Intelligent feeding method and system for feeding robot

Abstract

The present application relates to the technical fields of intelligent industrial control and robot automation, and particularly relates to an intelligent feeding method and system for a feeding robot, comprising: acquiring a reaction kettle liquid level program and a powder mass flow rate of an end effector, and extracting a maximum Lyapunov index; if the index is greater than zero, constructing a global state vector and a stochastic differential equation; inputting an acceleration control variable and a state vector into an operation cost function of an embedded dynamic Weber number, and constructing a global stochastic cost functional; defining a lower bound of the functional as an optimal value function, expanding the equation to generate a partial differential equation with a trace term and extracting a Hamiltonian; finding an extreme value of the Hamiltonian to generate an optimal stochastic feedback control law; substituting the control law into a robot inverse dynamics model to generate a comprehensive driving torque column vector of a joint servo motor, and controlling the end effector to retreat. The present application realizes an advanced probability prediction under a strong turbulent flow condition, and effectively avoids liquid medicine splashing caused by impact kinetic energy overload.

Description

Technical Field

[0001] This invention relates to the field of intelligent industrial control and robot automation technology, and in particular to an intelligent feeding method and system for a feeding robot. Background Technology

[0002] In advanced chemical production processes such as the synthesis of new energy battery materials or high-end biopharmaceuticals, automated feeding robots are often used to add easily agglomerated powdered catalysts or active ingredients into reactors containing highly corrosive solvents and subjected to high-speed stirring. Due to the influence of the high-speed stirring impeller, the liquid flow field inside the reactor exhibits a highly turbulent and chaotic state filled with white noise disturbances. The liquid level and local surface tension show extremely nonlinear random abrupt changes, and the falling powder often experiences a transient surge in mass flow rate due to the collapse of agglomerates. Traditional feeding equipment mostly adopts open-loop linear deceleration based on a fixed height threshold or a simple visual obstacle avoidance and tracking strategy. Since the computing power of microprocessors is difficult to directly analyze complex nonlinear models containing integral variables of random processes, the underlying control system cannot make probabilistic predictions and advance second-order anti-disturbance compensation for the chaotic evolution trend of the flow field. As a result, the end effector of the feeding robot is lagging and rigid when facing extreme working conditions where instantaneous material inrush and random liquid surface turbulence are superimposed. The unpredictable high-energy solid-liquid impact kinetic energy can easily break through the critical threshold of the fluid dynamic Weber number, resulting in safety production problems such as the overflow of highly corrosive liquid, loss of core reactant materials, and corrosion of mechanical hardware. Summary of the Invention

[0003] To overcome the above shortcomings, this invention provides an intelligent feeding method and system for feeding robots, aiming to improve the problem that traditional feeding equipment mostly adopts linear deceleration, which cannot predict the random changes of strong turbulence, resulting in solid-liquid impact kinetic energy overload and causing liquid splashing.

[0004] In a first aspect, the present invention provides the following technical solution: an intelligent feeding method for a feeding robot, comprising the following steps:

[0005] S1. Obtain the time series data of the liquid level elevation in the reactor and the instantaneous powder mass flow rate of the end effector of the feeding robot, and extract the maximum Lyapunov exponent of the liquid level elevation time series data;

[0006] S2. If the maximum Lyapunov exponent is greater than zero, construct a global state vector and a stochastic differential equation characterizing the evolution of the global state vector using the liquid level elevation time series data and the instantaneous powder mass flow rate.

[0007] S3. Obtain the acceleration control variables of the end effector, input the global state vector and the acceleration control variables into the running cost function with embedded dynamic Weber number, and construct a global stochastic cost functional;

[0008] S4. Define the infimum of the global stochastic cost functional as the optimal value function, expand the optimal value function along the stochastic differential equation to generate a partial differential equation with trace terms, and extract the Hamiltonian of the partial differential equation.

[0009] S5. Find the extreme value of the Hamiltonian with respect to the acceleration control variable to generate the optimal stochastic feedback control law;

[0010] S6. Substitute the optimal random feedback control law into the inverse dynamics model of the feeding robot to generate a comprehensive driving torque column vector of the joint servo motor, and control the end effector to retract.

[0011] By adopting the above technical solution, the stochastic differential equation of state evolution and the cost functional are used to solve the optimal control law, thereby controlling the nonlinear yield of the end effector. This improves the problem that most traditional feeding equipment uses linear deceleration, which cannot predict the random changes of strong turbulence, resulting in solid-liquid impact kinetic energy overload and causing liquid splashing.

[0012] Secondly, the present invention provides the following technical solution: an intelligent feeding system for a feeding robot, comprising the following modules:

[0013] The data acquisition and index extraction module is used to acquire time series data of liquid level elevation in the reactor and instantaneous powder mass flow rate of the end effector of the feeding robot, and extract the maximum Lyapunov index of the liquid level elevation time series data.

[0014] The state vector and equation construction module is used to construct a global state vector and a stochastic differential equation characterizing the evolution of the global state vector by using the liquid level elevation time series data and the instantaneous powder mass flow rate if the maximum Lyapunov exponent is greater than zero.

[0015] The cost functional construction module is used to obtain the acceleration control variables of the end effector, input the global state vector and the acceleration control variables into the running cost function with embedded dynamic Weber number, and construct a global stochastic cost functional.

[0016] The partial differential equation generation module is used to define the infimum of the global stochastic cost functional as the optimal value function, expand the optimal value function along the stochastic differential equation to generate a partial differential equation with trace terms, and extract the Hamiltonian of the partial differential equation.

[0017] The control law solving module is used to find the extreme value of the Hamiltonian with respect to the acceleration control variable and generate the optimal stochastic feedback control law;

[0018] The dynamic servo execution module is used to substitute the optimal random feedback control law into the inverse dynamics model of the feeding robot, generate a comprehensive driving torque column vector of the joint servo motor, and control the end effector to retract.

[0019] The present invention has the following beneficial effects:

[0020] 1. In this invention, by constructing a stochastic differential equation of state evolution and solving the optimal control law with a cost functional, the nonlinear yield of the end effector is controlled, thereby improving the problem that most traditional feeding equipment adopts linear deceleration, which causes liquid splashing due to the inability to predict the random changes of strong turbulence.

[0021] 2. In this invention, a running cost function is constructed by weighting the dynamic Weber number, which includes solid-liquid impact velocity and surface tension coefficient, with the square term of acceleration control variable, and then performing mathematical expectation operator operation. This generates a global stochastic cost functional that takes into account both physical splash risk boundary and mechanical servo energy consumption. This improves the problem that traditional feeding path planning mostly uses a single height distance threshold for judgment. Since it does not consider the hydrodynamic limit between the kinetic energy of the falling powder and the capillary force of the liquid surface, the end effector will blindly pursue the feeding speed when dealing with fluctuations, causing transient kinetic energy overload.

[0022] 3. In this invention, by using Itō's lemma to perform a second-order Taylor expansion to extract the Hessian matrix and generate trace terms, and by using the upwind difference scheme to find the extreme value of the Hamiltonian, a continuous nonlinear mapping from the global state vector to the next time-series optimal buffer acceleration is established. This improves the problem that traditional industrial robot trajectory control mostly adopts conventional deterministic linear feedback adjustment strategies. Since the computing power of microprocessors is difficult to directly analyze complex algebraic models containing integral variables of stochastic Wiener processes, the underlying controller suffers from computing power overload and delay in action command output when facing high-frequency chaotic flow fields.

[0023] 4. In this invention, by extracting the variance distribution parameters representing the uncertainty of fluctuations from the diffusion term matrix and solving the minimum direction of the splash probability density function in the Cartesian coordinate system, the joint servo motor is driven to control the end effector to accurately perform spatial offset deceleration in the coordinate of the minimum direction. This improves the problem that most traditional material feeding anti-collision systems adopt a blind vertical straight-line lifting obstacle avoidance mechanism. Since they cannot identify the random oscillation safety gaps existing in the three-dimensional chaotic flow field, the mechanical entity is stiff when avoiding sudden impacts and is still easily contaminated by splashes. Attached Figure Description

[0024] Figure 1 This is a flowchart of an intelligent feeding method for a feeding robot proposed in this invention;

[0025] Figure 2 This is a flowchart illustrating the control law solution and dynamic servo execution of an intelligent feeding method for a feeding robot proposed in this invention.

[0026] Figure 3 This is an architecture diagram of an intelligent feeding system for a feeding robot proposed in this invention. Detailed Implementation

[0027] The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0028] Example 1:

[0029] In a first embodiment of the present invention, the present invention provides an intelligent feeding method for a feeding robot, such as... Figure 1 As shown, it includes the following steps:

[0030] S1. Obtain the time series data of liquid level elevation in the reactor and the instantaneous powder mass flow rate of the end effector of the feeding robot, and extract the maximum Lyapunov exponent from the liquid level elevation time series data;

[0031] Furthermore, in S1, the time series data of the liquid level elevation in the reactor and the instantaneous powder mass flow rate of the end effector of the feeding robot are acquired. The maximum Lyapunov exponent of the liquid level elevation time series data is extracted, including:

[0032] Obtain the initial trajectory vector and nearby small perturbation vector of the liquid surface elevation time series data in phase space;

[0033] Within a set evolution time step, the initial orbit vector and the neighboring small perturbation vector are phase space evolution tracked to obtain the evolved phase space perturbation separation vector;

[0034] Calculate the ratio of the Euclidean norm of the phase space perturbation separation vector to the Euclidean norm of the neighboring small perturbation vector;

[0035] Perform the natural logarithm operation on the comparison values ​​and divide the result of the natural logarithm operation by the evolution time step;

[0036] The limit value of the natural logarithm operation is calculated as the time parameter approaches infinity, and the limit value is output as the maximum Lyapunov exponent.

[0037] Specifically, the model input parameters are the time-series data of the reactor liquid level elevation collected by sensors and other hardware, and the instantaneous powder mass flow rate of the end effector of the feeding robot. Since the reactor liquid level elevation time-series data is a one-dimensional time series, the underlying algorithm first performs delayed coordinate phase space reconstruction on the reactor liquid level elevation time-series data based on Takens' embedding theorem. Specifically, the system embedding dimension is set to... and the delay time is Mapping and reconstructing one-dimensional time series data of liquid level elevation in the reactor into A multidimensional phase space state sequence is constructed. Within this reconstructed multidimensional phase space, initial state points are further extracted as initial trajectory vectors, and state points within a preset neighborhood are selected to construct neighboring small perturbation vectors. Trajectory evolution tracking calculations are performed on the phase space state sequence, and the maximum Lyapunov exponent is finally calculated and output. The maximum Lyapunov exponent serves as a pre-existing physical quantitative definition standard for the system and is passed to subsequent modules to determine whether the flow field has entered a turbulent chaotic state.

[0038] To accurately extract the maximum Lyapunov exponent, a bottom-level phase space evolution tracking model is established. The calculation logic of the maximum Lyapunov exponent strictly satisfies the following mathematical relationship:

[0039] ;

[0040] in The maximum Lyapunov exponent, representing the final calculated output, is used to quantitatively characterize the exponential divergence rate of the liquid phase flow field inside the reactor in adjacent orbits in phase space. This represents the set evolution time step, and its value is usually matched to the controller's control cycle, ranging from 0.001 seconds to 0.1 seconds. This represents the small perturbation vector between the initial orbit vector established in phase space based on the time series data of the liquid level elevation in the reactor and the adjacent orbit. This represents the phase space perturbation separation vector determined after evolution tracking over an evolutionary time step. Represents the Euclidean norm operator, indicating the measurement of the absolute spatial Euclidean distance of the corresponding vectors in phase space. This represents the natural logarithm operator. The limit calculation represents the time parameter approaching infinity. In practical engineering digital discrete systems, the cutoff value of the observation time window with a long period step is used for approximation.

[0041] By tracking the phase space evolution of the high-order sequence of the liquid level inside the reactor and extracting the maximum Lyapunov exponent as a quantitative indicator for chaotic situational awareness, this method improves upon the shortcomings of traditional feeding techniques that rely on fixed height observation thresholds or linear filtering systems, which cannot effectively identify deep, strong turbulent nonlinear fluctuations. This avoids the problem of corrosive liquid splashing caused by the degradation or failure of the underlying control strategy when the end effector of the feeding robot faces a complex and disordered flow field, and provides a precise physical reference for triggering the subsequent nonlinear bias retreat mechanism.

[0042] S2. If the maximum Lyapunov exponent is greater than zero, construct a global state vector and a stochastic differential equation characterizing the evolution of the global state vector using liquid surface elevation time series data and instantaneous powder mass flow rate.

[0043] Furthermore, in S2, if the maximum Lyapunov exponent is greater than zero, the global state vector and the stochastic differential equations characterizing the evolution of the global state vector are constructed using the liquid level elevation time series data and the instantaneous powder mass flow rate, including:

[0044] Obtain the real-time elevation and descent speed of the end effector;

[0045] The liquid level elevation time series data, instantaneous powder mass flow rate, real-time elevation and descent velocity are matrix-stitched to generate a global state vector;

[0046] Extract the integral term describing the hydrodynamic trend of the stirred fluid in the reactor, and merge the integral term with the kinematic integral term of the end effector to generate a deterministic drift term vector;

[0047] The maximum Lyapunov exponent is used as the positive correlation mapping parameter to construct matrix elements, generating a diffusion term matrix that characterizes the intensity of chaotic flow field.

[0048] Establish the product of the deterministic drift term vector and the time differential term, and establish the product of the diffusion term matrix and the differential term of the standard multidimensional Wiener process;

[0049] By superimposing the product of the deterministic drift term vector and the time differential term, and the product of the diffusion term matrix and the differential term of the standard multidimensional Wiener process, a stochastic differential equation is constructed.

[0050] Specifically, the maximum Lyapunov exponent output by the receiving and judgment module is used. Under the physical condition that the maximum Lyapunov exponent is greater than zero, the extracted multidimensional physical quantities are imported into the equation construction module to perform model solving. The multidimensional physical quantity input data includes liquid surface elevation time series data, instantaneous powder mass flow rate, real-time elevation of the end effector, and descent velocity. This step ultimately outputs the global state vector and stochastic differential equations.

[0051] To achieve unified dimensionality reduction of the system's physical kinematics and environmental fluid dynamics variables, a matrix concatenation is performed to generate a global state vector. The concatenation expression is as follows:

[0052] ;

[0053] in This represents the generated global state vector. This represents the input time series data of liquid level elevation. This represents the instantaneous powder mass flow rate. This represents the real-time elevation of the end effector, which is acquired in real time. This represents the descent speed of the end effector, which is collected in real time. This represents the matrix transpose operator.

[0054] To accurately capture unpredictable disturbances in strongly turbulent environments, a stochastic differential equation characterizing the system's state evolution trajectory is constructed. The specific mathematical expression is:

[0055] ;

[0056] in It represents the differential evolution of the global state vector with respect to time parameters. The vector representing the deterministic drift term is used to describe the macroscopic deterministic motion law of the system's state evolution, and its complete mathematical expression is defined as:

[0057] ;

[0058] in and These represent the proportionality coefficient and integral coefficient in fluid dynamics, respectively. This represents the integral term describing the hydrodynamic trend of the stirred fluid inside the reactor; Represents the powder flow rate decay constant; This represents the descent speed of the end effector; Represents the kinematic constant of gravity; This represents the transpose of a matrix.

[0059] The diffusion term matrix represents the intensity of random chaos in the flow field within the reactor. The diffusion term matrix is ​​constructed strictly based on the maximum Lyapunov exponent, and its specific mathematical mapping matrix form is as follows:

[0060] ;

[0061] in Represents the operator for constructing diagonal matrices; The maximum Lyapunov index extracted; and This represents the amplification factor of the fluid disturbance as determined in the experiment. By constructing the aforementioned diagonal matrix, the abstract chaotic index is precisely mapped to the magnitude of the random fluctuation variance of the corresponding state variable dimension. The representative multidimensional Wiener process differential term is numerically set to follow a normal distribution with an expected value of zero and a variance equal to the time differential term, characterizing the completely random turbulent white noise disturbance of the intervened system.

[0062] By coupling the kinematic variables of the feed process with the fluid environment variables of the superimposed Wiener process into the same differential equation, the nonlinear characteristic loss caused by the reliance on linear filtering to process the flow field signal in traditional intelligent feed control schemes is improved. This underlying stochastic differential model transforms the random disordered characteristics of turbulence into a probabilistic evolution equation that can be mathematically expected, thus avoiding the ineffective high-frequency oscillations caused by the control actuator blindly tracking random liquid surface peaks. This provides an accurate controlled object model input for subsequent solution of the anti-disturbance value functional.

[0063] S3. Obtain the acceleration control variables of the end effector, input the global state vector and acceleration control variables into the running cost function with embedded dynamic Weber number, and construct the global stochastic cost functional.

[0064] Furthermore, in S3, the runtime cost function that incorporates the global state vector and acceleration control variables into the embedded dynamic Weber number includes:

[0065] Obtain the surface tension coefficient of the liquid solvent in the reactor and the instantaneous equivalent cross-sectional area of ​​the powder agglomerate in contact with the liquid surface;

[0066] Calculate the free fall velocity increment from the time the end effector detaches from the powder until the powder contacts the liquid surface;

[0067] The incremental free-fall velocity and the descent velocity are vector-superimposed to obtain the comprehensive solid-liquid impact velocity.

[0068] The dynamic Weber number, which characterizes the kinetic energy component, is obtained by multiplying the instantaneous powder mass flow rate with the square of the comprehensive solid-liquid impact velocity, and then dividing the result of the product by the product of the surface tension coefficient and the instantaneous equivalent cross-sectional area.

[0069] Assign splash suppression weight constants to the dynamic Weber number and energy consumption penalty weight constants to the squared terms of the acceleration control variables;

[0070] The running cost function is generated by weighting and summing the dynamic Weber number that assigns the splash suppression weight constant with the squared terms of the acceleration control variable that assigns the energy consumption penalty weight constant.

[0071] In S3, constructing the global stochastic cost functional includes:

[0072] Obtain the set feeding task termination time, and set the terminal state penalty function to constrain the elevation range of the end effector at the feeding task termination time;

[0073] Within the time domain from the current moment to the end of the feeding task, perform time integration on the running cost function to obtain the integral cost value;

[0074] The total global cost is obtained by adding the integral cost to the terminal state penalty function.

[0075] Under the constraint of the current global state vector as the initial condition, the mathematical expectation operator is performed on the sum of the values ​​of all stochastic evolution paths of the global total cost to construct the global stochastic cost functional.

[0076] Specifically, the system receives the global state vector and acceleration control variables from the preceding module as data inputs. Within the system's computational unit, the surface tension coefficient of the liquid solvent in the target reactor is obtained by querying the system's pre-set physical property database. Simultaneously, the system retrieves real-time visual images of powder falling from a high-speed industrial camera mounted on the end effector of the feeding robot. An image edge detection algorithm is used to extract the powder flow contour pixels from the visual image, and combined with the instantaneous powder mass flow rate and pre-calibrated powder apparent density parameters, the instantaneous equivalent cross-sectional area of ​​the powder agglomerate in contact with the liquid surface is calculated and output. After obtaining the above basic physical quantities, the system calculates the free-fall velocity increment from when the end effector detaches from the powder until the powder contacts the liquid surface. The free-fall velocity increment and the descent velocity are vector-superimposed to output the comprehensive solid-liquid impact velocity. The dynamic Weber number, characterizing the kinetic energy component, is extracted using the instantaneous powder mass flow rate, comprehensive solid-liquid impact velocity, surface tension coefficient, and instantaneous equivalent cross-sectional area. The dynamic Weber number of the splash suppression weight constant and the squared term of the acceleration control variable of the energy consumption penalty weight constant are weighted and summed to calculate the output running cost function.

[0077] The mathematical analytical expression of the operating cost function is defined as follows:

[0078] ;

[0079] in The output runtime cost function. This represents the splash suppression weight constant assigned to the user. This represents the instantaneous powder mass flow rate of the input. This represents the descent speed of the end effector. This represents the gravitational acceleration constant, which is taken as 9.8 meters per square second in actual physics calculations. This represents the real-time elevation of the end effector. This represents the instantaneous elevation of the liquid level inside the reactor. The surface tension coefficient represents the liquid solvent. It represents the instantaneous equivalent cross-sectional area of ​​the powder agglomerate in contact with the liquid surface. This represents the energy consumption penalty weight constant assigned to the allocation. This represents the acceleration control variable.

[0080] The generated operating cost function is obtained as the underlying integration parameter. The system reads the set termination time of the feeding task and performs time integration on the operating cost function within the time domain from the current time to the termination time of the feeding task, outputting the integral cost value. At the termination time of the feeding task, a terminal state penalty function is set to constrain the elevation interval of the end effector. The integral cost value and the terminal state penalty function are added to generate the global total cost. Under the constraint of the global state vector at the current time as the initial condition, the mathematical expectation operator is performed on the sum of the values ​​of all random evolution paths of the global total cost, and finally the global random cost functional is output.

[0081] The mathematical analytical expression of the global stochastic cost functional is defined as follows:

[0082] ;

[0083] in This represents the global stochastic cost functional of the constructed output. The mathematical expectation operator represents the execution. This represents the current moment in the system's evolution. This represents the end time of the set feeding task. This represents the time variable for integration. This represents the running cost function under the integral time variable. This represents the terminal state penalty function set at the time the feeding task ends. This represents the global state vector of the system at the moment the feeding task ends.

[0084] By constructing an operational cost function with an embedded dynamic Weber number and combining it with the integral of the mathematical expectation operator to generate a global stochastic cost functional, the shortcomings of traditional intelligent feeding technology, such as stiff robotic arm retreat and system adjustment lag caused by a single control objective and failure to consider the physical limits of fluid dynamic collisions, are improved. This avoids the problem of transient solid-liquid impact kinetic energy overload and violent liquid splashing caused by the end effector pursuing feeding speed in response to high-frequency random liquid surface fluctuations. It also establishes a quantitative evaluation standard for solving the optimal control strategy in probability space that takes into account both splash suppression and servo energy loss.

[0085] like Figure 2As shown in Figure S4, the infimum of the global stochastic cost functional is defined as the optimal value function. The optimal value function is expanded along the stochastic differential equation to generate a partial differential equation with trace terms, and the Hamiltonian of the partial differential equation is extracted.

[0086] Furthermore, in S4, the infimum of the global stochastic cost functional is defined as the optimal value function. The optimal value function is expanded along the stochastic differential equation to generate a partial differential equation with a trace term. The Hamiltonian of the partial differential equation is extracted, including:

[0087] We use Ito's lemma to perform a second-order Taylor expansion of the optimal value function along the evolution trajectory of the stochastic differential equation;

[0088] Calculate the partial derivative of the optimal value function with respect to time;

[0089] Calculate the Jacobian matrix and Hessian matrix of the optimal value function with respect to the global state vector;

[0090] Obtain the transpose of the diffusion term matrix, which characterizes the chaotic intensity of the flow field. Multiply the transpose of the diffusion term matrix, the Hessian matrix, and the diffusion term matrix together to obtain the second-order wave product matrix.

[0091] The trace of the matrix is ​​extracted by summing the diagonal elements of the second-order wave product matrix and multiplying the trace by the constant coefficients to generate the trace term.

[0092] By establishing the partial derivative of the optimal value function with respect to time, the running cost function, the product of the Jacobian matrix and the deterministic drift term vector, and the dynamic programming equality constraints between the trace terms, partial differential equations are generated.

[0093] Specifically, the system receives the global stochastic cost functional and the stochastic differential equation characterizing the system's evolution as basic data input parameters from the preceding module. After analysis by the underlying operator, the final output includes a partial differential equation containing the trace term and the extracted Hamiltonian.

[0094] In the computational process, the underlying logic first defines the infimum of the global stochastic cost functional under all physically permissible control input conditions as the optimal value function. It then performs an Itō lemma expansion along the evolutionary trajectory described by the stochastic differential equation for this optimal value function. Given that the system state variables contain Wiener process white noise, traditional calculus rules fail here, and the expansion must be strictly preserved down to the second-order Taylor expansion term. The system uses this to calculate the first-order partial derivatives of the optimal value function with respect to the time parameter, the first-order partial derivatives with respect to the global state vector (i.e., the Jacobian matrix), and the crucial second-order partial derivatives (i.e., the Hessian matrix). Subsequently, the transpose of the diffusion term matrix, which characterizes the chaotic intensity of the flow field, is extracted. The transpose of the diffusion term matrix, the Hessian matrix, and the diffusion term matrix are multiplied together to obtain a second-order wave product matrix. The sum of the main diagonal elements of this second-order wave product matrix is ​​extracted, and the trace operation is performed, multiplied by half the constant coefficient to generate the trace term. Finally, based on the dynamic programming principle, equality constraints are established to generate partial differential equations, and the set of polynomials on one side of the equality is directly extracted as the Hamiltonian and sent to the extremum solution module.

[0095] The analytical expression defining the optimal value function is:

[0096] ;

[0097] in This represents the optimal value function that is defined and solved. This represents the operator that takes the minimum value within the set of physically permissible acceleration control variables. This represents the global stochastic cost functional of the preceding input.

[0098] The mathematical expression of the generated core partial differential equation is: ;

[0099] in This represents the negative value of the first-order partial derivative of the optimal value function with respect to the time parameter. The running cost function represents the input. The Jacobian matrix represents the calculated optimal value function with respect to the global state vector. This represents the matrix transpose operator. This represents the vector of deterministic drift terms. These represent the constant coefficients generated by the second-order Taylor expansion. The trace operator for a matrix is ​​the summation of the elements along the main diagonal of the matrix. The transpose of the diffusion term matrix. The Hessian matrix represents the calculated optimal value function with respect to the global state vector. This represents the diffusion term matrix generated in the preceding sequence. The complete polynomial structure within the curly braces on the right side of the equation is extracted and defined as the Hamiltonian of the partial differential equation.

[0100] By introducing Itō's lemma for second-order calculus expansion and forcibly extracting trace terms, the cost functional, which originally contained stochastic integral variables and was difficult to solve numerically directly, is reduced in dimension to a partial differential equation in a deterministic state space. The second-order wave trace term embedded in the equation is specifically used for proactive probabilistic compensation of the disordered turbulent white noise within the reactor. This technique overcomes the limitation of conventional feeding robot path planning algorithms, which can only handle deterministic physical models, and provides the underlying control system with a probabilistic predictive basis for dealing with random fluid mutations in the near future. This removes the functional analytical barrier at the computational level for subsequent accurate solutions to the inverse dynamic compensation torque.

[0101] like Figure 2 As shown, S5, find the extreme value of the Hamiltonian with respect to the acceleration control variable to generate the optimal stochastic feedback control law;

[0102] Furthermore, in S5, the process of finding the extreme value of the Hamiltonian with respect to the acceleration control variable to generate the optimal stochastic feedback control law includes:

[0103] The state space and time domain of the partial differential equation are discretized by the upwind difference scheme to obtain the discrete time node network.

[0104] At the nodes in the discrete-time node network, extract the Hamiltonian expression from the partial differential equation;

[0105] Perform first-order partial derivative calculations on the Hamiltonian expression with respect to the acceleration control variable;

[0106] Set the result of the first-order partial derivative operation to zero, and simultaneously apply the boundary conditions of the global state vector to calculate the corresponding root space of the control variables;

[0107] Extract the elements that make the Hamiltonian reach a global minimum in the root space of the control variables, establish a continuous nonlinear mapping from the global state vector to the next time-series optimal buffer acceleration, and generate the optimal stochastic feedback control law.

[0108] Specifically, the system receives the data model from the preceding partial differential equation generation module as the underlying input parameters. The control terminal uses an upwind difference scheme to perform numerical grid discretization on the state space and continuous time domain contained in the partial differential equation, dividing the continuous domain into a discrete-time node network. At each node location within the discrete-time node network, the system independently extracts the Hamiltonian expression within the partial differential equation.

[0109] The extracted Hamiltonian expression is subjected to first-order partial derivative calculations with respect to the acceleration control variable. The result of the first-order partial derivative calculation is set to zero. Based on this, the system strictly establishes the global state vector physical boundary conditions of the feeding robot and the reactor system. The specific boundary condition constraints are as follows:

[0110] ;

[0111] ;

[0112] in This represents the set safety margin for solid-liquid impact resistance, used to ensure that the end effector must never be submerged below the fluid surface. and These represent the maximum reverse buffer speed limit and the maximum forward downward speed limit, respectively, determined by the servo motor hardware performance. Under the strict constraints of the above physical boundary conditions, the corresponding root space of control variables is obtained by solving.

[0113] The core extremum solving operations involved in this step satisfy the following mathematical relationship:

[0114] ;

[0115] ;

[0116] ;

[0117] in The expression representing the Hamiltonian for separation and extraction. This represents the global state vector constructed in the preceding sequence. This represents the acceleration control variable at the system's underlying level. It represents the Jacobian matrix of the optimal value function with respect to the global state vector. This represents the runtime cost function embedded within the system. This represents the matrix transpose operator. This represents the vector of deterministic drift terms. Represents a time variable. These represent the intrinsic constant coefficients resulting from the Taylor expansion of calculus. This represents the trace operator that extracts the sum of the elements on the main diagonal of a matrix. This represents the diffusion term matrix, which characterizes the intensity of chaos. The Hessian matrix represents the optimal value function with respect to the global state vector. This represents the first-order partial derivative operator with respect to the acceleration control variable. 0 represents the extremum search condition constant for the partial derivative to return to zero. This represents the optimal stochastic feedback control law that is ultimately generated and output. The table lists the solver operators for finding the minimum value of the corresponding variable within the constraint boundary. This represents the set of physically permissible boundaries for acceleration control variables determined based on the mechanical limits of robot hardware.

[0118] In the calculated root space of control variables, specific elements that guide the Hamiltonian expression to reach the global minimum are extracted. The underlying control algorithm uses these specific elements to establish a continuous nonlinear mapping from the current global state vector to the next time-series optimal buffer acceleration, generating the optimal stochastic feedback control law and outputting it to the downstream dynamic model.

[0119] In the intelligent material feeding and anti-splash system, it plays a crucial role in transforming abstract fluid dynamics functionals into executable machine instructions. An upwind difference scheme is introduced to discretize the partial differential equations into a grid, converting the complex differential calculations with random fluctuation matrices into an algebraic extremum solution task that can be scheduled in real time by the industrial controller. By forcing the first-order partial derivatives to zero and optimizing the global minimum elements, the system oscillation dead zone that is easily caused by conventional linear feedback strategies at strongly nonlinear turbulent boundaries is avoided. This nonlinear mapping mechanism establishes a solution channel from the white noise probability compensation parameters to the robotic arm acceleration, avoiding the action delay caused by computational overload of the underlying controller and ensuring that the material feeding robot has a millisecond-level execution response capability to match sudden changes in chaotic flow fields.

[0120] like Figure 2 As shown, S6, the optimal stochastic feedback control law is substituted into the inverse dynamics model of the feeding robot to generate the comprehensive driving torque column vector of the joint servo motor, and the end effector is controlled to retract.

[0121] Furthermore, in S6, the optimal stochastic feedback control law is substituted into the inverse dynamics model of the feeding robot to generate the comprehensive driving torque column vector of the joint servo motors, including:

[0122] Obtain the joint angle vectors of the feeding robot and calculate the spatial Jacobian matrix corresponding to the current pose;

[0123] The pseudo-inverse matrix is ​​obtained by inverting the spatial Jacobian matrix. The optimal stochastic feedback control law in Cartesian space is then converted into a multi-axis joint spatial acceleration command using the pseudo-inverse matrix.

[0124] Extract the system inertia matrix, Coriolis force and centrifugal force coupling matrix, and gravity feedforward compensation column vector that depend on the joint angle vector;

[0125] The multi-axis joint spatial acceleration command, system inertia matrix, Coriolis force and centrifugal force coupling matrix, and gravity feedforward compensation column vector are input into the rigid body inverse dynamics model equation for solution, generating a comprehensive driving torque column vector output to the joint servo motor.

[0126] In S6, controlling the end effector to retract includes:

[0127] The overall driving torque column vector is sent down to the servo motors of each joint.

[0128] Obtain the variance distribution parameters representing the wave uncertainty in the diffusion term matrix that characterizes the intensity of chaotic flow field;

[0129] The minimum direction and corresponding coordinates of the splash probability density function are calculated in Cartesian coordinates using variance distribution parameters.

[0130] The drive joint servo motor outputs torque, extracts the minimum direction coordinate, and controls the end effector to perform spatial offset deceleration towards the minimum direction coordinate to achieve yielding.

[0131] Specifically, the system receives the optimal stochastic feedback control law and the diffusion term matrix characterizing the chaotic intensity of the flow field as input data. The control terminal reads the underlying feedback data of the feeding robot to extract the joint angle vector and the joint angular velocity column vector. After spatial kinematic transformation, inverse dynamics calculation, and probability density distribution space search, the system outputs the comprehensive driving torque column vector to each execution hardware and outputs the minimum value direction coordinates to guide the physical space offset of the mechanical entity.

[0132] To achieve cross-domain conversion from abstract control laws to physical hardware drive instructions, the system introduces rigid body inverse dynamics model equations for computation. The underlying controller establishes the coupling relationship between the spatial Jacobian matrix and the system dynamic parameters, and the specific computations performed satisfy the following mathematical relationship:

[0133] ;

[0134] in This represents the column vector of the combined driving torque generated by the solution and output to the joint servo motor. This represents the system inertia matrix, which depends on the joint angle vector and is extracted based on the current feedback information. This represents the pseudo-inverse matrix obtained by performing an inversion operation on the spatial Jacobian matrix corresponding to the current pose. This represents the optimal stochastic feedback control law in Cartesian space, which is the input from the preceding module. Multiplying this term with the pseudo-inverse matrix essentially converts the Cartesian space parameters into multi-axis joint space acceleration commands. The matrix representing the coupling between the Coriolis force and the centrifugal force of the system itself. This represents the column vector of joint angular velocities of the feeding robot. This represents the gravity feedforward compensation column vector used to offset the weight of the mechanical entity.

[0135] After obtaining the underlying drive commands, the system directly sends the comprehensive drive torque column vector to each joint servo motor, generating the corresponding physical torque. The underlying algorithm module synchronously retrieves the diffusion term matrix and extracts the variance distribution parameters characterizing the uncertainty of the flow field fluctuations from the diagonal elements. Due to the introduction of Gaussian white noise, the system constructs a normally distributed splash probability density function in the vertical elevation dimension, using the current liquid surface elevation as the expectation and the variance distribution parameters as the variance. To ensure that the retreating action does not cause indefinite stagnation of the feeding task, a comprehensive safety objective function with an embedded task progress trade-off mechanism is established. The comprehensive safety objective function weights the evaluation value of the splash probability density function with a distance penalty term for deviation from the baseline feeding trajectory.

[0136] Minimum optimization is performed on the comprehensive safety objective function to calculate the minimum direction and corresponding coordinates of the splash probability density function. The located safety elevation minimum is then sent to the trajectory planner. Driven by the torque output of the joint servo motor, the end effector is controlled to perform a vertical offset deceleration along a single vertical axis towards the safety elevation minimum, with second-order anti-disturbance compensation. This accurately avoids the expected high-splash area while ensuring the continuity of the overall feeding progress.

[0137] This computation and execution process achieves a physical dimensionality reduction from high-dimensional fluid probabilistic functionals to physical mechanical motion. By combining the pseudo-inverse of the Jacobian matrix and the solution of the inverse dynamics model, a conversion channel is established between the acceleration command in the Cartesian probability space and the driving torque of the underlying servo motor. By searching for the minimum direction coordinates according to the variance distribution parameters and performing bias retreat, it breaks the rigid logic of conventional industrial robots that can only blindly perform vertical lifting to avoid obstacles when facing collision risks. The end effector cuts into the safety gap of the chaotic flow field along the path of the probability minimum, ensuring that the mechanical entity is protected from the physical damage of highly corrosive liquid splashes in the process of accurately dissolving the overload kinetic energy of solid-liquid impact caused by avalanche-style material impact, thus establishing a hardware-level high-risk protection closed loop.

[0138] Example 2:

[0139] In the synthesis of new energy battery materials or high-end biopharmaceutical applications, feeding robots need to add easily agglomerated powdered catalysts into deep reactors containing highly corrosive solvents and under high-speed stirring. Under these complex conditions, a significant challenge lies in physical splash prevention: the high-speed stirring impeller creates a highly turbulent and chaotic liquid flow field within the reactor, filled with white noise disturbances, resulting in highly nonlinear and random abrupt changes in liquid surface elevation and local surface tension. Simultaneously, the falling powder often experiences a sudden, avalanche-like surge in transient mass flow rate due to agglomeration collapse. When a sudden surge of material with extremely high impact kinetic energy violently impacts the disordered and turbulent liquid surface, it can easily breach the critical threshold of the fluid dynamic Weber number, triggering unpredictable, high-energy impact splashes. Existing automated equipment can only rely on lagging fixed-point ranging to perform rigid linear vertical lifting and lowering, completely unable to probabilistically predict the chaotic evolution trend of the flow field or provide advanced second-order anti-disturbance compensation. This passive yielding mechanism, lacking multidimensional physical and dynamic coupling, cannot dissipate sudden impact kinetic energy within microseconds, easily leading to the spillage of highly corrosive chemicals, loss and contamination of core reactants, and even severe corrosion of the robotic arm's end effector and safety accidents. To address these issues, this invention provides an intelligent feeding system for a feeding robot, the structure of which is as follows: Figure 3 As shown. The specific implementation process of this system is as follows:

[0140] The data acquisition and exponent extraction module, acting as a front-end sensing source, collects the liquid level sequence and instantaneous material flow rate. It quantitatively determines whether the reactor flow field has entered a disordered state by calculating the maximum Lyapunov exponent. Given the established physical premise of chaotic flow field characteristics, the state vector and equation construction module no longer treats the working environment as a conventional deterministic system. Instead, it integrates the robotic arm motion parameters and turbulent fluctuations to reconstruct a low-level state model with stochastic differential characteristics. This approach eliminates the signal lag caused by conventional linear filtering algorithms, transforming the unpredictability of the physical interface into a probabilistic evolution trend that the low-level controller can compute.

[0141] The cost functional construction module, based on the extracted dynamic Weber quantification of the physical limits of solid-liquid impacts that the liquid surface can withstand, combined with the acceleration energy consumption penalty boundary, establishes a global stochastic cost functional including a mathematical expectation metric. The partial differential equation generation module performs dimensionality reduction expansion calculations on this functional system, with internally forced trace terms specifically used for advance compensation of white noise disturbances within the flow field. The control law solving module extracts the extremum mapping space from the extracted Hamiltonian, and the system calculates the optimal feedback control strategy for the end effector of the feeding robot under the current adverse working conditions.

[0142] The dynamics servo execution module takes the abstract mathematical extreme value solution mentioned above and, through rigid body space inverse dynamics conversion, establishes it as the physical torque output command for each joint servo motor. The internal module logic of the overall system is tightly interlocked, reversing the disadvantage of traditional automated feeding equipment that relies on fixed height tracking and produces rigid movements when encountering sudden material impacts. Driven by the underlying servo commands, the end effector of the feeding robot performs nonlinear spatial bias buffer retreat in the direction of the minimum splash probability density. In the extremely short physical contact instant, the system strictly suppresses the impact kinetic energy of high-energy powder clumps below the surface tension boundary, curbing the risk of agitation and spillage of highly corrosive liquids under high-speed stirring, and ensuring the operational safety of equipment in deep chemical synthesis operations.

[0143] Finally, it should be noted that the above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art can still modify the technical solutions described in the foregoing embodiments or make equivalent substitutions for some of the technical features. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. An intelligent feeding method for a feeding robot, characterized in that, Includes the following steps: S1. Obtain the time series data of the liquid level elevation in the reactor and the instantaneous powder mass flow rate of the end effector of the feeding robot, and extract the maximum Lyapunov exponent of the liquid level elevation time series data; S2. If the maximum Lyapunov exponent is greater than zero, construct a global state vector and a stochastic differential equation characterizing the evolution of the global state vector using the liquid level elevation time series data and the instantaneous powder mass flow rate. S3. Obtain the acceleration control variables of the end effector, input the global state vector and the acceleration control variables into the running cost function with embedded dynamic Weber number, and construct a global stochastic cost functional; S4. Define the infimum of the global stochastic cost functional as the optimal value function, expand the optimal value function along the stochastic differential equation to generate a partial differential equation with trace terms, and extract the Hamiltonian of the partial differential equation. S5. Find the extreme value of the Hamiltonian with respect to the acceleration control variable to generate the optimal stochastic feedback control law; S6. Substitute the optimal random feedback control law into the inverse dynamics model of the feeding robot to generate a comprehensive driving torque column vector of the joint servo motor, and control the end effector to retract.

2. The intelligent feeding method for a feeding robot according to claim 1, characterized in that, In S1, the acquisition of time-series data of liquid level elevation in the reactor and instantaneous powder mass flow rate of the end effector of the feeding robot, and the extraction of the maximum Lyapunov exponent from the liquid level elevation time-series data, include: Obtain the initial trajectory vector and the nearby small perturbation vector of the liquid level elevation time series data in phase space; Within a set evolution time step, the initial orbit vector and the neighboring small perturbation vector are subjected to phase space evolution tracking to obtain the evolved phase space perturbation separation vector. Calculate the ratio of the Euclidean norm of the phase space perturbation separation vector to the Euclidean norm of the neighboring small perturbation vector; Perform a natural logarithm operation on the ratio, and divide the result of the natural logarithm operation by the evolution time step; The limit value of the natural logarithm operation result is calculated when the time parameter approaches infinity, and the limit value is output as the maximum Lyapunov exponent.

3. The intelligent feeding method for a feeding robot according to claim 1, characterized in that, In S2, if the maximum Lyapunov exponent is greater than zero, constructing a global state vector and a stochastic differential equation characterizing the evolution of the global state vector using the liquid level elevation time series data and the instantaneous powder mass flow rate includes: Obtain the real-time elevation and descent speed of the end effector; The liquid level elevation time series data, the instantaneous powder mass flow rate, the real-time elevation, and the descent velocity are matrix-concatenated to generate the global state vector; Extract the integral term describing the hydrodynamic trend of the stirred fluid in the reactor, and merge the integral term with the kinematic integral term of the end effector to generate a deterministic drift term vector; The maximum Lyapunov exponent is used as a positive correlation mapping parameter to construct matrix elements, generating a diffusion term matrix that characterizes the intensity of chaotic flow field. Establish the product of the deterministic drift term vector and the time differential term, and establish the product of the diffusion term matrix and the differential term of the standard multidimensional Wiener process; The stochastic differential equation is constructed by superimposing the product of the deterministic drift term vector and the time differential term, and the product of the diffusion term matrix and the standard multidimensional Wiener process differential term.

4. The intelligent feeding method for a feeding robot according to claim 3, characterized in that, In S3, the step of inputting the global state vector and the acceleration control variable into the embedded dynamic Weber number of the operating cost function includes: Obtain the surface tension coefficient of the liquid solvent in the reactor and the instantaneous equivalent cross-sectional area of ​​the powder agglomerate in contact with the liquid surface; Calculate the free fall velocity increment of the end effector from the time it leaves the powder until the powder contacts the liquid surface; The free fall velocity increment and the descent velocity are vector-superimposed to obtain the comprehensive solid-liquid impact velocity. The instantaneous powder mass flow rate is multiplied by the square of the comprehensive solid-liquid impact velocity, and the result of the multiplication is divided by the product of the surface tension coefficient and the instantaneous equivalent cross-sectional area to obtain the dynamic Weber number characterizing the kinetic energy component. Assign a splash suppression weight constant to the dynamic Weber number and an energy consumption penalty weight constant to the squared term of the acceleration control variable; The operating cost function is generated by weighting and summing the dynamic Weber number, which is assigned to the splash suppression weight constant, and the squared terms of the acceleration control variable, which is assigned to the energy consumption penalty weight constant.

5. The intelligent feeding method for a feeding robot according to claim 1, characterized in that, In S3, the construction of the global stochastic cost functional includes: Obtain the set feeding task termination time, and set the terminal state penalty function to constrain the elevation range of the end effector at the feeding task termination time; Within the time domain from the current moment to the termination time of the feeding task, perform time integration on the running cost function to obtain the integral cost value; The integral cost is added to the terminal state penalty function to obtain the total global cost; Under the constraint of the global state vector at the current moment as the initial condition, the mathematical expectation operator is performed on the sum of the values ​​of all random evolution paths of the global total cost to construct the global random cost functional.

6. The intelligent feeding method for a feeding robot according to claim 1, characterized in that, In S4, defining the infimum of the global stochastic cost functional as the optimal value function, expanding the optimal value function along the stochastic differential equation to generate a partial differential equation with a trace term, and extracting the Hamiltonian of the partial differential equation includes: The optimal value function is expanded using Ito's lemma along the evolution path of the stochastic differential equation; Calculate the partial derivative of the optimal value function with respect to time; Calculate the Jacobian matrix and Hessian matrix of the optimal value function with respect to the global state vector; Obtain the transpose of the diffusion term matrix that characterizes the chaotic intensity of the flow field, and perform a chain multiplication operation on the transpose of the diffusion term matrix, the Hessian matrix, and the diffusion term matrix to obtain the second-order wave product matrix. The trace of the matrix is ​​extracted by summing the diagonal elements of the second-order wave product matrix and multiplying the trace by the constant coefficients to generate the trace term. The partial differential equation is generated by establishing the partial derivative of the optimal value function with respect to time, the running cost function, the product of the Jacobian matrix and the deterministic drift term vector, and the dynamic programming equality constraints between the trace terms.

7. The intelligent feeding method for a feeding robot according to claim 1, characterized in that, In S5, the step of finding the extreme value of the Hamiltonian with respect to the acceleration control variable to generate the optimal stochastic feedback control law includes: The state space and time domain of the partial differential equation are discretized by a windward difference scheme to obtain a discrete time node network. At the nodes in the discrete-time node network, extract the Hamiltonian expression from the partial differential equation; Perform first-order partial derivative calculations on the Hamiltonian expression with respect to the acceleration control variable; Set the result of the first-order partial derivative operation to zero, and simultaneously apply the boundary conditions of the global state vector to calculate the corresponding root space of the control variables; Extract the elements that make the Hamiltonian reach a global minimum in the root space of the control variables, establish a continuous nonlinear mapping from the global state vector to the next time-series optimal buffer acceleration, and generate the optimal stochastic feedback control law.

8. The intelligent feeding method for a feeding robot according to claim 1, characterized in that, In S6, substituting the optimal stochastic feedback control law into the inverse dynamics model of the feeding robot to generate the comprehensive driving torque column vector of the joint servo motors includes: Obtain the joint angle vectors of the feeding robot and calculate the spatial Jacobian matrix corresponding to the current pose; The spatial Jacobian matrix is ​​inverted to obtain a pseudo-inverse matrix. The pseudo-inverse matrix is ​​then used to convert the optimal stochastic feedback control law in Cartesian space into a multi-axis joint spatial acceleration command. Extract the system inertia matrix, Coriolis force and centrifugal force coupling matrix, and gravity feedforward compensation column vector that depend on the joint angle vector; The multi-axis joint spatial acceleration command, the system inertia matrix, the Coriolis force and centrifugal force coupling matrix, and the gravity feedforward compensation column vector are input into the rigid body inverse dynamics model equation for solution, generating the comprehensive driving torque column vector output to the joint servo motor.

9. The intelligent feeding method for a feeding robot according to claim 1, characterized in that, In S6, controlling the end effector to retract includes: The comprehensive driving torque column vector is sent down to each of the joint servo motors; Obtain the variance distribution parameters representing the wave uncertainty in the diffusion term matrix that characterizes the intensity of chaotic flow field; The minimum direction and corresponding minimum direction coordinates of the splash probability density function are calculated in the Cartesian coordinate system using the variance distribution parameters. The joint servo motor is driven to output torque, the minimum direction coordinate is extracted, and the end effector is controlled to perform spatial offset deceleration towards the minimum direction coordinate to achieve the yielding.

10. An intelligent feeding system for a feeding robot, characterized in that, Includes the following modules: The data acquisition and index extraction module is used to acquire time series data of liquid level elevation in the reactor and instantaneous powder mass flow rate of the end effector of the feeding robot, and extract the maximum Lyapunov index of the liquid level elevation time series data. The state vector and equation construction module is used to construct a global state vector and a stochastic differential equation characterizing the evolution of the global state vector by using the liquid level elevation time series data and the instantaneous powder mass flow rate if the maximum Lyapunov exponent is greater than zero. The cost functional construction module is used to obtain the acceleration control variables of the end effector, input the global state vector and the acceleration control variables into the running cost function with embedded dynamic Weber number, and construct a global stochastic cost functional. The partial differential equation generation module is used to define the infimum of the global stochastic cost functional as the optimal value function, expand the optimal value function along the stochastic differential equation to generate a partial differential equation with trace terms, and extract the Hamiltonian of the partial differential equation. The control law solving module is used to find the extreme value of the Hamiltonian with respect to the acceleration control variable and generate the optimal stochastic feedback control law; The dynamic servo execution module is used to substitute the optimal random feedback control law into the inverse dynamics model of the feeding robot, generate a comprehensive driving torque column vector of the joint servo motor, and control the end effector to retract.

Images