CN109491389A - A kind of robot trace tracking method with constraint of velocity - Google Patents
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Abstract
The invention discloses a kind of robot trace tracking methods with constraint of velocity, including (1), and people moving region, starting point, barrier is arranged；(2) path planning is carried out, first obtains path with the random tree algorithm of improved rapid discovery, then path is optimized and curve matching, a smooth path is obtained；(3) according to the parameter of robot, constraint of velocity is established；(4) system prediction model is established, the optimal input speed of subsequent time is predicted according to path node；(5) step (4) are repeated, optimal input speed is found out；(6) it is moved according to optimal velocity input control robot.This method may be implemented Robot path and carry out quickly, smoothly move, and can sufficiently accurately be fitted planned path, and error is small, strong robustness.
Description
Technical field
The present invention relates to a kind of robot trace tracking methods, and in particular to the speed of a kind of pair of omni-directional mobile robots into
The trace tracking method of row control.
Background technique
Nowadays mobile robot all receives extensive research in every field, it is not only in industry, space flight, public utilities
Etc. applied, and service, there has also been develop on a large scale very much for sphere of life.With the double drive of traditional nonholonomic constraint
Wheeled robot is compared, and the wheel of the omni-directional mobile robots (OMR) with holonomic constriants can simultaneously and separately rotate, with reality
The translation and complicated arcuate movement of existing any direction, so causing the very big concern of researcher.Omni-directional mobile robots
Have many advantages, such as that flexible, modeling is simple, navigability is good, concentrates on point-to-point stabilization, path planning, track in terms of main research
Tracking, speed control etc..
Model Predictive Control (MPC) algorithm is a kind of computer control algorithm of industrial process control field earliest, now
As a kind of feedback control strategy by extensive discussions.MPC algorithm is mainly for multivariable, constraint object, and principle is as follows: each
Sampling instant, according to the metrical information of system, one finite time-domain open loop optimization problem of line solver can be in the hope of current time
With later control sequence, but first control variable is taken only to control current time, in subsequent time, repeat this process,
New optimization problem is handled with new metrical information.MPC algorithm only focuses on model function by it, does not focus on model form, transports
Reduced with rolling optimization uncertain, possess feedback compensation, the features such as algorithm is easily expanded is widely applied.Currently, by MPC
It is also largely effective that algorithm is applied to motion planning and robot control.However, carrying out the rail of robot in performance model predictive control algorithm
During mark tracking, carrying out control to the speed of robot is an emphasis.If do not constrained speed, machine
People static at each point of tracking can get off, then obtain speed in subsequent time, its speed in this way can change always,
And after carrying out speed control, the stabilization of speed may be implemented in robot, meets actual demand.
Summary of the invention
To solve the problems, such as omni-directional mobile robots track following in background technique, the invention discloses one kind to have speed
The omni-directional mobile robots trace tracking method of constraint.Assuming that between the beginning and end and starting point of known machine people movement
Existing obstacle first passes through the random tree algorithm of rapid discovery before robot motion and obtains the collisionless of a connection starting point
Feasible path, routing information is input in Model Predictive Control Algorithm.According to the actual information of robot and think application
Constraint of velocity information, establishes prediction model.According to the routing information of the prediction model and the moment established, lower a period of time is predicted
The optimal velocity at quarter is carried out the movement of robot by the speed predicted.In subsequent time, prediction steps are repeated, are thus obtained every
The speed of a moment robot.Because joined constraint of velocity in a model, it is possible to realize the stabilization of speed.
Technical solution: to achieve the goals above, the present invention adopts the following technical scheme: a kind of machine with constraint of velocity
Device people's trace tracking method, includes the following steps:
(1) people moving region, starting point, barrier are set；
(2) path planning is carried out, first obtains path with the random tree algorithm of improved rapid discovery, then optimize to path
And curve matching, obtain a smooth path；
(3) according to the three of robot speed envelopes of wheel and the motion range of robot, constraint of velocity is established；
(4) system prediction model is established, the optimal input speed of subsequent time is predicted according to path node；
(5) step (4) are repeated, the optimal input speed at each moment is found out；
(6) it is moved according to optimal velocity input control robot.
Rapid discovery random tree (RRT) algorithm is a kind of by being sampled in space come the random path planning side for constructing tree
Method, it has probability completeness., by taking a spanning tree at random in clear space, tree is not visited to most of in principle for it
It surveys region growing and finally finds out a feasible path from starting point to terminal so as to occupy most of free space.This
It is its innovatory algorithm --- RRT* used in invention, the random tree algorithm of improved rapid discovery in above-mentioned steps (2) is such as
Under:
Global context X is defined, wherein space with obstacle Xobstacle, clear space Xfree=X/Xobstacle, it is assumed that
The obstacle of space with obstacle is previously known and static；Starting point qinit and terminal qend is located in clear space；It plans
Path be a part for setting T, tree is constructed by the line E one by one between sampled point V and sampled point and is formed, and wherein sampled point claims
For leaf node, line is known as branch；
Random point qrand is taken in X, finds node qnear nearest with qrand in T, and connection forms vector Vector；
Step-length step is taken since qnear on Vector, forms new node qnew；If qnew and qnear line pass through collision detection
It was found that being collided, then this secondary growth is abandoned；
Node set is established near qnew, using qnew as the center of circle, preset R is round empty caused by radius work circle
Between, compare the accumulated costs that will be set after the tree node fallen into circle and qnew connection, selects the smallest node of cost as qnew
Father node qnear, be added tree in；
Assuming that the new node qnew that tree is added is father node, calculating is fallen into using it as the cost of the circle interior nodes of radius；Choosing
The smallest node qmin of cost is selected, by it and qnew connection, and deletes the branch with qmin connection originally；Son of the qmin as qnew
Node is added in tree；
It repeats the above steps, obtains a series of leaf nodes；When a certain node is less than step-length at a distance from terminal qend,
Link two o'clock, if between collisionless, have found one from starting point qinit to the feasible path of terminal qend.
System prediction model in above-mentioned steps (4) is obtained by following methods:
The kinematics model of omni-directional mobile robots is expressed asIts
InIt is state of the OMR in cartesian coordinate,It is state of the OMR in world coordinates, H is
Transformation matrix, θcFor steering angle；
According to the model of omni-directional wheel, obtainWherein matrix R is obtained by the parameter of omni-directional wheel, determines OMR
Omni-directional, [v1 v2 v3]TFor the speed of three wheels of robot；
The inverse kinematics equation of OMR is
Enable S=R-1, then
Derive continuous time system equation
To formula (1) discretization, obtainWherein T is the sampling time；
It is converted into separate manufacturing firms model, and obtains X (k+1)=AX (k)+BU (k), wherein X (k+1) is next
The state at moment, X (k) are the state at the moment, and U (k) is the variable quantity of speed, and A, B are coefficient matrix.
Output model is Y (k)=CX (k)+DU (k), and wherein C, D are coefficient matrix.According to the theory of rolling optimization, at certain
The input at one moment can not influence the output at the moment, so matrix D is 0 matrix, then Y (k)=CX (k).
So prediction model is
Optimal input speed in above-mentioned steps (5) is obtained by following methods:
Assuming that control input is Δ u (ki),Δu(ki+1),...,Δu(ki+Np- 1), total NpIt is a,
State is x (ki+1|ki),x(ki+2|ki),...,x(ki+Nc|ki),...,x(ki+Np|ki)；
By state-space model, obtain
Wherein A, B, C are different
Coefficient matrix.
Definition vector
Y=[y (ki+1|ki)y(ki+2|ki)y(ki+3|ki)...y(ki+Np|ki)]T
Δ U=[Δ u (ki)Δu(ki+1)Δu(ki+2)...Δu(ki+Nc-1)]T
So prediction output Y=Fx (ki)+Φ Δ U, wherein
Assuming that set point signal r (ki), and kiThe closed-loop characteristic adjustment parameter at moment is rω；It enables
And transition matrixSo cost function
By minimizing cost function, optimum control input is obtained, i.e., the output of minimum forecasting system and expectation are with reference to defeated
Difference between out；
Consider input constraint Δ umin≤Δu(k)≤ΔumaxWith output constraint Ymin≤Fx(ki)+ΦΔU≤Ymax；
It is constrained due to existing, the analytic solutions of optimization problem can not be obtained, solved using numerical optimization；
For having a constrained MPC algorithm, simplified objective function be it is secondary, dynamical equation and time-domain constraints are lines
Property, therefore it is quadratic programming (QP) problem.The form of the quadratic programming of belt restraining is
Quadratic programming problem is solved by calling function library, then obtains optimum control input.We add for QP algorithm
Addition of constraints, including the upper limit/lower limit constraint and reference constraint, so that speed can be stablized near a value, to realize speed
Control.
The invention has the following advantages that
(1) RRT* algorithm is utilized, can quickly obtain the accessible path of a connection origin-to-destination, which connects
Nearly optimal path.
(2) by Model Predictive Control Algorithm, omni-directional mobile robots can be made quickly to be moved along path, is transported
The error very little in the path that dynamic track and RRT* algorithm obtains.
(3) by improved model, constraint of velocity is added wherein, can make robot that stable speed be kept to be transported
It is dynamic, it tallies with the actual situation.
Detailed description of the invention
Fig. 1 is trace tracking method flow chart of the invention.
Fig. 2 is route programming result schematic diagram of the invention.
Fig. 3 is the rate curve emulation (not having constraint of velocity) based on dummy robot of the present invention movement.
Fig. 4 is the rate curve emulation (having constraint of velocity) based on dummy robot of the present invention movement.
Fig. 5 is the motion profile emulation based on dummy robot of the present invention.
Fig. 6 is the kinematic error emulation based on dummy robot of the present invention.
Specific embodiment
The invention will be further described with reference to the accompanying drawing and by specific embodiment, and following embodiment is descriptive
, it is not restrictive, this does not limit the scope of protection of the present invention.
A kind of robot trace tracking method with constraint of velocity, flow chart is as shown in Figure 1, specifically include following step
It is rapid: to include the following steps:
(1) people moving region, starting point, barrier are set；
(2) path planning is carried out, first obtains path with the random tree algorithm of improved rapid discovery, then optimize to path
And curve matching, obtain a smooth path；
(3) according to the three of robot speed envelopes of wheel and the motion range of robot, constraint of velocity is established；
(4) system prediction model is established, the optimal input speed of subsequent time is predicted according to path node；
(5) step (4) are repeated, the optimal input speed at each moment is found out；
(6) it is moved according to optimal velocity input control robot.
The collisionless feasible path of a connection starting point is obtained by the random tree algorithm of improved rapid discovery；
Set spatial dimension X that robot moved (in specific implementation motion range as 21m*21m, but not limited to this),
Starting point qinit and terminal qend (starting point is (0m, 0m) in specific implementation, and terminal is (20m, 20m), but not limited to this), and with
Machine sets the quantity and size of barrier, and barrier is shaped to circle, is black region in Fig. 2, and white area is
The movable region of robot.The size and shape for ignoring robot, is regarded as particle.It is obtained by the planning of RRT* algorithm
Path be curve composed by blue node in figure, optimize, can link and collisionless point connection again later
Get up, reduce the length in path, finally after curve matching, a smooth curve is obtained, for red curve in figure.
The kinematics model of omni-directional mobile robots is
According to the model of omni-directional wheel, we are obtained
Wherein the order of matrix R is 3, it shows that Omni-mobile, θ may be implemented in robotcFor steering angle.
So the inverse kinematics equation of OMR is
Enable S=R-1, then
Therefore we can derive continuous time system equation
To above formula discretization, obtainWherein T is that the sampling time, (T was in specific implementation
0.02s, but not limited to this).
It is converted into separate manufacturing firms model, and obtains X (k+1)=AX (k)+BU (k), i.e.,
Wherein X (k+1) is the state of subsequent time, and X (k) is the state at the moment, U (k)=[Δ v1 Δv2 Δv3]T
For the variable quantity of speed, r is the radius of wheels of robot.
Assuming that control input is Δ u (ki),Δu(ki+1),...,Δu(ki+Np- 1) total NpIt is a,
State is x (ki+1|ki),x(ki+2|ki),...,x(ki+Nc|ki),...,x(ki+Np|ki)。
By state-space model, obtain
Wherein A, B, C are different coefficient matrixes.
Definition vector
Y=[y (ki+1|ki)y(ki+2|ki)y(ki+3|ki)...y(ki+Np|ki)]T
Δ U=[Δ u (ki)Δu(ki+1)Δu(ki+2)...Δu(ki+Nc-1)]T
So prediction output Y=Fx (ki)+Φ Δ U, wherein
Assuming that set point signal r (ki), and kiThe closed-loop characteristic adjustment parameter at moment is rω.It enables
And transition matrixSo cost function
Therefore, by minimize cost function, can obtain optimum control input, that is, minimize forecasting system output and
It is expected that with reference to the difference between output.
Consider input constraint Δ umin≤Δu(k)≤Δumax(input constraint is each wheel of robot in specific implementation
Rotational velocity range [- 2m/s, 2m/s], but not limited to this) and output constraint Ymin≤Fx(ki)+ΦΔU≤Ymax(specific implementation
Middle output constraint is moving region range [- 20m, 20m], but not limited to this).
QP is solved the problems, such as followed by function library is called, and then can obtain optimum control input.
The embodiment of the present invention is as follows:
In the present embodiment, rectangular area between simulating area (0m, 0m) and (21m, 21m), the starting point of robot is
(0m, 0m), target endpoint are (20m, 20m), the centre coordinate of barrier be respectively (5m, 5m), (6m, 13m), (10m,
8.5m), (15m, 14m), (16m, 5m), radius are respectively 2m, 2.5m, 2m, 3.5m, 3m.It is advised by the RRT* algorithm optimized
The path drawn is as shown in Fig. 2, be a smooth curve.
Example has carried out track following, and each input speed is as shown in Figure 3 and Figure 4.Top subgraph is the reality of robot
Border movement velocity, intermediate subgraph are the velocity component of robot in the x and y direction, and lower part subgraph is the angular speed of robot.Figure
3 be the result of not speed control.As can be seen that robot obtains certain speed at each node, then slowly restrain
To zero, and new initial velocity is obtained at next node.Such case can only actually realize multiple point-to-point stabilizations, not
Global speed control.Moreover, robot can often stop, and damage to robot, no when robot is in actually walking
It tallies with the actual situation.Fig. 4 is by speed control results, it can be seen that then robot is protected in zero moment acquisition initial velocity
Stable motion is held, and the time moved greatly reduces compared to Fig. 3.Robot rate curve in the x and y direction and its angle speed
Line of writing music all is smoothed curve, this illustrates the validity of speed control.
The result for the track following that example is carried out is as shown in figure 5, thick line is cooked up by the RRT* algorithm of optimization in figure
Path, filament be robot practical run trace.As can be seen that the curve movement of robot has been fitted has been planned well
Path out, two curves realize coincidence substantially.The error of path and actual motion curve is as shown in Figure 6, it can be seen that accidentally
For difference generally between -0.04m and 0.04m, worst error is no more than 0.07m.
Those skilled in the art can to the present invention be modified or modification design but do not depart from think of of the invention
Think and range.Therefore, if these modifications and changes of the present invention belongs to the claims in the present invention and its equivalent technical scope
Within, then the present invention is also intended to include these modifications and variations.
Claims (4)
1. a kind of robot trace tracking method with constraint of velocity, which comprises the steps of:
(1) people moving region, starting point, barrier are set；
(2) path planning is carried out, first obtains path with the random tree algorithm of improved rapid discovery, then path is optimized and bent
Line fitting, obtains a smooth path；
(3) according to the three of robot speed envelopes of wheel and the motion range of robot, constraint of velocity is established；
(4) system prediction model is established, the optimal input speed of subsequent time is predicted according to path node；
(5) step (4) are repeated, the optimal input speed at each moment is found out；
(6) it is moved according to optimal velocity input control robot.
2. a kind of robot trace tracking method with constraint of velocity according to claim 1, which is characterized in that described
The random tree algorithm of improved rapid discovery in step (2) is as follows:
Global context X is defined, wherein space with obstacle Xobstacle, clear space Xfree=X/Xobstacle, it is assumed that obstacle
The obstacle in space is previously known and static；Starting point qinit and terminal qend is located in clear space；The road to be planned
Diameter is a part for setting T, and tree is constructed by the line E one by one between sampled point V and sampled point to be formed, and wherein sampled point is known as leaf
Child node, line are known as branch；
Random point qrand is taken in X, finds node qnear nearest with qrand in T, and connection forms vector Vector；?
Vector is upper to take step-length step since qnear, forms new node qnew；If qnew and qnear line are sent out by collision detection
It is now collided, then abandons this secondary growth；
Node set is established near qnew, using qnew as the center of circle, preset R is that radius makees circular space caused by circle, than
Compared with the accumulated costs that will be set after the tree node fallen into circle and qnew connection, the smallest node of cost is selected to save as the father of qnew
Point qnear is added in tree；
Assuming that the new node qnew that tree is added is father node, calculating is fallen into using it as the cost of the circle interior nodes of radius；Select generation
The smallest node qmin of valence by it and qnew connection, and deletes the branch with qmin connection originally；Child node of the qmin as qnew
It is added in tree；
It repeats the above steps, obtains a series of leaf nodes；When a certain node is less than step-length at a distance from terminal qend, connection
Two o'clock, if between collisionless, have found one from starting point qinit to the feasible path of terminal qend.
3. a kind of robot trace tracking method with constraint of velocity according to claim 1, which is characterized in that described
System prediction model in step (4) is obtained by following methods:
The kinematics model of omni-directional mobile robots is expressed asWhereinIt is state of the OMR in cartesian coordinate,It is state of the OMR in world coordinates, H is to become
Change matrix, θcFor steering angle；
According to the model of omni-directional wheel, obtainWherein matrix R is obtained by the parameter of omni-directional wheel, determines that OMR's is complete
Tropism, [v1 v2 v3]TFor the speed of three wheels of robot；
The inverse kinematics equation of OMR is
Enable S=R-1, then
Derive continuous time system equation
To formula (1) discretization, obtainWherein T is the sampling time；
It is converted into separate manufacturing firms model, and obtains X (k+1)=AX (k)+BU (k), wherein X (k+1) is subsequent time
State, X (k) be the moment state, U (k) be speed variable quantity, A, B be coefficient matrix；
Output model is Y (k)=CX (k)+DU (k), and wherein C, D are coefficient matrix；According to the theory of rolling optimization, in certain a period of time
The input at quarter can not influence the output at the moment, so matrix D is null matrix, then Y (k)=CX (k)；
So prediction model is
4. a kind of robot trace tracking method with constraint of velocity according to claim 1, which is characterized in that described
Optimal input speed in step (5) is obtained by following methods:
Assuming that control input is Δ u (ki),Δu(ki+1),...,Δu(ki+Np- 1), total NpIt is a,
State is x (ki+1|ki),x(ki+2|ki),...,x(ki+Nc|ki),...,x(ki+Np|ki)；
The state-space model obtained by step (4)?
Definition vector
Y=[y (ki+1|ki) y(ki+2|ki) y(ki+3|ki)...y(ki+Np|ki)]T
Δ U=[Δ u (ki) Δu(ki+1) Δu(ki+2)...Δu(ki+Nc-1)]T
So prediction output Y=Fx (ki)+Φ Δ U, wherein
Assuming that set point signal r (ki), and kiThe closed-loop characteristic adjustment parameter at moment is rω；It enablesWith turn
Change matrixSo cost function
By minimizing cost function, optimum control input is obtained, i.e., the output of minimum forecasting system and expectation are with reference to output
Between difference；
Consider input constraint Δ umin≤Δu(k)≤ΔumaxWith output constraint Ymin≤Fx(ki)+ΦΔU≤Ymax；
It is constrained due to existing, the analytic solutions of optimization problem can not be obtained, solved using numerical optimization；
The form of the quadratic programming of belt restraining is
Quadratic programming problem is solved by calling function library, then obtains optimum control input.
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| CN114237047A (en) * | 2021-12-10 | 2022-03-25 | 广东工业大学 | Time optimal speed planning method and system based on constraint classification |
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