Dexterous hand sensorless fingertip force estimation and control method based on joint probability evolution

Abstract

A dexterous hand sensorless fingertip force estimation and control method based on joint probability evolution belongs to the technical field of robot dexterous hand control, and only relies on motor current, position and speed signals to unify system state, parameters, disturbances and noise into random variables, builds a four-dimensional joint probability state space, and represents system probability evolution through Fokker-Planck equation; multi-time scale variational inference is used to decouple fast and slow subsystems, slow scale identifies slow time-varying model uncertainty, fast scale tracks dynamic load disturbance, and realizes joint optimal estimation of multiple types of uncertainty; the probability mapping and quantization of joint torque to fingertip force are completed combined with heterogeneous finger configuration; the active perception self-calibration is triggered through the model mismatch index, and the online correction model is stimulated with optimal information gain; the fingertip force probability distribution is introduced to construct the chance-constrained robust optimization, the analytical control law containing uncertain damping is derived, and the adaptive gain adjustment mechanism is designed and the closed-loop stability is guaranteed based on Lyapunov theory.

Description

Technical Field

[0001] This invention belongs to the field of robot dexterous hand control technology, specifically involving a sensorless fingertip force estimation and control method for dexterous hands based on joint probabilistic evolution. This method expands the system state from a "deterministic value" to a "probability distribution," constructing a four-in-one closed-loop enhancement framework of "state estimation—model learning—active sensing—robust control." This achieves high-precision force sensing and adaptive control with uncertainty quantification, making it particularly suitable for high-end applications with stringent requirements for force control reliability and dynamic performance, such as precision assembly, minimally invasive surgery, and biological sample grasping. Background Technology

[0002] The robot's dexterous hand is the core actuator for achieving precise grasping and dexterous manipulation. High-precision real-time sensing of fingertip contact force is a prerequisite for completing tasks such as precision assembly, non-destructive sorting of fragile items, and safe human-robot interaction. Current mainstream solutions for force sensing in dexterous fingers generally employ the addition of force / torque physical sensors to the fingertips, joints, or linkage structures to acquire force signals.

[0003] Such external physical sensors have inherent drawbacks: high hardware cost, large structure and complex integrated wiring, and are easily damaged under frequent mechanical contact, collision and alternating load conditions, which restricts the miniaturization, high reliability and large-scale application of dexterous hands.

[0004] To avoid the drawbacks of external sensors, sensorless force estimation technology has become the mainstream research direction. This type of technology only uses the current, position and speed signals that can be natively collected by the motor driver, and calculates the joint torque and infers the fingertip contact force through algorithms. It has the advantages of low cost, high integration and no risk of additional hardware damage.

[0005] Existing sensorless force estimation techniques mainly fall into two categories, both with inherent limitations: The first category is the mechanistic model observer approach, which theoretically boasts high static accuracy and fast dynamic response, but the algorithm heavily relies on an accurate mathematical model of system dynamics. In actual working conditions, the parameters of the dexterous hand model can experience slow time-varying drift due to changes in motor temperature rise, mechanical wear, and lubrication status, and can also suffer from step mismatches due to component replacement and sudden load changes. Observers designed with fixed nominal models show significantly degraded estimation performance under parameter mismatch conditions, potentially leading to observation divergence, system instability, and insufficient model robustness. The second category is the data-driven learning approach: it does not require an accurate explicit mechanistic model, but relies on offline training to establish an input-output mapping relationship, exhibiting a certain degree of adaptability to small model deviations. However, this approach relies on massive amounts of training data covering all working conditions, and the model obtained from the training is a static mapping relationship, which cannot be adapted to unfamiliar working conditions that were not trained; moreover, offline learning and online estimation are disconnected from each other, and it does not have the ability to make real-time online adaptive corrections; at the same time, the pure data-driven method has an inherent delay in dynamic response in strongly nonlinear systems, which makes it difficult to meet the real-time requirements of millisecond-level high-speed force closed-loop control.

[0006] Existing technologies often involve compromises between two approaches, such as using fixed-parameter perturbation observers. However, they cannot overcome the inherent contradiction between observation bandwidth and measurement noise suppression: reducing the observer bandwidth can suppress measurement noise, but it will cause a lag in dynamic perturbation estimation; increasing the bandwidth can improve the dynamic response, but it will amplify high-frequency measurement noise, and the force estimation value is prone to drastic jumps in the micro-force operating range, which cannot meet the requirements of practical engineering applications. Summary of the Invention

[0007] To overcome the shortcomings of existing technologies, this invention provides a sensorless fingertip force estimation and control method for a dexterous hand based on joint probabilistic evolution. A novel theoretical framework of "joint probabilistic evolution" is proposed, which treats joint load torque, model parameters, external disturbances, and measurement noise as random variables, constructing a unified joint probabilistic state space. The Focke-Planck equation describes the probabilistic evolution of the system state. Based on this, fingertip force estimation with uncertainty quantification, uncertainty-driven active sensing and self-calibration, and probabilistic robust control based on chance constraints are realized. These three aspects are deeply integrated to form an inseparable integrated "sensing-learning-control" system.

[0008] To solve the above-mentioned technical problems, the present invention provides the following technical solution: A sensorless fingertip force estimation and control method for a dexterous hand based on joint probabilistic evolution includes the following steps: Step 1: Construct a four-dimensional joint probabilistic state space and a probabilistic dynamic model: Construct a unified joint probabilistic state space by treating joint load torque, model parameters, total disturbance torque, and joint angles containing measurement noise as four types of random variables, and assume a Gaussian distribution for each random variable; Probabilistically process the dynamic equations of the single-joint motor of the dexterous hand, derive and establish a probabilistic dynamic model in the form of Iton stochastic differential equations, determine the system drift term and diffusion term, and uniformly incorporate various sources of uncertainty such as time-varying characteristics of the model, external disturbances, and measurement noise; In this invention, a four-dimensional joint probability state space of the system is constructed, and the basic state of the system is defined as a joint probability distribution containing four random variables: ; in, To follow a Gaussian distribution Joint load torque, This is a hyperparameter vector containing parameters of the Gaussian process kernel function, moment of inertia, damping coefficients, etc. The total disturbance torque includes unmodeled dynamics, external shocks, etc. The joint angles include measurement noise; based on this, and using the motor dynamics equations and probability and statistics theory, the system drift term, which can describe the deterministic evolution of the system state and the propagation of random uncertainty, is derived. With diffusion term ; Step 2: Solving the Fokker-Planck equation based on multi-timescale variational inference: Establish the Fokker-Planck equation characterizing the evolution of the joint probability distribution over time. Use a multi-timescale decomposition method to split the joint distribution into slow-timescale and fast-timescale sub-distributions. At the slow-timescale level, Gaussian process variational inference is used to update the model parameter distribution over a long period, learning the slow-time-varying model uncertainties caused by motor temperature rise and mechanical wear. At the fast-timescale level, a momentum-driven second-order extended state observer is used to update the system state and disturbance distribution over a short period, quickly tracking sudden load changes and external dynamic disturbances. The model parameter uncertainties obtained from the slow-timescale update are transferred to the fast-timescale, and the observer gain and bandwidth are adaptively adjusted to achieve the joint optimal probability estimation of model uncertainties and dynamic disturbances. In this invention, the Focke-Planck equation describing the evolution of the above four-dimensional joint probability distribution over time is established: ; Given the excessive computational cost of solving this equation precisely, multi-timescale variational inference is used to decompose the joint distribution into two conditionally independent sub-distributions: ; Among them, the distribution of model parameters updated at a specific period on a slow time scale It is used to learn slow time-varying model uncertainties such as parameter drift and mechanical wear caused by temperature rise, and is implemented using Gaussian process variational inference; the fast timescale updates the state and perturbation distribution with a period one order of magnitude faster than the slow timescale. This method is used to track rapidly changing load torque and dynamic disturbances, and is implemented in a probabilistic form using a momentum-driven second-order extended state observer. This step couples the model parameters obtained from slow-timescale updates with conditional probability distributions, directly transferring the uncertainty to fast-timescale updates and automatically adjusting the gain and bandwidth of the fast observer. Ultimately, this achieves the joint optimal estimation of model uncertainty and dynamic disturbances. Step 3: Perform joint torque to fingertip force probability mapping with uncertainty quantification: Extract the estimated mean and uncertainty variance of joint load torque from the evolved and updated joint probability distribution; adopt differentiated kinematic mapping strategies for the two-degree-of-freedom coupled configuration of the thumb of the dexterous hand and the single-degree-of-freedom configuration of the other fingers, respectively using the generalized inverse method of the complete Jacobian matrix and the simplified lever model; complete the conversion of the joint space torque probability distribution to the fingertip Cartesian space force probability distribution, and decompose and quantify the uncertainty of the fingertip normal clamping force and tangential friction force, outputting sensorless fingertip force estimation results with confidence intervals; In this invention, fingertip force mapping with uncertainty quantification is performed, and the mean value of joint load torque is extracted from the updated joint probability distribution. With variance A configuration optimization lightweight mapping method is adopted, through the formula , The joint space torque distribution is converted into the fingertip Cartesian space force distribution, where... The generalized inverse of the Jacobian matrix. Additional uncertainties are introduced into the mapping process; a differentiated mapping strategy is adopted for the heterogeneous configuration of the dexterous hand. The complete coupled Jacobian matrix is ​​used for the two-degree-of-freedom coupled thumb, while a simplified lever model is used for the other four single-degree-of-freedom fingers, ultimately yielding a Gaussian distribution. The fingertip force estimation result makes it fall within a very high probability. Within the range; Step 4: Construct an uncertainty-driven active perception and model self-calibration mechanism: Construct a dimensionless model mismatch evaluation index and introduce a minimum detectable force constraint to avoid index divergence under zero-load conditions; when the model mismatch exceeds a preset threshold, trigger the active perception calibration process; solve for the optimal micro-active motion based on maximizing information gain, setting a micro-reciprocating motion along the force direction of the fingertip as the excitation without interfering with normal grasping operations; collect motor current, joint angular velocity, and joint angle operation data under active excitation, and correct the model parameter distribution in real time according to the Bayesian inference criterion; iteratively update the model mismatch until the threshold requirement is met, then exit calibration and resume normal operations; if multiple calibrations still fail to meet the standard, trigger a mechanical fault alarm. In this invention, an active perception and self-calibration mechanism based on uncertainty is constructed. First, a model mismatch index is defined. In the formula, To minimize the detectable force, it avoids index divergence under zero-load conditions; when the model mismatch... Greater than the preset threshold The process of triggering active perception is based on information theory principles to solve for the optimal small active action that maximizes information gain. ,in, Characterize the execution action Back-observation y and load torque Mutual information is used between the systems. For dexterous hand configurations, the optimal active motion is set as a small reciprocating motion along the direction of fingertip force, which does not interfere with routine operations. After the active motion is executed, system response data is collected and analyzed using Bayesian criteria. Quickly correct the model parameter distribution until the model mismatch meets the requirements. When the time comes, the active sensing process ends and the system returns to normal operation. Step 5: Conduct probabilistic robust adaptive control design based on chance constraints: Integrate the probability distribution of fingertip force into the control architecture, with the optimization objective of minimizing the expected force tracking error, while applying probabilistic confidence constraints on the actual contact force tracking error; utilize the statistical properties of Gaussian distribution to transform the probabilistic constraints into deterministic constraints; construct the Lagrangian function to derive the analytical control law containing proportional control, derivative control, and uncertainty damping terms; design an adaptive adjustment rule for the control gain based on the uncertainty of fingertip force estimation: when the uncertainty is high, decrease the proportional and derivative gains and increase the damping gain to ensure system stability; when the uncertainty is low, improve the dynamic response speed of the system; use Lyapunov stability theory to verify the global asymptotic stability of the closed-loop system, achieving high-precision robust adaptive control of agile fingertip force without sensors; In this invention, a probabilistic robust control design based on chance constraints is carried out, directly incorporating the probability distribution of fingertip force into the control law framework, transforming the traditional force tracking control problem into a probabilistic robust control design based on chance constraints. With the goal, For a chance-constrained optimization problem, where For the desired contact force, To allow for force tracking error, To allow for failure probabilities, under the Gaussian distribution assumption, probabilistic chance constraints are equivalently transformed into deterministic constraints. This leads to the derivation of the analytical form of the probabilistic robust control law. and through , , To achieve adaptive adjustment of the control gain according to the estimation uncertainty, in the formula... The coefficient adjustment parameter is used to automatically reduce the proportional gain and differential gain and increase the uncertainty damping gain to ensure stability when the estimation uncertainty is high, and to improve the dynamic response speed of the system when the uncertainty is low.

[0009] The beneficial effects of this invention are as follows: The technical paradigm of "joint probabilistic evolution" is proposed, which extends the system state from "deterministic value" to "probability distribution", thus solving the fundamental contradiction of the inability to achieve both "accuracy" and "robustness" in existing technologies.

[0010] It realizes the quantification of uncertainty in sensorless force estimation, and can simultaneously output the estimated force value and confidence interval, providing a basis for decision-making in the control system.

[0011] By introducing active perception into the field of sensorless force estimation, the system can actively explore system characteristics, significantly shorten the model reconstruction time after load mutation, and keep the force estimation error within an acceptable range when there is extreme model mismatch.

[0012] By directly incorporating estimation uncertainty into the control law design, a deep integration of perception and control is achieved. Traditional sensorless force control systems are prone to instability when the model is mismatched, while the probabilistic robust control law of this invention can guarantee the stability of the system under any estimation uncertainty. Attached Figure Description

[0013] Figure 1 This is a schematic diagram of the process for constructing the four-dimensional joint probability state space of the stochastic dynamics of the motor in this invention.

[0014] Figure 2 This is a schematic diagram of the multi-timescale variational inference process for solving the Fock-Planck equations according to the present invention.

[0015] Figure 3 This is a schematic diagram of the active sensing and self-calibration process based on maximizing mutual information in this invention.

[0016] Figure 4 This is a schematic diagram of the probability-constrained probabilistic robust control law design and adaptive gain adjustment process of the present invention. Detailed Implementation

[0017] The invention will now be further described with reference to the accompanying drawings.

[0018] Reference Figures 1-4 A sensorless fingertip force estimation and control method for a dexterous hand based on joint probabilistic evolution includes the following steps: Step 1: The core of constructing the four-dimensional joint probabilistic state space is to extend the traditional deterministic dynamic model into a probabilistic dynamic model, building a unified state space that can encompass all sources of uncertainty. First, the definitions and reasonable distribution assumptions of various random variables are completed: the joint load torque... As the core state variable to be estimated, based on the central limit theorem and considering the engineering characteristic that the superposition of multiple independent random disturbances follows a Gaussian distribution, it is assumed that it follows a Gaussian distribution. Model parameters hyperparameter vector Signal variance covering Gaussian process kernel function Length scale matrix Noise variance and the equivalent rotational inertia of the motor Torque constant Viscous damping coefficient Key physical parameters, all of which are treated as random variables, with initial prior distributions set based on offline calibration results; total disturbance torque. The data includes various high-frequency disturbances such as unmodeled dynamics, external impacts, and reducer cogging torque, which follow a Gaussian distribution. Joint angle The measured values ​​are from the motor encoder, and the measured noise conforms to a zero-mean Gaussian distribution. Based on the definition of random variables, starting from the deterministic dynamic equations of a single-joint motor: ; in, The joint angular velocity, For nonlinear frictional torque, all parameters and variables in the equation are uniformly treated as random variables and probabilistically processed, resulting in a probabilistic dynamic equation in the form of Itō's stochastic differential equation: ; The system state vector is defined as follows: , The standard Wiener process vector; the drift term of the equation The expression is: ; Since the model parameters are slow time-varying parameters, and their dynamic characteristics are characterized by the diffusion term, the drift term is set to zero, while the diffusion term... It is a diagonal matrix, specifically in the form of: ; The diagonal elements of the matrix are the diffusion coefficients of each state variable, which are used to characterize the intensity of random fluctuations of each variable. The initial values ​​of the diffusion coefficients are determined by offline experiments and can be updated in real time during the operation through subsequent joint probability evolution steps.

[0019] Step 2: Solve the Fock-Planck equations through multi-timescale variational inference to complete the real-time update of the system's joint probability distribution. First, decompose the system into multiple timescales based on singular perturbation theory. Given that the evolution timescale of the model parameters is on the order of seconds to minutes, much slower than the millisecond-level changes in load torque, disturbances, etc., the system can be divided into fast and slow subsystems. The slow subsystem is used to characterize the evolution law of the model parameters and satisfies the Fock-Planck partial differential equations: ; in, For slow subsystems, the Fokker-Planck operator is used. For fast subsystems, it is used to characterize the evolution of joint states and perturbations under given model parameters. The corresponding equation is: ; in, The system employs the Fokker-Planck operator for fast subsystems that depends on model parameters. Based on this, a Gaussian process variational inference algorithm is used periodically to update parameters on a slow timescale. Specifically, this is achieved by maintaining a sliding data window of length N to store the latest observation data. Combining the prior distribution of model parameters Calculate the lower bound of evidence: ; in, The initial prior distribution of the model parameters, To determine the KL divergence, we then use stochastic gradient descent to maximize the lower bound of evidence, thus completing the variational distribution of the model parameters. Iterative updates, and the uncertainty of the updated model parameters. The data is passed to the fast timescale module to provide a basis for adaptive adjustment of the fast observer gain. At the fast timescale level, a probabilistic momentum-driven second-order extended state observer with an update period of 1ms is used to achieve rapid state and perturbation updates. First, joint momentum is defined. The original dynamic equations are reconstructed into momentum domain form: ; At the same time, the total disturbance and its rate of change Set as the expansion state, construct the expansion state vector. Further design of a probabilistic second-order extended state observer: ; The adaptively adjustable observer gain matrix satisfies: ; The nominal gain matrix, This is the gain adjustment factor. This mechanism, which uses matrix trace operations, enables dynamic gain adjustment. Specifically, it increases the observation gain to enhance perturbation tracking when model uncertainty increases, and decreases the gain to suppress noise amplification when uncertainty decreases. Ultimately, it updates the fast-state conditional probability distribution in real time based on the observer error covariance matrix. ; Complete the hierarchical evolution update of the entire joint probability distribution.

[0020] Step 3: Implement fingertip force mapping with uncertainty quantification. This step accurately converts the torque probability distribution in joint space into the force probability distribution in fingertip Cartesian space. A differentiated mapping strategy is adopted for the heterogeneous configurations of the robotic hand fingers. For the thumb, which has a 2-DOF coupled configuration, its kinematic chain is constructed using the DH parameter method, based on the thumb joint angle. , With the length of the connecting rod , The corresponding Jacobian matrix is ​​derived as follows: ; in, , , , Combining the mapping relationship between joint torque and fingertip force

[0021] ; The fingertip force is solved using generalized inverse operations: ; To effectively solve the rank deficiency problem near the singular configuration of the Jacobian matrix, for the single-degree-of-freedom configuration of the other four fingers, a simplified lever model with the fingertip force perpendicular to the linkage axis is adopted, based on the joint angle of each finger. With the length of the connecting rod The fingertip force is calculated using the following formula: , ; This simplified model significantly reduces computational load and is suitable for embedded real-time operating scenarios. It quantifies uncertainty propagation based on mapping computation, and the mean fingertip force is obtained by mapping the mean joint torque through the Jacobian matrix, satisfying… The variance of fingertip force takes into account both the propagation of joint torque uncertainty and the error of the mapping model itself. The calculation formula is as follows: ; Among them, mapping error uncertainty Calibration was performed through offline experiments.

[0022] Based on the geometric characteristics of the contact point, a unit normal vector n is defined. The fingertip force is decomposed into a normal clamping force and a tangential frictional force. The decomposition formula is as follows: , ; Simultaneously, the corresponding uncertainty decomposition is completed, through... and The uncertainty variances of the normal force and the tangential force are obtained respectively, and the precise mapping of fingertip force with uncertainty quantification is fully realized, which takes into account both accuracy and real-time performance.

[0023] Step 4: Utilize the uncertainty information of force estimation to drive the system to perform minute active actions, thereby quickly suppressing and reducing model uncertainty and correcting model mismatch problems. First, define a model mismatch index with the ratio of the standard deviation to the mean of the joint load torque as the core: ; Among them, a minimum detectable force of 0.01N is introduced. This effectively avoids the problem of index divergence under zero-load conditions, while setting a mismatch threshold. ,when When a system is deemed to have a severe model mismatch, an active sensing calibration process is triggered. To maximize the calibration effect, the optimal active action solution criterion is constructed with the goal of maximizing the mutual information gain of the model parameters after the action is executed. ; in, Using the information entropy function and considering the characteristics of dexterous hand force estimation, a small reciprocating motion along the fingertip force direction is selected as the optimal excitation action. The selection principle is that this excitation action will not cause the gripped object to slip, and can efficiently extract model correction information without interfering with normal operation. After completing the active motion excitation, system observation data including current, angular velocity, and joint angles are collected. Based on Bayes' theorem: ; The model parameter distribution was updated. Considering the limited amount of active action data, a Laplace approximation was introduced to fit the posterior distribution to a Gaussian distribution, and an analytical solution was obtained to achieve millisecond-level rapid updates. Finally, a comprehensive process exit and fault determination mechanism was set up, and the model mismatch was recalculated after active calibration. ,like If the calibration is completed, the active sensing process is exited and the system returns to normal operation. If the model mismatch still exceeds the standard after three consecutive active calibrations, the system is determined to be abnormal and a mechanical fault alarm is triggered. This realizes a closed-loop complete control logic of uncertainty perception, active excitation, parameter self-calibration and fault diagnosis.

[0024] Step 5: Directly integrate the obtained fingertip force probability distribution into the control law design to ensure that the actual contact force accurately meets the operation control requirements under a specified confidence level. First, a deterministic transformation of the chance-constrained optimization problem is carried out, which differs from traditional force tracking control that only minimizes the expected value of the square of the force tracking error. To achieve this objective, this method adds a probability constraint, requiring the actual contact force to be no less than [a certain value]. The probability falls within the preset allowable error range, that is, it satisfies... Since the actual contact force follows a Gaussian distribution Based on Gaussian distribution The criterion can transform stochastic chance constraints into deterministic constraints in an equivalent form: ; Based on this, the Lagrange function is constructed as follows: ; Solving constrained optimization problems, for control variables Taking the partial derivatives and setting them to zero, we derive the analytical form of the robust probability control law: ; This control law introduces an uncertainty damping term based on the traditional proportional-derivative control structure. It can effectively suppress control oscillations caused by force estimation uncertainty and improve system robustness; to further adapt to dynamically changing model uncertainties, a design based on force estimation uncertainty is proposed. The adaptive gain adjustment mechanism, wherein the proportional gain, differential gain, and uncertainty damping gain satisfy the following conditions: ; ; ; in, , , The nominal gain tuned for offline experiments. , With a fixed adjustment coefficient, this adaptive mechanism enables dynamic adaptive adjustment of the gain. When the estimation uncertainty is high, it reduces the proportional and derivative gains exponentially and increases the uncertainty damping gain exponentially to ensure system stability. When the estimation uncertainty is low, the control law approaches traditional PID control, preserving the system's fast response capability. Finally, based on Lyapunov stability theory, the stability of the control system is proven, and a Lyapunov function incorporating force tracking error and uncertainty terms is constructed. ; By differentiating it and substituting it into the designed probabilistic robust control law, it can be proved that for any time... All meet This fully verifies that the probabilistic robust control system possesses global asymptotic stability.

[0025] Reference Figure 1 First, the original signals of motor current, rotation angle, and angular velocity are collected, and four types of Gaussian distributed random variables are defined: load torque, flux linkage, disturbance torque, and rotation angle. Based on the motor dynamics equations, Iton's stochastic differential equations are derived, and the drift terms representing deterministic evolution are solved. With the diffusion term characterizing the propagation of random uncertainty Finally, a four-dimensional joint probability state space is constructed. This enables probabilistic state modeling of motors under multi-source uncertainty coupling.

[0026] Reference Figure 2 With a four-dimensional initial probability space As input, the global probability distribution is decomposed into a slow-scale parameter distribution and a fast-scale perturbation state distribution through multi-timescale variational decomposition; multi-scale decomposition is implemented based on the Fock-Planck equation to construct a slow-scale model parameter learning branch and a fast-scale perturbation observation branch respectively; the output parameter uncertainty covariance of the slow-scale branch is... Adaptive gain calculation using fast-scale branch combined with parameter uncertainty The multi-scale coupled joint probability distribution is updated after probabilistic information fusion. It then outputs to the downstream process to complete the hierarchical joint estimation of the time-varying uncertainty of motor speed.

[0027] Reference Figure 3 Input torque probability features , ,pass Calculate the model mismatch index; if the index does not exceed the threshold, exit the self-calibration process; if the index exceeds the threshold, trigger active detection; generate the optimal detection action based on maximizing mutual information and output the angle excitation. Collect observation data Complete the Bayesian parameter update and output the updated magnet linkage. The probability distribution is fed back to the mismatch calculation stage to achieve closed-loop self-calibration of model parameters.

[0028] Reference Figure 4 Input the average fingertip force ,variance Expectation ,Establish Chance-constrained optimization model; constructing the Lagrangian function for solution, and deriving the probabilistic robust control law. Based on force variance Adaptive tuning of proportional gain Differential gain Uncertainty damping gain The control law is substituted to generate motor control commands, and the system stability is verified using the Lyapunov method.

[0029] The method in this embodiment is applicable to applications of robot dexterity fingertip force perception and robust control in scenarios such as precision assembly, minimally invasive surgery, biological sample grasping, non-destructive sorting of fragile items, and safe human-computer interaction.

[0030] The embodiments described in this specification are merely illustrative examples of specific implementations of the technical concept of the present invention. The scope of protection of the present invention should not be limited to the specific technical solutions disclosed in these embodiments, but also covers all equivalent technical means that can be obtained by those skilled in the art through conventional deduction, equivalent substitution, or simple modification based on the overall concept of the present invention.

Claims

1. A sensorless fingertip force estimation and control method for a dexterous hand based on joint probabilistic evolution, characterized in that, The method includes the following steps: Step 1: Construct a unified joint probability state space by treating the joint load torque, model parameters, total disturbance torque, and joint angle with measurement noise as four types of random variables, and assume a Gaussian distribution for each random variable; perform probabilistic processing based on the dynamic equation of the single joint motor of the dexterous hand, derive and establish a probabilistic dynamic model in the form of Iton stochastic differential equations, determine the system drift term and diffusion term, and uniformly incorporate various sources of uncertainty such as model time-varying characteristics, external disturbances, and measurement noise; Step 2: Establish the Fokker-Planck equation characterizing the evolution of the joint probability distribution over time. Use a multi-timescale decomposition method to split the joint distribution into a slow-timescale sub-distribution and a fast-timescale sub-distribution. Transfer the uncertainty of the model parameters obtained from the slow-timescale update to the fast-timescale, and adaptively adjust the observer gain and bandwidth to achieve the joint optimal probability estimation of model uncertainty and dynamic disturbance. Step 3: Extract the estimated mean and uncertainty variance of joint load torque from the evolved and updated joint probability distribution; adopt a differentiated kinematic mapping strategy for the two-degree-of-freedom coupled configuration of the thumb and the single-degree-of-freedom configuration of the other fingers, using the generalized inverse method of the complete Jacobian matrix and the simplified lever model respectively; complete the conversion of the joint space torque probability distribution to the fingertip Cartesian space force probability distribution, and decompose and quantify the uncertainty of the fingertip normal clamping force and tangential friction force, outputting the sensorless fingertip force estimation results with confidence intervals; Step 4: Construct a dimensionless model mismatch evaluation index and introduce a minimum detectable force constraint. When the model mismatch exceeds the preset threshold, trigger the active sensing calibration process. Iterate and update the model mismatch until the threshold requirement is met, then exit the calibration and resume normal operation. If multiple calibrations still fail to meet the standard, trigger a mechanical fault alarm. Step 5: Integrate the fingertip force probability distribution into the control architecture, with the optimization objective of minimizing the expected force tracking error, while applying a probabilistic confidence constraint on the actual contact force tracking error; based on the statistical characteristics of the Gaussian distribution, the probabilistic constraint is equivalently transformed into a deterministic constraint condition; construct the Lagrangian function to derive the analytical control law containing proportional control terms, differential control terms, and uncertainty damping terms; design an adaptive adjustment rule for the control gain according to the uncertainty of fingertip force estimation, and use Lyapunov stability theory to verify the global asymptotic stability of the closed-loop system, thus achieving high-precision robust adaptive control of agile fingertip force without sensors.

2. The sensorless fingertip force estimation and control method for dexterous hands based on joint probabilistic evolution as described in claim 1, characterized in that, In step 1, the four-dimensional joint probability state space expression is constructed as follows: ； in, To follow a Gaussian distribution Joint load torque, This is a hyperparameter vector containing parameters of the Gaussian process kernel function, moment of inertia, damping coefficients, etc. The total disturbance torque, For joint angles that include measurement noise; The probabilistic dynamics model employs Itō's stochastic differential equations: ； in, For system drift term, For system diffusion terms, This is the standard Wiener process vector.

3. The sensorless fingertip force estimation and control method for dexterous hands based on joint probabilistic evolution as described in claim 1 or 2, characterized in that, In step 2, the slow timescale level uses Gaussian process variational inference to update the model parameter distribution over a long period, learning the uncertainties of the slow time-varying model caused by motor temperature rise and mechanical wear; the fast timescale level uses momentum-driven second-order extended state observers to update the system state and disturbance distribution over a short period, quickly tracking sudden load changes and external dynamic disturbances.

4. The sensorless fingertip force estimation and control method for dexterous hands based on joint probabilistic evolution as described in claim 3, characterized in that, In step 2, the multi-timescale variational inference decomposes the joint distribution as follows: ； Slow timescales maximize the lower bound of evidence: ； Iteratively update the model parameter distribution; The adaptive gain of the fast timescale observer satisfies: ； in, For the parameter distribution of the slow time-scale model; The distribution of state conditions on a fast timescale; The nominal gain matrix of the observer; This is the gain adjustment factor; For matrix trace operations; Let be the model parameter covariance matrix.

5. The sensorless fingertip force estimation and control method for dexterous hands based on joint probabilistic evolution as described in claim 1 or 2, characterized in that, In step 3, the probability mapping relationship between joint torque and fingertip force is as follows: ； ； The force at the fingertips ultimately follows a Gaussian distribution: ； in, The generalized inverse of the Jacobian matrix; , These represent the mean and variance of the joint load torque, respectively. , These represent the mean and variance of fingertip force, respectively. Additional uncertainty variance introduced into the kinematic mapping process.

6. The sensorless fingertip force estimation and control method for dexterous hands based on joint probabilistic evolution as described in claim 1 or 2, characterized in that, In step 4, the optimal small active motion is solved by maximizing information gain. A small reciprocating motion along the direction of force on the fingertip is set as the excitation and does not interfere with the normal grasping operation. The motor current, joint angular velocity and joint angle operation data under active excitation are collected, and the model parameter distribution is corrected in real time according to the Bayesian inference criterion.

7. The sensorless fingertip force estimation and control method for dexterous hands based on joint probabilistic evolution as described in claim 6, characterized in that, In step 4, the model mismatch index is defined as: ； The optimal active action is determined by maximizing information gain. ； The posterior update of model parameters follows the Bayesian criterion: ； in, This represents the minimum detectable force of the system. Mutual information function; The optimal small active joint rotation angle; This refers to system observation data collected under active stimulation.

8. The sensorless fingertip force estimation and control method for dexterous hands based on joint probabilistic evolution as described in claim 1 or 2, characterized in that, In step 5, a rule is designed to adaptively adjust the control gain according to the uncertainty of the fingertip force estimation. When the uncertainty is high, the ratio and differential gain are reduced and the damping gain is increased to ensure system stability. When the uncertainty is low, the dynamic response speed of the system is improved.

9. The sensorless fingertip force estimation and control method for dexterous hands based on joint probabilistic evolution as described in claim 8, characterized in that, In step 5, the probabilistic chance constraint is equivalently transformed into a deterministic constraint: ； The analytical form of the probabilistic robust control law is derived as follows: ； The adaptive adjustment formula for control gain is: ； ； ； in, To achieve the desired fingertip contact force; The upper limit of allowable error for force tracking; , This is the gain adjustment coefficient; , , These are the nominal gains for proportional, derivative, and uncertainty-damped loads, respectively. , , For real-time adaptive control of gain.

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