CN107168064B - Wheel type mobile stage robot online optimization stabilization control method - Google Patents
Wheel type mobile stage robot online optimization stabilization control method Download PDFInfo
- Publication number
- CN107168064B CN107168064B CN201710467447.3A CN201710467447A CN107168064B CN 107168064 B CN107168064 B CN 107168064B CN 201710467447 A CN201710467447 A CN 201710467447A CN 107168064 B CN107168064 B CN 107168064B
- Authority
- CN
- China
- Prior art keywords
- stage robot
- mobile stage
- wheeled mobile
- time
- control
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Active
Links
Images
Classifications
-
- G—PHYSICS
- G05—CONTROLLING; REGULATING
- G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
- G05B13/00—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion
- G05B13/02—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric
- G05B13/04—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric involving the use of models or simulators
- G05B13/042—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric involving the use of models or simulators in which a parameter or coefficient is automatically adjusted to optimise the performance
Abstract
An online optimization and stabilization control method for a wheeled mobile stage robot aims at the requirement of achieving stabilization control of the wheeled mobile stage robot under the incomplete constraint condition, firstly, a discrete time three-order dynamics model of the wheeled mobile stage robot and a randomly selected initial time limited time window control sequence are defined, a stabilization control error sequence in a time window and the gradient of the error sequence relative to a control input sequence are calculated, an updating mechanism of each sampling time control sequence is established by utilizing a Newton method, and the control input quantity at each sampling time is calculated by combining a rolling optimization control principle, so that stabilization control of the wheeled mobile stage robot is achieved. The design method has the advantages of simplicity in understanding, few setting parameters, strong universality and simplicity and convenience in online calculation, and meets the real-time requirement of rapid stabilization control of the wheeled mobile stage robot.
Description
Technical Field
The invention relates to an online optimization and stabilization control method for a wheeled mobile stage robot.
Background
The stage performance art becomes an important component of the daily cultural life of China, wherein the wheel type mobile stage robot is one of important props for presenting the high-quality stage performance art. Generally, when a song is performed, the stage robot needs to move quickly to a designated target position according to the change of the song of the performance. The mobile stage robot can quickly reach the designated position, and the stabilization control problem of the mobile robot can be considered. The goal of the calm control is to obtain a feedback control law so that the mobile stage robot approaches the target position gradually. However, the wheeled mobile stage robot has incomplete constraint limitation, and any smooth continuous time-invariant static state feedback control law cannot drive the wheeled mobile stage robot to reach a specified target position, which provides a challenge for the stabilization control of the wheeled mobile stage robot. Through the search of documents of the existing wheeled mobile robot stabilization control method, the wheeled mobile stage robot stabilization control method mainly comprises the following steps: discontinuous stabilization control, time-varying stabilization control, hybrid stabilization control and model prediction stabilization control, but the discontinuous stabilization control, the time-varying stabilization control and the hybrid stabilization control cannot process physical constraints and movement interval limits of a wheel type mobile stage robot executing mechanism, a Hessian matrix of a target function needs to be constructed on line in the model prediction stabilization control, the online calculation amount is large, the control methods are complex to understand, and the convergence rate of the control effect is slow. Because the wheeled mobile stage robot needs to arrive at a designated stage position on time according to the change of songs, the requirement on control real-time performance is high, and the wheeled mobile stage robot is a typical incomplete constraint control system, although the wheeled mobile stage robot achieves some achievements in the stabilization control research, relevant scholars and performance experts still conduct a great deal of careful research and discussion on the challenging important problem in recent years so as to meet the urgent requirement of the current high-quality stage performance art on the simple and flexible stabilization control of the wheeled mobile stage robot.
Disclosure of Invention
In order to overcome the defects of multiple setting parameters, complex online calculation and difficult realization of the existing wheeled mobile stage robot stabilization control method, the invention provides the wheeled mobile stage robot online optimization stabilization control method which is intuitive to understand, simple in design and easy to calculate online.
The technical scheme adopted by the invention for solving the technical problems is as follows:
an online optimization and stabilization control method for a wheeled mobile stage robot comprises the following steps:
1) establishing a discrete time dynamics model of the moving process of the wheeled moving stage robot, and referring to formula (1):
wherein the normal number TsRepresents the sampling period, and the variable k represents the sampling time; x is the number of1(k) And x2(k) Respectively representing the position coordinates of the wheeled mobile stage robot in the X direction and the Y direction in a stage rectangular coordinate system at the moment k; x is the number of3(k) Representing the azimuth angle of the wheeled mobile stage robot in the rectangular coordinate system at the moment k; u. of1(k) And u2(k) Respectively representing the linear velocity and the angular velocity of the wheeled mobile stage robot at the moment k; considering model equation (1), a state column vector x ═ x of the wheeled mobile stage robot is defined1x2x3]TAnd control column vector u ═ u1u2]TWhere the symbol T represents the transpose of the vector;
2) and the model formula (1) is abbreviated as formula (2):
x(k+1)＝f(x(k),u(k)) (2)
wherein f (x), (k), u (k) ═ f1(x(k),u(k))f2(x(k),u(k))f3(x(k),u(k))]T，f1(x(k),u(k))＝x1(k)+Tsu1(k)cosx3(k)，f2(x(k),u(k))＝x2(k)+Tsu1(k)sinx3(k)，f3(x(k),u(k))＝x3(k)+Tsu2(k) Establishing a discrete time prediction model of the wheeled mobile stage robot, and referring to formula (3):
x(k+j+1|k)＝f(x(k+j|k),u(k+j|k)),j＝0,1,...,M-1 (3)
wherein x (k + j | k) represents a prediction vector of the wheeled mobile stage robot control system at the time k to the state of k + j at the future time; the positive integer M represents the optimized time window;
3) let us makeu k,M＝[uT(k|k)uT(k+1|k)…uT(k+M-1|k)]TIndicating a control sequence consisting of 2M elements at time k, willu k,MAnd (3) substituting the formula (3) to obtain a predicted state vector at the moment k + M, and referring to the formula (4):
x(k+M|k)＝φM(x(k|k),u k,M) (4)
wherein the symbol phiMRepresenting model function f in model equation (2)Combining functions for M times;
4) let xdA moving target balance point of the wheeled mobile stage robot is represented, and a calm control error of the wheeled mobile stage robot is defined, which is shown in formula (5):
ek,M＝φM(x(k|k),u k,M)-xd(5)
and calculate the error ek,MFor input sequenceu k,MSee formula (6):
wherein, the symbol xkRepresents a state measurement value of the wheeled mobile stage robot at the time k, and xk＝x(k|k)；
5) And updating the control sequence at time k by using Newton's method and equation (6), see equation (7):
wherein, the symbolv k,M＝[vT(k|k)vT(k+1|k)…vT(k+M-1|k)]TVariable η, which represents the control sequence updated at time kkRepresents an update step size, satisfies 0<ηk<1, symbol Dk +Represents DkThe generalized inverse matrix of (2);
6) considering equation (7), a control amount of the wheeled moving stage robot at time k is defined, and see equation (8):
u(k)＝[I 202… 02]2×2M v k,M(8)
wherein, the symbol I2Denotes an identity matrix of order 2, symbol 02Represents a zero matrix of order 2;
7) applying the control quantity (8) to the wheeled mobile stage robot, detecting the motion state x (k +1) of the wheeled mobile stage robot after the next sampling time k +1 is reached, and updating the initial control sequence at the time k +1
Wherein, the symbol
Expressing a 2-dimensional column vector with random values, then making k equal to k +1 and returning to the step 3), and repeating the steps until the wheeled mobile stage robot moves to a given mobile target balance point xdTo the position.
The technical conception of the invention is as follows: aiming at the requirement of realizing stabilization control of the wheeled mobile stage robot under the incomplete constraint condition, firstly, a discrete time three-order dynamics model of the wheeled mobile stage robot and a randomly selected initial time limited time window control sequence are defined, a stabilization control error sequence in an optimized time window and the gradient of the error sequence relative to a control input sequence are calculated, then, an updating mechanism of the control sequence at each sampling time is established by utilizing a Newton method, and the control input quantity at each sampling time is calculated by combining a rolling optimization control principle, so that the stabilization control of the wheeled mobile stage robot is realized. The design method has the advantages of simple understanding, few setting parameters, strong universality and simple and convenient online calculation.
The main execution part of the invention is operated and implemented on the motion control computer of the wheeled mobile stage robot. The application process of the method can be roughly divided into 3 stages:
1. setting parameters: initializing a control sequence by random values in a parameter import interfaceu 0,MInputting the target position xdSampling period TsOptimized time window M and step size factor ηkAfter the input parameters are confirmed, the control computer sends the setting data into a computer storage unit RAM for storage;
2. off-line debugging, clicking the 'debugging' button in the configuration interface, controlling the system to enter the off-line simulation debugging stage of the controller, and adjusting the step length coefficient η in the configuration interfacekObserving the control effect of the state variable, namely the position and the direction angle of the wheeled mobile stage robot, determining a step length which can well realize the stabilization control of the wheeled mobile robotValue, optimized time window M and step size factor ηkThe value-taking rule of (1): m is a finite natural number and 0<ηk<1, optimizing the adjustment rules of the time window and the step length coefficient, namely increasing M to improve the stability of the wheeled mobile stage robot in the motion process and increase the calculation amount of online optimization, and conversely, decreasing M to improve the rapidity of the wheeled mobile stage robot in the motion process and easily generate the oscillation of the wheeled mobile stage robot state response, and increasing ηkThe value of (3) will shorten the adjustment time of the state response of the wheeled mobile stage robot, but will cause the oscillation of the state response of the wheeled mobile stage robot, otherwise, the value of (η) is reducedkThe value of (1) is to smooth the state response speed and the control quantity of the wheeled mobile stage robot, but prolong the adjustment time of the state response of the wheeled mobile stage robot, so that when the time window and the step length coefficient are actually debugged and optimized, the comprehensive performance among the overshoot, the adjustment time, the damping effect and the control quantity of the state response of the wheeled mobile stage robot is balanced;
3. and (3) online operation: clicking a 'run' button on a configuration interface to start a CPU reading initialization control sequence of a motion control computer of the wheeled mobile stage robotu 0,MSampling period TsOptimized time window M and step size factor ηkAnd executing a wheel type mobile stage robot stabilization control program, controlling the linear speed and the angular speed of the wheel type mobile stage robot by measuring the position and the azimuth angle of the wheel type mobile stage robot on line, realizing the stabilization control of the wheel type mobile stage robot on the specified target, measuring the actual position and the azimuth angle of the wheel type mobile stage robot on line when the next sampling period arrives, and repeating the whole execution process and the cycles to realize the stabilization control of the wheel type mobile stage robot on the specified target.
The method for the online optimized stabilization control of the complete set of wheeled mobile stage robot can be completed on a configuration interface of a wheeled mobile stage robot control system, and the process can be applied by referring to examples provided in the specification. Compared with the traditional wheeled mobile stage robot stabilization control method, the wheeled mobile stage robot online optimization stabilization control method provided by the invention has the greatest characteristics that an optimization objective function and a Hessian matrix thereof do not need to be solved in the design process of an optimization controller, and only 2 required setting parameters are needed, so that the calculation rapidity, the stability and the online implementation simplicity of the wheeled mobile stage robot online optimization stabilization control are greatly improved. The following specific implementation method takes the wheel type mobile stage robot target origin stabilization control as an example to illustrate the practical effects of the present invention, but the application scope of the present invention is not limited to the wheel type mobile stage robot origin stabilization control in this embodiment.
The invention has the following beneficial effects: 1. the design is simple, the understanding is easy, the online implementation is simple, and the universality is strong; 2. in the design process of the optimization controller, an optimization objective function and a Hessian matrix thereof do not need to be solved, the calculation rapidity and the stability of the wheel type mobile stage robot for online optimization stabilization control are improved, and the requirement on the rapid control instantaneity of the mobile stage robot is met.
Drawings
Fig. 1 is a schematic diagram of a linear velocity variation curve of a wheeled mobile stage robot.
Fig. 2 is a schematic diagram of an angular velocity variation curve of the wheeled moving stage robot.
Fig. 3 is a schematic diagram of a motion trajectory curve of the wheeled mobile stage robot on the stage plane.
Detailed Description
The invention is further described below with reference to the accompanying drawings.
Referring to fig. 1 to 3, a wheeled mobile stage robot online optimization stabilization control method includes the following steps:
1) establishing a discrete time dynamics model of the moving process of the wheeled moving stage robot, and referring to formula (1):
wherein the normal number TsRepresents the sampling period, and the variable k represents the sampling time; x is the number of1(k) And x2(k) Respectively representing the position coordinates of the wheeled mobile stage robot in the X direction and the Y direction in a stage rectangular coordinate system at the moment k; x is the number of3(k) Representing the azimuth angle of the wheeled mobile stage robot in the rectangular coordinate system at the moment k; u. of1(k) And u2(k) Respectively representing the linear velocity and the angular velocity of the wheeled mobile stage robot at the moment k; considering model equation (1), a state column vector x ═ x of the wheeled mobile stage robot is defined1x2x3]TAnd control column vector u ═ u1u2]TWhere the symbol T represents the transpose of the vector;
2) and the model formula (1) is abbreviated as formula (2):
x(k+1)＝f(x(k),u(k)) (2)
wherein f (x), (k), u (k) ═ f1(x(k),u(k))f2(x(k),u(k))f3(x(k),u(k))]T，f1(x(k),u(k))＝x1(k)+Tsu1(k)cosx3(k)，f2(x(k),u(k))＝x2(k)+Tsu1(k)sinx3(k)，f3(x(k),u(k))＝x3(k)+Tsu2(k) Establishing a discrete time prediction model of the wheeled mobile stage robot, and referring to formula (3):
x(k+j+1|k)＝f(x(k+j|k),u(k+j|k)),j＝0,1,...,M-1 (3)
wherein x (k + j | k) represents a prediction vector of the wheeled mobile stage robot control system at the time k to the state of k + j at the future time; the positive integer M represents the optimized time window;
3) let us makeu k,M＝[uT(k|k)uT(k+1|k)…uT(k+M-1|k)]TIndicating a control sequence consisting of 2M elements at time k, willu k,MAnd (3) substituting the formula (3) to obtain a predicted state vector at the moment k + M, and referring to the formula (4):
x(k+M|k)＝φM(x(k|k),u k,M) (4)
wherein the symbol phiMAn M-th order combination function representing the model function f in the model formula (2);
4) let xdA moving target balance point of the wheeled mobile stage robot is represented, and a calm control error of the wheeled mobile stage robot is defined, which is shown in formula (5):
ek,M＝φM(x(k|k),u k,M)-xd(5)
and calculate the error ek,MFor input sequenceu k,MSee formula (6):
wherein, the symbol xkRepresents a state measurement value of the wheeled mobile stage robot at the time k, and xk＝x(k|k)；
5) And updating the control sequence at time k by using Newton's method and equation (6), see equation (7):
wherein, the symbolv k,M＝[vT(k|k)vT(k+1|k)…vT(k+M-1|k)]TVariable η, which represents the control sequence updated at time kkRepresents an update step size, satisfies 0<ηk<1, symbol Dk +Represents DkThe generalized inverse matrix of (2);
6) considering equation (7), a control amount of the wheeled moving stage robot at time k is defined, and see equation (8):
u(k)＝[I202… 02]2×2M v k,M(8)
wherein, the symbol I2Denotes an identity matrix of order 2, symbol 02Represents a zero matrix of order 2;
7) applying the control quantity (8) to the wheeled mobile stage robot, detecting the motion state x (k +1) of the wheeled mobile stage robot after the next sampling time k +1 is reached, and updating the initial control sequence at the time k +1
Wherein, the symbol
Representing a 2-dimensional random column vector with the mean value of zero, then making k equal to k +1 and returning to the step 3), and repeating the steps until the wheeled mobile stage robot moves to a given mobile target balance point xdTo the position.
This example is wheeled mobile stage robot target initial point calming process, and specific operation process is as follows:
firstly, in a parameter setting interface, inputting a target position xd0, sampling period Ts0.1 second, optimized time window M, step factor ηkAnd initializing the control sequence with a random valueu 0,M；
Secondly, clicking a 'debugging' button on a configuration interface to enter a debugging interface, starting a CPU of a wheel type mobile stage robot motion control computer to call a controller calculation program which is programmed in advance to solve a controller, wherein the specific calculation process is as follows according to given M and ηkCalculating and updating an optimized control sequence (7), defining an optimized controller (8) of the linear velocity and the angular velocity of the wheeled mobile stage robot at the moment k according to M and ηkComparing the response result of the position and the azimuth angle of the wheeled mobile stage robot with the calculation result of the control quantity, and debugging to obtain M10 and ηkSaving the debugging result into a computer storage unit RAM (random access memory) when the debugging result is 0.5;
thirdly, clicking a 'running' button on a configuration interface to start a CPU of a wheeled mobile stage robot control computer to read a target position xdInitializing a control sequenceu 0,MSampling period TsOptimized time window M and step size factor ηkAnd executing a wheel type mobile stage robot stabilization control program, controlling the linear speed and the angular speed of the wheel type mobile stage robot by measuring the position and the azimuth angle of the wheel type mobile stage robot on line, realizing the stabilization control of the wheel type mobile stage robot on the target position, and measuring the wheel type mobile stage robot stabilization control on line when the next sampling period arrivesAnd the actual position and the azimuth angle of the stage moving robot are moved, and then the whole execution process is repeated in cycles, so that the stabilization control of the wheeled stage moving robot on the target position is realized.
The above illustrates the good motion performance of the target origin online optimization and stabilization control example of the wheeled mobile stage robot provided by the invention. It should be noted that the above-mentioned examples are intended to illustrate rather than to limit the invention, and that any modifications made to the invention within the spirit and scope of the claims fall within the scope of the invention.
Claims (1)
1. The utility model provides a wheeled mobile stage robot optimizes calm control method on line which characterized in that: the control method comprises the following steps:
1) establishing a discrete time dynamics model of the moving process of the wheeled moving stage robot, and referring to formula (1):
wherein the normal number TsRepresents the sampling period, and the variable k represents the sampling time; x is the number of1(k) And x2(k) Respectively representing the position coordinates of the wheeled mobile stage robot in the X direction and the Y direction in a stage rectangular coordinate system at the moment k; x is the number of3(k) Representing the azimuth angle of the wheeled mobile stage robot in the rectangular coordinate system at the moment k; u. of1(k) And u2(k) Respectively representing the linear velocity and the angular velocity of the wheeled mobile stage robot at the moment k; considering model equation (1), a state column vector x ═ x of the wheeled mobile stage robot is defined1x2x3]TAnd control column vector u ═ u1u2]TWhere the symbol T represents the transpose of the vector;
2) and the model formula (1) is abbreviated as formula (2):
x(k+1)＝f(x(k),u(k)) (2)
wherein f (x), (k), u (k) ═ f1(x(k),u(k))f2(x(k),u(k))f3(x(k),u(k))]T，f1(x(k),u(k))＝x1(k)+Tsu1(k)cosx3(k)，f2(x(k),u(k))＝x2(k)+Tsu1(k)sinx3(k)，f3(x(k),u(k))＝x3(k)+Tsu2(k) Establishing a discrete time prediction model of the wheeled mobile stage robot, and referring to formula (3):
x(k+j+1|k)＝f(x(k+j|k),u(k+j|k)),j＝0,1,...,M-1 (3)
wherein x (k + j | k) represents a prediction vector of the wheeled mobile stage robot control system at the time k to the state of k + j at the future time; the positive integer M represents the optimized time window;
3) let us makeu k,M＝[uT(k|k)uT(k+1|k)…uT(k+M-1|k)]TIndicating a control sequence consisting of 2M elements at time k, willu k,MAnd (3) substituting the formula (3) to obtain a predicted state vector at the moment k + M, and referring to the formula (4):
x(k+M|k)＝φM(x(k|k),u k,M) (4)
wherein the symbol phiMAn M-th order combination function representing the model function f in the model formula (2);
4) let xdA moving target balance point of the wheeled mobile stage robot is represented, and a calm control error of the wheeled mobile stage robot is defined, which is shown in formula (5):
ek,M＝φM(x(k|k),u k,M)-xd(5)
and calculate the error ek,MFor input sequenceu k,MSee formula (6):
wherein, the symbol xkRepresents a state measurement value of the wheeled mobile stage robot at the time k, and xk＝x(k|k)；
5) And updating the control sequence at time k by using Newton's method and equation (6), see equation (7):
wherein, the symbolv k,M＝[vT(k|k) vT(k+1|k) … vT(k+M-1|k)]TVariable η, which represents the control sequence updated at time kkRepresents an update step size, satisfies 0<ηk<1, symbol Dk +Represents DkThe generalized inverse matrix of (2);
6) considering equation (7), a control amount of the wheeled moving stage robot at time k is defined, and see equation (8):
u(k)＝[I202… 02]2×2M v k,M(8)
wherein, the symbol I2Denotes an identity matrix of order 2, symbol 02Represents a zero matrix of order 2;
7) applying the control quantity (8) to the wheeled mobile stage robot, detecting the motion state x (k +1) of the wheeled mobile stage robot after the next sampling time k +1 is reached, and updating the initial control sequence at the time k +1
Wherein, the symbol
Expressing a 2-dimensional column vector with random values, then making k equal to k +1 and returning to the step 3), and repeating the steps until the wheeled mobile stage robot moves to a given mobile target balance point xdTo the position.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201710467447.3A CN107168064B (en) | 2017-06-20 | 2017-06-20 | Wheel type mobile stage robot online optimization stabilization control method |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201710467447.3A CN107168064B (en) | 2017-06-20 | 2017-06-20 | Wheel type mobile stage robot online optimization stabilization control method |
Publications (2)
| Publication Number | Publication Date |
|---|---|
| CN107168064A CN107168064A (en) | 2017-09-15 |
| CN107168064B true CN107168064B (en) | 2020-08-04 |
Family
ID=59819789
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CN201710467447.3A Active CN107168064B (en) | 2017-06-20 | 2017-06-20 | Wheel type mobile stage robot online optimization stabilization control method |
Country Status (1)
| Country | Link |
|---|---|
| CN (1) | CN107168064B (en) |
Families Citing this family (1)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN108107885B (en) * | 2017-11-24 | 2020-06-02 | 浙江工业大学 | Method for tracking and controlling cycloid of wheeled mobile stage robot |
Citations (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN105929849A (en) * | 2016-04-28 | 2016-09-07 | 东南大学 | Wheeled mobile robot target tracking control method based on point stabilization |
| CN106292290A (en) * | 2016-09-28 | 2017-01-04 | 浙江工业大学 | A kind of wheeled mobile robot point is calmed rolling optimization control method |
-
2017
- 2017-06-20 CN CN201710467447.3A patent/CN107168064B/en active Active
Patent Citations (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN105929849A (en) * | 2016-04-28 | 2016-09-07 | 东南大学 | Wheeled mobile robot target tracking control method based on point stabilization |
| CN106292290A (en) * | 2016-09-28 | 2017-01-04 | 浙江工业大学 | A kind of wheeled mobile robot point is calmed rolling optimization control method |
Non-Patent Citations (3)
| Title |
|---|
| Nonholonomic Motion Planning Based on Newton Algorithm with Energy Optimization;Ignacy Duleba and Jurek Z. Sasiadek;《IEEE TRANSACTIONS ON CONTROL SYSTEMS TECHNOLOGY》;20030531;第11卷(第3期);全文 * |
| 双臂空间机器人姿态调整运动的最优控制规划;唐晓腾 等;《空间科学学报》;20061231;第33卷(第5期);第405页-第406页 * |
| 基于速度空间的移动机器人同时避障和轨迹跟踪方法;张启彬 等;《控制与决策》;20170228;第32卷(第2期);全文 * |
Also Published As
| Publication number | Publication date |
|---|---|
| CN107168064A (en) | 2017-09-15 |
Similar Documents
| Publication | Publication Date | Title |
|---|---|---|
| CN102385342B (en) | Self-adaptation dynamic sliding mode controlling method controlled by virtual axis lathe parallel connection mechanism motion | |
| CN103538068A (en) | Fuzzy sliding mode trajectory tracking control method for SCARA robot | |
| CN104317195B (en) | Improved extreme learning machine-based nonlinear inverse model control method | |
| CN103419198A (en) | Robot program changing device | |
| CN105915121A (en) | Servo system inertia identification method adopting genetic algorithm for optimization | |
| CN103645725A (en) | Teaching track planning method and system for robot | |
| CN109213175A (en) | A kind of mobile robot visual servo track tracking prediction control method based on primal-dual neural network | |
| CN107168064B (en) | Wheel type mobile stage robot online optimization stabilization control method | |
| CN116184813B (en) | Method, device, equipment and storage medium for controlling posture of boosting gliding rocket | |
| CN105186959A (en) | Parameter setting method of sliding mode controller of servo system | |
| CN104048777A (en) | Temperature value and resistance value conversion method for NTC-type thermistor | |
| CN106716423A (en) | Thermal circuit simulations using convolution and iterative methods | |
| CN106292290A (en) | A kind of wheeled mobile robot point is calmed rolling optimization control method | |
| CN108828959A (en) | A kind of novel bridge crane is anti-sway with position control method and device | |
| CN110744552A (en) | Flexible mechanical arm motion control method based on singular perturbation theory | |
| US11747773B2 (en) | Sequential deterministic optimization based control system and method | |
| CN114502338A (en) | Techniques for generating controllers for robots | |
| CN104749956A (en) | Structure optimization method of industrial robot based on harmony search algorithm | |
| CN114114903B (en) | Cricket system integral terminal sliding mode control method based on variable exponent power approach law | |
| CN116512256A (en) | Robot optimal man-machine interaction impedance control method based on joint learning, storage medium and robot | |
| CN108107885B (en) | Method for tracking and controlling cycloid of wheeled mobile stage robot | |
| Lu | Iterative learning control algorithm for optimal path industrial manipulator | |
| CN103064286A (en) | Control method of industrial process and equipment | |
| Zheng et al. | Neurodynamics Adaptive Reward and Action for Hand-to-Eye Calibration with Deep Reinforcement Learning | |
| WO2023216581A1 (en) | Controller training method, trajectory tracking method, terminal device, and storage medium |
Legal Events
| Date | Code | Title | Description |
|---|---|---|---|
| PB01 | Publication | ||
| PB01 | Publication | ||
| SE01 | Entry into force of request for substantive examination | ||
| SE01 | Entry into force of request for substantive examination | ||
| GR01 | Patent grant | ||
| GR01 | Patent grant |