CN106292290B - A kind of calm rolling optimization control method of wheeled mobile robot point - Google Patents
A kind of calm rolling optimization control method of wheeled mobile robot point Download PDFInfo
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Abstract
A kind of calm rolling optimization control method of the point of wheeled mobile robot, kinetic model based on mobile robot under global coordinate system, utilize State Feedback Type model predictive control method, control constraints and state constraint are integrated in the design of a stability controller, by using variable replacement, final design goes out the smooth stabilization control law expression formula of Mobile Robot Control System, solve the problems, such as that mobile robot puts the stability problem of point stabilization as caused by the nonholonomic constraint of itself, the stability problem of point point stabilization caused by executing the acceleration that system certainly exists and constraint of velocity limitation displacement, and from external environment it is various uncertainty caused by point point stabilization stability problem, while guaranteeing to obtain good moveable robot movement track, more effectively improve movement Rapidity and accuracy.
Description
Technical Field
The invention relates to a point-stabilizing rolling optimization control method for a wheeled mobile robot.
Background
With the rapid increase of the application range of the wheeled mobile robot, the real-time performance and the rapid response capability of the motion control of the robot are continuously improved, and the motion control method is paid more and more attention. The aim of motion control of the wheeled mobile robot is to solve the problems of motion planning and stabilization control of the mobile robot, wherein the stabilization control drives the robot to gradually move to a target point through a feedback control law, but the wheeled mobile robot usually has incomplete constraint limitation, and a continuous smooth control law is not existed to gradually stabilize the mobile robot, so that the stabilization control of the wheeled mobile robot becomes a challenging problem. Through the search of the documents of the conventional wheeled mobile robot point stabilization control method, the wheeled mobile robot point stabilization control method mainly comprises the following steps: discontinuous stability control, time-varying stability control and hybrid stability control are adopted, but in the design process of a motion control system of the wheeled mobile robot, the physical constraints of an actuating mechanism of the wheeled mobile robot and the limitation of a moving interval of the robot are not considered in the control methods, and the control methods are complex to understand and slow in convergence rate of control effects. In practical control application of the wheeled mobile robot, the robot is required to meet physical constraints of an actuating mechanism and limits of a moving speed and a moving interval, a motion control system of the wheeled mobile robot is required to meet system states and control constraints, and the wheeled mobile robot is a typical incomplete constraint control system.
Disclosure of Invention
In order to overcome the defects that the existing wheeled mobile robot point stabilization control method is complex in understanding and difficult to realize, and the calculated control quantity does not meet the constraint requirement of a robot system, the invention provides the wheeled mobile robot point stabilization rolling optimization control method which is intuitive in understanding, simple in design and capable of enabling the calculated control quantity to meet the constraint requirement of the robot system.
The technical scheme adopted by the invention for solving the technical problems is as follows:
a point-stabilized rolling optimization control method for a wheeled mobile robot comprises the following steps:
1) establishing a three-order dynamic model of continuous time in the motion process of the wheeled mobile robot, and referring to formula (1):
wherein the variable t represents time; x is the number of1(t) and x2(t) respectively indicating the position coordinates of the wheeled mobile robot in the X direction and the Y direction in the rectangular coordinate system at the time t; x is the number of3(t) represents an azimuth angle of the wheeled mobile robot in the rectangular coordinate system at the time t; u. of1(t) and u2(t) respectively indicating the linear velocity and the angular velocity of the wheeled mobile robot at the time t; considering model equation (1), a state column vector x ═ x of the wheeled mobile robot is defined1 x2 x3]TAnd control column vector u ═ u1 u2]TWhere the symbol T represents the transpose of the vector;
2) considering model equation (1), an expression function of the control vector u is defined, see equation (2):
wherein, gijIs an unknown parameter, i ═ 1,2, j ═ 1,2, 3; matrix arraySubstituting formula (2) into model formula (1) to obtain formula (3):
3) with a sampling period TsPerforming discrete time conversion on the model type (3) to obtain a three-order discrete time dynamics model of the wheeled mobile robot, and referring to the formula (4):
and model formula (4) is abbreviated as formula (5):
x(k+1)＝f(x(k),Gx(k)) (5)
wherein f (x (k), gx (k) ═ f1(x(k),Gx(k))f2(x(k),Gx(k))f3(x(k),Gx(k))]T，f1(x(k),Gx(k))＝x1(k)+Ts[g11x1(k)+g12x2(k)+g13x3(k)]cosx3(k)，f2(x(k),Gx(k))＝x2(k)+Ts[g11x1(k)+g12x2(k)+g13x3(k)]sinx3(k)，f3(x(k),Gx(k))＝x3(k)+Ts[g21x1(k)+g22x2(k)+g23x3(k)]；
4) And establishing a dynamic prediction model of the wheeled mobile robot by considering the model formula (5), wherein the dynamic prediction model is shown in the formula (6):
x(k+j+1|k)＝f(x(k+j|k),Gx(k+j|k)),j＝0,1,...,N-1 (6)
wherein x (k + j | k) represents a prediction vector of the wheeled mobile robot control system at the time k to the state of the future time k + j; the positive integer N is the prediction time window; considering the state of the wheeled mobile robot and the boundary constraint of the control amplitude, see equations (7) and (8):
wherein,xandurespectively representing the lower bound of the state and control,andupper bounds representing state and control, respectively;
5) considering equation (6), a quadratic objective function is defined, see equation (9):
wherein Q and R are positive definite weighting matrixes respectively used for punishing a state variable and a control variable; detecting the state x (k) at the current k moment, and defining an optimization control problem, see formula (10):
wherein matrix G is a decision variable; the symbol "s.t." denotes a constraint; the equation x (k | k) ═ x (k) is referred to as the initial condition of the optimization problem; the optimization problem (10) is solved by applying a numerical optimization algorithm to obtain an optimal matrix value G*And optimizing the control amount, see formula (11):
applying the control quantity (11) to the wheeled mobile robot, detecting the motion state x (k +1) of the wheeled mobile robot after the next sampling time k +1 is reached, updating the initial condition of the optimization control problem (10) according to the state, and then optimizing and calculating the optimal matrix value G at the current time*And optimizing the control quantity, and repeating the steps until the wheeled mobile robot moves to the target origin position.
The technical conception of the invention is as follows: aiming at the point stabilization control problem required by the wheeled mobile robot under the incomplete constraint and state and control constraint conditions, the three-order kinetic model of the wheeled mobile robot is taken as a basis, the optimization control problem of limited prediction time is established by defining a robot control input function and a discrete time three-order kinetic model, and the point stabilization control of the wheeled mobile robot is realized by calculating the control input quantity with the optimal parameter at each sampling moment by combining a rolling optimization control principle. The design method has the advantages of simple understanding, strong universality and capability of meeting the constraint limit of the wheeled mobile robot by the control quantity.
The main execution part of the invention is operated and implemented on the wheel type mobile robot motion control computer. The application process of the method can be roughly divided into 3 stages:
1. setting parameters: in the parameter import interface, a sampling period T is inputsLower bound for, status and controlxAnduupper bound on state and controlAndpredicting a time window N, a weighting matrix Q and a weighting matrix R, and after input parameters are confirmed, sending set data into a computer storage unit RAM by a control computer for storage;
2. off-line debugging: clicking a 'debugging' button in a configuration interface, enabling a control system to enter a controller offline simulation debugging stage, adjusting weighting matrixes Q and R in the configuration interface, observing the control effect of state variables, namely positions and direction angles, of the wheeled mobile robot, and determining a group of weighting matrix values capable of well realizing point stabilization control of the wheeled mobile robot; the value rules of the weighting matrixes Q and R are as follows: q is a third-order positive definite diagonal matrix, and R is a second-order positive definite diagonal matrix; adjustment rules for the weighting matrices Q and R: increasing the value of the matrix Q shortens the adjustment time of the state response of the wheeled mobile robot, but increases the overshoot and the control quantity of the state response of the wheeled mobile robot, and conversely, decreasing the value of the matrix Q eases the state response speed and the control quantity of the wheeled mobile robot, but prolongs the adjustment time of the state response of the wheeled mobile robot; increasing the value of the matrix R increases the adjustment time of the state response of the wheeled mobile robot, but shortens the overshoot and the control quantity of the state response of the wheeled mobile robot, and conversely, decreasing the value of the matrix R increases the state response speed and the control quantity of the wheeled mobile robot, but shortens the adjustment time of the state response of the wheeled mobile robot, so that when the weighting matrices Q and R are actually debugged, the comprehensive performance among the overshoot, the adjustment time, the damping effect and the control quantity of the state response of the wheeled mobile robot is balanced;
3. and (3) online operation: clicking a 'run' button on a configuration interface to start a CPU (central processing unit) of a motion control computer of the wheeled mobile robot to read a sampling period TsLower bound for, status and controlxAnduupper bound on state and controlAndpredicting a time window N and weighting matrixes Q and R, executing a 'wheeled mobile robot point stabilization control program', controlling linear speed and angular speed entering the wheeled mobile robot by measuring the position and the azimuth angle of the wheeled mobile robot on line, realizing the point stabilization control of the wheeled mobile robot on a target origin, measuring the actual position and the azimuth angle of the wheeled mobile robot on line when the next sampling period arrives, and then repeating the whole execution process,and the point stabilization control of the wheeled mobile robot to the target origin is realized in a circulating way.
The complete set of wheel-type mobile robot point-stationary control method can be completed on a configuration interface of a wheel-type mobile robot control system, and the process can be applied by referring to examples provided in the specification below. Compared with the traditional point stabilization control method for the wheeled mobile robot, the point stabilization rolling optimization control method for the wheeled mobile robot has the greatest characteristics that incomplete constraint, state and control constraint of the wheeled mobile robot are explicitly considered in the design process of the controller, and a function of a control variable of the wheeled mobile robot is designed in advance, so that the safety, the rapidity and the stability of point stabilization movement of the wheeled mobile robot are improved. The following embodiment describes the practical effects of the present invention by taking the origin stabilizing control of the wheeled mobile robot as an example, but the application scope of the present invention is not limited to the origin stabilizing control of the wheeled mobile robot in the present embodiment.
The invention has the following beneficial effects: 1. the design is simple, the understanding is easy, and the universality is strong; 2. incomplete constraints and states and control constraints can be clearly processed in the design process of the motion control system of the wheeled mobile robot, and the safety, the rapidity and the stability of point stabilizing motion of the wheeled mobile robot are improved by designing a control variable function of the wheeled mobile robot in advance.
Drawings
Fig. 1 is a schematic diagram of a motion trail curve of a wheeled mobile robot in an X-Y plane.
Fig. 2 is a schematic diagram of a linear velocity profile of the wheeled mobile robot.
Fig. 3 is a schematic view of an angular velocity change curve of the wheeled mobile robot.
Detailed Description
The invention is further described below with reference to the accompanying drawings.
Referring to fig. 1 to 3, a wheeled mobile robot point-stationary rolling optimization control method includes the following steps:
1) establishing a three-order dynamic model of continuous time in the motion process of the wheeled mobile robot, and referring to formula (1):
wherein the variable t represents time; x is the number of1(t) and x2(t) respectively indicating the position coordinates of the wheeled mobile robot in the X direction and the Y direction in the rectangular coordinate system at the time t; x is the number of3(t) represents an azimuth angle of the wheeled mobile robot in the rectangular coordinate system at the time t; u. of1(t) and u2(t) respectively indicating the linear velocity and the angular velocity of the wheeled mobile robot at the time t; considering model equation (1), a state column vector x ═ x of the wheeled mobile robot is defined1 x2 x3]TAnd control column vector u ═ u1 u2]TWhere the symbol T represents the transpose of the vector;
2) considering model equation (1), an expression function of the control vector u is defined, see equation (2):
wherein, gijIs an unknown parameter, i ═ 1,2, j ═ 1,2, 3; matrix arraySubstituting formula (2) into model formula (1) to obtain formula (3):
3) adopting computer control principle to sample period TsPerforming discrete time conversion on the model type (3) to obtain a three-order discrete time dynamics model of the wheeled mobile robot, and referring to the formula (4):
and model formula (4) is abbreviated as formula (5):
x(k+1)＝f(x(k),Gx(k)) (5)
wherein f (x (k), gx (k) ═ f1(x(k),Gx(k)) f2(x(k),Gx(k)) f3(x(k),Gx(k))]T，f1(x(k),Gx(k))＝x1(k)+Ts[g11x1(k)+g12x2(k)+g13x3(k)]cosx3(k)，f2(x(k),Gx(k))＝x2(k)+Ts[g11x1(k)+g12x2(k)+g13x3(k)]sinx3(k)，f3(x(k),Gx(k))＝x3(k)+Ts[g21x1(k)+g22x2(k)+g23x3(k)]；
4) And establishing a dynamic prediction model of the wheeled mobile robot by considering the model formula (5), wherein the dynamic prediction model is shown in the formula (6):
x(k+j+1|k)＝f(x(k+j|k),Gx(k+j|k)),j＝0,1,...,N-1 (6)
wherein x (k + j | k) represents a prediction vector of the wheeled mobile robot control system at the time k to the state of the future time k + j; the positive integer N is the prediction time domain; considering the state of the wheeled mobile robot and the boundary constraint of the control amplitude, see equations (7) and (8):
wherein,xandurespectively representing the lower bound of the state and control,andupper bounds representing state and control, respectively;
5) considering equation (6), a quadratic objective function is defined, see equation (9):
wherein Q and R are positive definite weighting matrixes respectively used for punishing a state variable and a control variable; detecting the state x (k) at the current k moment, and defining an optimization control problem, see formula (10):
wherein matrix G is a decision variable; the symbol "s.t." denotes a constraint; the equation x (k | k) ═ x (k) is referred to as the initial condition of the optimization problem; the optimization problem (10) is solved by applying a numerical optimization algorithm to obtain an optimal matrix value G*And optimizing the control amount, see formula (11):
applying the control quantity (11) to the wheeled mobile robot, detecting the motion state x (k +1) of the wheeled mobile robot after the next sampling time k +1 is reached, updating the initial condition of the optimization control problem (10) according to the state, and then optimizing and calculating the optimal matrix value G at the current time*And optimizing the control quantity, and repeating the steps until the wheeled mobile robot moves to the target origin position.
The example is a wheeled mobile robot origin calming process, and the specific operation process is as follows:
1. in the parameter setting interface, a sampling period T is inputs0.25s, lower bound of statex＝[-10 -10 0]TAnd upper boundLower bound of controlu＝[-0.47 -3.77]TAnd upper boundPrediction time window N22, weighting matrix Q and R.
2. Clicking a debugging button on a configuration interface to enter the debugging interface, starting a CPU (central processing unit) of a motion control computer of the wheeled mobile robot to call a controller calculation program which is programmed in advance to solve a controller, wherein the specific calculation process is as follows: solving an optimization control problem (10) according to given weighting matrices Q and R to obtain a set of optimal solutions G of parameters G*Defining an optimal controller (11) of the linear velocity and the angular velocity of the wheeled mobile robot at the moment k, comparing the position and the azimuth angle response result of the wheeled mobile robot with the control quantity calculation result according to the values and the adjustment rules of Q and R, and debugging Q and R to obtain
Saving the debugging result into a computer storage unit RAM;
3. clicking a 'run' button on a configuration interface to start a CPU (central processing unit) of a wheeled mobile robot control computer to read a sampling period TsLower bound for, status and controlxAnduupper bound on state and controlAndpredicting a time window N and weighting matrixes Q and R, executing a 'wheel type mobile robot point stabilization control program', controlling the linear speed and the angular speed of the wheel type mobile robot by measuring the position and the azimuth angle of the wheel type mobile robot on line, realizing the point stabilization control of the wheel type mobile robot on a target origin, measuring the actual position and the azimuth angle of the wheel type mobile robot on line when the next sampling period arrives, and repeating the whole execution process and repeating the steps to realize the point stabilization control of the wheel type mobile robot on the target origin.
The point-stabilized control effect of the wheeled mobile robot on the target origin, which is shown to be excellent in performance by one embodiment of the present invention, is explained above. It should be noted that the above-mentioned embodiments illustrate rather than limit the invention, and that any modifications made within the spirit of the invention and the scope of the appended claims fall within the scope of the invention.
Claims (1)
1. A point-stabilized rolling optimization control method for a wheeled mobile robot is characterized by comprising the following steps: the control method comprises the following steps:
1) establishing a three-order dynamic model of continuous time in the motion process of the wheeled mobile robot, and referring to formula (1):
wherein the variable t represents time; x is the number of1(t) and x2(t) respectively indicating the position coordinates of the wheeled mobile robot in the X direction and the Y direction in the rectangular coordinate system at the time t; x is the number of3(t) represents an azimuth angle of the wheeled mobile robot in the rectangular coordinate system at the time t; u. of1(t) and u2(t) respectively indicating the linear velocity and the angular velocity of the wheeled mobile robot at the time t; considering model equation (1), a state column vector x ═ x of the wheeled mobile robot is defined1 x2 x3]TAnd control column vector u ═ u1 u2]TWhere the symbol T represents the transpose of the vector;
2) considering model equation (1), an expression function of the control vector u is defined, see equation (2):
wherein, gijIs an unknown parameter, i ═ 1,2, j ═ 1,2, 3; matrix arraySubstituting formula (2) into model formula (1) to obtain formula (3):
3) with a sampling period TsPerforming discrete time conversion on the model type (3) to obtain a three-order discrete time dynamics model of the wheeled mobile robot, and referring to the formula (4):
and model formula (4) is abbreviated as formula (5):
x(k+1)＝f(x(k),Gx(k)) (5)
wherein f (x (k), gx (k) ═ f1(x(k),Gx(k)) f2(x(k),Gx(k)) f3(x(k),Gx(k))]T，f1(x(k),Gx(k))＝x1(k)+Ts[g11x1(k)+g12x2(k)+g13x3(k)]cosx3(k)，f2(x(k),Gx(k))＝x2(k)+Ts[g11x1(k)+g12x2(k)+g13x3(k)]sinx3(k)，f3(x(k),Gx(k))＝x3(k)+Ts[g21x1(k)+g22x2(k)+g23x3(k)]；
4) And establishing a dynamic prediction model of the wheeled mobile robot by considering the model formula (5), wherein the dynamic prediction model is shown in the formula (6):
x(k+j+1|k)＝f(x(k+j|k),Gx(k+j|k)),j＝0,1,...,N-1 (6)
wherein x (k + j | k) represents a prediction vector of the wheeled mobile robot control system at the time k to the state of the future time k + j; the positive integer N is the prediction time window; considering the state of the wheeled mobile robot and the boundary constraint of the control amplitude, see equations (7) and (8):
wherein,xandurespectively representing the lower bound of the state and control,andupper bounds representing state and control, respectively;
5) considering equation (6), a quadratic objective function is defined, see equation (9):
wherein Q and R are positive definite weighting matrixes used for respectively representing penalty state variables and control variables; detecting the state x (k) at the current k moment, and defining an optimization control problem, see formula (10):
wherein matrix G is a decision variable; the symbol "s.t." denotes a constraint; the equation x (k | k) ═ x (k) is referred to as the initial condition of the optimization problem; the optimization problem (10) is solved by applying a numerical optimization algorithm to obtain an optimal matrix value G*And optimizing the control amount, see formula (11):
applying the control quantity (11) to the wheeled mobile robot, detecting the motion state x (k +1) of the wheeled mobile robot after the next sampling time k +1 is reached, updating the initial condition of the optimization control problem (10) according to the state, and then optimizing and calculating the optimal matrix value G at the current time*And optimizing the control quantity, and repeating the steps until the wheeled mobile robot moves to the target origin position.
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| CN107168058B (en) * | 2017-05-27 | 2020-04-07 | 杭州电子科技大学 | Robot rolling optimization control method based on cooperation control mechanism |
| CN107168064B (en) * | 2017-06-20 | 2020-08-04 | 浙江工业大学 | Wheel type mobile stage robot online optimization stabilization control method |
| 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 |
| CN108839026B (en) * | 2018-07-19 | 2021-04-06 | 浙江工业大学 | Visual servo tracking prediction control method for mobile robot |
| CN109213175A (en) * | 2018-10-31 | 2019-01-15 | 浙江工业大学 | A kind of mobile robot visual servo track tracking prediction control method based on primal-dual neural network |
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