A method and system for admittance control of an underwater robotic leg without end force sensors

Abstract

The application relates to the technical field of robots and proposes an underwater mechanical leg admittance control method and system without a terminal force sensor, the method comprising the following steps: acquiring joint torque and motion state information; on-line identifying and updating sealed friction model parameters based on the information, calculating a friction torque estimation value; compensating a sensor measurement value based on the friction torque estimation value to obtain a joint net output torque; mapping the joint net output torque to a foot end space, combining a dynamics model to calculate a virtual terminal contact force; inputting the virtual terminal contact force into an admittance control outer ring to generate a desired net output torque; and finally, combining the desired net output torque and the friction estimation value, and calculating a driving instruction through a motor dynamics model. The method breaks the dependence on the terminal force sensor through on-line friction identification and compensation, virtual force estimation and an admittance control closed loop, effectively suppresses sealed nonlinear interference, and significantly improves the force sensing precision and compliant interaction ability of the underwater mechanical leg in a complex environment.

Description

Technical Field

[0001] This application relates to the field of robot control technology, and in particular to an admittance control method and system for an underwater mechanical leg without an end effector force sensor. Background Technology

[0002] Underwater robotic legs are core components of underwater operational equipment such as seabed crawling robots and pile foundation maintenance robots. They need to achieve stable support, compliant walking, and precise operation in complex seabed terrain. Admittance control, as a force-potential hybrid control strategy, can achieve compliant interaction with the environment by adjusting the dynamic behavior of the robotic leg, and is a key technology to prevent foot slippage, sinking, or impact on the seabed ecosystem. However, the practical application of admittance control in the special underwater environment faces severe challenges, especially the lack of force sensing and insufficient interference compensation, which seriously restricts the autonomy and reliability of underwater robotic legs.

[0003] The primary challenge lies in the lack of end-effector force sensing. Traditional admittance control frameworks heavily rely on end-effector six-dimensional force sensors to directly measure the interaction force between the foot and the environment, using this as feedback input for control. However, the operating environment of underwater robotic legs is harsh, and end-effector six-dimensional force sensors are not only expensive and structurally fragile, but also face challenges in reliable sealing; high pressure and corrosive seawater can easily cause sensor failure, increasing system complexity and failure rate. Therefore, in practical underwater robotic legs, such sensors are usually not installed at the foot, causing traditional admittance control to lose a direct source of force feedback information and thus becoming unusable.

[0004] Another core bottleneck is the distortion of joint torque transmission. Underwater robotic leg joints commonly employ dynamic seals, such as rotary shaft seals or magnetohydrodynamic seals, to prevent seawater intrusion. However, this sealing process introduces significant and time-varying nonlinear frictional torque. This interference severely disrupts the transmission process from the motor output torque to the joint's net output torque, making it difficult to accurately obtain the actual torque acting on the linkage. Without end-effector force sensors, the accuracy of the joint output torque becomes the only reliable basis for indirectly estimating the end-effector interaction force. If the sealing friction is not accurately compensated, systematic errors will occur in the foot-end force estimation, especially under low-speed movement or high sealing pressure conditions.

[0005] To address the force sensing problem without end effectors, existing technologies mainly employ two approaches: one is indirect force estimation based on joint torque sensors, which estimates foot force by installing torque sensors at the output of the joint actuator and combining them with a kinematic model. However, this method does not consider the torque consumed by dynamic sealing, directly treating the sensor measurement as the net torque and ignoring the losses caused by sealing friction. The other approach is disturbance observation based on motor current, which calculates the output torque using the motor current and estimates the total disturbance using an extended state observer. However, this method couples sealing friction, load changes, and hydrodynamics into a single total disturbance, making it impossible to separate and specifically compensate for sealing friction. This results in a coarse model and unstable compensation effects when sealing characteristics change.

[0006] In summary, existing technologies have failed to effectively solve the dual challenges of "lack of end force sensor" and "sealing interference," resulting in insufficient force sensing and control precision, which prevents underwater robotic legs from achieving high-precision compliant force control in real marine environments. Summary of the Invention

[0007] In view of this, this application proposes an admittance control method and system for an underwater mechanical leg without an end-effector force sensor, aiming to solve the technical problem that underwater mechanical legs cannot achieve high-precision compliant force control due to the inability to install end-effector force sensors and interference from joint seals.

[0008] The technical solution of this application is implemented as follows: This application provides a...

[0009] In a first aspect, this application discloses a method for controlling the admittance of an underwater mechanical leg without an end-effector force sensor, comprising the following steps: Acquire the joint torque sensor measurements and joint motion status information of the target joint; Based on the joint motion state information and preset environmental parameters, the model parameters of the parameterized friction model of the dynamic sealing link of the target joint are updated through an online identification algorithm; using the updated model parameters and the joint motion state information, the estimated value of the friction torque is calculated through the parameterized friction model. The estimated value of the frictional torque is used to compensate for the measured value of the joint torque sensor to obtain the net joint output torque of the linkage driven by the target joint. The net output torque of the joint is mapped to the foot end operating space of the mechanical leg, and the virtual end contact force of the foot end is calculated based on the dynamic model of the mechanical leg. The virtual end contact force is input into the admittance control outer loop to generate the desired net output torque of the target joint; Based on the sum of the expected net output torque and the estimated value of the friction torque, and combined with the motor dynamics model, the motor command torque for driving the target joint is calculated.

[0010] In some embodiments, the parameterized friction model is: ,in, This is an estimated value for the frictional torque. and q These are the joint angular velocity and joint angular position, respectively, from the joint motion state information. P and T These are water depth, pressure, and temperature, respectively. The sealing condition coefficient is determined based on the aforementioned pressure and temperature. Let be the Coulomb friction coefficient. and v s These are the amplitude coefficients and characteristic velocities that describe the Stribek effect, respectively. The coefficient of viscous friction, and These are the stiffness coefficient and shape factor, respectively, describing the micro-deformation of the seal pre-tightening.

[0011] In some embodiments, the sealing condition coefficient For the water depth pressure obtained through offline calibration p With temperature T The function; during online control, based on real-time measured water depth and pressure. p With temperature T This can be achieved by querying a mapping table built based on offline calibration data or by calculating the function. The value is obtained by taking the value.

[0012] In some embodiments, the online identification algorithm employs a recursive least squares method with a forgetting factor. When the mechanical leg is in a swing phase with no contact at the foot end, the model parameters of the parameterized friction model are updated online using the condition that the net output torque of the joint is approximately equal to the torque calculated by the link model.

[0013] In some embodiments, mapping the net output torque of the joint to the foot operating space and calculating the virtual end contact force based on the dynamic model specifically includes: mapping the net output torque vector of the joint to the foot operating space through the pseudo-inverse operation of the Jacobian matrix of the mechanical leg, and subtracting the joint space internal force vector calculated based on the dynamic model, thereby calculating the virtual end contact force.

[0014] In some embodiments, the force vector within the joint space includes the gravity term of the mechanical leg, and one or more of the inertial force term, the Coriolis eccentric term, and the estimated hydrodynamic term.

[0015] In some embodiments, the admittance control outer loop generates the desired net output torque in the joint space based on the desired foot pose, the actual foot pose, and the deviation between the desired foot force and the estimated contact force. This process is defined by the following second-order admittance model: ,in, M d , B d , K d These represent the admittance mass, damping, and stiffness matrices, respectively. , , These represent the desired foot position, velocity, and acceleration, respectively. , , These are the actual foot position, velocity, and acceleration, respectively. This is an estimate of the foot contact force extracted from the virtual end contact force. The desired foot contact force; The desired net output torque By mapping the operational space forces output by the admittance model to the joint space and combining them with gravity compensation, its expression is as follows: ,in, Let be the Jacobian matrix of the mechanical leg. For the transpose of the Jacobian matrix of the mechanical leg, Let be the gravity term of the mechanical leg.

[0016] In some embodiments, the calculation of the motor command torque by combining the motor dynamics model specifically includes: adding the expected net output torque to the estimated value of the friction torque to compensate for sealing friction loss; then dividing by the reduction ratio to convert it into an equivalent command at the motor shaft end; and finally superimposing a feedforward compensation term based on the motor rotor dynamics to obtain the final motor command torque.

[0017] Secondly, this application discloses an underwater mechanical leg admittance control system without an end-effector force sensor, comprising: The data acquisition module is used to acquire the joint torque sensor measurement values ​​and joint motion state information of the target joint; The friction torque estimation module is used to update the model parameters of the parameterized friction model of the dynamic sealing link based on the joint motion state information and preset environmental parameters through an online identification algorithm, and to calculate the estimated value of the friction torque using the updated model parameters and the joint motion state information. The torque compensation module is used to compensate the measured value of the joint torque sensor using the estimated value of the friction torque, so as to obtain the net joint output torque of the linkage driven by the target joint. The virtual force estimation module is used to map the net output torque of the joint to the foot end operating space of the robotic leg, and calculate the virtual end contact force of the foot end based on the dynamic model of the robotic leg. The admittance control module is used to input the virtual end contact force into the admittance control outer loop to generate the desired net output torque of the target joint; The motor command synthesis module is used to calculate, based on the sum of the expected net output torque and the estimated value of the friction torque, and in conjunction with the motor dynamics model, to obtain the motor command torque for driving the target joint.

[0018] Thirdly, this application discloses an electronic device, including a processor and a memory; the memory stores a computer program, wherein the computer program, when executed by the processor, implements the underwater mechanical leg admittance control method without end force sensor described in the first aspect.

[0019] This application has the following advantages over the prior art: (1) The method disclosed in this application obtains accurate joint net torque by online identification and compensation of dynamic sealing friction, thereby virtually estimating the end contact force and using this force signal to drive the admittance control outer loop. Finally, motor commands are generated in the inner loop, which includes feedforward friction compensation, forming a complete sensing and control chain. This method completely eliminates the dependence on the six-dimensional force sensor at the end and effectively suppresses the interference of nonlinear sealing friction, significantly improving the realism and accuracy of force sensing and force control of the underwater robotic leg in unknown and complex seabed environments. Ultimately, it enables the underwater robotic leg to have stable, compliant, and adaptive movement and operation capabilities in complex seabed environments.

[0020] (2) By organically combining the efficient algorithm of recursive least squares with forgetting factor, which can track time-varying characteristics, the wise timing of execution limited to the oscillating phase with minimal disturbance, and the reliable physical condition of using known link dynamics as the update reference, the system can stably, reliably, and automatically complete the online calibration and tracking of the sealing friction model parameters in complex underwater working cycles by utilizing the periodically occurring oscillating phase window. This effectively addresses the characteristic drift of the seal caused by long-term operation and changes in environmental pressure and temperature, thereby maintaining the long-term accuracy and robustness of the entire control system.

[0021] (3) A second-order admittance model is used to clearly define the dynamic compliance relationship between force and pose deviation. Accurate joint-layer torque commands are generated using Jacobi transpose mapping and gravity compensation, thus constructing a core decision-making and conversion hub connecting virtual force sensing and the underlying joint actuator. It transforms the upstream estimated end-effector contact force into an executable joint desired net torque, enabling the entire system to achieve high-quality compliant position and force hybrid control based on force feedback even without end-effector force sensors. This is a key control law guarantee for ensuring safe, stable, and adaptive interaction between the underwater robotic leg and the uncertain environment.

[0022] (4) By combining the desired net torque command generated by the admittance control outer loop with the online identified sealing friction compensation, transmission ratio conversion, and motor self-dynamic feedforward compensation, the final motor command is synthesized. This step ensures that the actual output torque of the motor, after passing through the reducer and overcoming all losses, can highly accurately reproduce the joint net output torque expected by the admittance controller, thereby reliably implementing the entire sensorless force sensing and compliant control scheme into physical execution, ensuring that the underwater mechanical leg achieves high-precision compliant movement. Attached Figure Description

[0023] To more clearly illustrate the technical solutions in the embodiments of this application or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0024] Figure 1 This application discloses a flowchart of an underwater mechanical leg admittance control method without an end force sensor. Detailed Implementation

[0025] To make the objectives, technical solutions, and advantages of this application clearer, the technical solutions of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, not all embodiments. Based on the embodiments of this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.

[0026] like Figure 1 As shown, the first embodiment of this application discloses an admittance control method for an underwater mechanical leg without an end-effector force sensor, comprising the following steps: Step S1: Obtain the joint torque sensor measurement value and joint motion state information of the target joint.

[0027] This step is fundamental to data acquisition and sensing. A joint torque sensor installed at the output end of the actuator in the target joint (such as the hip or knee joint) measures the raw signal reflecting the torque of the reducer's output shaft in real time. Simultaneously, position sensors such as encoders acquire the angular position and angular velocity information of the joint. This real-time data collectively constitutes the direct input to all subsequent estimation, identification, and control algorithms, serving as the signal source for the entire control method to be implemented.

[0028] Step S2: Based on the joint motion state information and preset environmental parameters, update the model parameters of the parameterized friction model of the dynamic sealing link through an online identification algorithm; using the updated model parameters and the joint motion state information, calculate the estimated value of the friction torque through the parameterized friction model.

[0029] This step is the core of achieving high-precision sealing friction compensation. First, the system utilizes motion state information such as joint angular velocity, as well as environmental parameters such as current water depth and temperature obtained through pressure and temperature sensors, to drive an online adaptive identification algorithm. This algorithm is activated during the swing phase when the mechanical leg's foot is not in contact with the ground. Taking advantage of the physical condition that the net output torque of the joint at this time is mainly determined by the known inertial dynamics of the connecting rod, the algorithm continuously iteratively updates the internal parameters of the mathematical model describing the nonlinear friction behavior of the target joint's dynamic seal. This process allows the friction model to track in real time the drift in friction characteristics caused by wear of the target joint's seals, changes in lubrication status, and fluctuations in water pressure and temperature, maintaining the model's accuracy. Immediately afterwards, the system substitutes the updated model parameters and the current joint motion state information into the parameterized friction model, performs a forward calculation, and outputs a precise estimate of the dynamic seal friction torque corresponding to the current operating condition of the target joint.

[0030] Step S3: Compensate the measured value of the joint torque sensor using the estimated value of the friction torque to obtain the net joint output torque of the linkage driven by the target joint.

[0031] This step aims to reconstruct the true and effective driving torque from the raw sensor signals. The joint torque sensor measurements essentially include the effective torque used to drive the linkage and the frictional torque consumed by the sealing element. By subtracting the estimated frictional torque calculated in step S2 from the raw measurements, systematic interference from sealing friction can be eliminated. The net output torque of the joint obtained from this subtraction operation represents the pure torque actually applied to the mechanical linkage connected to the joint's output shaft to generate motion or resist environmental forces, providing accurate input for subsequent indirect estimation of foot-end forces.

[0032] Step S4: Map the net output torque of the joint to the foot end operating space of the mechanical leg, and calculate the virtual end contact force of the foot end based on the dynamic model of the mechanical leg.

[0033] This step virtually reconstructs crucial force interaction information without the need for physical end-effector sensors. The system utilizes the Jacobian matrix from robot kinematics to establish a mechanical mapping from joint space to foot operating space. Through this mapping, the net joint output torque obtained in step S3 is converted to the foot, forming an equivalent generalized force in the foot operating space. Subsequently, based on the dynamic model of the robotic leg, the internal force terms generated by link gravity, inertial forces, and Coriolis centrifugal forces are calculated under the current configuration and motion state of the robotic leg. These internal force terms are subtracted from the equivalent force mapped to the foot, and the estimated underwater hydrodynamic effects are further considered. Finally, a virtual end-effector contact force estimate reflecting the actual interaction between the foot and the seabed environment can be obtained. This step successfully replaces the function of the six-dimensional force sensor at the end-effector.

[0034] Step S5: Input the virtual end contact force into the admittance control outer loop to generate the desired net output torque of the target joint.

[0035] This step implements compliant interaction decision-making based on virtual force perception. The admittance control outer loop is a second-order dynamic model whose inputs are the deviation between the desired foot contact force and the virtual end-effector contact force estimated in step S4, and the deviation between the desired foot trajectory and the actual trajectory. Based on preset admittance mass, damping, and stiffness parameters, the model simulates a desired compliant physical interaction behavior and, considering the aforementioned deviations, determines the force adjustment amount applied to the foot to achieve this compliant behavior. Subsequently, through the transpose of the Jacobian matrix, this force adjustment amount in the foot operating space is mapped back to the joint space, and combined with a gravity compensation term, the desired net output torque command that the target joint should output is finally generated. This command defines the mechanical goal that the joint needs to achieve to realize compliant walking or work.

[0036] Step S6: Based on the sum of the estimated values ​​of the desired net output torque and the friction torque, and combined with the motor dynamics model, calculate the motor command torque used to drive the target joint.

[0037] This step is the final synthesis and execution of control commands, ensuring the precise achievement of the desired mechanical objective. To ensure that the actual net output torque generated by the joint accurately tracks the desired net output torque generated in step S5, the losses from sealing friction must be compensated. Therefore, the desired net output torque is added to the friction torque estimated in step S2 to obtain the total torque required by the motor at the reducer input. This total torque is then divided by the reduction ratio and converted to the motor shaft. Furthermore, a dynamic feedforward compensation term is added to counteract the effects of the motor rotor's own inertia and damping. Finally, the precise command torque to be sent to the joint drive motor is calculated. This command ensures that the actual output torque of the motor, after passing through the transmission chain and overcoming sealing friction, is exactly equal to the joint net output torque desired by the admittance controller, thus forming a complete closed-loop control from force sensing and decision-making to execution, ensuring that the mechanical leg achieves the predetermined compliant interaction behavior.

[0038] The method disclosed in this application obtains precise joint net torque by online identification and compensation of dynamic sealing friction. Based on this, the end-effector contact force is virtually estimated, and this force signal drives the admittance control outer loop. Finally, motor commands are generated in the inner loop, which includes feedforward friction compensation, forming a complete sensing and control chain. This method completely eliminates the dependence on a six-dimensional force sensor at the end and effectively suppresses the interference of nonlinear sealing friction, significantly improving the realism and accuracy of force sensing and force control of the underwater robotic leg in unknown and complex seabed environments. Ultimately, this enables the underwater robotic leg to possess stable, compliant, and adaptive movement and operational capabilities in complex seabed environments.

[0039] In some embodiments, the parametric friction model is fully defined by the following mathematical formula: This model is a comprehensive and enhanced nonlinear frictional mathematical model designed to describe with high fidelity the complex time-varying frictional behavior exhibited by the dynamic sealing links of underwater mechanical leg joints.

[0040] The model output is an estimate of the frictional torque. Its input variables include directly measurable joint angular velocities. Joint angle position q、 water depth pressure P and temperature T .

[0041] The first part of the model, namely It is mainly used to characterize static friction and low-speed region characteristics related to the direction of motion. Among them, It's about water depth and pressure. P and temperature TThe sealing condition coefficient is used as an environmental scaling factor to incorporate the macroscopic effects of pressure and temperature on the basic frictional characteristics of the seal into the model, enabling the model to adapt to different underwater depths and temperature environments. Let be the Coulomb friction coefficient. and v s To describe the amplitude coefficients and characteristic velocities of the Stribek effect. (Term) This represents classic Coulomb friction, where the magnitude of the torque is constant and the direction is always opposite to the direction of the joint's velocity. This is used to characterize the Stribek effect, a phenomenon observed during the low-speed start-up phase: the frictional torque is not constant, but rather decreases as the speed increases from zero. This exponential decay term is related to the characteristic velocity. v s Together they provided a detailed description of this nonlinear transition process.

[0042] The second part of the model, namely This characterizes viscous friction. This is the coefficient of viscous friction, which is related to the joint angular velocity. It is proportional to the velocity, simulating the resistance generated by the shear motion of fluid media such as lubricant within the sealed cavity, and is linearly related to the velocity. It is the main part of the model that handles frictional behavior in the medium-to-high speed region.

[0043] The third part of the model, namely Used to describe the position relative to the joint angle q The relevant frictional characteristics mainly reflect the effects of preload and minute deformation on the seal. Hyperbolic tangent function. It is a smooth, bounded odd function that can simulate the symmetrical and asymptotically saturated additional frictional resistance generated by the compression deformation and springback of the seal when the joint makes small reciprocating movements near zero. (Coefficient) The stiffness coefficient is the value of the seal pre-tightening micro-deformation. The shape factor controls the rate at which this effect changes with position.

[0044] The parameterized friction model disclosed in this application is not a simple, single model, but a composite nonlinear model that integrates environmental adaptation, Coulomb friction, the Stribeck effect, linear viscous friction, and preload micro-deformation effects. The parameters in the model include the Coulomb friction coefficient. Stribeck effect parameters and v s viscous friction coefficient and pre-tightening micro-deformation parameters and All parameters are updated in real time using the online identification algorithm described in step S2. This model design enables the system to characterize and predict time-varying and nonlinear sealing friction torque with extremely high accuracy, thus laying a crucial model foundation for subsequent accurate torque compensation and virtual force estimation.

[0045] In some embodiments, the sealing condition coefficient For the water depth pressure obtained through offline calibration p With temperature T The function; during online control, based on real-time measured water depth and pressure. p With temperature T This can be achieved by querying a mapping table built based on offline calibration data or by calculating the function. The value is obtained by taking the value.

[0046] Specifically, sealing condition coefficient It is a combination of environmental conditions (water depth and pressure) p With temperature T This is mapped to a function of the friction characteristic scaling factor. Its core function is to enable the parametric friction model to adapt to the environment. The working depth of the underwater mechanical leg varies significantly with the sea temperature, and the friction characteristics of the seal, especially the static friction component (such as Coulomb friction), will change systematically with the increase of external water pressure on the seal and the changes in material properties and lubrication state caused by temperature changes. If the friction model parameters remain constant, it will lead to significant force sensing and control errors at different depths and temperatures. The purpose is to establish an a priori compensation mechanism within the model that reflects the impact of the environment on the basic friction level.

[0047] The specific functional relationship of this coefficient is obtained in advance through offline calibration experiments of the system. The calibration process is usually carried out in a controlled environment simulation device in the laboratory. The target joint is placed in the device, and different water pressures are independently adjusted and precisely set. p With temperature T These combinations constitute a series of typical operating points. In each fixed ( p, T Under the operating condition, the drive joint performs low-speed, uniform reciprocating motion. At this time, after compensating for known factors such as gravity, the readings of the joint torque sensor mainly reflect the sealing friction torque under that specific pressure and temperature. Through data acquisition and processing (such as using least squares fitting), the basic Coulomb friction coefficient in the friction model under this operating condition can be extracted. coefficient of friction with adhesive tape .

[0048] Under a certain standard working condition ( p 0 ,T0 Using the parameters of ) as a benchmark, the relative change ratio of the Coulomb friction coefficient under all other working conditions is calculated, thus obtaining a series of discrete values. W(p, T) Values. Ultimately, these discrete data are constructed into a pressure-temperature-scaling factor mapping table, or further fitted to a concise binary function model, such as a linear form: ,in, a p and a T The pressure and temperature coefficients were obtained through calibration. This offline calibration process ensures... W(p, T) The function accurately reflects the changes in the physical properties of a specific sealing structure under the influence of environmental variables.

[0049] During actual online control operation of the robotic leg, the system uses onboard pressure and temperature sensors to obtain real-time information about the current working water depth and pressure. p With ambient temperature T Subsequently, the system quickly determines the current status using one of two optional methods. W (p, T) Values: First, table lookup and interpolation, that is, based on real-time measurements. (p, T) The approach involves two methods: first, querying the discrete mapping table generated by offline calibration and obtaining the corresponding scaling factor through a two-dimensional interpolation algorithm; second, direct function calculation, where if the offline calibration data has been fitted into a well-defined functional form (such as the linear model mentioned above), then the real-time data is directly calculated. p , T Substitute the values ​​into the function formula to perform the calculation. Obtain the current... W(p, T) After obtaining the value, it is used as a multiplicative factor in the parameterized friction model, thereby compensating for the environmental conditions of the model's basic friction level in real time and a priori.

[0050] In some embodiments, the online identification algorithm employs a recursive least squares method with a forgetting factor. When the mechanical leg is in the swing phase with no contact at the foot end, the model parameters of the parameterized friction model are updated online using the condition that the net output torque of the joint is approximately equal to the torque calculated by the link model.

[0051] In this embodiment, the core idea of ​​recursive least squares is to recursively update the parameter estimates based on the previous time step whenever a new set of input-output observation data is obtained. This method is computationally efficient and suitable for online real-time operation. Introducing a "forgetting factor" (typically between 0.95 and 0.99) is a key optimization. This factor assigns an exponentially decaying weight to historical data, allowing the algorithm to gradually "forget" data from the distant past, thus giving it the ability to track time-varying parameters. During the long-term underwater operation of the robotic leg, the sealing friction characteristics will slowly change due to wear and lubrication conditions. The recursive least squares method with a forgetting factor ensures that the identified model parameters can follow these slow time-varying characteristics, maintaining the model's accuracy and avoiding model rigidity and inability to adapt to new working conditions due to excessive weighting of past data.

[0052] It is worth noting that the online update of the parameterized friction model parameters is performed when the robotic leg is in the swing phase, where the foot is not in contact with the ground. The swing phase refers to the stage in which the foot of the robotic leg lifts up, detaches from the seabed or ground, and swings forward. During this phase, the foot has no mechanical contact with the external environment, i.e., the foot contact force is zero. This state has significant technical implications: it greatly simplifies the force situation on the joint. At this time, the torque acting on the joint mainly consists of two parts: one is the known or calculable part used to overcome the weight and inertial force of the connecting rod, and the other is the sealing friction torque that needs to be identified. Choosing to update the parameters during the swing phase can effectively avoid the serious interference caused by the complex, unknown, and time-varying ground contact forces during the support phase, creating an ideal diagnostic window for obtaining pure and reliable friction parameter estimates.

[0053] The update condition is that the net output torque of the joint is approximately equal to the torque calculated by the link model. This is the physical basis and mathematical basis for realizing online parameter identification. Under the condition of swing phase and no contact at the foot end, the net output torque of the joint (i.e. the torque acting on the link after compensating for sealing friction) should theoretically be used entirely to drive the link motion. Its value can be calculated by a precise dynamic model that includes the link mass, moment of inertia, current attitude and acceleration.

[0054] The torque calculated by the linkage model mentioned here specifically refers to the torque calculated based on the currently acquired joint motion state information, including joint angle position. q angular velocity and angular acceleration The torque value was calculated using the dynamic model of the mechanical leg linkage. The complete dynamic model expression is as follows: .in, M(q) Here is the inertia matrix of the mechanical leg system. For terms that include both Coriolis force and centrifugal force, This refers to the gravity term. When the mechanical leg is in the swing phase without foot contact, the motion is usually planned and relatively smooth, so the influence of the velocity-acceleration coupling term is relatively small. Therefore, in the simplified analysis for parameter identification, the inertial force term can be mainly considered. and gravity term .

[0055] This torque value, calculated based on the model, provides a reliable reference value for the parameter identification algorithm. The online identification algorithm operates by substituting the currently estimated friction model parameters into the model to calculate the predicted friction torque. Combined with other known quantities, the predicted net joint output torque can be obtained. The algorithm continuously adjusts the friction model parameters to minimize the sum of squared errors (least squares principle) between the predicted net joint output torque and the "reference value" calculated by the dynamic model. Through this continuous comparison and correction, the model parameters converge to values ​​that best reflect the actual sealing friction characteristics.

[0056] By employing the above technical solution, the efficient algorithm of recursive least squares with a forgetting factor, capable of tracking time-varying characteristics, is organically combined with the wise timing of execution during the oscillating phase with minimal disturbance, and the reliable physical condition of using known link dynamics as the update reference. This ensures that, during complex underwater operating cycles, the system can stably, reliably, and automatically complete the online calibration and tracking of the sealing friction model parameters using the periodically occurring oscillating phase window. This effectively addresses the characteristic drift of the seal caused by long-term operation and changes in environmental pressure and temperature, thereby maintaining the long-term accuracy and robustness of the entire control system.

[0057] In some embodiments, the net joint output torque is mapped to the foot operating space, and the virtual end contact force is calculated based on a dynamic model. Specifically, this includes: performing a pseudo-inverse operation on the Jacobian matrix of the robotic leg to obtain the net joint output torque vector. τ net The virtual end-effector contact force is calculated by mapping the force to the foot's operating space and subtracting the joint space internal force vector calculated based on the dynamic model. The expression is; ,in, J(q) Let be the Jacobian matrix of the mechanical leg. Let be the transpose of the Jacobian matrix of the mechanical leg. This indicates a pseudo-inverse operation. This refers to the joint space internal force vector calculated based on the aforementioned dynamic model.

[0058] In this embodiment, the Jacobian matrix J(q)It is a core tool in robot kinematics, establishing a linear mapping between joint space velocities and the operational space velocities of the end effector (in this case, the foot). Its transpose... This establishes a dual relationship between the force in the operating space and the torque in the joint space, namely the principle of virtual work.

[0059] However, direct inversion may not be feasible for redundant or non-square Jacobian matrices. Therefore, this embodiment employs pseudo-inversion operations. This is a generalized inverse that can be used for a given joint torque vector. τ net Solve for the best-fitting foot operation space force in the least squares sense. This step forms the geometric foundation of virtual force perception, transforming the mechanical information of local joints into the global foot manipulation space.

[0060] In this embodiment, the net output torque of the joint τ net Not all of these forces are generated by the interaction between the foot and the external environment. They include all the internal forces required to drive the mechanical leg's own movement (such as overcoming gravity and generating acceleration). Joint space internal force vector. The torque required to generate the current mechanical leg motion (i.e., to overcome gravity, inertial forces, Coriolis forces, etc.) is calculated based on a multibody dynamics model. By subtracting the internal force term from the net output torque of the joint to separate the external contact forces, the system removes the internal forces generated by the movement of the link itself from the total torque. The remaining torque component, ideally, is entirely generated by the interaction (contact, support, collision) between the foot and the external environment.

[0061] In some embodiments, the force vector within the joint space Gravity term including the mechanical leg and inertial force term Coriolis term Estimated fluid dynamics terms One or more of them.

[0062] Specifically, It is a composite internal force vector that can be dynamically configured according to the actual motion state of the robotic leg and the underwater environment. Its design purpose is to achieve a net output torque from the joint. τ net The internal force components generated by non-contact forces due to the movement of the robotic leg itself and its environment are precisely isolated, thus purifying the external torque generated solely by the interaction between the foot and the environment. The physical meanings of each internal force component are as follows:

[0063] Gravity term This reflects the mass of each link in the mechanical leg under different joint configurations.q Below, the static equilibrium torque generated at each joint due to gravity. It is The most basic component that must be included in any posture is used to compensate for the continuous effect of gravity on joint torque.

[0064] Inertial force term With the motion acceleration of the mechanical leg Directly related, among which This is the inertia matrix of the robotic leg, which describes the mass distribution of the system. When the robotic leg accelerates or decelerates, the joints need to provide corresponding torques to overcome the inertia of the links. This is crucial in dynamic movements (such as rapid swinging and dramatic adjustments in body posture).

[0065] Coriolis term The speed of movement of the mechanical leg This is caused by the Coriolis force and centrifugal force effects. When there is a velocity at the joint and the robotic arm configuration is asymmetrical, these velocity coupling terms generate additional joint torques. This is particularly significant during high-speed motion and is an important component of accurate dynamic models.

[0066] Estimated hydrodynamic terms This is a compensation term specific to underwater working environments. When the robotic leg moves in water, it is subjected to hydrodynamic forces such as water resistance and additional mass forces. These distributed forces are ultimately equivalent to hydrodynamic torques acting on the joints. Since hydrodynamic forces are difficult to measure directly and accurately, they are usually estimated online using an observer based on a hydrodynamic model (such as the Morison equation). And include internal force compensation.

[0067] In practical control, the system can intelligently combine these internal force terms based on the current motion phase of the robotic leg and the task requirements. For example, in low-speed motion or static support phases, when acceleration and velocity are relatively small, the gravity term is mainly considered. and estimated hydrodynamic terms In some extremely low-speed cases, even the hydrodynamic terms are ignored to simplify calculations.

[0068] During high-speed dynamic oscillation phases or body maneuvers, the gravity term must be fully included. Inertial force term Coriolis term Estimated fluid dynamics terms This is to achieve the most accurate deduction of internal force.

[0069] In some embodiments, the admittance control outer loop generates the desired net output torque in the joint space based on the desired foot pose, the actual foot pose, and the deviation between the desired foot force and the estimated contact force. This process is defined by the following second-order admittance model: .

[0070] This model is used in robot control to simulate a virtual dynamic system in which... M d , B d , K d These are the admittance mass, damping, and stiffness matrices, which together define a virtual mass-damper-stiffness system to simulate the desired end-effector compliance. , , These represent the desired foot position, velocity, and acceleration, respectively. , , These represent the actual foot pose, velocity, and acceleration, respectively. The left end of the model represents the desired foot trajectory ( , , ) and the actual measured or estimated foot movement trajectory ( , , The deviation between the two is processed by the dynamic response generated by the virtual system, and the right side of the model is the estimated foot contact force extracted from the virtual end contact force. The expected foot contact force given by the plan or task The deviation between them.

[0071] It is worth noting that the estimated foot contact force value From virtual end contact force It is obtained by extracting the corresponding components based on the current motion state of the robotic leg (mainly whether the foot is in contact with the ground).

[0072] In admittance control, the outer loop requires the actual, perpendicular support force or contact force between the foot and the ground (or the work object), used to match the desired support force. F d The comparison generates a compliant adjustment instruction.

[0073] Virtual end contact force As a general force estimate, when the foot is in the support phase (i.e., in contact with the ground and bearing weight), the normal force component perpendicular to the ground in the foot coordinate system is the foot contact force of interest. Therefore, the extraction operation is usually technically manifested as follows:

[0074] In the support phase: through coordinate transformation, the contact force is obtained from the virtual end. Extract its normal force component and use it directly as the estimated value of the foot contact force. Sometimes, components in a specific direction may be extracted based on control requirements.

[0075] In the oscillating phase: when the foot is not in contact with the environment, the theoretical estimated value of the foot contact force is... It should be zero. The system can... Set to zero, or ignore this feedback.

[0076] This equation establishes the dynamic relationship between motion deviation and force deviation, and is the essence of admittance control. Its physical meaning can be interpreted as: when the estimated contact force at the foot tip... Desired foot contact force When there is inconsistency (i.e., there is a force deviation) The system does not forcibly maintain the preset position trajectory. , , Instead, it is based on this force deviation, through a virtual dynamic system. M d , B d , K d Calculate the allowable pose adjustment amount produced by the foot. This transforms force errors into acceptable trajectory correction instructions, which is the core mechanism for achieving active compliance. For example, when the actual force on the foot is greater than the expected force, the admittance model generates an instruction to "yield" the foot position, thereby reducing the contact force and achieving compliant force tracking.

[0077] After defining the desired pose adjustment, the system needs to convert it into executable instructions in joint space. Force deviations in the operand space are mapped to the joint space via Jacobian matrix transpose, and combined with gravity compensation, to obtain the desired net output torque. Expected net output torque The generating expression is: .

[0078] The execution of this formula consists of two steps. The first step is to apply the desired foot contact force in the admittance model equation. Compared with the calculated virtual force based on motion deviation Addition, formula Mathematically equivalent to In control theory, this represents the total target operating force expected to be applied to the foot for tracking admittance model. The second step involves transposing the Jacobian matrix. This target force in the foot-end operating space is mapped to the joint space to obtain the equivalent torque required to generate this target force in the joint space. Finally, the gravity term of the robotic leg is added. Compensation is necessary because gravity constantly acts on the system, and the joints must continuously provide torque to balance it. This torque is independent of admittance interaction and therefore needs to be added separately. The final calculated... In order to track the desired compliant interaction behavior, the joint needs to generate the desired net output torque. It is the set value of the effective torque that the joint should output to achieve compliant interaction.

[0079] A second-order admittance model explicitly defines the dynamic compliance relationship between force and pose deviation. Precise joint-layer torque commands are generated using Jacobi transpose mapping and gravity compensation, thus constructing a core decision-making and conversion hub connecting virtual force sensing and the underlying joint actuators. It transforms the upstream estimated end-effector contact force into an executable desired net joint torque, enabling the entire system to achieve high-quality compliant position and force hybrid control based on force feedback even without end-effector force sensors. This is a key control law guaranteeing safe, stable, and adaptive interaction between the underwater robotic leg and uncertain environments.

[0080] In some embodiments, the calculation of the motor command torque by combining the motor dynamics model specifically includes: adding the expected net output torque to the estimated value of the friction torque to compensate for sealing friction loss; then dividing by the reduction ratio to convert it into an equivalent command at the motor shaft end; and finally superimposing a feedforward compensation term based on the motor rotor dynamics to obtain the final motor command torque.

[0081] The final motor command torque is obtained. Calculated using the following formula: This formula is the final link in the control command chain. Its purpose is to generate a precise motor current or torque setpoint to ensure that, after complex transmission and losses, the net torque actually output by the joint to the connecting rod can strictly track the desired net output torque generated by the admittance control outer loop. The calculation process can be broken down into three physical operations performed sequentially.

[0082] First, the desired net output torque is added to the estimated friction torque to compensate for sealing friction losses. This is the core compensation operation for achieving high-precision torque tracking. Admittance control of the outer loop output... This is the expected effective net torque acting on the connecting rod. However, the total torque actually required by the motor must be greater than this value because a portion of the torque is consumed by friction in the dynamic sealing element of the joint during transmission. Therefore, the control system uses the sealing friction torque estimated online in the previous steps. and The sum represents the total torque required at the reducer output (i.e., the torque sensor mounting location). It takes into account the loss from sealing friction and is a kind of feedforward compensation.

[0083] Second, divide by the reduction ratio to convert the total torque command from the reducer output to the motor shaft. Since joints typically use high-reduction-ratio gearboxes (such as harmonic reducers) for torque amplification, the torque required to be output from the motor shaft is much smaller than that from the output. Therefore, the total torque command obtained in the previous step needs to be converted... Dividing by the reduction ratio N yields the equivalent command torque referred to the motor shaft. This step completes the instruction mapping from the joint output space to the motor drive space.

[0084] Third, by superimposing feedforward compensation terms based on motor rotor dynamics, it is also necessary to compensate for the motor rotor's own dynamic characteristics in order to achieve fast, zero-steady-state-error tracking of the command torque. (The formula contains...) This is the feedforward compensation term. Among them, and These are the moment of inertia and damping coefficient of the motor rotor, respectively. and These are the reference acceleration and actual velocity of the motor shaft, respectively. Used to provide the torque needed to overcome the inertia of the motor rotor, enabling the motor to accelerate or decelerate rapidly; Item These are used to compensate for the resistance torque generated by damping when the motor rotates. Adding these two feedforward compensations can significantly improve the dynamic response performance of the motor to time-varying torque commands and reduce tracking delay and error.

[0085] By employing the above technical solution, the desired net torque command generated by the admittance control outer loop is combined with online identification of seal friction compensation, transmission ratio conversion, and motor self-dynamic feedforward compensation to synthesize the final motor command. This step ensures that the actual torque output by the motor, after passing through the reducer and overcoming all losses, can highly accurately reproduce the joint net output torque expected by the admittance controller. This reliably translates the entire sensorless force sensing and compliant control scheme into physical execution, guaranteeing high-precision compliant movement of the underwater robotic leg.

[0086] The second embodiment of this application also discloses an underwater mechanical leg admittance control system without an end-effector force sensor, comprising: The data acquisition module is used to acquire the joint torque sensor measurement values ​​and joint motion state information of the target joint; The friction torque estimation module is used to update the model parameters of the parameterized friction model of the dynamic sealing link based on the joint motion state information and preset environmental parameters through an online identification algorithm, and to calculate the estimated value of the friction torque through the parameterized friction model using the updated model parameters and the joint motion state information. The torque compensation module is used to compensate the measured value of the joint torque sensor using the estimated value of the friction torque, so as to obtain the net joint output torque of the linkage driven by the target joint. The virtual force estimation module is used to map the net output torque of the joint to the foot end operating space of the robotic leg, and calculate the virtual end contact force of the foot end based on the dynamic model of the robotic leg. The admittance control module is used to input the virtual end contact force into the admittance control outer loop to generate the desired net output torque of the target joint; The motor command synthesis module is used to calculate, based on the sum of the expected net output torque and the estimated value of the friction torque, and in conjunction with the motor dynamics model, to obtain the motor command torque for driving the target joint.

[0087] This application also provides an electronic device. It includes a processor and a memory; the memory stores a computer program, wherein the computer program, when executed by the processor, implements the aforementioned sensorless underwater mechanical leg admittance control method.

[0088] Specifically, the processor may include, for example, a general-purpose microprocessor, an instruction set processor and / or an associated chipset and / or a special-purpose microprocessor (e.g., an application-specific integrated circuit (ASIC)), etc. The processor may also include onboard memory for caching purposes. The processor may be a single processing unit or multiple processing units for performing different actions of the method flow according to embodiments of this application.

[0089] Memory can be any medium capable of containing, storing, transmitting, propagating, or transmitting instructions. For example, memory can include, but is not limited to, electrical, magnetic, optical, electromagnetic, infrared, or semiconductor systems, devices, instruments, or propagation media. Specific examples of memory include: magnetic storage devices such as magnetic tape or hard disk drives (HDDs); optical storage devices such as optical discs (CD-ROMs); and also random access memory (RAM) or flash memory; and / or wired / wireless communication links.

[0090] This application also provides a computer-readable medium storing a computer program that, when executed by a processor, implements the aforementioned sensorless underwater mechanical leg admittance control method. This computer-readable medium may be included in the device / apparatus / system described in the above embodiments; or it may exist independently and not assembled into that device / apparatus / system. The aforementioned computer-readable medium carries one or more programs, which, when executed, implement the method according to the embodiments of this application.

[0091] According to embodiments of this application, a computer-readable medium may be a computer-readable signal medium or a computer-readable storage medium, or any combination thereof. A computer-readable storage medium may be, for example, but not limited to, an electrical, magnetic, optical, electromagnetic, infrared, or semiconductor system, apparatus, or device, or any combination thereof. More specific examples of a computer-readable storage medium may include, but are not limited to: an electrical connection having one or more wires, a portable computer disk, a hard disk, random access memory (RAM), read-only memory (ROM), erasable programmable read-only memory (EPROM or flash memory), optical fiber, portable compact disk read-only memory (CD-ROM), optical storage device, magnetic storage device, or any suitable combination thereof. In this application, a computer-readable storage medium may be any tangible medium containing or storing a program that can be used by or in conjunction with an instruction execution system, apparatus, or device. In this application, a computer-readable signal medium may include a data signal propagated in baseband or as part of a carrier wave, carrying computer-readable program code. Such propagated data signals may take various forms, including but not limited to electromagnetic signals, optical signals, or any suitable combination thereof. Computer-readable signal media can also be any computer-readable medium other than computer-readable storage media, which can send, propagate, or transmit a program for use by or in connection with an instruction execution system, apparatus, or device. The program code contained on the computer-readable medium can be transmitted using any suitable medium, including but not limited to: wireless, wired, optical fiber, radio frequency signals, etc., or any suitable combination thereof.

[0092] The above description is merely a preferred embodiment of this application and is not intended to limit this application. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of this application should be included within the protection scope of this application.

Claims

1. A method for controlling the admittance of an underwater mechanical leg without an end-effector force sensor, characterized in that, Includes the following steps: Acquire the joint torque sensor measurements and joint motion status information of the target joint; Based on the joint motion state information and preset environmental parameters, the model parameters of the parameterized friction model of the dynamic sealing link of the target joint are updated through an online identification algorithm; using the updated model parameters and the joint motion state information, the estimated value of the friction torque is calculated through the parameterized friction model. The estimated value of the frictional torque is used to compensate for the measured value of the joint torque sensor to obtain the net joint output torque of the linkage driven by the target joint. The net output torque of the joint is mapped to the foot end operating space of the mechanical leg, and the virtual end contact force of the foot end is calculated based on the dynamic model of the mechanical leg. The virtual end contact force is input into the admittance control outer loop to generate the desired net output torque of the target joint; Based on the sum of the expected net output torque and the estimated value of the friction torque, and combined with the motor dynamics model, the motor command torque for driving the target joint is calculated.

2. The underwater mechanical leg admittance control method without end force sensor as described in claim 1, characterized in that: The parameterized friction model is defined by the following formula: ,in, This is an estimated value for the frictional torque. and q These are the joint angular velocity and joint angular position, respectively, from the joint motion state information. P and T These are water depth, pressure, and temperature, respectively. The sealing condition coefficient is determined based on the aforementioned pressure and temperature. Let be the Coulomb friction coefficient. and v s These are the amplitude coefficients and characteristic velocities that describe the Stribek effect, respectively. The coefficient of viscous friction, and These are the stiffness coefficient and shape factor, respectively, describing the micro-deformation of the seal pre-tightening.

3. The underwater mechanical leg admittance control method without end force sensor as described in claim 2, characterized in that: The sealing condition coefficient For the water depth pressure obtained through offline calibration p With temperature T The function; during online control, based on real-time measured water depth and pressure. p With temperature T This can be achieved by querying a mapping table built based on offline calibration data or by calculating the function. The value is obtained by taking the value.

4. The underwater mechanical leg admittance control method without end force sensor as described in claim 1, characterized in that: The online identification algorithm employs a recursive least squares method with a forgetting factor. When the mechanical leg is in the swing phase with no contact at the foot end, the model parameters of the parameterized friction model are updated online using the condition that the net output torque of the joint is approximately equal to the torque calculated by the link model.

5. The underwater mechanical leg admittance control method without end force sensor as described in claim 1, characterized in that: The process of mapping the net output torque of the joint to the foot operating space and calculating the virtual end-effector contact force based on the dynamic model specifically includes: By performing a pseudo-inverse operation on the Jacobian matrix of the mechanical leg, the net output torque vector of the joint is mapped to the foot operating space, and the internal force vector of the joint space calculated based on the dynamic model is subtracted, thereby calculating the virtual end contact force.

6. The underwater mechanical leg admittance control method without end force sensor as described in claim 5, characterized in that: The force vector within the joint space includes the gravity term of the mechanical leg, as well as one or more of the inertial force term, Coriolis eccentric term, and estimated hydrodynamic term.

7. The underwater mechanical leg admittance control method without end force sensor as described in claim 1, characterized in that: The admittance control outer loop generates the desired net output torque in the joint space based on the desired foot pose, the actual foot pose, and the deviation between the desired foot force and the estimated contact force. This process is defined by the following second-order admittance model: ,in, M d , B d , K d These represent the admittance mass, damping, and stiffness matrices, respectively. , , These represent the desired foot position, velocity, and acceleration, respectively. , , These are the actual foot position, velocity, and acceleration, respectively. This is an estimate of the foot contact force extracted from the virtual end contact force. The desired foot contact force; The desired net output torque By mapping the operational space forces output by the admittance model to the joint space and combining them with gravity compensation, its expression is as follows: ,in, Let be the Jacobian matrix of the mechanical leg. For the transpose of the Jacobian matrix of the mechanical leg, Let be the gravity term of the mechanical leg.

8. The underwater mechanical leg admittance control method without end force sensor as described in claim 7, characterized in that: The calculation of the motor command torque by combining the motor dynamics model specifically includes: adding the expected net output torque to the estimated value of the friction torque to compensate for sealing friction loss; then dividing by the reduction ratio to convert it into an equivalent command at the motor shaft end; and finally superimposing a feedforward compensation term based on the motor rotor dynamics to obtain the final motor command torque.

9. A sensorless underwater mechanical leg admittance control system, characterized in that, include: The data acquisition module is used to acquire the joint torque sensor measurement values ​​and joint motion state information of the target joint; The friction torque estimation module is used to update the model parameters of the parameterized friction model of the dynamic sealing link based on the joint motion state information and preset environmental parameters through an online identification algorithm, and to calculate the estimated value of the friction torque through the parameterized friction model using the updated model parameters and the joint motion state information. The torque compensation module is used to compensate the measured value of the joint torque sensor using the estimated value of the friction torque, so as to obtain the net joint output torque of the linkage driven by the target joint. The virtual force estimation module is used to map the net output torque of the joint to the foot end operating space of the robotic leg, and calculate the virtual end contact force of the foot end based on the dynamic model of the robotic leg. The admittance control module is used to input the virtual end contact force into the admittance control outer loop to generate the desired net output torque of the target joint; The motor command synthesis module is used to calculate, based on the sum of the expected net output torque and the estimated value of the friction torque, and in conjunction with the motor dynamics model, to obtain the motor command torque for driving the target joint.

10. An electronic device, characterized in that: It includes a processor and a memory; the memory stores a computer program, wherein the computer program, when executed by the processor, implements the underwater mechanical leg admittance control method without end force sensor as described in any one of claims 1 to 8.

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