control efficiency.

[0004] To address the aforementioned issues, some improvements have been attempted in existing technologies. For example, some researchers have used feedforward disturbance observers to estimate and compensate for external disturbances in order to improve the anti-interference capability of trajectory tracking. However, this method still has limitations in its adaptive capability and compensation accuracy when dealing with time-varying disturbances with rapidly changing amplitudes. At the same time, the traditional saturation function introduced to suppress chattering is often non-differentiable, affecting the smoothness of the control signal, and fails to fundamentally solve the overshoot and chattering problems caused by the dynamic characteristics of the reaching law and integral saturation. Summary of the Invention

[0005] The technical problem to be solved by the present invention is to provide a trajectory tracking method and system for a caisson tracked robot. Through differential saturation processing, dynamic sliding surface control, adaptive approach law and online disturbance compensation, high-precision and fast convergence trajectory tracking of the caisson tracked robot in complex underwater environments is achieved.

[0006] To solve the above-mentioned technical problems, the technical solution of the present invention is as follows: In a first aspect, a trajectory tracking method for a caisson-mounted tracked robot, the method comprising: The original control input is processed by a differentiable saturation function based on the Gaussian error function to obtain a smooth saturated control signal; the difference between the smooth saturated control signal and the original control input is calculated to obtain a saturation error compensation signal. Using the smooth saturation control signal, saturation error compensation signal, and initial state, a basic framework for the sliding surface is constructed through a feedforward function; a nonlinear feedback function is introduced into the basic framework, and the sliding surface state is adjusted in stages through this function to suppress steady-state overshoot, thereby obtaining the sliding surface state variables; Based on the absolute value of the sliding surface state variable, the dynamic logarithmic gain that changes with the state is calculated; using the dynamic logarithmic gain, the speed approaching the sliding surface is adjusted to obtain a reaching law output with dynamic damping characteristics. Using the approach law output as input, the upper bound of the time-varying disturbance in the underwater environment is estimated online through finite-time adaptive technology to obtain the estimated value of the upper bound of the time-varying disturbance; using the estimated value of the upper bound of the time-varying disturbance, the approach law output is fed forward to compensate, the final control law is synthesized and output to the actuator to drive the robot to complete trajectory tracking.

[0007] Secondly, a trajectory tracking system for a caisson-mounted tracked robot includes: The saturation compensation module is used to process the original control input with a differentiable saturation function based on the Gaussian error function to obtain a smooth saturated control signal; and to calculate the difference between the smooth saturated control signal and the original control input to obtain a saturation error compensation signal. The adjustment module is used to construct the basic framework of the sliding surface through a feedforward function using the smooth saturation control signal, the saturation error compensation signal, and the initial state; a nonlinear feedback function is introduced into the basic framework, and the sliding surface state is adjusted in stages through the function to suppress steady-state overshoot and obtain the sliding surface state variables. The dynamic adjustment module is used to calculate the dynamic logarithmic gain that changes with the state based on the absolute value of the sliding surface state variable; and to adjust the speed approaching the sliding surface using the dynamic logarithmic gain to obtain a reaching law output with dynamic damping characteristics. An adaptive module is used to take the output of the reaching law as input, estimate the upper bound of the time-varying disturbance of the underwater environment online through finite-time adaptive technology, and obtain the estimated value of the upper bound of the time-varying disturbance; using the estimated value of the upper bound of the time-varying disturbance, feedforward compensation is performed on the output of the reaching law, synthesize the final control law and output it to the actuator to drive the robot to complete trajectory tracking.

[0008] Thirdly, a computing device includes: One or more processors; A storage device for storing one or more programs that, when executed by one or more processors, cause the one or more processors to implement the method.

[0009] Fourthly, a computer-readable storage medium storing a program that, when executed by a processor, implements the method.

[0010] The above-described solution of the present invention has at least the following beneficial effects: By employing a differentiable saturation function based on a Gaussian error function to process the original control input, the generated smooth saturated control signal avoids the discontinuous abrupt changes of traditional saturation functions. This ensures a smooth transition of the control signal even when approaching the actuator's limits, reducing the impact of signal abrupt changes on the actuator. Simultaneously, the difference between the smooth saturated control signal and the original control input is calculated to obtain a saturation error compensation signal, which supplements the control deviation generated during saturation, ensuring that the control signal's adjustment capability is not weakened by saturation. The smooth saturated control signal, saturation error compensation signal, and initial state are used to construct the sliding surface basic framework through a feedforward function. This allows the basic framework to directly link the initial motion state with the pre-processed control signal, making the initial setting of the sliding surface more closely match the robot's actual motion requirements and reducing the deviation between the framework and the actual state. Introducing a nonlinear feedback function into the basic framework and performing phased adjustments allows for dynamic adjustment of the feedback intensity according to different stages of the sliding surface state. The follow-up state is calculated based on the absolute value of the sliding surface state variables. The dynamic logarithmic gain of the state change allows the gain value to be directly related to the magnitude of the state deviation, enabling adaptive adjustment of the gain without the need for a preset fixed gain value. Using this dynamic logarithmic gain to adjust the approach speed to the sliding surface, when the sliding surface state variable is large, increasing the gain can boost the approach speed and accelerate deviation convergence; when the state variable is small, decreasing the gain can slow down the approach speed and avoid jitter caused by excessive speed. Using the approach law output as input, the upper bound of time-varying disturbances is estimated online using finite-time adaptive technology. This allows for real-time processing of the disturbance information implicit in the approach law output, dynamically updating the estimated value of the disturbance upper bound, and ensuring that the estimation result is synchronized with the changing rhythm of underwater environmental disturbances. Using the estimated value to perform feedforward compensation on the approach law output and synthesizing the final control law, the disturbance rejection compensation term can be organically integrated with the basic approach adjustment data. This allows the final control law to retain the core function of approaching the sliding surface while also possessing the ability to counteract time-varying disturbances, without the need for additional complex feedback corrections, enabling the control signal to directly respond to the impact of underwater disturbances. Attached Figure Description

[0011] Figure 1 This is a schematic flowchart of a trajectory tracking method for a caisson tracked robot provided in an embodiment of the present invention.

[0012] Figure 2 This is a schematic diagram of a caisson tracked robot trajectory tracking system provided in an embodiment of the present invention. Detailed Implementation

[0013] Exemplary embodiments of the present disclosure will now be described in more detail with reference to the accompanying drawings. While exemplary embodiments of the present disclosure are shown in the drawings, it should be understood that the present disclosure may be implemented in various forms and should not be limited to the embodiments set forth herein. Rather, these embodiments are provided so that this disclosure will be thorough and complete, and will fully convey the scope of the disclosure to those skilled in the art.

[0014] like Figure 1 As shown, an embodiment of the present invention proposes a trajectory tracking method for a caisson tracked robot, the method comprising the following steps: Step 1: Process the original control input using a differentiable saturation function based on the Gaussian error function to obtain a smoothed saturated control signal; calculate the difference between the smoothed saturated control signal and the original control input to obtain the saturation error compensation signal; Step 2: Using the smooth saturation control signal, saturation error compensation signal, and initial state, construct the basic framework of the sliding surface through a feedforward function; introduce a nonlinear feedback function into the basic framework, and use this function to adjust the state of the sliding surface in stages to suppress steady-state overshoot, thereby obtaining the state variables of the sliding surface. Step 3: Calculate the dynamic logarithmic gain that varies with the state based on the absolute value of the sliding surface state variable; use the dynamic logarithmic gain to adjust the speed approaching the sliding surface to obtain a reaching law output with dynamic damping characteristics. Step 4: Using the approach law output as input, estimate the upper bound of the time-varying disturbance in the underwater environment online using finite-time adaptive technology to obtain the estimated value of the upper bound of the time-varying disturbance; use the estimated value of the upper bound of the time-varying disturbance to perform feedforward compensation on the approach law output, synthesize the final control law and output it to the actuator to drive the robot to complete trajectory tracking.

[0015] In this embodiment of the invention, by processing the original control input with a differentiable saturation function based on a Gaussian error function, the control signal can maintain its smooth characteristics during data processing, avoiding signal fluctuations caused by non-smooth processing methods and ensuring the stability of control signal transmission. Simultaneously, calculating the difference between the smoothed saturated control signal and the original control input allows for precise capture of the differences between the two signals, and the resulting saturation error compensation signal provides accurate error data reference for subsequent control stages. Constructing the basic framework of the sliding surface using a feedforward function allows for the integration of multiple key signals and initial state information at the initial stage of data processing, making the initial structure of the sliding surface more closely match actual control requirements. Introducing a nonlinear feedback function to adjust the sliding surface state in stages allows for flexible adjustment of the data processing intensity based on different values ​​of the sliding surface state variables. Calculating the dynamic logarithmic gain based on the absolute value of the sliding surface state variables allows for the correlation between gain data and state. The real-time changes of variables are closely correlated, enabling dynamic adaptation of the gain magnitude. This dynamic logarithmic gain is used to adjust the speed of approaching the sliding surface. When the absolute value of the state variable is large, the approach speed is increased to shorten the approach time; when the absolute value of the state variable is small, the approach speed is decreased to reduce fluctuations, giving the approach process dynamic damping characteristics and reducing system jitter. Using the approach law output as input, the upper bound of time-varying disturbances in the underwater environment is estimated online through finite-time adaptive technology. This allows for real-time processing of disturbance data in the underwater environment, continuously updating the estimated value of the upper bound of the disturbance, ensuring that the estimation result is synchronized with the actual trend of disturbance change. Using this estimated value to perform feedforward compensation on the approach law output allows for the integration of accurate disturbance-related data into the control signal processing process. This enables the synthesized final control law to specifically address underwater time-varying disturbances, providing the actuator with more suitable control commands and driving the robot to stably complete trajectory tracking.

[0016] In a preferred embodiment of the present invention, step 1 above, which involves processing the original control input with a differentiable saturation function based on a Gaussian error function to obtain a smoothed saturated control signal; and calculating the difference between the smoothed saturated control signal and the original control input to obtain a saturation error compensation signal, includes: Step 11: Based on the original control input and the absolute value of the input limit, calculate the function value using the Gaussian error function; multiply the function value by the absolute value of the input limit to obtain the smooth saturated control signal. Specifically, this includes: first determining the two core input parameters for this step, namely the original control input generated during the trajectory tracking control of the caisson tracked robot, denoted as... And the absolute value of the input limit determined based on the physical properties of the robot actuator, denoted as It should be noted that the absolute value of the input limit here is not an abstract parameter, but rather a specific physical input constraint corresponding to the robot's actuator. Specifically, it can refer to the maximum control signal amplitude that the power unit driving the track movement (such as a drive motor or hydraulic motor) can withstand, or the maximum allowable command input range when the actuator moves (e.g., the upper limit of the control voltage corresponding to the maximum output torque of the motor, the peak value of the control current corresponding to the maximum extension of the hydraulic actuator, etc.). Its value is determined by the hardware physical performance of the actuator (such as the rated power of the motor and the rated pressure of the hydraulic system), and satisfies the following conditions: ,in , These represent the maximum positive and negative input values ​​allowed by the actuator, respectively. Their core function is to define the maximum input range within which the actuator can operate safely and stably, providing a clear physical constraint benchmark for subsequent calculations.

[0017] Furthermore, the original control input obtained above and the absolute value of the input limit are used together as the input parameters of the Gaussian error function, denoted as erf(·). A smooth saturation function based on the Gaussian error function is constructed and processed to obtain the smooth saturation control signal, denoted as . The specific form of the smooth saturation function is as follows: ,in, This represents the saturation control signal after smoothing. Represents at discrete time points The original control input signal, This represents the absolute values ​​of the upper and lower limits of the saturation of control inputs that the system's actuators (such as motors and thrusters) can accept. It is a positive constant. It defines the boundary of the saturation function, erf(·), which is a special function commonly used in mathematics and engineering, and its definition is: The graph of this function is an S-shaped curve. Error function The input parameter is a scaling factor. The core purpose of designing this smooth saturation function based on the Gaussian error function is to utilize the differentiability and smooth continuity inherent in the Gaussian error function to avoid the signal abrupt change problem that traditional non-smooth saturation functions (such as step saturation functions) are prone to when processing control signals. Specifically, the function curve of the Gaussian error function has a continuous and smooth changing trend. By quantizing the correlation between the original control input and the absolute value of the input limit, the smooth saturation control signal obtained by calculation can naturally have smooth transition characteristics.

[0018] Subsequently, since the absolute value of the input limit is directly related to the input capability boundary of the actuator, the design of multiplying the result of the Gaussian error function with the absolute value of the input limit in the above function is essentially to limit the amplitude of the final generated smooth saturation control signal within the maximum input range that the actuator can withstand through the physical constraint of the absolute value of the input limit (i.e., satisfying | |≤ The reason why this technique can achieve both meeting the input requirements of the actuator and possessing smoothness is that, on the one hand, the differentiability of the Gaussian error function ensures the smoothness of the smooth saturated control signal, avoiding discontinuities or abrupt changes in the signal after processing by non-smooth functions; on the other hand, the introduction of the absolute value of the input limit ensures that the smooth saturated control signal does not exceed the physical input limit of the actuator, so that the final smooth saturated control signal simultaneously meets the two core requirements of not exceeding the physical limit and signal smoothness. This signal can be directly used for signal transmission and processing in subsequent control stages.

[0019] Step 12 involves calculating the difference between the smoothed saturation control signal and the original control input to obtain a saturation error compensation signal used to compensate for the saturation effect of the input. Specifically, this includes: firstly, determining that the calculation basis comes from the processing results of step 11 and the initial input parameters, namely the smoothed saturation control signal generated in step 11 and the original control input obtained in the initial stage of trajectory tracking control. These two signals together constitute the calculation basis of step 12, ensuring the continuity of the calculation process and the consistency of the data.

[0020] Next, in order to capture the error information caused by the input saturation phenomenon, the above-mentioned smoothing saturation control signal needs to be adjusted. With raw control input The difference operation is performed by constructing a calculation formula for the saturation error compensation signal, which is denoted as... The specific form of ) is ,in It is a pre-defined positive constant, and must satisfy... , The maximum allowable error compensation range for the actuator is matched with the absolute value of the input limit. The saturation error compensation signal obtained through this formula is essentially an error function used to quantify the impact of input saturation. The core purpose and function of setting this error function is to accurately quantify the deviation caused by the actuator's input saturation constraints. Specifically, the original control input is the ideal control command generated based on trajectory tracking requirements, while the smoothed saturation control signal is the actual usable command after being constrained by the actuator's physical input limits. The two are related by the formula... The calculated difference This directly reflects the extent to which the ideal instruction is adjusted due to the input capability limitations of the actuator. This extent is the error correlation information caused by the input saturation phenomenon, and normal numbers... The introduction of this feature can further optimize the stability of error compensation and avoid over- or under-compensation.

[0021] It should be further explained that this error function is not simply a result of difference calculation; its core value lies in its linkage with the actual saturated input function. Combined with the generation logic of the smoothing saturation control signal in step 11, the actual saturated input function can be further expressed as: = + This formula shows that the saturation error compensation signal can be directly applied in reverse to the original control input, providing a clear basis for compensation in subsequent control stages. The error function presents the deviation caused by input saturation in a quantified form, and the subsequent control logic can directly call the deviation data to adjust the control strategy in a targeted manner to offset the adverse effects of input saturation on the system control accuracy. This reduces the interference of input saturation on the trajectory tracking control effect of the caisson tracked robot, ensuring that subsequent control actions can achieve more accurate trajectory correction based on the error information.

[0022] In a preferred embodiment of the present invention, step 2 above involves using the smoothing saturation control signal, the saturation error compensation signal, and the initial state to construct the basic framework of the sliding surface through a feedforward function; introducing a nonlinear feedback function into the basic framework, and using this function to adjust the sliding surface state in stages to suppress steady-state overshoot, thereby obtaining the sliding surface state variables, including: Step 21: Input the smoothing saturation control signal, saturation error compensation signal, and initial state into the attenuation feedforward function to construct the basic framework of the sliding surface including initial error compensation. Specifically, this includes: first, determining the core formula definition corresponding to the construction of the basic framework of the sliding surface, namely the formula related to the attenuation nonlinear global integral sliding surface (NANGISMS), specifically including the basic term formula of the sliding surface. With the formula for disturbance compensation term ,in, To attenuate the feedforward nonlinear global integral sliding surface, i.e., the final designed sliding surface, For discrete time points The system tracking error, This is the proportional gain coefficient. The initial tracking error of the system, Let be the decay function acting on the initial error. This is the integral gain coefficient. The output of the nonlinear feedback function, It is a nonlinear integral term. For feedforward compensation term, The derivative (or rate of change) of the desired trajectory. For the decay function acting on the desired trajectory dynamics, The initial derivative (or rate of change) of the desired trajectory is given. The proportional and integral coefficients in the formula are pre-set according to the accuracy requirements of the caisson tracked robot trajectory tracking. The real-time trajectory state data corresponds to the fusion value of the pre-processed smooth saturated control signal and the saturation error compensation signal. The initial trajectory state data is the quantized value of the initial position, velocity and other parameters when the robot starts. The trajectory attenuation coefficient function and the disturbance attenuation coefficient function are used to dynamically weaken the influence of the initial deviation. The real-time disturbance correlation data and the initial disturbance correlation data are the quantized values ​​of underwater environmental disturbances acquired in real time and initially, such as water flow velocity and water flow impact force. The above parameters together constitute the basis of the formula calculation.

[0023] Secondly, the robot's initial state (initial position coordinates, initial motion velocity) is quantized and converted into trajectory initial state data. At the same time, initial underwater environmental disturbance data (such as initial water flow velocity) is collected and quantized into initial disturbance correlation data to ensure that both are consistent with the definition of the corresponding state parameters in the formula. Then, the smooth saturation control signal obtained in step 11 and the saturation error compensation signal obtained in step 12 are weighted and fused. The weights are set according to the control priority, such as 0.6 for the smooth saturation control signal and 0.4 for the saturation error compensation signal. The fusion result is the real-time trajectory state data in the formula. Simultaneously, real-time underwater disturbance data (such as real-time water flow impact force) is collected and quantized into real-time disturbance correlation data. The real-time trajectory state data and real-time disturbance correlation data are normalized to ensure that their numerical magnitudes are consistent with the proportional coefficients and integral coefficients in the formula, such as adjusting them to the range of 0 to 1 to avoid deviations in formula calculation due to differences in magnitude.

[0024] Further, the disturbance compensation term is calculated first. The proportional coefficient, disturbance attenuation coefficient function, real-time disturbance correlation data, initial disturbance correlation data, and integral coefficient from the formula are substituted into the disturbance compensation term formula. The disturbance attenuation coefficient function is designed to increase with tracking time, such as using an exponential decay function, to gradually reduce the impact of initial disturbances on the sliding surface as the robot runs. Then, the sliding surface basic term is calculated. The proportional coefficient, real-time trajectory state data, trajectory attenuation coefficient function, trajectory initial state data, integral coefficient, and the calculated disturbance compensation term from the formula are substituted into the sliding surface basic term formula. Here, the trajectory attenuation coefficient function adopts the same type of attenuation function as the disturbance attenuation coefficient function to weaken the cumulative effect of initial trajectory error. Through the above formula calculations, the basic framework data of the sliding surface containing initial error compensation and preliminary disturbance compensation (i.e., the calculation result of the sliding surface basic term formula) is finally generated.

[0025] Step 22 involves introducing a nonlinear feedback function into the basic framework of the sliding surface to construct a composite sliding surface with phased adjustment capabilities. Specifically, this includes: first, identifying the technical limitations of the basic framework of the sliding surface constructed in Step 21 (i.e., the calculation results of the basic formula for the sliding surface). It only handles the preset initial error and static disturbance through feedforward formula logic. For sudden dynamic deviations in trajectory tracking, such as sudden changes in real-time trajectory state data caused by instantaneous strong water flow, it cannot be corrected in real time using existing formulas. Therefore, a nonlinear feedback function formula needs to be introduced. To improve the dynamic adjustment function of the sliding surface, among which, The output of the nonlinear feedback function, For symbolic functions, The absolute value of the tracking error. The nonlinear adjustment coefficient is one. The nonlinear adjustment coefficient is 2; the gain base coefficient and gain adjustment rate coefficient in the formula are set according to the robot's response sensitivity requirements to errors, such as the gain base coefficient being 1.2 and the gain adjustment rate coefficient being 0.8.

[0026] Secondly, the output values ​​of the sliding surface base frame and the corresponding real-time trajectory state data are acquired in real time through the data acquisition unit. The real-time trajectory state data is directly used as the input parameter of the nonlinear feedback function and substituted into the nonlinear feedback function formula. At this point, it is crucial to verify whether the numerical range of the real-time trajectory state data is suitable for the formula calculation. If the absolute value of the real-time trajectory state data exceeds the effective calculation range of the exponent term in the formula, such as if the absolute value is greater than 5 causing the exponent term to approach 0, then the real-time trajectory state data needs to be limited to ensure the validity of the formula calculation result. Subsequently, the formula expression of the composite sliding surface is constructed. The output value of the nonlinear feedback function is used as the feedback correction term and superimposed with the output value of the sliding surface base frame to obtain the state formula of the composite sliding surface. This formula enables the sliding surface to have dynamic adjustment capabilities through the logic of feedforward basis (output value of the sliding surface basic frame) plus feedback correction (output value of nonlinear feedback function).

[0027] Finally, the key focus is on checking whether the settings of the gain base coefficient and gain adjustment rate coefficient in the formula meet the requirements of phased adjustment. When the absolute value of the real-time trajectory state data is small, the exponential term in the formula approaches 1, and the formula result of the nonlinear feedback function increases rapidly with the increase of the absolute value of the real-time trajectory state data, reflecting the trend of gain enhancement. When the absolute value of the real-time trajectory state data is large, the exponential term in the formula approaches 0, and the formula result of the nonlinear feedback function approaches a fixed value, that is, the product of the sign function and the logarithmic term related to the gain base coefficient, reflecting the trend of gain limitation, ensuring that the composite sliding surface formula has the core function of phased adjustment.

[0028] Step 23 involves real-time adjustment of the composite sliding surface state using the nonlinear feedback function. Under small error conditions, the gain value is increased to accelerate the convergence process, while under large error conditions, the gain value is limited to avoid excessive accumulation of integrals and to suppress steady-state overshoot. This ultimately yields the sliding surface state variables used for trajectory tracking control. Specifically, this includes: firstly, based on the composite sliding surface formula... This formula is the core expression of the attenuated feedforward nonlinear sliding surface, where The output value is the sliding surface basic framework with attenuation feedforward logic constructed in step 21. The values ​​are nonlinear feedback functions. Together, they form a sliding surface that combines attenuation feedforward and nonlinear feedback. A real-time adjustment operation flow is established: the data acquisition unit continuously collects real-time trajectory state data and the current output value of the composite sliding surface according to the robot control cycle, such as 0.1 seconds / cycle. The acquisition frequency is consistent with the discrete time step in the formula to ensure that each step of the operation is based on the latest state data, which provides a guarantee for the adjustment accuracy. At the same time, it also provides real-time data support for the dynamic attenuation effect of the attenuation feedforward logic and the staged adjustment of the nonlinear feedback function.

[0029] Secondly, the phased adjustment operation is performed based on the nonlinear feedback function formula. This process is the core link of the attenuation feedforward nonlinear sliding surface to achieve small error amplification and accelerated convergence, and large error saturation to avoid integral accumulation: First, the absolute value of the real-time trajectory state data is compared with the preset error threshold. The preset error threshold is determined by the allowable error range of trajectory tracking and matches the values ​​of the gain base coefficient and gain adjustment rate coefficient in the nonlinear feedback function. For example, the threshold is 0.5, which is used to divide the error adjustment interval. If the absolute value of the real-time trajectory state data is less than or equal to the threshold, it is determined to be a small error state, and then substituted into the nonlinear feedback function formula: At this time, the exponential term in the formula approaches 1, making the result of the nonlinear feedback function approximately the product of the sign function and the gain base coefficient, gain adjustment rate coefficient and the logarithmic term related to the absolute value of the real-time trajectory state data. This result grows logarithmically with the increase of the absolute value of the real-time trajectory state data. This growth characteristic is the implementation logic of small error amplification. On the one hand, in step 21 The attenuation feedforward logic has weakened the cumulative effect of the initial error through the attenuation coefficient, clearing away the initial deviation interference for precise adjustment in the small error stage. On the other hand, the logarithmic growth output of the nonlinear feedback function will have a gain amplification effect on the current small error, transforming the small trajectory deviation into a more significant sliding surface adjustment amount. The first-type corrected composite sliding surface state value obtained after substituting it into the composite sliding surface formula can drive the sliding surface to converge to the ideal state more quickly, thereby achieving the effect of amplifying small errors and accelerating convergence.

[0030] If the absolute value of the real-time trajectory status data exceeds the threshold, it is determined to be a large error state. In this case, the exponential term in the formula approaches 0, making the nonlinear feedback function result approximately the product of the sign function and the logarithmic term related to the gain base coefficient, which is a fixed value. This fixed-value output is the implementation logic for large error saturation: on the one hand, the attenuation feedforward logic... The attenuation coefficient function in the formula has already weakened the initial impact of large errors in the early stage, avoiding the large errors from directly acting on the sliding surface and causing adjustment imbalance. On the other hand, the fixed output value of the nonlinear feedback function limits the further increase of the gain, so that the second-type corrected composite sliding surface state value obtained after substituting into the composite sliding surface formula will not be excessively amplified by large errors. This avoids the excessive accumulation of the integral term corresponding to the integral coefficient in the formula. This integral term is used to improve steady-state accuracy, but the excessive amplification of the adjustment amount under large errors will cause the integral data to continue to accumulate, ultimately achieving the effect of avoiding integral accumulation when large errors saturate.

[0031] Furthermore, the first and second types of corrected composite sliding surface state values ​​are substituted into the accuracy judgment condition, namely, the absolute value of the state value must be less than or equal to the allowable fluctuation threshold of the sliding surface state. This threshold is set according to the trajectory tracking accuracy requirements. For example, if the threshold is 0.1, if this condition is met, the current composite sliding surface state value is determined to meet the trajectory tracking control requirements and is identified as the final sliding surface state variable. If it is not met, the latest real-time trajectory state data and the output value of the sliding surface basic framework are re-acquired, and the above-mentioned phased adjustment calculation is repeated. This verification and iteration process further ensures that the attenuated feedforward nonlinear sliding surface maintains a stable and reliable effect of amplifying small errors to accelerate convergence and saturating large errors to avoid integral accumulation under different error states. It will not fail to adjust due to fluctuations in operating conditions. The final sliding surface state variable obtained is the composite sliding surface state value that meets the accuracy requirements.

[0032] In this embodiment of the invention, by inputting the smoothing saturation control signal, the saturation error compensation signal, and the initial state into the decay feedforward function, the integrated processing of multiple types of key data is achieved. The smoothing saturation control signal provides basic control data that conforms to the physical constraints of the actuator; the saturation error compensation signal carries quantified error data related to input saturation; and the initial state reflects the initial working condition data of the robot trajectory tracking. The coordinated input of these three ensures that the decay feedforward function can fully utilize the effective data from the previous processing and the initial working condition information, thereby constructing a sliding surface basic framework that includes initial error compensation. This framework incorporates initial error compensation logic at the data level in advance, avoiding the cumulative impact of initial state deviations on subsequent adjustments of the sliding surface, making the initial structure of the sliding surface more closely match the control requirements of the robot during actual startup. Introducing a nonlinear feedback function into the sliding surface basic framework essentially adds a dynamic feedback adjustment data dimension to the original feedforward data processing logic. Compared to a single feedforward data processing mode, the nonlinear feedback function can receive data in real time. The state data of the basic sliding surface framework is collected, and adjustment signals are dynamically output based on changes in the state data. Through a collaborative data processing mode of feedforward foundation and feedback adjustment, a composite sliding surface with staged adjustment capability is constructed. This composite sliding surface overcomes the limitations of single-frame data processing and can flexibly adjust the processing strategy according to the dynamic changes of actual state data during subsequent adjustment. The state of the composite sliding surface is adjusted in real time through a nonlinear feedback function, the core of which is to realize differentiated data processing based on the error magnitude. Under small error conditions, the function enhances the adjustment of error data by increasing the gain value, accelerates the convergence speed of error data, and shortens the time for the sliding surface state to reach stability. Under large error conditions, the function controls the adjustment amplitude of error data by limiting the gain value, avoiding excessive accumulation of integral data caused by continuous input of large errors, and preventing control deviation caused by integral accumulation. This differentiated data processing method ensures fast convergence efficiency under small errors and avoids the problem of excessive integrals under large errors, effectively suppressing steady-state overshoot.

[0033] In a preferred embodiment of the present invention, step 3 above, which calculates the dynamic logarithmic gain as the state changes based on the absolute value of the sliding surface state variable, and adjusts the approaching velocity using the dynamic logarithmic gain to obtain a reaching law output with dynamic damping characteristics, includes: Step 31: Add the absolute value of the sliding surface state variable to a preset gain constant to form the input term of the logarithmic function. Specifically, this includes: first determining the sliding surface state variable here, denoted as... This is the composite sliding surface state value determined after validity verification in step 23, which meets the trajectory tracking accuracy requirements. It directly reflects the deviation between the current trajectory and the ideal trajectory of the caisson tracked robot. Secondly, the key preset parameters involved are determined, namely the preset gain constant, denoted as... The value of this constant needs to be determined by combining the response sensitivity of the robot actuator and the operational characteristics of the logarithmic function. The core purpose is to avoid non-positive values ​​in the input terms of the logarithmic function when the absolute value of the sliding surface state variable approaches zero. Since the logarithmic function is only defined for positive values, it is usually a decimal greater than 0, such as 0.1 or 0.2. Specifically, it needs to be verified through multiple simulation tests to ensure that the input terms can still maintain stable positive values ​​when the absolute value of the state variable is minimized.

[0034] Furthermore, specific operations are performed to form the logarithmic function input term, and the corresponding calculation formula is input term = + First, the absolute value of the sliding surface state variables is calculated to eliminate the influence of the positive or negative sign of the state variables, since gain calculation only needs to focus on the magnitude of the deviation and does not need to distinguish the direction of the deviation. Then, the obtained absolute value of the state variable is added to the preset gain constant. This addition operation ensures the positive definiteness of the input term and, through the numerical supplementation of the gain constant, avoids the problem of insufficient discrimination of the subsequent logarithmic operation results due to the narrow value of the input term when the absolute value of the state variable is too small. The final addition result is the input term adapted to the subsequent logarithmic operation. This input term has the characteristics of dynamically adjusting with the changes of the state variable and always maintaining a positive value.

[0035] Step 32: Calculate the natural logarithmic value of the logarithmic function input term to obtain the basic dynamic gain component. This specifically includes: first determining the technical attributes of the operand, the logarithmic function input term, i.e. + Its numerical value is directly related to the sliding surface state variables. The degree of deviation is such that when the deviation of the state variable increases, the value of the input item increases accordingly, and when the deviation decreases, the value of the input item decreases synchronously. This correlation is the core premise for realizing dynamic adjustment of gain according to state.

[0036] Secondly, based on the logic of logarithmic operations, the natural logarithm is chosen as the operation function, and an adjustment coefficient is introduced. Perform the specific calculation, that is, the basic dynamic gain component = Its function curve exhibits a smooth, non-linear growth characteristic. Compared to other logarithmic forms, such as the commonly used logarithm, it is better suited to the dynamic gain's requirement for a smooth response, avoiding drastic fluctuations in gain as the input term changes; parameters The introduction of this factor is used to adjust the gain weight of the logarithmic term. Its value needs to be determined in conjunction with the dynamic response capability of the actuator, such as a value between 0.5 and 2.0, to ensure that the logarithmic output can adapt to the adjustment requirements under different operating conditions. In specific calculations, the input term obtained in step 31 is substituted into the natural logarithm function, and then... Multiplication transforms the linear change of the input term into a smooth, nonlinear change of the fundamental dynamic gain component. For example, when the input term increases significantly due to the increase in S-bias, the result of the operation becomes... The gain increases only gradually to avoid excessive amplification that could lead to a sudden change in the rate of convergence. When the input term shrinks due to the decrease in deviation, the basic dynamic gain component also decreases gradually to ensure the continuity of gain adjustment.

[0037] At the same time, the calculation results need to be validated for reasonableness. The validation includes whether the numerical range of the basic dynamic gain component is within the preset range. This range is determined based on the maximum gain tolerance of the actuator, such as 0.5 to 5. If it exceeds the range, the preset value in step 31 needs to be adjusted retrospectively. such as increasing To increase the value of the input item, thereby raising the lower limit of the basic component; or to decrease it. This reduces the input values ​​and lowers the upper limit of the base components, ensuring that the base dynamic gain components are always within a reasonable and effectively adjustable range.

[0038] Step 33: Combine the basic dynamic gain component with another preset fixed gain coefficient to obtain the dynamic logarithmic gain. Specifically, this includes: first determining another key preset parameter, the fixed gain coefficient. Both technologies are functionally identical, providing stable base gain support for dynamic logarithmic gain and avoiding the limitations of relying solely on the base dynamic gain component. If the deviation is too small, the values ​​of the basic components will be too low, which will lead to problems such as insufficient overall gain and slow approach speed.

[0039] parameter The value of this value should be determined in accordance with the requirements of the formula provided: it needs to be determined based on the basic approximation requirements of robot trajectory tracking, and is usually a fixed positive number, such as 0.8 or 1.0. Furthermore, it needs to be adjusted through compatibility testing with the basic dynamic gain components to ensure that the gain, when combined, can adapt to the robot's trajectory tracking needs. Dynamically adjust to changes in state, without being affected by... Excessive gain leads to an overall high gain.

[0040] Secondly, perform basic dynamic gain component and Combinatorial operations, i.e., dynamic logarithmic gain = The combination method uses direct superposition, through... Numerical supplementation ensures the basic level of overall gain; the core logic of this combined operation is the dynamic component, i.e. It provides state adaptability and fixed coefficients to provide a stable foundation, so that the combined result can be adjusted in real time according to the deviation of the sliding surface state variables, and the overall gain can be prevented from going out of the effective control range due to the fluctuation of dynamic components.

[0041] Furthermore, verify the simulation of different sliding surface states (such as large deviation, small deviation, and near-zero deviation), and observe whether the combined dynamic logarithmic gain can exhibit the characteristics of moderately increasing gain with large deviation, gradually decreasing gain with small deviation, and maintaining the basic level of gain near zero deviation; if the verification fails, step 32 needs to be adjusted accordingly. (Indirectly adjusting the basic dynamic components) and this step Until the dynamic logarithmic gain fully meets the technical requirements of dynamic adaptation and stability with respect to the state, the final determined combined operation result is... .

[0042] Step 34: Using the aforementioned dynamic logarithmic gain, adjust the speed of approaching the sliding surface. When the sliding surface state variable is large, increase the gain to accelerate the approach; when the sliding surface state variable is small, decrease the gain to suppress jitter, thus obtaining a approach law output with dynamic damping characteristics. Specifically, this includes: first, determining the formula for the novel logarithmic gain approach law, the specific expression of which is the approach law output. ,in For sliding surface The rate of change of the first derivative with time. For the sliding surface state variables, For adjustment coefficients, For logarithmic parameters, For fixed coefficients, It is the natural logarithm function. ( The sign function (S) is used to determine the approach direction, taking the value 1 or negative 1 depending on the sign of S. Secondly, the correlation logic between the formula and the approach sliding surface velocity is established. In the trajectory tracking control of the caisson tracked robot, the magnitude of the approach velocity is determined by the superposition of the two adjustment terms, and the direction is determined by... Positive and negative ( The first part of the adjustment term is determined collaboratively through dynamic logarithmic gain. and The product of these terms enables dynamic adjustment of the basic approach velocity; the second part of the adjustment term is achieved through... and The product of these factors enhances the damping effect under small deviation conditions, thus preventing chattering.

[0043] Furthermore, based on the complete formula, the approach speed is dynamically adjusted according to different scenarios. The first scenario involves the sliding surface state variable. When the trajectory deviation is large, that is, when the trajectory deviation is large. The increase of will Significant growth, driving the first part The overall increase leads to a significant increase in the magnitude of the first adjustment term; simultaneously, The increase of Approaching 0, As ln(1) approaches 0, the magnitude of the second part of the adjustment term approaches 0. At this time, the approach speed is mainly dominated by the first part of the adjustment term, which pushes the robot to accelerate towards the ideal trajectory, shortens the transition time from large deviation to small deviation, and achieves the effect of accelerated approach.

[0044] The second scenario involves sliding surface state variables. When the value is small, that is, the trajectory deviation is small. The reduction of Growth slowed, and the magnitude of the first adjustment item stabilized; while The reduction of Increase As the adjustment increases, the magnitude of the second adjustment term also increases synchronously. When this part is superimposed on the first part, it avoids the adjustment magnitude from being affected by other factors. Excessive shrinkage can lead to a slow approach speed. However, the dynamic damping in the second part can suppress fluctuations in the adjustment amplitude, making the approach speed smooth and preventing the robot from repeatedly overshooting due to sudden speed changes near the ideal trajectory, i.e., jittering, thus achieving the effect of suppressing jitter.

[0045] During the switching between the two scenarios, the nonlinear characteristics of the logarithmic function in the formula and , The synergistic effect ensures continuous change of the adjustment amplitude, thereby making the adjustment of the approach velocity smooth and without abrupt changes, avoiding system instability caused by velocity fluctuations; finally, the approach law output with dynamic damping characteristics is generated through the complete formula, which can not only adapt to the dynamic changes of trajectory deviation in the underwater environment, but also balance the requirements of approach efficiency and process stability.

[0046] In this embodiment of the invention, adding the absolute value of the sliding surface state variable to a preset gain constant ensures that the resulting logarithmic function input term always remains positive, avoiding meaningless or abnormal results in logarithmic operations due to the absolute value of the sliding surface state variable approaching zero. Simultaneously, the introduction of the gain constant allows for flexible adjustment of the starting point of the input term's value, enhancing its adaptability to subsequent logarithmic operations. Calculating the natural logarithmic value of the logarithmic function input term yields the basic dynamic gain component, utilizing the nonlinear, gradual growth characteristic of the natural logarithmic function to transform the linear change of the absolute value of the sliding surface state variable into a gradual, nonlinear change of the basic gain component. Combining the basic dynamic gain component with another preset fixed gain coefficient ensures that the final dynamic logarithmic gain is consistent with... It possesses both flexibility in adapting to state changes and stability in its basic output. The basic dynamic gain component ensures that the gain can be adjusted in real time according to changes in the sliding surface state variables, while the fixed gain coefficient provides stable basic numerical support for the dynamic logarithmic gain. Adjusting the approach speed to the sliding surface using the dynamic logarithmic gain allows for targeted data adjustment of the approach speed through differentiated outputs. When the sliding surface state variables are large, increasing the dynamic logarithmic gain can drive up the approach speed, accelerating the process of the sliding surface approaching the ideal state and shortening the approach time. When the sliding surface state variables are small, decreasing the dynamic logarithmic gain can control the approach speed to slow down, avoiding frequent fluctuations of the sliding surface near the ideal state due to excessive speed, effectively suppressing jitter.

[0047] In a preferred embodiment of the present invention, step 34 above, utilizing the dynamic logarithmic gain to adjust the speed of approaching the sliding surface, increases the gain to accelerate the approach when the sliding surface state variable is large, and decreases the gain to suppress jitter when the sliding surface state variable is small, thereby obtaining a approach law output with dynamic damping characteristics, including: Step 341 involves multiplying the dynamic logarithmic gain by the sliding surface state variable to form the basic approximation term. Specifically, this includes: first, determining the dynamic logarithmic gain as the gain value determined in step 33 after functional verification, composed of dynamic components and fixed coefficients, which directly reflects the adjustment intensity required to be adapted under the current sliding surface state; the sliding surface state variable is the composite sliding surface state value verified in step 23, whose magnitude and sign correspond to the degree and direction of trajectory deviation, respectively. Both constitute the core parameters for the basic approximation term calculation. Secondly, preprocessing the input parameters before calculation is required to avoid calculation deviations caused by differences in parameter characteristics: on the one hand, for the dynamic logarithmic gain... The magnitude of the logarithmic gain and the sliding surface state variable is checked separately to ensure that their magnitudes are consistent, for example, both are in the range of 0 to 10. If there is a difference in magnitude, such as the gain being 0.5 to 5 and the state variable being 10 to 100, the state variable needs to be normalized, such as by dividing it by 10 to adjust it to the range of 1 to 10, to avoid abnormal product results due to magnitude imbalance. On the other hand, the sign of the sliding surface state variable is confirmed to clarify the direction of the trajectory deviation it reflects, such as positive values ​​leading the ideal trajectory and negative values ​​lagging the ideal trajectory, to ensure that subsequent multiplication operations can retain the deviation direction information, so that the basic approach term has both adjustment amplitude and adjustment direction attributes.

[0048] Furthermore, a multiplication operation is performed between the dynamic logarithmic gain and the sliding surface state variable to form the basic approach term. The core purpose of this multiplication operation is to allow the basic approach term to simultaneously carry the dual information of the deviation degree and the adaptation gain. When the sliding surface state variable is large, the dynamic logarithmic gain has increased synchronously, and the amplitude of the basic approach term formed by the product of the two is increased accordingly, which can provide a stronger adjustment force to push the system closer to the ideal trajectory. When the state variable is small, the dynamic logarithmic gain decreases synchronously, and the amplitude of the product is reduced accordingly to avoid excessive adjustment force leading to system fluctuations. At the same time, the rationality of the calculation result needs to be verified. For example, a maximum and minimum threshold for the basic approach term (such as -20 to 20) is set. If the calculation result exceeds the threshold, the fixed coefficient in step 33 is adjusted retrospectively to indirectly correct the dynamic logarithmic gain and ensure that the basic approach term is always within the range that the actuator can effectively respond to.

[0049] Step 342: Based on the absolute value of the sliding surface state variable and preset parameters, a nonlinear damping term is generated through a calculation involving a logarithmic function. Specifically, this includes: First, determining that the absolute value of the sliding surface state variable is the result of the absolute value calculation of the sliding surface state variable in step 341. This value only reflects the magnitude of the trajectory deviation (excluding directional information) and is the core basis for generating the damping term. The preset parameter values ​​need to be determined comprehensively by combining the damping response sensitivity of the robot actuator and the disturbance intensity of the underwater environment. For example, the parameters used for the logarithmic calculation basis are usually decimals of 0.1 to 0.5 to ensure that the logarithmic calculation still has effective output when the deviation is small. The weight parameters used for damping intensity adjustment are usually values ​​of 0.8 to 1.2 to avoid excessive or insufficient damping. Furthermore, multiple sets of working condition simulation tests are required to verify that the parameter values ​​can adapt to the damping requirements under different deviation states.

[0050] Secondly, parameter combination and logarithmic operations are performed to generate nonlinear damping terms. The operation process needs to be carried out in stages to ensure the accuracy of the damping characteristics: The first stage is parameter combination, which adds the absolute value of the sliding surface state variable to the preset logarithmic basic parameters to form the input term of the logarithmic function. The core purpose of this operation is to avoid the logarithmic input term from having a non-positive value when the absolute value of the state variable approaches zero. At the same time, by supplementing the value of the basic parameters, it is ensured that the input term still has sufficient value to drive the logarithmic operation to output effective damping information when the deviation is small. The second stage is logarithmic operation, which substitutes the combined input term into the... In the logarithmic function, the linear change of the input term is transformed into a nonlinear output through logarithmic operations. For example, when the absolute value of the state variable is small, such as 0.1 to 0.5, the logarithmic operation can amplify the impact of the change of the input term on the output, making the damping term output a larger value to enhance the damping effect. When the absolute value of the state variable is large, such as 5 to 10, the logarithmic operation can weaken the impact of the change of the input term, making the damping term output a smaller value to reduce the damping effect. The third stage is damping strength adaptation, which multiplies the logarithmic operation result with the preset damping weight parameters, and adjusts the overall strength of the damping term through the weight parameters.

[0051] Meanwhile, by simulating the change of the sliding surface state variable from large to small, such as gradually decreasing from 10 to 0.1, we can observe whether the nonlinear damping term exhibits the characteristic of gradually decreasing when the deviation is large and rapidly increasing when the deviation is small. If the verification finds that the damping term has abnormal characteristics in a certain deviation range, such as slow growth when the deviation is small, then the preset logarithmic base parameter or weight parameter needs to be adjusted until the damping term fully meets the technical requirements of strong damping for small deviations and weak damping for large deviations.

[0052] Step 343 involves synthesizing the basic approach term and the nonlinear damping term to obtain a approach law output with dynamic damping characteristics. When the sliding surface state variable is large, the basic approach term dominates to accelerate the approach; when the sliding surface state variable is small, the nonlinear damping term dominates to suppress jitter. Specifically, this includes: firstly, completing pre-synthesis preparations for the basic approach term and the nonlinear damping term to ensure effective coordination: on one hand, performing time synchronization verification to confirm that the acquisition and calculation cycles of both parameters are consistent with the control cycle of the robot trajectory tracking, avoiding the synthesis result failing to reflect the current sliding surface state in real time due to time differences (e.g., the basic approach term is the current cycle data, and the damping term is the previous cycle data); on the other hand, performing sign matching processing. Since the nonlinear damping term is only generated through absolute value calculation of the state variable and has no direction information, the damping term is assigned the same sign according to the positive or negative sign of the basic approach term (e.g., when the basic approach term is positive, the damping term is also assigned a positive value, synchronously suppressing in the opposite direction, ensuring that the adjustment directions of the two are consistent, and avoiding the cancellation of adjustment effects after synthesis due to sign conflicts.

[0053] Secondly, the two parameters are combined using direct superposition. Based on their consistent adjustment direction and synergistic effect, the core logic is to achieve scenario-specific adaptive dominance through the superposition of the basic adjustment force and the damping correction force: When the sliding surface state variable is large, such as when the trajectory deviation is greater than 5, the basic approach term generated in step 341 has a large amplitude due to the correlation between large deviation and large gain, such as 15 to 20, while the nonlinear damping term generated in step 342 only shows a small amplitude due to the large deviation and weak damping characteristics, such as 2 to 5. After the two are superimposed, the adjustment effect of the basic approach term is much stronger than that of the damping term, naturally forming a basic approach term-dominated adjustment mode, which can quickly push the system closer to the ideal trajectory and ensure approach efficiency; When the sliding surface state variable is small, such as when the trajectory deviation is less than 1, the amplitude of the basic approach term is significantly reduced, such as 1 to 3, while the amplitude of the nonlinear damping term is relatively increased due to the small deviation and strong damping characteristics, such as 4 to 6. After the superposition, the correction effect of the damping term dominates, which can effectively suppress repeated overshoot caused by excessive adjustment force and ensure approach stability.

[0054] Furthermore, functional verification requires simulating common underwater operating conditions, such as static deviations and dynamic deviations caused by instantaneous disturbances, to observe whether the output can exhibit the characteristics of rapid convergence under large deviations and smooth, non-vibrating operation under small deviations. Boundary verification requires setting extreme deviation scenarios, such as state variables far exceeding the normal range, to confirm that the output will not exceed the maximum adjustment capability of the actuator, such as the upper limit of the control signal corresponding to the maximum torque of the drive motor. If abnormal output is found during verification, the gain parameters or preset damping parameters need to be adjusted retrospectively until the reaching law output fully meets the technical requirements of dynamic damping and efficient speed stabilization, and finally the reaching law output is determined.

[0055] In this embodiment of the invention, the dynamic logarithmic gain is multiplied by the sliding surface state variable to form a basic approaching term. The dynamic logarithmic gain itself has the characteristic of changing with the magnitude of the sliding surface state variable. After multiplying with the state variable, the magnitude of the basic approaching term directly reflects the synergistic effect of the deviation degree and gain adjustment. Based on the absolute value of the sliding surface state variable and preset parameters, a nonlinear damping term is generated through operations involving a logarithmic function. The key is to utilize the nonlinear characteristics of the logarithmic function and the adaptability of the preset parameters to achieve differentiated adjustment of the damping effect. The synthesis of the basic approaching term and the nonlinear damping term is essentially a process of using the basic approaching term to achieve ... The collaborative data processing mode of basic regulation and damping correction balances approaching efficiency and process stability. During the synthesis process, scenario-specific dominance can be achieved without additional complex logic: when the sliding surface state variable is large, the basic approaching term has formed a large amplitude due to the gain-state correlation, and its regulatory effect is much stronger than that of the nonlinear damping term, naturally dominating the approaching process and driving the system to quickly approach the ideal trajectory, ensuring approaching efficiency; when the state variable is small, the amplitude of the basic approaching term weakens, and the nonlinear damping term highlights its regulatory effect due to its strong damping characteristics with small deviations, naturally dominating the process. Damping correction suppresses excessively fast approaching speed and avoids repeated overshoot.

[0056] In a preferred embodiment of the present invention, step 4 above, using the approach law output as input, estimates the upper bound of the time-varying disturbance in the underwater environment online using finite-time adaptive technology to obtain an estimated value of the upper bound of the time-varying disturbance; using the estimated value of the upper bound of the time-varying disturbance, feedforward compensation is performed on the approach law output to synthesize the final control law and output it to the actuator to drive the robot to complete trajectory tracking, including: Step 41: Using the approach law output as the input of the finite-time adaptive technique, the upper bound of the time-varying disturbance of the underwater environment is estimated online through a calculation process including the hyperbolic tangent function and the adaptive parameter update law. Specifically, this includes: first, determining the input parameter approach law output, which is the control basis data generated in step 34 after dynamic damping adjustment, possessing the characteristics of large deviation acceleration and small deviation stabilization. This data directly reflects the dynamic adjustment requirements during the sliding surface approach process, and also implicitly contains the influence of underwater environmental disturbances on the sliding surface state. Therefore, using it as the input of the finite-time adaptive technique can ensure that the disturbance estimation is closely related to the actual control requirements.

[0057] The core operation uses an adaptive law formula: ,in, The upper bound estimate of the disturbance The update rate (derivative). This is an online estimate of the upper bound of the time-varying perturbation. For the sliding surface variable, This is the hyperbolic tangent function, used for smoothing. It is a positive smoothing parameter. This is the adaptive gain coefficient (a positive constant). For σ-correction term coefficients (positive constants). The known nonlinear function is related to the system state. The hyperbolic tangent function is used for preprocessing to smooth and suppress abnormal data in the approach law output. Due to sudden disturbances such as instantaneous strong currents in the underwater environment, the approach law output may have sharp outliers. If used directly for parameter updates, it may cause oscillations in the estimated values. After substituting the approach law output into the hyperbolic tangent function, its value range will be limited to the interval [-1, 1], and it has a significant smoothing effect on extreme outliers. For example, the sharp peaks such as 5 and -5 in the original output will approach 1 and -1 after processing. At the same time, the overall trend of the output data is preserved, such as the trend of increased output caused by enhanced disturbances.

[0058] The upper bound estimation of disturbances based on adaptive parameter update laws requires the initialization of update law parameters. An initial estimate is preset, typically set based on the intensity of normal underwater disturbances, such as 0.5 to 1.0. An update rate coefficient controls the sensitivity of the estimate to disturbance changes, such as 0.01 to 0.05. An excessively high rate will cause the estimate to oscillate, while an excessively low rate will fail to adapt to disturbance changes in a timely manner. Then, iterative updates are performed according to the robot control cycle (e.g., 0.1 seconds / cycle): the approach law output data processed by the hyperbolic tangent function is compared with the current upper bound estimate of the disturbance to obtain the deviation data. The deviation data is then multiplied by the update rate coefficient to obtain the parameter adjustment amount. Finally, the current estimate and the adjustment amount are superimposed to obtain a new upper bound estimate of the disturbance. For example, when the disturbance increases, causing the approach law output to increase, the deviation data is positive, the adjustment amount is positive, and the estimate increases accordingly; when the disturbance decreases, causing the output to decrease, the deviation data is negative, the adjustment amount is negative, and the estimate decreases synchronously, achieving real-time linkage between disturbance change, output adjustment, and estimate adaptation.

[0059] At the same time, upper and lower limits are set for the estimated value. The lower limit is 0 to avoid negative upper limits of disturbance. The upper limit is set according to the maximum disturbance rejection capability of the actuator, such as 5.0. If the estimated value exceeds the upper limit, it is clamped to the upper limit value to avoid excessive compensation in the future. If it is lower than the lower limit, it is reset to the initial estimated value to avoid estimation failure. This verification ensures that the estimated value is always within a reasonable range that can effectively support subsequent compensation calculations, and the final obtained estimated value is the verified value.

[0060] Step 42 involves performing a feedforward compensation operation on the estimated value of the time-varying disturbance upper bound and the approach law output to obtain the anti-disturbance compensation term. Specifically, this includes: determining that the estimated value of the time-varying disturbance upper bound reflects the maximum impact intensity of the current underwater environmental disturbance, and that the approach law output reflects the basic adjustment requirements for the sliding surface approach; the core operation uses the feedforward compensation control law formula: ,in, For the final feedforward compensation control term, The inverse of the system control gain matrix is... For smooth switching terms based on sliding surfaces, For proportional feedback items, This is the upper bound estimate of the perturbation from the adaptive law.

[0061] Before computation, two key preprocessing steps are required. The first is magnitude adaptation. Since the units of the estimated upper bound of the time-varying disturbance (e.g., N, N·m) differ from the units of the reaching law output (e.g., V, A, corresponding to the actuator drive signal), a coefficient conversion is necessary. This coefficient is determined based on the force / torque-signal conversion characteristics of the actuator, such as the torque-current coefficient of a motor. The estimated upper bound of the disturbance is converted into signal data of the same magnitude as the reaching law output. For example, a disturbance torque estimate of 0.8 N·m is converted to a signal magnitude of 0.4 A using a coefficient of 0.5 A / (N·m), avoiding excessively strong or weak compensation terms due to magnitude differences. The second step is direction matching. It is necessary to determine the direction of the disturbance's impact on the robot's trajectory, such as the direction in which water flow causes the robot to deviate from the ideal trajectory, and to determine the reverse adjustment direction of the compensation term. For example, if the disturbance causes the robot to shift in the positive X-axis direction, and the reaching law output has already generated a basic adjustment signal in the negative X-axis direction, then the anti-disturbance compensation term should also be set in the negative X-axis direction, consistent with the reaching law output direction, to enhance the ability to cancel the disturbance through unidirectional superposition. The direction judgment basis can be extracted from the changing trend of the reaching law output. For example, if the disturbance causes the reaching law output to continuously increase in a certain direction, then that direction is the direction of the disturbance's influence, ensuring that the compensation direction is opposite to the direction of the disturbance's influence and consistent with the basic adjustment direction.

[0062] After preprocessing, the magnitude-adapted upper bound estimate of the disturbance is weighted and calculated with the reaching law output. The weights are set according to the principle of prioritizing basic adjustment, such as a weight of 0.7 for the reaching law output and a weight of 0.3 for the disturbance upper bound estimate. The core logic of this weight allocation is to prioritize the basic adjustment role of the reaching law output, while supplementing it with the weighted upper bound estimate of the disturbance to enhance the disturbance resistance capability. For example, if the reaching law output is 1.0A (negative X-axis direction) and the magnitude-adapted upper bound estimate of the disturbance is 0.4A (negative X-axis direction), then the compensation term = 1.0 × 0.3 + 0.4 × 0.7 = 0.3 + 0.28 = 0.58A (negative X-axis direction).

[0063] Finally, the verification criteria are that the magnitude of the compensation term is less than or equal to 50% of the output magnitude of the reaching law, so as to avoid the compensation term being too strong and masking the basic regulation, and the direction of the compensation term is consistent with the output direction of the reaching law. If the verification criteria are not met, the magnitude conversion coefficient or weight allocation ratio is adjusted retrospectively until the compensation term meets the technical requirements of assisting in disturbance rejection and not interfering with the basic regulation, and the disturbance rejection compensation term is finally determined.

[0064] Step 43: The approach law output and the disturbance rejection compensation term are superimposed and synthesized to obtain a composite control signal containing disturbance rejection compensation, which serves as the final control law. Specifically, this includes: First, determining the core logic of the synthesis operation. The approach law output and the disturbance rejection compensation term do not act independently, but rather work together through the functions of basic adjustment and disturbance rejection supplementation to form a composite control signal that combines approach efficiency and disturbance rejection capability. Therefore, two key preparatory tasks need to be completed before synthesis to ensure that the two can be effectively superimposed.

[0065] The first preparatory step is time synchronization verification: Since the calculation cycles of the approach law output and the disturbance rejection compensation term must be consistent with the robot control cycle, such as 0.1 seconds / cycle, it is necessary to verify whether the generation timestamps of the two data items are completely matched, such as both being generated at 0.1 seconds of the 100th control cycle. This is to avoid the synthesized data reflecting control requirements at different times due to time differences, such as the approach law output being the current cycle data and the compensation term being the previous cycle data, which would lead to a disconnect between the control signal and the actual working condition. If there is a time difference, it is necessary to wait for the compensation term to generate the current cycle data before performing the synthesis to ensure the time consistency of the synthesized data.

[0066] The second preparatory step is sign verification: reconfirm that the direction of the anti-disturbance compensation term is consistent with the direction of the approach law output. For example, if both are in the negative X-axis direction, avoid the sign being reversed due to the direction judgment error in step 42, which would lead to the cancellation of the adjustment amplitude after synthesis. The verification method is to compare the sign labels of the two data. If the signs are inconsistent, the sign of the compensation term is immediately corrected to keep it consistent with the sign of the approach law output, ensuring that the adjustment direction is unified after synthesis.

[0067] After completing the preparation work, the superposition and synthesis operation is performed: a direct addition operation is adopted. Based on the characteristics of the two being in the same direction and functionally coordinated, the approach law output and the disturbance rejection compensation term are added to obtain the composite control signal. For example, if the approach law output is 1.0A (negative X-axis direction) and the disturbance rejection compensation term is 0.58A (negative X-axis direction), then the composite control signal = 1.0 + 0.58 = 1.58A (negative X-axis direction). The technical advantage of this addition operation is that it can directly superimpose the basic adjustment amount and the disturbance rejection compensation amount without additional complex logic. When the disturbance increases, the compensation term increases synchronously, and the disturbance rejection capability of the synthesized signal is enhanced accordingly. When the disturbance decreases, the compensation term decreases synchronously, and the synthesized signal is still dominated by the basic adjustment amount, ensuring the dynamic adaptability of functional coordination.

[0068] After synthesis, two key verifications are required for the composite control signal: First, amplitude boundary verification. An upper limit for the signal amplitude is set based on the maximum driving capability of the actuator, such as a maximum motor drive current of 2.0A. If the synthesized signal exceeds this limit, it is clamped to the upper limit value to prevent overload damage to the actuator. If it is below the lower limit, such as 0.1A, which is below the actuator's minimum response threshold, it is raised to the lower limit value to ensure effective actuator response. Second, functional characteristic verification. Two typical operating conditions are simulated: a large disturbance condition and a small disturbance condition. The characteristics of the synthesized signal are observed. Under the large disturbance condition, the synthesized signal should exhibit a reaching law output. The characteristics of the base amplitude and the compensation term enhancement amplitude, such as a base amplitude of 1.0A plus a compensation term of 0.8A equaling 1.8A, can quickly cancel out disturbances. Under small disturbance conditions, the synthesized signal should exhibit the characteristics of a dominant approach law output and a weak compensation term, such as a base amplitude of 0.5A plus a compensation term of 0.1A equaling 0.6A, to avoid over-adjustment leading to oscillations. If the verification fails, the compensation term weight in step 42 or the disturbance estimation update rate in step 41 is adjusted retrospectively until the synthesized signal simultaneously meets the requirements of amplitude compliance and functional adaptation. Finally, the verified composite control signal is the final control law that can be output to the actuator.

[0069] Step 44: Output the final control law to the actuator to achieve robot trajectory tracking by real-time compensation for time-varying disturbances. Specifically, this includes: First, determining the adaptation logic between the final control law and the actuator. The final control law currently exists in the form of abstract control signals, such as current A and voltage V. It needs to be converted into physical drive signals that the actuator can directly recognize, such as the PWM signal of the motor and the opening control signal of the hydraulic valve, in order to drive the actuator to move. Therefore, the first step is to perform signal format conversion.

[0070] Signal format conversion requires specific methods depending on the type of actuator: If the actuator is a DC drive motor, such as a robot thruster motor, the current signal of the final control law, such as 1.58A, needs to be converted into a PWM (Pulse Width Modulation) signal. The conversion is based on the correspondence between the motor's current and the PWM duty cycle, such as 0A corresponding to 0% duty cycle and 2.0A corresponding to 100% duty cycle. The appropriate duty cycle is obtained through linear interpolation, such as 1.58A corresponding to 79% duty cycle. If the actuator is a hydraulic valve, such as a robot posture adjustment hydraulic valve, the voltage-based control law signal, such as 3.0V, needs to be converted into a valve position opening signal, such as 0V corresponding to 0% opening and 5.0V corresponding to 100% opening. Ensure that the converted signal is fully compatible with the hardware interface protocol of the actuator. For example, the frequency of the PWM signal needs to be set to 1kHz, consistent with the receiving frequency of the motor drive board.

[0071] After the format conversion is completed, the control signal is output in real time: the output cycle strictly follows the robot control cycle, such as 0.1 seconds / cycle, that is, the converted physical drive signal is sent to the actuator once every 0.1 seconds to ensure that the signal output rhythm is synchronized with the disturbance change rhythm and the sliding surface approach rhythm. For example, if the underwater disturbance changes in intensity once every 0.1 seconds, the control signal is also updated once every 0.1 seconds. Dynamic compensation for disturbance is achieved through real-time output and real-time response.

[0072] The system collects actual action data of the actuator through feedback interfaces such as motor current feedback and hydraulic valve position feedback. For example, the actual motor current is 1.56A and the actual hydraulic valve opening is 78%. The difference between these data and the theoretical data corresponding to the final control law (e.g., 1.58A and 79%) is calculated to obtain the deviation data. If the deviation data is less than a preset threshold, such as 5%, the system is considered to be operating normally and continues to output signals periodically. If the deviation data exceeds the threshold, such as when the actual motor current is only 1.0A and the deviation is 30%, the system immediately triggers an exception handling mechanism, suspends the current signal output, re-executes the calculations from steps 41 to 43, and checks the hardware status of the actuator, such as whether there is any blockage, to avoid trajectory tracking failure due to execution anomalies.

[0073] Ultimately, through a closed-loop process of signal conversion, real-time output, and feedback monitoring, the final control law is transformed into the actual actions of the actuator: when underwater disturbances increase, the amplitude of the control law signal increases synchronously, and the actuator outputs a stronger driving force (such as increasing the motor speed) to counteract the disturbances; when the disturbances decrease, the signal amplitude decreases, and the actuator's actions become smoother, ensuring that the robot always moves along the ideal trajectory and achieving high-precision trajectory tracking in time-varying underwater environments.

[0074] In this embodiment of the invention, the reaching law output is used as the input to the finite-time adaptive technique. The core of the technique involves collaborative data processing using the hyperbolic tangent function and the adaptive parameter update law to achieve online estimation of the upper bound of the time-varying disturbance. The hyperbolic tangent function can smooth and suppress abnormal fluctuations in the reaching law output, preventing abnormal data from interfering with the estimation results. Simultaneously, the boundedness of its value range ensures that intermediate computational data remains within a stable range. The adaptive parameter update law dynamically adjusts the estimation parameters based on the real-time input reaching law output data. Based on the estimated upper bound of the time-varying disturbance, a feedforward compensation operation is performed with the reaching law output to generate an anti-disturbance compensation term. Its proactive predictive compensation logic design differs from post-event correction feedback compensation. The feedforward compensation operation directly utilizes the estimated upper bound of the disturbance data, preemptively converting the disturbance's impact on the trajectory into targeted compensation data. For example, when it is estimated that a water flow disturbance will cause the robot's trajectory to deviate, the compensation term will generate data in advance that is opposite in direction and matches the amplitude of the disturbance's impact, integrating it into the control process through a feedforward approach. Simultaneously, during the operation, the estimated upper bound of the disturbance and the reaching law output are compared... The magnitude of the compensation term is adapted to match the adjustment range of the approach law output, ensuring that insufficient compensation fails to offset the disturbance and excessive compensation does not cause new trajectory deviations. The approach law output and the anti-disturbance compensation term are superimposed to obtain the final control law. The approach law output carries the core function of driving the sliding surface to quickly approach the ideal state, ensuring the efficiency of trajectory tracking. The anti-disturbance compensation term carries the auxiliary function of offsetting the influence of underwater time-varying disturbances, ensuring the stability of trajectory tracking. When the two are superimposed, no additional complex weight allocation is required; functional synergy can be achieved simply by direct synthesis. The final control law is output to the actuator, and trajectory tracking is achieved by compensating for time-varying disturbances in real time. The control law output data is formatted according to the response characteristics of the actuator, converting the control signal data into drive data that the actuator can directly recognize, ensuring that the data can be effectively executed. The output process is synchronized with the control cycle of the actuator. For example, if the actuator receives a control command every 0.1 seconds, the control law data is output in real time according to that cycle, ensuring that the compensation data is consistent with the time rhythm of disturbance changes.

[0075] like Figure 2 As shown, embodiments of the present invention also provide a trajectory tracking system for a caisson-mounted tracked robot, comprising: The saturation compensation module is used to process the original control input with a differentiable saturation function based on the Gaussian error function to obtain a smooth saturated control signal; and to calculate the difference between the smooth saturated control signal and the original control input to obtain a saturation error compensation signal. The adjustment module is used to construct the basic framework of the sliding surface through a feedforward function using the smooth saturation control signal, the saturation error compensation signal, and the initial state; a nonlinear feedback function is introduced into the basic framework, and the sliding surface state is adjusted in stages through the function to suppress steady-state overshoot and obtain the sliding surface state variables. The dynamic adjustment module is used to calculate the dynamic logarithmic gain that changes with the state based on the absolute value of the sliding surface state variable; and to adjust the speed approaching the sliding surface using the dynamic logarithmic gain to obtain a reaching law output with dynamic damping characteristics. An adaptive module is used to take the output of the reaching law as input, estimate the upper bound of the time-varying disturbance of the underwater environment online through finite-time adaptive technology, and obtain the estimated value of the upper bound of the time-varying disturbance; using the estimated value of the upper bound of the time-varying disturbance, feedforward compensation is performed on the output of the reaching law, synthesize the final control law and output it to the actuator to drive the robot to complete trajectory tracking.

[0076] It should be noted that this system is a system corresponding to the above method. All implementation methods in the above method embodiments are applicable to this embodiment and can achieve the same technical effect.

[0077] Embodiments of the present invention also provide a computing device, including: a processor and a memory storing a computer program, wherein the computer program, when executed by the processor, performs the method described above. All implementations in the above method embodiments are applicable to this embodiment and can achieve the same technical effects.

[0078] Embodiments of the present invention also provide a computer-readable storage medium storing instructions that, when executed on a computer, cause the computer to perform the method described above. All implementations in the above method embodiments are applicable to this embodiment and can achieve the same technical effects.

[0079] Those skilled in the art will recognize that the units and algorithm steps of the various examples described in conjunction with the embodiments disclosed herein can be implemented in electronic hardware, or a combination of computer software and electronic hardware. Whether these functions are implemented in hardware or software depends on the specific application and design constraints of the technical solution. Those skilled in the art can use different methods to implement the described functions for each specific application, but such implementations should not be considered beyond the scope of this invention.

[0080] Furthermore, it should be noted that in the apparatus and method of the present invention, it is obvious that the components or steps can be decomposed and / or recombined. These decompositions and / or recombinations should be considered equivalent solutions of the present invention. Moreover, the steps performing the above series of processes can naturally be executed in the order described, but are not necessarily required to be executed in chronological order; some steps can be executed in parallel or independently of each other. Those skilled in the art will understand that all or any step or component of the method and apparatus of the present invention can be implemented in any computing device (including processors, storage media, etc.) or network of computing devices, in hardware, firmware, software, or a combination thereof. This can be achieved by those skilled in the art using basic programming skills after reading the description of the present invention.

[0081] Therefore, the object of the present invention can also be achieved by running a program or a set of programs on any computing device. The computing device can be a known general-purpose device. Therefore, the object of the present invention can also be achieved simply by providing a program product containing program code implementing the method or apparatus. That is, such a program product also constitutes the present invention, and the storage medium storing such a program product also constitutes the present invention. Obviously, the storage medium can be any known storage medium or any storage medium developed in the future. It should also be noted that in the apparatus and method of the present invention, it is obvious that the components or steps can be decomposed and / or recombined. These decompositions and / or recombinations should be considered equivalent to the present invention. Furthermore, the steps performing the above series of processes can naturally be performed in the order described, but are not necessarily required to be performed in chronological order. Some steps can be performed in parallel or independently of each other.

[0082] The above description represents the preferred embodiments of the present invention. It should be noted that those skilled in the art can make various improvements and modifications without departing from the principles of the present invention, and these improvements and modifications should also be considered within the scope of protection of the present invention.

Claims

1. A trajectory tracking method for a caisson-type tracked robot, characterized in that, The method includes: The original control input is processed by a differentiable saturation function based on the Gaussian error function to obtain a smooth saturated control signal; the difference between the smooth saturated control signal and the original control input is calculated to obtain a saturation error compensation signal. Using the smooth saturation control signal, saturation error compensation signal, and initial state, a basic framework for the sliding surface is constructed through a feedforward function; a nonlinear feedback function is introduced into the basic framework, and the sliding surface state is adjusted in stages through this function to suppress steady-state overshoot, thereby obtaining the sliding surface state variables; Based on the absolute value of the sliding surface state variable, the dynamic logarithmic gain that changes with the state is calculated; using the dynamic logarithmic gain, the speed approaching the sliding surface is adjusted to obtain a reaching law output with dynamic damping characteristics. Using the approach law output as input, the upper bound of the time-varying disturbance in the underwater environment is estimated online through finite-time adaptive technology to obtain the estimated value of the upper bound of the time-varying disturbance; using the estimated value of the upper bound of the time-varying disturbance, the approach law output is fed forward to compensate, the final control law is synthesized and output to the actuator to drive the robot to complete trajectory tracking.

2. The trajectory tracking method for a caisson-type tracked robot according to claim 1, characterized in that, The original control input is processed by a differentiable saturation function based on the Gaussian error function to obtain a smooth saturated control signal; Calculate the difference between the smoothed saturation control signal and the original control input to obtain the saturation error compensation signal, including: Based on the original control input and the absolute value of the input limit, a function value is obtained by calculating using the Gaussian error function; the function value is then multiplied by the absolute value of the input limit to obtain the smooth saturation control signal. The difference between the smoothed saturation control signal and the original control input is calculated to obtain a saturation error compensation signal used to compensate for the influence of input saturation.

3. The trajectory tracking method for a caisson-tracked robot according to claim 2, characterized in that, Using the smooth saturation control signal, saturation error compensation signal, and initial state, a basic framework for the sliding surface is constructed through a feedforward function. A nonlinear feedback function is introduced into this basic framework to adjust the sliding surface state in stages, suppressing steady-state overshoot, thus obtaining the sliding surface state variables, including: The smooth saturation control signal, the saturation error compensation signal, and the initial state are input into the attenuation feedforward function to construct a sliding surface basic framework that includes initial error compensation. By introducing a nonlinear feedback function into the basic framework of the sliding surface, a composite sliding surface with staged adjustment capability is constructed. The state of the composite sliding surface is adjusted in real time by the nonlinear feedback function. Under small error conditions, the gain value is increased to accelerate the convergence process, while under large error conditions, the gain value is limited to avoid excessive accumulation of integrals and to suppress steady-state overshoot. Finally, the sliding surface state variables used for trajectory tracking control are obtained.

4. The trajectory tracking method for a caisson-tracked robot according to claim 3, characterized in that, The dynamic logarithmic gain that varies with the state is calculated based on the absolute value of the sliding surface state variable. By utilizing the aforementioned dynamic logarithmic gain, the velocity approaching the sliding surface is adjusted to obtain a reaching law output with dynamic damping characteristics, including: The absolute value of the sliding surface state variable is added to a preset gain constant to form the input term of the logarithmic function; Calculate the natural logarithm of the input term of the logarithmic function to obtain the basic dynamic gain component; The basic dynamic gain component is combined with another preset fixed gain coefficient to obtain the dynamic logarithmic gain; By utilizing the dynamic logarithmic gain, the speed of approaching the sliding surface is adjusted. When the state variable of the sliding surface is large, the gain is increased to accelerate the approach, and when the state variable of the sliding surface is small, the gain is decreased to suppress jitter, thus obtaining a approach law output with dynamic damping characteristics.

5. The trajectory tracking method for a caisson-tracked robot according to claim 4, characterized in that, Using the aforementioned dynamic logarithmic gain, the speed of approaching the sliding surface is adjusted. When the sliding surface state variable is large, the gain is increased to accelerate the approach; when the sliding surface state variable is small, the gain is decreased to suppress jitter, resulting in a approach law output with dynamic damping characteristics, including: The dynamic logarithmic gain is multiplied by the sliding surface state variables to form the basic approach term; Based on the absolute value of the sliding surface state variables and preset parameters, a nonlinear damping term is generated through operations involving logarithmic functions; The basic approach term and the nonlinear damping term are synthesized to obtain an approach law output with dynamic damping characteristics. When the sliding surface state variable is large, the basic approach term dominates to accelerate the approach, and when the sliding surface state variable is small, the nonlinear damping term dominates to suppress jitter.

6. The trajectory tracking method for a caisson-tracked robot according to claim 5, characterized in that, Using the reaching law output as input, the upper bound of the time-varying disturbance in the underwater environment is estimated online using finite-time adaptive technology to obtain an estimated value of the upper bound of the time-varying disturbance; using the estimated value of the upper bound of the time-varying disturbance, feedforward compensation is performed on the reaching law output to synthesize the final control law and output it to the actuator to drive the robot to complete trajectory tracking, including: Using the output of the reaching law as the input of the finite-time adaptive technique, the upper bound of the time-varying disturbance of the underwater environment is estimated online through an operation process that includes the hyperbolic tangent function and the adaptive parameter update law, and the estimated value of the upper bound of the time-varying disturbance is obtained. The estimated value of the time-varying disturbance upper bound and the output of the reaching law are used to perform feedforward compensation operation to obtain the disturbance resistance compensation term; The approach law output is superimposed and synthesized with the anti-disturbance compensation term to obtain a composite control signal containing disturbance compensation, which serves as the final control law. The final control law is output to the actuator, and the robot's trajectory tracking is achieved by real-time compensation for time-varying disturbances.

7. A trajectory tracking system for a caisson-mounted tracked robot, wherein the system implements the method as described in any one of claims 1 to 6, characterized in that, include: The saturation compensation module is used to process the original control input with a differentiable saturation function based on the Gaussian error function to obtain a smooth saturated control signal; and to calculate the difference between the smooth saturated control signal and the original control input to obtain a saturation error compensation signal. The adjustment module is used to construct the basic framework of the sliding surface through a feedforward function using the smooth saturation control signal, the saturation error compensation signal, and the initial state; a nonlinear feedback function is introduced into the basic framework, and the sliding surface state is adjusted in stages through the function to suppress steady-state overshoot and obtain the sliding surface state variables. The dynamic adjustment module is used to calculate the dynamic logarithmic gain that changes with the state based on the absolute value of the sliding surface state variable; and to adjust the speed approaching the sliding surface using the dynamic logarithmic gain to obtain a reaching law output with dynamic damping characteristics. An adaptive module is used to take the output of the reaching law as input, estimate the upper bound of the time-varying disturbance of the underwater environment online through finite-time adaptive technology, and obtain the estimated value of the upper bound of the time-varying disturbance; using the estimated value of the upper bound of the time-varying disturbance, feedforward compensation is performed on the output of the reaching law, synthesize the final control law and output it to the actuator to drive the robot to complete trajectory tracking.

8. A computing device, characterized in that, include: One or more processors; A storage device for storing one or more programs that, when executed by one or more processors, cause the one or more processors to implement the method as described in any one of claims 1 to 6.

9. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores a program that, when executed by a processor, implements the method as described in any one of claims 1 to 6.

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