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42 results about "Iterative learning algorithm" patented technology
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High potential user buying intention prediction method based on big data user behavior analysis
ActiveCN107944913AReduce data redundancyPrecision marketingCharacter and pattern recognitionMarket data gatheringIterative learning algorithmData set
The invention provides a high potential user buying intention prediction method based on big data user behavior analysis. The high potential user buying intention prediction method comprises the following steps: 101 data preprocessing: the historical behavior data set of the e-commerce user is preprocessed; 102 sample defining and marking: samples are constructed with the interacted user product pairs to act as the keywords according to the historical consumption behavior of the user; 103 division of a training set and a test set: the historical data are divided into the training set and the test set by using a time window division method; 104 feature construction: feature engineering construction of the historical behavior data of the user is performed; and 105 algorithm design and implementation: feature selection of the feature group and unbalanced data processing of the data set are performed and then the final result of two-layer model iterative learning algorithm prediction is put forward. The prediction model is established on the basis of the historical behavior data of the e-commerce user of the time span of 45 days so that whether the user places an order of the commodityin the candidate commodity set P in the following 5 days can be predicted.
Owner:上海普瑾特信息技术服务股份有限公司
Method for creating expert knowledge base for automatically training lower artificial limbs
InactiveCN102119877ASignificant progressGet rid of adverse effects of controlSpecial data processing applicationsProsthesisIterative learning algorithmMicrocontroller
The invention discloses a method for creating an expert knowledge base for automatically training lower artificial limbs, which relates to lower artificial limb control. All hardware comprises an artificial limb knee joint, an acceptance chamber, a pelma pressure sensor, a control device and a control circuit, wherein the control device comprises a cylinder, a piston, an air channel, a pin valve and a straight stepping motor. Pelma pressure signals from the pelma pressure sensor are collected and calculated by a single chip in the control circuit, and an iteration study algorithm is adopted to create the expert knowledge base used for controlling the artificial limb knee joint. A portable acquisition system is adopted in the method. The calculation is automatically accomplished by the single chip, which is accurate and efficient. The iteration study method is adopted to find out the minimum period phase difference of the walking status of the artificial limbs and health limbs, and people who wear the artificial limbs can walk without the assist of professionals. The system can automatically generate the optimal symmetry of knee joint controlling amount at different walking speeds, so that the expert knowledge base for automatically training lower artificial limbs can be created.
Owner:HEBEI UNIV OF TECH
Iterative learning algorithm for trajectory tracking of wheeled robot
InactiveCN103631142ASolve the selection problemEasy to trackAdaptive controlPosition/course control in two dimensionsIterative learning algorithmProportion integration differentiation
The invention relates to a method for controlling trajectory tracking of a mobile robot, which solves the problem of selection of gain parameters. The method comprises the following steps: (1) a state of an actual trajectory is participated in iterative operation each time on the basis of conventional proportion integration differentiation (PID) iterative learning control, so that the control effect is close to an expected value; (2) a form of a learning gain matrix in a model algorithm learning law is introduced into a learning gain matrix of a PID algorithm. The problem that the gain matrix is difficult to acquire is solved. According to the controller, the trajectory tracking of a wheeled robot can be well realized.
Owner:TIANJIN POLYTECHNIC UNIV
Iterative learning correction-based aero-engine intelligent rotation peed control method
ActiveCN109162813AGuaranteed stabilityGuaranteed generalization abilityTurbine/propulsion fuel controlIterative learning algorithmAviation
The invention discloses an iterative learning correction-based aero-engine intelligent rotation speed control method. The method comprises the following steps of: establishing an NARMA-L2 model of a rotation speed control system by adoption of a neural network; and designing an iterative learning algorithm-based online rotation speed correction model by combining the NARMA-L2 model, so as to obtain an aero-engine rotation speed controller with self-regulation ability in a certain working condition range in envelopes. The method is capable of solving the problems that difficulties exist in traditional neural network-based prediction model establishment and online control rate solution and control quality of controllers expanded and applied in envelopes is reduced, is suitable for controlling rotation speeds of engines at different working points in certain flight envelopes, and has positive promotion effect for eliminating steady-state errors of engine control systems and improving engine rotation speed control quality.
Owner:NANJING UNIV OF AERONAUTICS & ASTRONAUTICS
Spacecraft ACS on-orbit reconstruction method oriented to multi-task multi-index optimization constraints
ActiveCN108594638AImprove task performanceImprove failure response capabilitiesAdaptive controlIterative learning algorithmTask completion
The invention discloses a spacecraft ACS on-orbit reconstruction method oriented to multi-task multi-index optimization constraints, and belongs to the technical field of spacecraft attitude control.According to the method, for a spacecraft with on-orbit time relevant multi-task constraint, the state and the motion under the multi-task constraint are defined, a utility function about the state-motion is designed and a performance index function is determined, and then an optimal reconstruction strategy in the form of the HJB equation is obtained. Aiming at the problem that the HJB equation isdifficult to solve accurately, an approximate solution method based on the BOADP is provided, the task network and the energy consumption network are designed for estimating two performance index functions, and the convergence of neural network estimation errors is achieved through an iterative learning algorithm, so that an approximate solution of the HJB equation is achieved, and then an optimal reconstruction strategy is obtained, and the maximization of the task earnings is achieved by controlling the energy consumption as few as possible. According to the invention, the multi-task completion capability and the fault response capability of the spacecraft are improved.
Owner:NANJING UNIV OF AERONAUTICS & ASTRONAUTICS
Linear servo system mechanical resonance control method
InactiveCN105929865ASolve the problem of resonance suppressionSimple control methodAC motor controlMechanical oscillations controlIterative learning algorithmSystem requirements
The invention discloses a linear servo system mechanical resonance control method which belongs to the field of mechanical equipment control. According to a control method in the prior art, on-line automatic adjustment of control parameters of a notch filter cannot be realized; a mechanical resonance suppression effect is poor; and the system requirements of high speed and high precision linear servo cannot be met. The invention provides a secant-based iterative learning algorithm to optimize the control parameters of the notch filter to solve the problem of resonance suppression of a linear servo system. The control method provided by the invention is simple, practical and highly precise.
Owner:ZHEJIANG SCI-TECH UNIV
Static pressure control method of variable air volume (VAV) air-conditioning system fan on basis of iterative learning
ActiveCN104850679AImplement trackingSmall overshootSpace heating and ventilation safety systemsLighting and heating apparatusIterative learning algorithmVariable air volume
The invention discloses a static pressure control method of a variable air volume (VAV) air-conditioning system fan on the basis of iterative learning and proposes that an iterative learning control algorithm is applied to the static pressure control of the VAV air-conditioning system fan. The static pressure control method comprises the following steps: firstly, establishing a state-space model of the VAV air-conditioning system fan, furthermore, converting the continuous state-space model into a discrete state-space model of a system, and verifying the astringency of the control method on the basis of the model to obtain a system astringency condition; and secondarily, according to the obtained system astringency condition, designing a specific iterative learning algorithm, and proving the effectiveness of the algorithm through a simulation experiment. Proved theoretically, the static pressure control method has the characteristics that the steady-state performance and the dynamic performance of the system are greatly improved than a traditional PID (Proportion Integration Differentiation) algorithm, and the static pressure control method has important theoretical guiding significance and practical value.
Owner:深圳市华富可节能技术有限公司
Temperature control method for continuous casting billet induction heating process, based on iterative learning control
ActiveCN104407642ASuppress uncertaintySuppress mismatchTemperature control using electric meansIterative learning algorithmTemperature control
The invention discloses a temperature control method for a continuous casting billet induction heating process, based on iterative learning control. The method comprises the steps that historical process data is preprocessed, and an input and output trajectory of the latest operation process is taken as a reference trajectory; a historical data trajectory subtracts the reference trajectory, a large amount of nonlinearity is removed, and a perturbation model variable is obtained; a revised dataset is processed through the partial least-squares regression method, and a linearized perturbation model around the reference trajectory is obtained; the control input voltage of the operation is calculated according to a learning law of iterative learning control; the control input voltage obtained through calculation is applied to the induction heating process, so that the billet outlet temperature of the process is obtained; newly obtained process data is added into a historical database, an old data is removed, and the next iteration cycle begins. The method sufficiently utilizes the characteristic of the repeatability of the induction heating process, introduces the iterative learning algorithm, and enables an output temperature trajectory to furthest track an expected temperature trajectory.
Owner:杭州四达电炉成套设备有限公司
Intelligent weighing control method based on genetic algorithm and iterative learning method
InactiveCN101414157AImprove robustnessStrong real-timeAdaptive controlIterative learning algorithmControl signal
The invention discloses an intelligent weighing control method based on a genetic algorithm and an iterative learning method. The weighing control method is characterized by comprising the following steps: firstly, substituting a difference value ek(t) between an actual weight value measured at any time t and an expected value to an iterative learning algorithm formula as an iteration deviation; then computing a control semaphore in a real-time manner according to the characteristic that the iterative learning control method which is designed and optimized by the genetic algorithm has stronger robustness, and outputting the control semaphore to a valve driving mechanism to achieve weighing control. In the weighing control method, time for controlling opening of a valve is determined only according to the weighing derivation without depending on the material level change of a storage bin and the random change of material flow rate in every moment; and the method has the advantages of good real-time characteristic and high control precision.
Owner:PLA UNIV OF SCI & TECH
Method for creating expert knowledge base for automatically training lower artificial limbs
InactiveCN102119877BImprove tracking performanceSignificant progressSpecial data processing applicationsProsthesisIterative learning algorithmMicrocontroller
Owner:HEBEI UNIV OF TECH
Stable operation process control method for free piston engine
ActiveCN109488471AAvoid influenceImprove job stabilityElectrical controlMachines/enginesIterative learning algorithmFree-piston engine
The invention discloses a stable operation process control method for a free piston engine. The control method comprises the following steps of: monitoring a pressure signal and a displacement signalin a free piston engine cylinder in real time; utilizing an iterative learning algorithm to control a compression stroke end point by a controller according to a cylinder pressure signal and the displacement signal; when the engine works in expanding stroke, estimating energy generated by current cyclic combustion by the controller according to in-cylinder combustion peak value pressure; giving power generation amount of a current circulating stroke motor according to the estimated current cyclic combustion energy, thereby guaranteeing that a piston assembly can move to a predetermined position to start next cycle under influences of a random combustion cyclical fluctuation. The control method disclosed by the invention can overcome inherent combustion cyclical fluctuation of a gasoline internal combustion engine, so that continuous and stable operation of the free piston engine is guaranteed.
Owner:NANJING UNIV OF SCI & TECH
Mechanical arm accurate path planning method based on man-machine cooperation and visual inspection
ActiveCN114536346AAvoid difficultyAvoid workloadProgramme-controlled manipulatorTotal factory controlIterative learning algorithmVision based
The invention discloses a mechanical arm precise path planning method based on man-machine cooperation and visual inspection. The method specifically comprises the steps that an initial path of a workpiece to be machined is obtained based on a visual assistance algorithm, and tracking error calculation of an end effector is detected in real time; the operation path point deviation and interaction force data of the mechanical arm are obtained through bottom layer control design; according to the obtained tracking error, the mechanical arm operation path point deviation and the interaction force data, iterative learning is carried out according to a set spatial iterative learning algorithm updating rate to update a path; and the mechanical arm starts to track along the new path coordinates until the path tracking effect is acceptable, and the accurate coordinates of the workpiece machining path in the space are obtained. According to the method, the problems of high program design difficulty, large workload and the like caused by offline teaching programming can be avoided, and the problem that the machining path of the shielded part of the workpiece cannot be detected under a traditional visual method can also be solved.
Owner:SOUTHWEST JIAOTONG UNIV
Superspeed wire rod extension processing equipment control system
The invention discloses a superspeed wire rod extension processing equipment control system. The superspeed wire rod extension processing equipment control system comprises pass mechanisms, a rolling mechanism and a control device; the control device comprises a reference speed given module and a plurality of pass control units; in each pass control unit, the reference speed given module is connected with each parallel connection gain module; the parallel gain module is connected with a first positive input end of a speed control convergence node; the output of a position error controller is connected with a first negative input end of the speed control convergence node; the output end of the speed control convergence node is connected with an electrical transmission mechanism; the pass control unit also comprises an iteration controller; series connection gain initial value of a mth pass is set as shown in the formula in the specification by using an iteration learning law with reference to (1) and (2); and based on a 2D dynamic model, the speed compensation control variable iteration learning arithmetic control rate of moment t of a kth processing cycle of the m pass is shown inthe specification with reference to (3) and (4). The system has high tracking control accuracy.
Owner:ZHEJIANG UNIV OF TECH
Two-phase orthogonal inversion power source control method enabling delay compensation function
ActiveCN107017796AImprove responsivenessQuality is easy to controlAc-dc conversionIterative learning algorithmControl system
The present invention discloses a two-phase orthogonal inversion power source control method enabling a delay compensation function. According to the method, an iterative learning algorithm is added to the feedback control link of current; the quick compensation output of the current can be realized through repeatedly applying information obtained in previous experiments, and therefore, the response performance of the output alternating current of a PWM inverter can be improved, and control quality can be also improved; as for a condition that the delay of a control system influences output current dynamic tracking performance and the stability of a system, a Smith predictor is introduced to eliminate the delay influence of the control system; and in fact, the Smith predictor estimates a lag link and makes appropriate compensation, so that a closed-loop characteristic equation does not contain the lag link, thus the dynamic characteristic and stability of the system can be improved. The control method of the present invention can significantly improve the stability and response speed of a system as for electromagnetic stirring which requires frequent positive and negative rotation alternation.
Owner:HUNAN UNIV
Air Conditioning Control System and Method Based on Variable Speed Integral PID Iterative Learning Algorithm
ActiveCN105627529BSmall steady state errorImprove dynamic performanceMechanical apparatusSpace heating and ventilation safety systemsIterative learning algorithmDifferentiator
Owner:XI'AN UNIVERSITY OF ARCHITECTURE AND TECHNOLOGY
A Control Method of Two-phase Orthogonal Inverter Power Supply with Delay Compensation Function
ActiveCN107017796BImprove responsivenessQuality is easy to controlAc-dc conversionIterative learning algorithmControl system
Owner:HUNAN UNIV
Servo motor control method and system based on fractional iterative learning
ActiveCN108736785ARunning speed is stableImprove real-time performanceElectronic commutation motor controlVector control systemsIterative learning algorithmThree-phase
The invention discloses a servo motor control method and system based on fractional iterative learning. The method comprises the following steps: using a fractional iterative learning to track a set motor operation speed value to obtain a speed controlled quantity; carrying out coordinate transformation on the speed controlled quantity through a matrix transform method so as to obtain the three-phase current control value of a motor; detecting three-phase current for motor operation; obtaining the weak current signal of motor three-phase voltage according to the three-phase current control value of the motor and the three-phase current for motor operation; and carrying out amplification processing on the weak current signal of motor three-phase voltage to obtain the strong current signal of motor three-phase voltage so as to control a servo motor. The system comprises a speed control module, a vector transformation module, a current detection module, a current control module and an inverter module. The system is high in instantaneity, the motor can keep stable operation speed under the condition of disturbance, the reliability is high, and the system can be widely applied to technical field of servo motor control.
Owner:GUANGZHOU HKUST FOK YING TUNG RES INST
LC serial-type three-phase PWM rectifier current iterative learning control method
ActiveCN104836465AImprove responsivenessOvercoming the capacitive inertial damping effectAc-dc conversionIterative learning algorithmPower compensation
The invention discloses an LC serial-type three-phase PWM rectifier current iterative learning control method. The power converter not only can rectify output power to power a load, but also can compensate reactive and harmonic currents generated by an adjacent nonlinear load. For the compensation for the adjacent nonlinear load, effective integration of a PWM rectification function and a power compensation function is achieved by using an LC serial filter, and high-power reactive and harmonic compensation output is realized. Through adoption of an iterative learning algorithm, the response performance of the control system is improved, and the capacitive inertia damping effect of the LC serial filter is overcome.
Owner:新源智储能源发展(北京)有限公司
Spacecraft formation orbit fault-tolerant control method based on learning neural network sliding mode
ActiveCN114879512ASolve the problem of maintaining controlInternal combustion piston enginesAdaptive controlIterative learning algorithmDynamic models
The invention discloses a spacecraft formation orbit fault-tolerant control method based on a learning neural network sliding mode, and the method comprises the following steps: 1, building a nonlinear relative dynamic model of a spacecraft formation system in consideration of space perturbation and thruster faults; 2, designing a learning neural network sliding mode observer by combining a P-type iterative learning algorithm, a radial basis function neural network model and a sliding mode algorithm, and performing robust reconstruction on a thruster fault; and 3, in combination with the learning neural network model and a sliding mode control algorithm, designing a learning neural network sliding mode fault-tolerant controller, and realizing high-precision maintenance control on nominal configuration when the spacecraft formation system is subjected to space perturbation and thruster faults.
Owner:NANJING UNIV OF AERONAUTICS & ASTRONAUTICS
Nonlinear system fault detection and estimation method and device based on adaptive iterative learning algorithm
InactiveCN113625677AConvergence vs AccuracyGood precisionProgramme controlElectric testing/monitoringIterative learning algorithmAlgorithm
The invention discloses a nonlinear system fault detection and estimation method and device based on an adaptive iterative learning algorithm. The method comprises the following steps: establishing a nonlinear continuous time system model; based on the nonlinear continuous time system model, designing a fault estimation observer of the system in continuous time; applying a fourth-order Runge-Kutta algorithm to the fault estimation observer to solve an observation system state differential equation; calculating a system state and an output estimation error of the kth iterative learning algorithm based on the solving result, calculating a virtual fault through a fault estimation algorithm, and determining a starting condition of a fault estimation observer; and using an H infinity method, designing a constraint inequality according to the bounded real lemma and the influence on the fault change rate, and solving a learning gain parameter matrix. By means of the method, the fault estimation error is effectively reduced, and the convergence speed of the fault estimation observer is improved.
Owner:HENAN UNIVERSITY
Control system for dynamic locking test of seat slide rail
PendingCN114754998ARealize self-learningRealize online controlVehicle testingMachine part testingIterative learning algorithmData acquisition
Owner:苏州市德智电子有限公司
Air conditioner control system and method based on variable speed integral PID type iterative learning algorithm
ActiveCN105627529ASmall steady state errorImprove dynamic performanceMechanical apparatusSpace heating and ventilation safety systemsIterative learning algorithmIntegrator
The invention discloses an air conditioner control system and method based on the variable speed integral PID type iterative learning algorithm. The control system comprises a subtractor, a differentiator, an integrator, a variable speed integral controller, an iterative learning controller, a storage memorizer and a pressure sensor used for detecting the value of static pressure in an air supply pipeline in an air conditioner; the output end of the pressure sensor is connected to the input end of the subtractor, the output end of the subtractor is connected to the input end of the iterative learning controller, the input end of the variable speed integral controller, the input end of the integrator and the input end of the differentiator, the output end of the integrator, the output end of the differentiator, the output end of the variable speed integral controller and the output end of the storage memorizer are connected to the input end of the iterative learning controller, and the output end of the iterative learning controller is connected to the input end of the storage memorizer and the control end of a frequency conversion can in the air conditioner. According to the air conditioner control system and method, the variable static pressure value of the air conditioner can be adjusted dynamically, and the energy saving performance of the air conditioner is good.
Owner:XI'AN UNIVERSITY OF ARCHITECTURE AND TECHNOLOGY
Distributed autonomous optimization method for cooperative reconnaissance coverage of unmanned aerial vehicle cluster
ActiveCN114200964AImprove stabilityIncrease flexibilityPosition/course control in three dimensionsIterative learning algorithmSimulation
The invention discloses a distributed autonomous optimization method for cooperative reconnaissance coverage of an unmanned aerial vehicle cluster, and the method comprises the steps: enabling earnings obtained when an unmanned aerial vehicle executes different position strategies and power strategies to be virtualized, and enabling the earnings to be virtualized to drive the autonomous decision of the action of the unmanned aerial vehicle; the position strategy and the power strategy of the unmanned aerial vehicles are optimized through a distributed autonomous iterative learning algorithm, the virtual revenue obtained by the unmanned aerial vehicle group is maximized, the unmanned aerial vehicle group can autonomously cooperate in a reconnaissance area, reconnaissance resources are reasonably distributed, the stability and the flexibility of the unmanned aerial vehicle group are improved, and the reconnaissance efficiency is improved. And the stable reconnaissance comprehensive efficiency can be kept in different environments.
Owner:NANJING UNIV OF INFORMATION SCI & TECH
Distributed optical fiber temperature prediction method based on Kalman filtering and iterative learning
ActiveCN111256873ADemodulation temperatureSave resourcesThermometers using physical/chemical changesComplex mathematical operationsIterative learning algorithmRaman scattering
The invention discloses a distributed optical fiber temperature prediction method based on Kalman filtering and iterative learning. A laser emits optical pulses, the optical pulse enters a sensing optical fiber through a wavelength division multiplexer; when the temperature changes, a backward Raman scattering signal in the optical fiber is changed along with the change; then, the optical pulse isseparated into Stokes light and anti-Stokes light through a wavelength division multiplexer; the light is converted into an electric signal through a photoelectric detector; the electric signal is acquired by an acquisition card, the acquired data of each point is processed through Kalman filtering, all sampling points are gathered together, a curve with the temperature changing along with the distance in real time can be obtained, iterative learning algorithm processing is conducted on the curve, then a temperature curve at the next moment can be obtained, and therefore, the real-time monitoring and prediction of the temperature are achieved. According to the invention, the temperature value measured by a distributed optical fiber temperature measurement system can be closer to a real value, and the temperature prediction of the next moment can be realized.
Owner:NANCHANG HANGKONG UNIVERSITY
A method for controlling the stable operation process of a free-piston engine
ActiveCN109488471BImprove job stabilityControl piston movementElectrical controlMachines/enginesFree-piston engineIterative learning algorithm
Owner:NANJING UNIV OF SCI & TECH
The optimal control method of reconstructable robot decentralized nerves based on judging identification structure
ActiveCN109581868BLighten the computational burdenSmall steady state errorAdaptive controlIterative learning algorithmRobotic systems
Owner:CHANGCHUN UNIV OF TECH
Control system for dynamic locking test of seat slide rail
InactiveCN114397099ARealize self-learningRealize online controlVehicle testingMachine part testingIterative learning algorithmData acquisition
The invention discloses a control system for a seat slide rail dynamic locking test, and the system comprises a servo module which is used for pushing a seat slide rail and a load to move at a set speed, and carrying out the expected force loading after the dynamic locking; the motion control module drives the servo module; the strain type force sensor module is used for converting and feeding back expected force; the pull rope type displacement sensor module is used for tracking and feeding back the position of the seat slide rail; the data acquisition module is used for performing high-speed acquisition on data of the sensor module; and the software module comprises an embedded program based on a P-type iterative learning algorithm. And the control system comprises a processor embedded with a real-time operating system and a host. The control system for the seat slide rail dynamic locking test can be directly applied to multi-specification seat slide rail, variable load and dynamic locking test, realizes self-learning and online control, improves data dynamic response, and is high in economic benefit.
Owner:苏州市德智电子有限公司
A Thickness Control Method for Hot Continuous Rolling Based on Improved Internal Model Controller
ActiveCN110538881BAchieve adaptiveImprove control qualityGeometric CADRoll mill control devicesIterative learning algorithmMathematical model
The invention relates to a hot continuous rolling thickness control method based on an improved internal mold controller. The method comprises the steps that a mathematical model of a machine frame hydraulic roll gap control system (HGC) is established, and the HGC system model is identified through a particle swarm optimization algorithm (PSO); a traditional internal model monitoring AGC controller is designed based on the model, and the traditional internal model monitoring AGC controller is improved into a two-degree-of-freedom controller; and an iterative learning algorithm is introduced into a monitoring AGC system based on the improved internal model controller. The iterative learning algorithm can make full use of historical cycle information of the monitoring AGC system, and modifythe control quantity of the internal model monitoring AGC system through a certain learning law, so that the monitoring AGC system automatically adapt to the model parameter mismatch condition duringhot continuous rolling. According to the technical scheme provided by the embodiments of the present invention, the control quality and robustness of the hot continuous rolling monitoring AGC systemcan be improved.
Owner:HUAQIAO UNIVERSITY
Energy consumption optimization method of unmanned aerial vehicle hierarchical mobile edge computing network based on game theory
ActiveCN113676917AImprove battery lifeSolve the problem of energy consumptionPower managementNetwork planningIterative learning algorithmSimulation
Owner:NANJING UNIV OF AERONAUTICS & ASTRONAUTICS
An Adaptive Force Tracking Control Method Based on Iterative Learning
ActiveCN113043266BAchieving Stable Force TrackingImprove robustnessProgramme-controlled manipulatorTotal factory controlIterative learning algorithmContact model
Owner:NAT INST OF INTELLIGENT ROBOTICS SHENYANG CO LTD +2
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