69 results about "Constraint control" patented technology

The invention discloses an improved FWN-based torque double-domain constraint control method for a flexible arm space robot, and the method comprises the steps: constructing a dynamic model of a flexible arm space robot system, and constructing a torque double-domain constraint control system mathematical model in combination with the posture of a body and the constraint of the amplitude and the amplitude change rate of the control torque of a joint hinge; a torque double-domain constraint controller based on the improved fuzzy wavelet network is constructed, the torque double-domain constraint controller meets a torque double-domain constraint control system mathematical model, and corresponding control laws comprise an improved fuzzy wavelet network control law and an improved fuzzy wavelet network parameter self-adjusting control law; and the body attitude angle and the joint angle of the robot and the deformation coordinate and the vibration amplitude of the flexible arm are adjusted through the control torque which is generated by the torque double-domain constraint controller and subjected to double-domain constraint till the control target is achieved. According to the method, the problems of saturation effect and dynamic performance degradation of the actuator caused by insufficient consideration of double-domain constraints of the torque amplitude and the change rate of the joint driving mechanism are solved.

The invention belongs to the technical field of stage equipment boundary safety protection control, and particularly relates to a variable constraint control method for stage equipment based on risk perception and a dynamic safety domain. The characteristic that stage equipment is usually in a fixed application scene in the performance process is utilized, the inherent safety level and active protection capacity of a stage equipment system are greatly improved through tight combination of real-time collection and variable constraint, and therefore safer, more accurate and more smooth control is achieved. According to the method, a construction algorithm is embedded in software, a dynamic region division and segmentation threshold adjustment strategy is utilized, and a multi-stage braking redundancy cooperation mechanism is triggered, so that the anti-interference capability and fault tolerance performance of the control system are effectively enhanced, the implementation cost is low, a large amount of manpower and material debugging can be saved, and the system is suitable for large-scale popularization and application. And a high-precision and high-robustness safety control scheme is provided for large stage machinery such as a seat vehicle platform and a rotating stage.

The invention discloses an unmanned ship target tracking constraint control method based on an exponential time-varying performance function, and relates to the technical field of state tracking control, in particular to the technical field of performance constraint control, comprising the following steps: step (1), establishing an unmanned ship motion three-degree-of-freedom mathematical model; step (2): constructing an exponential time-varying function; (3) constructing an exponential time-varying performance function; (4) introducing a time-varying auxiliary function; (5) designing a transfer function; (6) designing a fixed time performance constraint heading controller based on an exponential time-varying performance function; (7) designing a fixed time performance constraint surging controller based on an exponential time-varying performance function; and (8) performing simulation verification. According to the method, mainly starting from the design of a novel time-varying performance function, the problem that the state error of the traditional performance function constraint control at the initial moment is limited by the performance boundary is solved, so that the transient performance and the steady-state performance of the state tracking error of the unmanned ship are remarkably improved; and the overall control performance of unmanned ship target tracking control is further improved.

The invention discloses a random micro-geometric constraint virtual fixture, a dynamic control method and a system, and the random micro-geometric constraint virtual fixture is characterized in that the geometric form of the virtual fixture can be given in an analytical form, and at least two orders are differentiable; under the condition that the geometric form of the constraint only depends on the spatial position, a scalar constraint equation and a constraint control quantity of the virtual fixture are defined, a multi-constraint joint Jacobian matrix is constructed, and reference constraint control input is calculated by adopting PD control based on a constraint control expected value and a constraint control error value. According to the arbitrary micro-geometric constraint virtual fixture dynamic control method, null space control input of a mechanical arm is calculated based on a dynamic model, reference constraint control input is calculated through a virtual fixture, and compensation is carried out after estimated torque is projected to a task space corresponding to virtual fixture constraint through a disturbance observer. According to the virtual fixture, the problems of poor universality and heavy calculation burden are solved, calculation is simplified, and the universality is improved.

The invention provides a flexible intelligent material driver output constraint control method considering butterfly-shaped hysteresis input for an output constraint flexible intelligent material driving system with butterfly-shaped hysteresis input, aims to realize high-precision control in different application scenes, and comprises the following steps of: on the basis of a traditional KP model, selecting a KP model; according to the invention, a new butterfly-shaped KP (Butterfly Kranoselskii-Pokrovskii, BKP) kernel is obtained through derivation, and the KKP (Butterfly Kranoselskii-Pokrovskii, BKP) kernel is used as a kernel of the KKP. A new BKP model is established to describe butterfly hysteresis in the flexible intelligent material driver by performing weighted stacking on the BKP core; an unknown time delay function in the system is approached by using a radial basis function neural network and a finite coverage lemma, and the time delay problem of the control system is solved; a high-gain K-filter is designed to overcome the problem that the state in the system cannot be measured, and the problem of output constraint control of the butterfly hysteresis system is solved by combining a barrier Lyapunov function and an adaptive dynamic surface output feedback control algorithm; a butterfly pseudo-inverse algorithm is designed, the requirement for solving a hysteresis inverse model is avoided, and butterfly hysteresis nonlinearity is weakened to a great extent. Compared with a traditional control scheme, the method has a better effect on tracking performance and tracking errors, the tracking errors are effectively reduced, the control precision is remarkably improved, and precise control over the intelligent material driving system is achieved.

A method of controlling a robot manipulator for operating in a shared workspace with human(s) is provided. The method includes: determining a safety control set with respect to a safety condition between selected part(s) of the robot manipulator and selected part(s) of the human(s) using a safety control function: determining a hard constraint control set with respect to hard constraint(s) in trajectory tracking in DOF(s) of a component of the robot manipulator for a task using a hard constraint function: determining a soft constraint control set with respect to soft constraint(s) in trajectory tracking in DOF(s) of the component for the task using a soft constraint function: and performing control input optimization based on the safety control set. the hard constraint control set and the soft constraint control set to determine a control input for controlling the robot manipulator. In particular, the safety control function is configured to determine the safety control set: based on a control model for the robot manipulator that is configured in a control affine form based on a control mode of the robot manipulator, and for each part pair of part pair(s) of a selected part of the selected part(s) of the robot manipulator and a selected part of the selected part(s) of the human(s): based on a safety distance function associated with the part pair which corresponds to a control barrier function, and based on a sliding manifold associated with the part pair configured based on the safety distance function and a relative degree of the safety distance function with respect to the control input to the robot manipulator.

The invention provides a finite time position tracking control method of a magnetic suspension system with output constraint, which comprises the following steps of: establishing a mathematical model of the magnetic suspension system, determining an error system, and obtaining upper and lower bounds of suspension air gap constraint and system state information; designing a fractional obstacle Lyapunov function by considering upper and lower bounds of suspension air gap constraint, and solving partial derivative to obtain a constraint processing mechanism function; designing a continuous finite time state feedback constraint controller by using system state information based on a constraint processing mechanism function by applying a finite time control technology and a homogeneous system theory; and based on the constraint processing mechanism function, when the system speed state information cannot be measured, designing a non-smooth filter, and designing a finite time output feedback controller by using the filter output information and the system output information. Unified finite time control of the magnetic suspension system under symmetric / asymmetric suspension gap constraint is realized, and the method has high tracking precision, strong anti-interference robustness and engineering practicability.

A vehicle includes a vehicle engine, a steering control unit, an on-board sensor network and a navigational constraint control system. The vehicle engine generates a torque output of the vehicle. The steering control unit controls a steering angle of the vehicle. The on-board sensor network is programmed to detect external objects within a detection zone. The navigational constraint control system has a memory for storing a path index for the vehicle's navigation. The processor is programmed to determine a reference trajectory from the path index. The processor is further programmed to calculate navigational constraints for the determined reference trajectory to determine a nominal trajectory based on information detected by the on-board sensor network. The processor is programmed to control at least one of the vehicle engine and the steering control unit in accordance with the nominal trajectory.

The invention discloses a mechanical arm dynamic constraint control method and system oriented to model uncertainty compensation, and the method specifically comprises the steps: building a mathematical model of a mechanical arm system, and introducing a barrier function to convert a state constraint control problem of the system into a stability control problem; designing a neural network estimator based on the multilayer feedforward neural network, and estimating matching and non-matching endogenous disturbances suffered by the system; designing a disturbance observer based on a neural network estimator, and estimating other matching and non-matching disturbances of the system; designing a mechanical arm dynamic constraint intelligent controller and a neural network adaptive law; and selecting an initial value of a neural network weight parameter, the adaptive law matrix and a controller parameter, and carrying out dynamic constraint control on the mechanical arm. According to the method, the uncertainty of the model can be effectively compensated, meanwhile, high-precision trajectory tracking is achieved, it is strictly guaranteed that the system state does not exceed the dynamic constraint range, and the control precision, adaptability and reliability of the mechanical arm system under the complex working condition are improved.

This disclosure provides a method and system for selecting the site of pumped storage power stations based on spatial constraints and elastic buffers, relating to the field of data processing technology. The method includes: acquiring a set of spatial constraint elements corresponding to the pumped storage power station; determining the constraint control rules corresponding to each spatial constraint element in the set; applying range constraints to each associated spatial constraint element based on the constraint control rules; generating at least one elastic buffer corresponding to each spatial constraint element; determining engineering requirement indicators and geological assessment indicators; and filtering the elastic buffer based on the engineering requirement indicators and geological assessment indicators to obtain the target effective construction area. This solution enables differentiated management of different types of spatial constraint elements, thereby ensuring the safety of pumped storage power station construction, and allows for multi-dimensional filtering of elastic buffers to determine the target effective construction area, ensuring the accuracy and practicality of the target effective construction area.

The invention discloses a piezoelectric driving system constraint control method based on a predetermined time observer, and the method comprises the steps: designing a predetermined time interference observer in combination with a predetermined time performance function, and guaranteeing that an interference estimation error is converged to a bounded range within a predetermined time; a state conversion function is designed based on the obstacle Lyapunov function, so that the system output can also realize preset time output constraint under the condition that the initial state does not meet the constraint condition; a predetermined time adaptive controller is designed by using a neural network approximation technology, a dynamic surface control technology, a constraint control technology and a predetermined time interference observer technology, so that a closed-loop system realizes predetermined time stability. The problem that an existing disturbance observer cannot be used for preset time control is solved, and the assumption that initial conditions of constrained variables need to meet constraint conditions in constraint control is avoided.

The invention discloses a unified design method for a suboptimal controller of an aircraft system under multiple constraints, and the method comprises the steps: carrying out the modeling of an aircraft system and various constraint conditions in a control process; secondly, converting the aircraft system model into a form of an affine nonlinear system, and representing various constraints as state inequality constraints, input amplitude inequality constraints or input time delay constraints; then, respectively converting the state inequality constraint and the input amplitude inequality constraint into state equality constraints; meanwhile, a system containing input time delay is converted into a system without input time delay; then, establishing an unconstrained augmentation system comprising a no-input time-delay system and state equality constraints; and finally, designing a sub-optimal controller based on reinforcement learning for the unconstrained augmentation system by adopting an execution-evaluation network framework. By means of the multi-constraint control method, various constraints can be processed at the same time, and the multi-constraint control method is high in universality and can be used for diversified actual application scenes.

The invention discloses an interconnected autonomous vehicle formation dynamic constraint control method based on TSSZNN-DC1 / 2. The method comprises the following steps: constructing a dynamic constraint control system of an interconnected autonomous vehicle formation; and constructing a TSSZNN-DC1 discrete model and a TSSZNN-DC2 discrete model, and realizing more optimized dynamic constraint control of the interconnected autonomous vehicle formation under a certain condition. According to the method, a time-varying bounded attenuation coefficient based on topology feedback is designed and adopted in the design of a TSSZNN-DC1 discrete model and a TSSZNN-DC2 discrete model, so that the model has a higher convergence speed, meanwhile, the system burden caused by overlarge data is reduced, and meanwhile, a strong bounded constraint function based on error norm gain is designed; dynamic constraint control is carried out on the vehicle formation, the formation condition in an actual traffic scene is better met, the step-by-step gain coefficient based on errors is adopted, the anti-interference performance of the model is enhanced, and the model has the advantages of being high in convergence speed, high in precision, low in time delay, high in anti-interference capacity and the like.

The present application relates to biped robot control technical field, especially relate to a kind of robust constraint tracking control method of biped robot based on parameter optimization.The present application uses improved inverted pendulum model, while making full use of the advantages of single mass model, still can reflect the important characteristics of biped robot, avoid a series of errors and interference problems due to model oversimplification.The key parameters of the improved inverted pendulum model are set to be variable in the present application, which is convenient for adjusting its dynamic characteristics.The present application designs a kind of robust constraint control method, considers the motion equation of the limited mechanical system of equality constraint and inequality constraint, and makes the control input satisfy Gauss principle and d'Alembert principle, so as to produce moderate control force in the real world to meet system performance.

The application discloses a mobile manipulator control method and device based on online learning and fuzzy neural dynamics, and relates to the technical field of mobile manipulator control. The method comprises the following steps: acquiring an actual pose of an end effector, a desired pose trajectory and joint speed; introducing an excitation signal formed after superimposing random noise, updating a current Jacobian matrix estimation value of the mobile manipulator; inputting each data into a fuzzy neural dynamic solver; the fuzzy neural dynamic solver is configured to take a quadratic form as an optimization objective, take a differential kinematics tracking equation as an equality constraint, and take a non-convex feasible region as an inequality constraint; and finally outputting a control signal of the joint speed obtained by solving the fuzzy neural dynamic solver to drive the mobile manipulator to move. The application solves the technical problems of low control precision of the mobile manipulator under the conditions of parameter uncertainty and non-convex constraints without an accurate prior model, and realizes high-precision model-free pose control.

The application relates to the field of automatic control of intelligent agricultural equipment, and particularly discloses a constraint control method for an intelligent mower based on fixed-time convergence. First, a kinematic model and a heading subsystem of a differential steering intelligent mower are established; a fractional time conversion function is constructed to complete time dimension conversion scheduling of the heading subsystem; a nonlinear mapping function is used to convert the constrained heading system into an unconstrained system; and finally, a nonlinear heading constraint controller based on the backstepping method is designed to realize fixed-time convergence. The application can guarantee that the heading angle converges to the expected value within a fixed time, and the constraint boundary is not exceeded throughout the whole process, thereby improving the response speed, control accuracy and operation safety of the heading control of the intelligent mower.

The present invention provides a two-stage speed control method for a belt conveyor, which relates to the field of belt conveyor control and specifically includes the following steps: establishing a dynamic model with equality constraints; treating the speed of the control target as a constraint and designing robust control for the equality constraint portion in conjunction with the dynamic model; transforming the dynamic model so that it conforms to the state form of the inequality constraints; performing inequality constraint control design on the transformed dynamic model; and performing simulation verification on the belt conveyor system. The technical solution of the present invention overcomes the problem in the prior art of being unable to accurately limit the speed error of a belt conveyor system to within a desired range.

The application discloses a kind of transformer fault ride-through control method, system, equipment and medium, belong to the technical field of fault ride-through control, method includes: obtaining grid-connected voltage constructs observation model and solves stable phase;Multi-dimensional constraint model is constructed, locks amplitude when overcurrent and anchors phase, simultaneously triggers integral freezing mechanism.System includes state observation module, phase solving module, constraint model configuration module, instruction generation module, collaborative control module.The application constructs virtual magnetic flux observation model, uses integral filtering characteristic to filter out noise and analyzes high robustness synchronous phase;Combined with multi-dimensional constraint control model, lock current amplitude under current limiting condition and force anchor phase, simultaneously trigger integral freezing mechanism to block error accumulation.Thereby effectively solve the problem of transient synchronization instability, inhibit the control signal dithering, and eliminate the oscillation phenomenon in fault recovery period.

The invention discloses a performance constraint control method and system for multi-robot collaborative carrying of large workpieces. The method comprises the steps that firstly, a unit quaternion is adopted to establish a coupling dynamic model containing closed-chain constraint under a task reference coordinate system; secondly, designing a completely distributed finite time observer, and performing consistency estimation on a global reference trajectory only through neighborhood communication; secondly, designing a consistency indicator function based on the estimated value, gradually activating a performance constraint function only after an observation error is converged so as to apply transient and steady-state performance boundaries, and generating an expected motion state of each robot; and finally, designing a distributed robust adaptive controller to realize trajectory tracking. According to the method, singularity is avoided through quaternion modeling, controller design of a task reference coordinate system is achieved through rigid body transformation, dependence on a centroid coordinate system is avoided, the requirement for a priori track is eliminated through a distributed observer, constraint conflicts are avoided through a strategy of'feasibility first and then constraint ', and the robustness of the system is improved. And the safety, the precision and the robustness of collaborative carrying are effectively improved.

The application discloses a control method of an under-actuated two-wheel mobile robot based on constraint following, and the method comprises the following steps: a dynamics model of the under-actuated two-wheel mobile robot is established based on a Lagrange modeling method; a motion control problem of the under-actuated two-wheel mobile robot is expressed as a constraint following control problem, a constraint mathematical model is established according to expected control performance, and the constraint mathematical model is expressed in the form of servo constraint; the servo constraint is analyzed, a first-order or second-order servo constraint is obtained, and a controller not considering initial constraint deviation is designed; based on the controller not considering initial constraint deviation, an additional control action is added to process possible initial constraint deviation, a robust controller is designed, and a robust control strategy is constituted; and the complete constraint and non-complete constraint control design is constituted by taking the constraint following as a guide. The application can solve the under-actuated control design problem of the two-wheel mobile robot, the control design does not need auxiliary variables or pseudo variables, and the control efficiency and control precision are improved.

The application discloses a kind of active suspension nonlinear mapping constraint control methods based on fixed time, comprising the following steps: step 1: constructing nonlinear mapping function: by nonlinear mapping function, asymmetric time-varying constraint to system state variable is realized by coordinate conversion;The application is by constructing nonlinear mapping function to carry out coordinate conversion, and the constraint problem of original system state is converted into the bounded problem of new system state, while realizing asymmetric time-varying state constraint, avoid the limitation of feasibility condition to control design.On this basis, combined with fixed time stability theory to construct backstepping controller, so that closed-loop system realizes fixed time stability under time-varying asymmetric constraint condition, and its convergence time avoids dependence on initial state, so as to improve the rapidity, robustness and safety of active suspension system.

This invention relates to a management method, system, and electronic equipment for power grid systems, belonging to the technical field of power grid systems. The invention aggregates the electricity consumption data predicted by the load forecasting model of each edge node and introduces a constraint theory. Key constraint nodes are selected based on node importance and controllability. Non-constrained nodes synchronize data with the constraint nodes. Finally, based on the constraint optimization results and the electricity consumption data predicted by the load forecasting model of each edge node, the power supply in the target area is dynamically coordinated and optimized. Addressing the complexity of multi-node power grids, this invention introduces constraint control theory, selecting key constraint nodes based on node importance and controllability. Non-constrained nodes synchronize with the constraint nodes through a constraint matrix, significantly reducing the control dimension and communication burden. In practical applications, the online learning mechanism enables the controller to adapt to changes in grid topology and fluctuations in operating conditions in real time, achieving efficient frequency control.

The invention discloses a dual constraint control method, device and equipment of an unmanned aerial vehicle, a storage medium and a computer program product, and relates to the technical field of unmanned aerial vehicle control, and the method comprises the steps: building a model constraint optimization problem of model parameter estimation and a controller constraint optimization problem of controller parameter estimation based on an expected output signal of the unmanned aerial vehicle; constructing a first Lagrange function based on the model constraint optimization problem, and constructing a second Lagrange function based on the controller constraint optimization problem; performing dual conversion on the first Lagrange function to obtain a model parameter estimation value; performing dual conversion on the second Lagrange function to obtain a controller parameter estimation value; and calculating a target control quantity of the unmanned aerial vehicle based on the model parameter estimation value and the controller parameter estimation value, and controlling the unmanned aerial vehicle based on the target control quantity. The generated control quantity is determined through the Lagrange function and dual optimization, and the control performance of the unmanned aerial vehicle under the constraint condition is improved.

The invention relates to the technical field of cable welding, and discloses an in-cabinet cable self-adaptive welding device with an elastic restraint mechanism, the in-cabinet cable self-adaptive welding device comprises a supporting base, the top end of the supporting base is fixedly provided with a six-axis manipulator mechanism, and the top end of the six-axis manipulator mechanism is connected with an elastic restraint supporting mechanism and two restraint control mechanisms; by integrating the elastic constraint supporting mechanism and the constraint control mechanism, motion interference is effectively avoided, it is ensured that efficient and accurate welding operation is carried out in a compact electrical cabinet, and the risks of equipment collision shutdown and welding track deviation are reduced; and the elastic constraint supporting mechanism is combined with the six-axis manipulator mechanism, so that the dynamic adjustment and accurate fixation of the cable angle are realized. The first driving motor drives the positioning gear to rotate on the positioning gear ring, the elastic restraining base can flexibly rotate along the supporting ring, the cable is accurately adjusted to the needed angle, and the cable butt joint precision and consistency are improved.

The application discloses a robot contact force constraint control method based on a control barrier function, and an affine nonlinear system model containing contact force is constructed based on a kinematics model, a dynamics model and a contact force model of the robot, which has better dynamic performance compared with a single contact force model, the control barrier function is applied to robot contact force safety constraint control, compared with existing position safety constraint control methods, the application of the control barrier function in the robot field is widened, the control barrier function can be combined with various existing force-position control methods, has good contact force constraint effect, high flexibility, good real-time performance, strong robustness, simple application, and effectively improves the problem that traditional force-position control is difficult to constrain contact force.

This application relates to a dynamic safety domain prediction and adaptive constraint control method for human-robot collaboration in live-line work, applicable to the field of automatic control technology. The method includes: acquiring robot operating state data, human state data, and a spatial model of the live conductor; performing coordinate transformation and time alignment on the operating state data, state data, and spatial model to obtain a target data frame; determining the human's intent confidence level, predicting the human's actions, and obtaining the predicted position and prediction uncertainty information; constructing the human's future occupancy area; generating a dynamic safety domain and determining the target minimum safety distance; constructing control constraints based on the dynamic safety domain and the target minimum safety distance; modifying the acquired nominal control commands according to the control constraints to obtain target control commands, and controlling the robot's operation according to the target control commands. This method can improve the safety of robot operation control.

The present application provides an air-cushion vehicle multi-constraint control method based on a preset performance function with composite error transformation, which relates to the technical field of air-cushion vehicle motion control. The method establishes a motion mathematical model of a fully-lifted air-cushion vehicle, designs an observer to estimate and compensate for system uncertainties in real time, and introduces a non-linear mapping function and a biological excitation model to handle asymmetric time-varying constraints; based on the preset performance function with composite error transformation, a position control law and a speed control law are designed, effectively avoiding the problems of side-slip and tail-swing during high-speed navigation, and improving the trajectory tracking accuracy and system stability; in addition, through the disturbance observer and the composite error transformation technology, the dependence on initial conditions is eliminated, and the robustness of the system is enhanced. The present invention can significantly improve the trajectory tracking accuracy, stability and safety of the air-cushion vehicle in complex environments, is applicable to various complex environments such as water surfaces, land, swamps, etc., and has broad application prospects.

The invention provides a time constraint control method for multiple uncertainties of a p-normative system, and relates to modeling of the nonlinear system and signal bounded judgment lemma design with more loose parameter constraint. According to the method, the requirements of system stability control on high precision, high speed, low energy consumption and the like are comprehensively analyzed, and a controller algorithm is designed based on a Lyapunov theory system and by fusing a sign function, a Nussbaum function and a self-adaptive backstepping technology. The method comprises the following steps: firstly, establishing a p normative nonlinear system model with multiple uncertainties; introducing coordinate transformation, and designing a corresponding adaptive law and a controller algorithm by means of a backstepping technology, a sign function and a Nussbaum function; secondly, establishing an event triggering mechanism and a controller which meet the requirements of the p standard type nonlinear system; and finally, selecting a proper Lyapunov function, and proving the system stability by using a signal bounded judgment lemma and a finite time stability lemma. The method can be used for a ship steering system.

The invention relates to a steering under-constrained multi-axle vehicle sensitivity analysis and transverse dynamics constraint control method, which comprises the following steps of: calculating an ideal yaw velocity and a side slip angle when a multi-axle vehicle tracks an expected path according to expected path information, vehicle real-time position information and vehicle state information; establishing a multi-axle vehicle transverse dynamic model and a state tracking-oriented decoupling control model; calculating the sensitivity index of each rotation angle input to the yaw velocity and the side slip angle of the vehicle under different working conditions, analyzing the influence degree and the coupling relation of each rotation angle to the transverse dynamic performance of the vehicle, and obtaining a key control rotation angle; constructing an integral sliding mode state constraint controller based on the obstacle Lyapunov function; and according to a multi-axle vehicle turning angle signal output by the controller, an instruction is issued to the actuator, so that the turning angle of each axle is adjusted to a required angle, the motion state of the vehicle is changed, and tracking control is realized. The method can ensure safe and stable driving of the vehicle while realizing accurate tracking control of the multi-axle vehicle.