CN109597310B - Wheeled mobile robot track tracking method based on disturbance observer - Google Patents
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Abstract
The invention discloses a wheel type mobile robot track tracking method based on a disturbance observer, which introduces a slip degree in the design of a kinematics controller, and expresses the difference between an actual pose and an expected pose, if a mobile wheel type robot can be stabilized within a limited time, namely the actual motion track and the expected motion track can be overlapped within the limited time, and based on the result, a kinematics linear speed controller and an kinematics angular speed controller are designed; in the design of the dynamic torque controller, lumped disturbance is introduced firstly, an observer is designed to estimate the disturbance, and the dynamic torque controller is designed on the basis; the stability was demonstrated using the lyapunov function. The method solves the problem of how to track the track of the wheeled mobile robot under the conditions of slipping, external interference and the like, thereby realizing track tracking control of the robot.
Description
Technical Field
The invention belongs to the field of mobile robot trajectory tracking control, and particularly relates to a wheeled mobile robot trajectory tracking control method based on a disturbance observer.
Background
In recent years, the robot technology has been rapidly developed and is receiving more and more attention, and since the last century, robots are widely applied to various fields, and bring much convenience to the life of people. The robot integrates a plurality of high-tech technologies, is widely applied to various dangerous environments such as geographic survey, mine sweeping, rescue and the like, can complete a plurality of tasks which cannot be competed by human beings, and is an important mark of human social progress. Meanwhile, in the field of industrial production, the robot helps people to improve the production efficiency, reduce the production cost and promote social progress.
Wheeled mobile robots are one of the most important and challenging problems in the field of robots, which means that the robots are no longer fixed in a certain position for corresponding operations, which makes the robot work more flexible. In recent years, many scholars have conducted extensive research in the field of mobile wheeled robots, and have achieved certain results. At present, the wheeled mobile robot has incomparable advantages in the fields of material handling, dangerous area detection, industrial transportation assembly, moon and mars detection and the like, so that the wheeled mobile robot is widely applied.
The feedback control of the wheeled mobile robot is mainly divided into three aspects of point stabilization, path following and track tracking, wherein the point stabilization means that the robot starts from a set initial position to an end position, the path following means that a specified track is followed all the way from the initial position, and the track tracking means that a reference track can be tracked in real time. The scheme mainly utilizes adaptive control to research the track tracking. The core content of the scheme is how to stabilize the motion state within a limited time when the mobile wheeled robot slides with the ground because the external environment of the robot cannot be unchanged in the motion process.
Disclosure of Invention
The invention aims to provide a method for tracking a track of a wheeled mobile robot based on a disturbance observer, which solves the problem of tracking the track of the wheeled mobile robot under the conditions of slipping, external interference and the like, so that the robot can realize track tracking control.
In order to achieve the above purpose, the solution of the invention is:
a wheeled mobile robot track tracking method based on a disturbance observer comprises the following steps:
and 3, superposing the sum of external disturbances which can cause speed change, namely the lumped disturbance eta, designing a disturbance observer to estimate the disturbance eta, and designing a dynamic torque controller based on the disturbance observer to drive the wheeled mobile robot to generate corresponding speed.
After the scheme is adopted, the invention introduces the slip degree S in the design of the kinematic controllerL,SRBy using SL,SRAnd expressing the difference between the actual pose and the expected pose, and designing a kinematic linear velocity controller and an angular velocity controller based on the fact that the actual motion track and the expected motion track can be overlapped in a limited time if the mobile wheeled robot can be stable in the limited time. In the design of the dynamic torque controller, firstly, lumped disturbance eta is introduced, an observer is designed to estimate the disturbance eta, and the dynamic torque controller is designed on the basis. The stability is proved by utilizing the Lyapunov function, and through analysis, the track tracking control method for the mobile wheeled robot system with the interference, wheel slip, parameter perturbation and the like can stabilize the whole system and has a good tracking effect.
Drawings
Fig. 1 is a schematic view of a model of a mobile wheeled robot according to the present invention;
FIG. 2 is a schematic diagram of the actual trajectory and the expected trajectory of the mobile wheeled robot in the present invention;
fig. 3 is a schematic diagram showing the change of the slip degree of the left and right wheels of the mobile wheeled robot with time;
FIG. 4 is a left wheel torque controller τ of the wheeled mobile robotlA time-varying situation diagram;
FIG. 5 is a right wheel torque controller τ of the wheeled mobile robotrA time-varying situation diagram;
fig. 6 is a trend graph of a difference between an expected pose and an actual pose of the wheeled mobile robot over time;
fig. 7 is a graph showing the variation of angular velocity and linear velocity of the wheeled mobile robot with time;
fig. 8 is a schematic diagram of the present invention.
Detailed Description
The technical solution and the advantages of the present invention will be described in detail with reference to the accompanying drawings.
As shown in fig. 8, the present invention provides a method for tracking a trajectory of a wheeled mobile robot based on a disturbance observer, including the following steps:
wherein the kinematic model of the wheeled mobile robot is represented as:
wherein q is [ x, y, θ ]]TAnd (5) representing poses, v and w respectively representing linear velocity and angular velocity of the wheeled mobile robot.
The desired trajectory of the wheeled mobile robot is:
wherein q isr＝[xr,yr,θr]T(vi) represents the expected pose, (v)r,wr) Is the expected linear velocity and the angular velocity, so that the error q between the expected track and the actual motion track can be obtainedeComprises the following steps:
considering the slip, the constraint conditions are:
wherein u is a lateral slip speed,
the angular velocities of the left and right wheels of the robot,
representing the angular velocity of the left and right wheels caused by the slip, the distance between the two wheels of the robot being 2b, r being the radius of the left and right wheels of the robot, as shown in fig. 1, the above equation can be rewritten as
Wherein R [ -u, -R ζ1,-rζ2]T，
J (q) is the null-space matrix of A (q). Thus, the posture expression can be rewritten as
Wherein
Is a mismatched perturbation vector caused by perturbation non-integrity constraint, z ═ v, ω]T。
wherein v isL,vRRepresenting the actual speed of the left and right wheels of the robot, which can be obtained by an encoder; v. ofL',vR' indicates the speed of the left and right wheels when the robot slips.
Due to the fact that at SL,SRIn the formula (III), vL',vR' unknown, so v, ω is re-expressed to give:
substitute it into
Can be obtained from
This gives:
as shown in fig. 3, a kinematic model of the difference between the actual pose and the expected pose of the robot can be obtained at this time:
utilizing kinematic trajectory errors to design a Lyapunov function as follows:
if the system is stable, the Lyapunov function should be greater than or equal to 0, and its derivative should be less than 0.
Based on Lyapunov function and kinematic error model
In order to make the error asymptotically approach to 0, the kinematic controller (including the linear velocity controller and the angular velocity controller) is designed as follows:
wherein v isr,ωrDesired linear and angular velocities, k, respectively, of the wheeled mobile robotx,kyIs a normal number, qe＝[xe,ye,θe]TIs the pose difference between the actual pose and the expected pose of the robot.
Substituting the designed kinematic controller into the derivative of the Lyapunov function
In (1), obtaining:
wherein M (q) is a positive definite symmetric inertial matrix,
is a centripetal Coriolis matrix, G (q) is a gravity vector, τdIs the unknown disturbance, B (q) is the input transformation matrix, λ is the constraint force vector, and τ is the input moment.
After conversion, the following are obtained:
wherein z is [ v, ω ═ v]T，ξ＝[ξ1,ξ2]T，ξ1＝r(ζ1+ζ2) Per 2 is the longitudinal slip speed, xi2＝r(ζ1-ζ2) And/2 b is the yaw rate disturbance caused by wheel slip, G is the gravity vector,
is composed of
C is a centripetal coriolis matrix and Δ C is the direction due to slipThe difference in the cardiac coriolis matrix is,
j (q) is the null-space matrix of A (q);
and (3) taking the sum of all external interferences causing the speed change of the robot as lumped disturbance eta, and transforming the above formula to obtain a new dynamic model:
wherein the content of the first and second substances,
is that
An estimate of (d).
wherein the content of the first and second substances,
Γ＝γdiag{1,1}，
gamma > 0, for phiiThere are maximum and minimum values, i.e. 0 < phiimin＜Φi＜ΦimaxAnd is and
the above adaptation law satisfies the following conditions: (1)
is continuous; (2) if it is
Then
Satisfy the requirement of
(3)
Based on the above dynamic model, the disturbance observer is designed as follows:
wherein the content of the first and second substances,
to aggregate an estimate of the disturbance η, L is the gain matrix of the observer. Derived from adaptive control laws
Is a diagonally symmetric matrix and is invertible.
And 5, designing the self-adaptive torque controller based on the step 4 as follows:
wherein the content of the first and second substances,
sgn (·) is a sign function,
u＝[xe,sinθe]T. In the kinetic model, v ≠ vc,ω≠ωc. The control torque of the left and right wheels changes with time when the wheeled mobile robot encounters a slip as shown in fig. 4 to 5.
The lyapunov function is designed as follows:
wherein the content of the first and second substances,
substituting dynamic torque controller into derivative of Lyapunov function
In (1), obtaining:
wherein the content of the first and second substances,
in summary, it can be seen that:
since the wheel-type mobile robot is insensitive when it encounters external disturbance and the speed cannot rapidly change relatively greatly, it is possible to obtain that, when t → ∞,
meanwhile, assuming that all external disturbances and the first-order derivatives thereof are bounded, the speed change caused by external disturbance and sliding is far less than the normal moving speed of the robot. If a suitable gain matrix L is selected such that
Becoming a hervitz matrix. By the Lyapunov function
Can be obtained if
Then
From the above analysis, when t → ∞,
therefore l2When the content is more than or equal to 0, the content can be satisfied
Under the action of the kinematics controller and the dynamics moment controller, the effect of the wheeled mobile robot tracking the circular track is shown in fig. 2, the change of the pose difference along with the time is shown in fig. 6, and the linear velocity and the angular velocity of the mobile robot are shown in fig. 7.
In summary, the present invention is composed of a kinematics controller, a disturbance observer, and a dynamic torque controller. The kinematic controller is composed of linear speed and angular speed controllers, and introduces the slip degree S of the left and right wheels into the kinematic modelL,SRThe parameter represents the difference between the actual pose and the expected pose of the wheeled mobile robot, and if the robot can realize track tracking, the robot can realize track tracking within a limited time SL,SRBased on this, a kinematic controller was designed to be 0. When designing a dynamic torque controller, firstly, the sum of external disturbances which can cause speed change is called as lumped disturbance eta, and a disturbance observer is designed to estimate the external disturbances. Simulation experiments show that the controller provided by the invention can enable the wheeled mobile robot to reach a stable state within a limited time when slipping, and has good robustness.
The above embodiments are only for illustrating the technical idea of the present invention, and the protection scope of the present invention is not limited thereby, and any modifications made on the basis of the technical scheme according to the technical idea of the present invention fall within the protection scope of the present invention.
Claims (6)
1. A wheeled mobile robot track tracking method based on a disturbance observer is characterized by comprising the following steps:
step 1, establishing a kinematic model and a dynamic model of a wheeled mobile robot;
step 2, introducing the slip degree S of the left wheel and the right wheel of the wheeled mobile robotL,SRRepresenting a kinematics model of the wheeled mobile robot, further obtaining the difference between the actual pose and the expected pose of the robot, and designing a kinematics controller;
step 3, superposing the sum of external disturbances which can cause speed change, namely lumped disturbance eta, designing a disturbance observer to estimate the disturbance eta, and designing a dynamic torque controller based on the disturbance observer to drive the wheeled mobile robot to generate corresponding speed; based on the lumped disturbance eta, the expression of the obtained dynamic model is as follows:
wherein the content of the first and second substances,
is that
Is determined by the estimated value of (c),
representing the adaptive control law, j (q) is the null-space matrix of a (q), m (q) is the positive definite symmetric inertial matrix, τ is the input moment, B is the input transformation matrix, z ═ v, ω]TV, ω respectively represent the linear velocity and angular velocity of the wheeled mobile robot;
wherein xi is ═ xi [1,ξ2]T，
Representing the angular velocity of the left and right wheels caused by the slip; c is the centripetal coriolis matrix and,
is the mismatched perturbation vector caused by perturbation incomplete constraint, G is the gravity vector, τdIs an unknown disturbance.
2. The method of claim 1, wherein: in step 1, the kinematic model of the wheeled mobile robot is expressed as:
wherein q is [ x, y, θ ]]TAnd (5) representing poses, v and w respectively representing linear velocity and angular velocity of the wheeled mobile robot.
3. The method of claim 1, wherein: in the step 1, the kinetic model of the wheeled mobile robot is:
wherein M (q) is a positive definite symmetric inertial matrix,
is a centripetal Coriolis matrix, G (q) is a gravity vector, τdIs an unknown disturbance, B (q) is an input transformation matrix, λ is a constraint force vector, AT(q) is the transpose of A (q), the matrix A (q) being:
4. the method of claim 1, wherein: in the step 2, the slip degree SL,SRIs defined as:
wherein v isL,vRRepresenting the actual speed, v, of the left and right wheels of the robotL',vR' indicates the speed of the left and right wheels when the robot slips.
5. The method of claim 1, wherein: in the step 2, the designed kinematics controller is as follows:
wherein v isr,ωrDesired linear and angular velocities, k, respectively, of the wheeled mobile robotx,kyIs a normal number, xe,ye,θeIs the difference between the actual pose and the expected pose of the robot.
6. The method of claim 1, wherein: in the step 3, the designed disturbance observer is as follows:
wherein beta is an intermediate variable, has no actual physical meaning,
is the derivative of the beta-value of,
b is the input matrix and B is the input matrix,
to aggregate an estimate of the disturbance η, L is the gain matrix of the observer.
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| CN113835339B (en) * | 2021-07-29 | 2023-10-27 | 东南大学 | Super-spiral sliding mode track tracking method for wheeled mobile robot |
| CN114609911B (en) * | 2022-03-15 | 2022-11-25 | 中国科学院重庆绿色智能技术研究院 | Anti-interference self-adaptive force and position coordination control method |
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