CN108153309B - Control method for tracked robot and tracked robot - Google Patents
Control method for tracked robot and tracked robot Download PDFInfo
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Abstract
The invention relates to the field of motion control of mobile robots and discloses a control method for a tracked robot and the tracked robot. The crawler robot is regarded as a cascade system consisting of a motor driving system and a vehicle body motion system, an adaptive integral sliding mode switching function of variable inclination parameters is constructed, adaptive sliding mode tracking control based on equivalent control and switching control is provided according to the adaptive integral sliding mode switching function, the obtained time-varying uncertain parameters of the driving motor are identified on line according to the speed of the robot, errors between the obtained time-varying uncertain parameters and target poses in a kinematic model are fed back to a controller of the driving system, and then the expected speed of each motor is decomposed according to the kinematic relationship, so that stable motion control of the robot is realized.
Description
Technical Field
The present invention relates to a mobile robot motion control, and more particularly, to a control method for a tracked robot and a tracked robot.
Background
With the wide application of Agricultural Tracked Robots (ATR), higher requirements are put forward on the adaptability, the control accuracy and the motion stability of a Robot system. However, the farmland topography is complex, the environment is variable, and the design and use difficulty of the ATR control system is increased due to the strong coupling and model uncertainty of the ATR system.
Therefore, scholars at home and abroad deeply research the trajectory tracking control, some scholars put forward various trajectory tracking controls, mainly utilize kinematic models or models combining kinematics or dynamics, and some scholars put forward a linear feedback method, a PID control method, a moment calculation method, a backstepping method, a sliding mode control method, a neural network control method, a fuzzy control method and the like. The linear feedback method is a common control method, and the ATR model is nonlinear, so the control precision is low; the PID control method has poor control effect on a nonlinear and structure uncertain system because the control parameters are fixed; the moment calculation method depends on a dynamic model of a controlled object, and the dynamic modeling is very complex and difficult to construct, so the theoretical and practical significance of the method is not great; although the neural network method can overcome the uncertainty and unknown disturbance of the system, the control algorithm is complex; the fuzzy control does not need to establish an accurate mathematical model, is suitable for the control of a nonlinear time-varying and lagging system, but the selection of the fuzzy rule lacks systematicness and is difficult to adjust on line; the backstepping method uses virtual control quantity and carries out iterative derivation, so that the structure of the controller is very complex and the engineering realization difficulty is high.
The complexity of the farm environment makes there a lot of uncertainty in the ATR campaign, such as: parameter perturbations and load disturbances, as well as measurement errors from the sensors, can cause the ATR's trajectory to deviate from the reference path. The conventional control method is difficult to meet the requirement of high-precision trajectory tracking control. The modular variable structure control has the advantages of robustness of quick transient response, independence on an accurate mathematical model of a controlled object, insensitivity to parameter and environmental change and simple engineering realization, thereby being suitable for the control of the robot in the farmland environment.
Disclosure of Invention
The invention aims to provide a control method for a tracked robot, which realizes the control of the motion track of the tracked robot by establishing an adaptive sliding mode tracking control model and improves the control precision.
In order to achieve the above object, the present invention provides a control method for a tracked robot, comprising the steps of:
acquiring the pose of the tracked robot in the current state;
setting a reference track of the tracked robot, wherein the reference track comprises a pose instruction and a speed instruction;
establishing a kinematic model for describing a constraint relation between the pose of the tracked robot and the speed of the tracked robot, wherein the speed comprises an angular speed and a linear speed;
establishing a pose error model of the tracked robot according to the pose in the current state and the set reference track;
establishing a pose error differential model of the tracked robot according to the kinematics model and the pose error model;
establishing a driving model of a left motor for driving a left driving wheel and a right motor for driving a right driving wheel of the tracked robot, wherein the driving model comprises a moment driving model and a potential balance model;
obtaining dynamic models of the left motor and the right motor according to the moment driving model and the potential balance model;
establishing a self-adaptive sliding die cutting and changing model which changes along with parameter adjustment;
obtaining an expected speed of the tracked robot according to the pose error differential model and the self-adaptive sliding die cutting model, wherein the expected speed comprises an expected linear speed and an expected angular speed;
and obtaining the expected angular speeds of the left motor and the right motor according to the expected speed of the tracked robot.
Preferably, the control method further includes:
establishing a switching control model for correcting the expected speed of the tracked robot;
correcting the expected speed of the tracked robot by adopting a switching control model and obtaining the corrected expected speed of the tracked robot;
obtaining the expected angular speeds of the left motor and the right motor according to the corrected expected speed;
and calculating the driving voltages of the left motor and the right motor according to the expected angular speeds of the left motor and the right motor and the dynamic models of the left motor and the right motor.
Preferably, the kinematic model describing the constraint relationship between the pose of the tracked robot and the speed of the tracked robot is represented by equation (1):
wherein X and y are respectively the position coordinates of the barycenter of the crawler robot in an XOY coordinate system, theta is the included angle between the motion direction of the crawler robot and an X axis, v and omega are respectively the linear velocity and the angular velocity of the crawler robot, d is the distance between the barycenter of the crawler robot and a geometric center,
and
the derivatives of x, y, and θ, respectively, with respect to time;
according to the pose of the tracked robot in the current state and the set reference track, the established pose error model of the tracked robot is represented by the formula (2):
wherein, (x, y, theta)TThe pose of the tracked robot in the current state is shown, X and y are coordinates of the current position of the mass center of the tracked robot respectively, and theta is an included angle between the motion direction of the tracked robot and an X axis in the current state, (X is the included angle between the motion direction of the tracked robot and the X axis)r,yr,θr)TAs a pose instruction, xr、yrAre respectively provided withCoordinates of a target position, theta, being the center of mass of the crawler robotrIs the included angle between the moving direction of the crawler robot and the X axis when the crawler robot reaches the target position, XeIs the error value of the current position of the mass center of the crawler robot and the target position along the current movement direction of the crawler robot, yeThe error value of the current position of the mass center of the crawler robot and the error value of the target position in the direction perpendicular to the current motion direction of the crawler robot is thetaeIs theta and thetarAn error value therebetween;
the pose error differential model of the crawler robot is established according to the kinematic model and the pose error model:
wherein the content of the first and second substances,
are respectively xe、yeAnd thetaeThe time derivative, v and omega are respectively the linear velocity and the angular velocity of the crawler robot in the current state, (v)r,ωr)TFor speed command, vrAnd ωrRespectively, the linear velocity and the angular velocity when the crawler robot reaches the target position, and d is the distance between the centroid and the geometric center of the crawler robot.
Preferably, the torque balance models of the right motor and the left motor are represented by equations (4) and (5), respectively:
wherein, Jr(t)、Jl(t) the rotational inertia of the rotating shafts of the right motor and the left motor, respectively, F the viscous friction coefficient on the output shafts of the left motor and the right motor, and ktOf left and right motorsCoefficient of electromagnetic torque, Tdr(t)、Tdl(t) the disturbing moments, omega, respectively experienced by the right and left motorsr(t)、ωl(t) the angular speeds of the rotation of the rotating shafts of the left motor and the right motor respectively,
and
are respectively omegar(t) and ωl(t) derivative with time, ir(t)、il(t) armature currents of the right motor and the left motor, respectively;
the potential balance models of the right motor and the left motor are respectively expressed by an equation (6) and an equation (7):
wherein L is the armature inductance of the left motor and the right motor, R is the armature resistance of the left motor and the right motor, keIs the back electromotive force coefficient of the left and right motors, and ke＝0.10472kt，ktIs the electromagnetic torque coefficient of the left motor and the right motor,
and
are respectively ir(t) and il(t) derivative with time, ur(t) and ul(t) driving voltage of the right motor and driving voltage of the left motor, respectively;
the dynamic models of the right motor and the left motor obtained from the torque driving model and the potential balance model are expressed by equations (8) and (9):
wherein, Tl(t)＝RJl(t)/(RF+kTke)，Tr(t)＝RJr(t)/(RF+kTke)，
k1＝kt/(RF+kTke)，k2＝R/(RF+kTke) R is the armature resistance of the left and right motors, Jr(t)、Jl(t) the rotational inertia of the rotating shafts of the right motor and the left motor, respectively, F the viscous friction coefficient on the output shafts of the left motor and the right motor, and ktIs the electromagnetic torque coefficient, T, of the left and right motorsdr(t)、TdlAnd (t) the interference torque suffered by the right motor and the left motor respectively.
Preferably, the established adaptive sliding die switching model which changes along with parameter adjustment is represented by an equation (10):
wherein alpha is1And alpha2In order to be a parameter of the tilt,
c1、c2、c3、c4、kk1、kk2are all normal numbers, s1And s2Are each with respect to xeAnd thetaeThe switching function of (2);
preferably, the expected speed of the crawler robot obtained according to the pose error differential model and the adaptive sliding die swap model is represented by equation (11):
wherein v isdAnd ωdRespectively, a desired linear velocity and a desired angular velocity of the crawler robot.
Preferably, the switching control model is represented by equation (12):
wherein, beta1、β2Switching gain, β, greater than zero1、β2、Δ1And Δ2Are empirical values, sat is a saturation function;
the corrected desired speed of the crawler robot is represented by equation (13):
wherein, v'dAnd ω'dRespectively the corrected desired linear velocity and the corrected desired angular velocity of the crawler robot,
is v isrDerivative with respect to time, beta1、β2Switching gain, β, greater than zero1、β2、Δ1And Δ2Are empirical values, sat is a saturation function;
the desired angular velocities of the right and left motors are represented by equations (14) and (15), respectively:
ωrd＝(v′d+ω′dA)r-1formula (14)
ωld＝(v′d-ω′dA)r-1Formula (15)
Wherein, ω isrdAnd ωldA desired angular velocity of the right motor and a desired angular velocity of the left motor, respectively, a being half of the distance between the left and right drive wheels,r is the radius of the left and right drive wheels.
In another aspect, embodiments of the present invention also provide a crawler robot, including: the left driving wheel is used for driving the left crawler; a right drive wheel for driving the right track; the left motor is used for driving the left driving wheel; a right motor for driving the right driving wheel; the sensor is used for detecting the pose of the tracked robot in the current state, and the pose comprises the position and the inclination angle of the tracked robot in an appointed coordinate system; and a controller for executing the above-described control method for the track robot.
According to the technical scheme, the crawler robot is regarded as a cascade system consisting of a motor driving system and a vehicle body motion system, a self-adaptive integral sliding mode switching function with variable inclination parameters is constructed, self-adaptive sliding mode tracking control based on equivalent control and switching control is provided according to the self-adaptive integral sliding mode switching function, the time-varying uncertain parameters of the obtained driving motor are identified on line at the speed of the robot, errors between the obtained driving motor and a target pose in a kinematic model are fed back to a controller of the driving system, then the expected speed of each motor is decomposed according to the kinematic relationship, and stable motion control of the robot is achieved.
Additional features and advantages of the invention will be set forth in the detailed description which follows.
Drawings
The accompanying drawings, which are included to provide a further understanding of the invention and are incorporated in and constitute a part of this specification, illustrate embodiments of the invention and together with the description serve to explain the principles of the invention and not to limit the invention. In the drawings:
fig. 1 is a flowchart of a control method for a tracked robot according to an embodiment of the present invention;
fig. 2 is a flowchart of a control method for a tracked robot according to an embodiment of the present invention;
fig. 3 illustrates a model diagram of a crawler robot according to an embodiment of the present invention;
FIG. 4 illustrates a pose error model diagram for a tracked robot according to an embodiment of the present invention;
FIG. 5 shows a response curve for the angular velocity of the left motor;
FIG. 6 shows a tracking error curve for the angular velocity of the left motor;
FIG. 7 shows a voltage output curve for the left motor;
fig. 8 shows a broken line movement locus of the crawler robot;
fig. 9 shows a tracking error curve of a polygonal line movement locus of the crawler robot;
FIG. 10 shows angular velocity response curves for left and right motors;
fig. 11 shows a circular motion trajectory of the crawler robot;
fig. 12 shows a tracking error curve of a circular motion trajectory of the crawler robot;
FIG. 13 shows angular velocity response curves for left and right motors;
fig. 14 shows a movement locus of a crawler robot when the ASMTC control method is adopted; and
fig. 15 shows a pose error curve of a motion trajectory of the crawler robot when the ASMTC control method is employed.
Detailed Description
The following detailed description of embodiments of the invention refers to the accompanying drawings. It should be understood that the detailed description and specific examples, while indicating the present invention, are given by way of illustration and explanation only, not limitation.
Fig. 1 is a flowchart of a control method for a tracked robot according to an embodiment of the present invention. As shown in fig. 1, an embodiment of the present invention provides a control method for a tracked robot, which may include the steps of:
in step S101, a pose of the tracked robot in the current state is acquired;
in step S102, a reference trajectory of the tracked robot is set, where the reference trajectory includes a pose instruction and a speed instruction;
in step S103, establishing a kinematic model describing a constraint relationship between the pose of the tracked robot and the speed of the tracked robot, the speed including an angular speed and a linear speed;
in step S104, a pose error model of the tracked robot is established according to the pose in the current state and the set reference trajectory;
in step S105, a pose error differential model of the tracked robot is established according to the kinematic model and the pose error model;
in step S106, a driving model of a left motor for driving a left driving wheel and a right motor for driving a right driving wheel of the tracked robot is established, the driving model including a moment driving model and a potential balance model;
in step S107, dynamic models of the left motor and the right motor are obtained from the torque drive model and the potential balance model;
in step S108, an adaptive sliding die conversion model that changes with parameter adjustment is established;
in step S109, a desired speed of the tracked robot is obtained according to the pose error differential model and the adaptive sliding die shift model, and the desired speed includes a desired linear speed and a desired angular speed.
In step S110, desired angular velocities of the left and right motors are obtained according to a desired velocity of the tracked robot.
Fig. 3 illustrates a model diagram of a crawler robot according to an embodiment of the present invention. As shown in fig. 3, the pose of the tracked robot refers to the position and posture (inclination degree) of the tracked robot in the XOY coordinate system, and p ═ x, y, θ is adopted in the present inventionTThe pose of the tracked robot is shown.
The reference track of the tracked robot refers to a specified position to which the tracked robot is to reach, and the inclination angle, the running linear speed and the running angular speed of the tracked robot when the tracked robot reaches the specified position.
As shown in FIG. 3, point m is the center of mass of the tracked robot, and point OaFor the geometric center of the crawler robot, a kinematic model describing a constraint relationship between the pose of the crawler robot and the velocity of the crawler robot may be represented by, for example, equation (1):
wherein X and y are respectively the position coordinates of the barycenter of the crawler robot in an XOY coordinate system, theta is the included angle between the motion direction of the crawler robot and an X axis, v and omega are respectively the linear velocity and the angular velocity of the crawler robot, d is the distance between the barycenter of the crawler robot and a geometric center,
and
the derivatives of x, y and theta with respect to time, respectively.
Fig. 4 shows a pose error model diagram of a tracked robot according to an embodiment of the present invention. As shown in fig. 4, the pose error model of the tracked robot, which is established according to the pose of the tracked robot in the current state and the set reference trajectory, may be represented by equation (2):
wherein, (x, y, theta)TThe pose of the tracked robot in the current state is shown, X and y are coordinates of the current position of the mass center of the tracked robot respectively, and theta is an included angle between the motion direction of the tracked robot and an X axis in the current state, (X is the included angle between the motion direction of the tracked robot and the X axis)r,yr,θr)TAs a pose instruction, xr、yrCoordinates of the target position, theta, respectively, of the center of mass of the crawler robotrIs the included angle between the moving direction of the crawler robot and the X axis when the crawler robot reaches the target position, XeIs the error value of the current position of the mass center of the crawler robot and the target position along the current movement direction of the crawler robot, yeThe error value of the current position of the mass center of the crawler robot and the error value of the target position in the direction perpendicular to the current motion direction of the crawler robot is thetaeIs theta and thetarTo an error value therebetween.
Differentiating the formula (2) and obtaining a pose error differential model of the tracked robot by combining the formula (1), wherein the pose error differential model can be represented by a formula (3) for example:
wherein the content of the first and second substances,
are respectively xe、yeAnd thetaeThe time derivative, v and omega are respectively the linear velocity and the angular velocity of the crawler robot in the current state, (v)r,ωr)TFor speed command, vrAnd ωrRespectively the linear velocity and the angular velocity when the crawler robot reaches the target position.
The driving actuator of the tracked robot is a left motor for driving the left driving wheel and a right motor for driving the right driving wheel, and the left motor and the right motor may be, for example, direct current motors. Under different road conditions, the left motor and the right motor rotate in a coordinated mode according to different control targets to drive the tracked robot to move, and therefore the movement control of the tracked robot is the coordinated control of the left motor and the right motor.
The torque balance models of the right motor and the left motor can be represented by, for example, equations (4) and (5), respectively:
wherein, Jr(t)、Jl(t) the rotational inertia of the rotating shafts of the right motor and the left motor, respectively, F the viscous friction coefficient on the output shafts of the left motor and the right motor, and ktIs the electromagnetic torque coefficient, T, of the left and right motorsdr(t)、Tdl(t) each isFor the disturbing moment, omega, to which the right and left motors are subjectedr(t)、ωl(t) the angular speeds of the rotation of the rotating shafts of the right motor and the left motor respectively,
and
are respectively omegar(t) and ωl(t) derivative with time, ir(t)、ilAnd (t) armature currents of the right motor and the left motor respectively.
The potential balance models of the right motor and the left motor can be represented by, for example, equations (6) and (7), respectively:
wherein L is the armature inductance of the left motor and the right motor, R is the armature resistance of the left motor and the right motor, keIs the back electromotive force coefficient of the left and right motors, and ke＝0.10472kt，ktIs the electromagnetic torque coefficient, omega, of the left and right motorsr(t)、ωl(t) angular velocities of rotation of the rotating shafts of the right motor and the left motor, ir(t)、il(t) armature currents of the right motor and the left motor respectively,
and
are respectively ir(t) and il(t) derivative with time, ur(t) and ulAnd (t) are respectively the driving voltage of the right motor and the driving voltage of the left motor.
Since the left motor and the right motor are the executing mechanisms of the crawler robot, the response speed is high, and the dynamic models of the right motor and the left motor can be represented by equations (8) and (9) under the condition of neglecting the armature inductance of the motors:
wherein, Tl(t)＝RJl(t)/(RF+ktke)，Tr(t)＝RJr(t)/(RF+ktke)，
k1＝kt/(RF+ktke)，k2＝R/(RF+ktke) R is the armature resistance of the left and right motors, Jr(t)、Jl(t) the rotational inertia of the rotating shafts of the right motor and the left motor, respectively, F the viscous friction coefficient on the output shafts of the left motor and the right motor, and ktIs the electromagnetic torque coefficient, T, of the left and right motorsdr(t)、TdlAnd (t) the interference torque suffered by the left motor and the right motor respectively.
Due to the characteristics of multiple inputs and nonlinearity of the pose error differential model, in one embodiment of the invention, the self-adaptive sliding die switching model which changes along with parameter adjustment is established, so that the integral term can be limited under the condition of large pose error, a certain amplification effect is realized under the condition of small pose error, and the control precision is improved.
The adaptive sliding die switching model that varies with parameter adjustment can be represented by, for example, equation (10):
wherein alpha is1And alpha2In order to be a parameter of the tilt,
vris the linear velocity when the crawler robot reaches the target position, c1、c2、c3、c4、kk1、kk2Are all normal numbers, s1And s2Are each with respect to xeAnd thetaeThe switching function of (2);
the derivative of time for equation (10) can yield equation (11):
wherein, the first and second guide rollers are arranged in a row,
and
are respectively s1And s2Derivative with respect to time.
Formula (12) can be obtained by bringing formula (3) into formula (11):
wherein the content of the first and second substances,
is v isrThe derivative with respect to time,.
Making equation (12) equal to zero may result in a desired speed of the tracked robot, which may be represented by equation (13), for example:
wherein v isdAnd ωdRespectively, a desired linear velocity and a desired angular velocity of the crawler robot.
Fig. 2 is a flowchart of a control method for a tracked robot according to an embodiment of the present invention. As shown in fig. 2, in an embodiment of the present invention, a control method for a tracked robot is provided, and the control method shown in fig. 2 may further include the following steps compared with the control method shown in fig. 1:
in step S210, a switching control model for correcting a desired speed of the tracked robot is established;
in step S211, correcting the desired speed of the tracked robot by using the switching control model and obtaining the corrected desired speed of the tracked robot;
in step S212, obtaining desired angular velocities of the left motor and the right motor according to the corrected desired velocity;
in step S213, the driving voltages of the left and right motors are calculated from the desired angular velocities of the left and right motors and the dynamic models of the left and right motors.
In an embodiment of the present invention, the switching control model for correcting the desired speed of the tracked robot can be represented by, for example, equation (12):
wherein, beta1、β2Switching gain, β, greater than zero1、β2、Δ1And Δ2Are empirical values, sat is a saturation function, s1And s2Are each with respect to xeAnd thetaeThe switching function of (2); (ii) a
The corrected desired speed of the coupled tracked robot (13) is expressed by equation (15):
wherein, v'dAnd ω'dThe corrected expected linear speed and the corrected expected angular speed of the crawler robot are respectively;
the desired angular velocities of the right and left motors are represented by equations (14) and (15), respectively:
ωrd＝(v′d+ω′dA)r-1formula (14)
ωld＝(v′d-ω′dA)r-1Formula (15)
Wherein, ω isrdAnd ωldThe desired angular velocity of the right motor and the desired angular velocity of the left motor, respectively, a is half of the distance between the left drive wheel and the right drive wheel, and r is the radius of the left drive wheel and the right drive wheel.
β1And beta2The value of (D) may be taken to be 0.01%, Δ1The value of (d) may be taken as. + -. 0.01%, Δ2The value of (d) may be taken as. + -. 0.01%.
Desired angular velocity ω of the right motorrdAnd desired angular velocity ω of the left motorldThe driving voltage u to be applied to the right motor can be calculated by respectively substituting the dynamic model formula (8) of the left motor and the dynamic model formula (9) of the right motorr(t) should be applied to the driving voltage u of the left motorl(t)。
Although specific steps of the control method for the tracked robot are shown in a specific order in fig. 1 and 2, it will be understood by those skilled in the art that the control method does not necessarily have to be executed according to the steps shown in the figures unless there is a logical precedence relationship.
An embodiment of the present invention also provides a crawler robot, which may include:
the left driving wheel is used for driving the left crawler; a right drive wheel for driving the right track;
a left motor for driving the left drive wheel; a right motor for driving the right driving wheel;
the sensor is used for detecting the pose of the tracked robot in the current state, and the pose comprises the position and the inclination angle of the tracked robot in an appointed coordinate system; and
and a controller for executing the control method for the tracked robot in any of the above embodiments.
In order to verify the effectiveness of the control method for the tracked robot according to the embodiment of the present invention, the present invention provides the following examples.
In an embodiment of the present invention, the parameters of the left motor and the right motor of the crawler robot may be, for example: j. the design is a squarer＝Jl＝0.155kg·m2，L＝0.45·10-3h，ke＝0.265V/rad，kt＝2.52nm/A,R＝3.68Ω,F＝0.001，k1＝2，k2And 2, the control voltage u of the left motor and the right motor meets the condition that | u | is less than or equal to 15V. The individual parameters of the tracked robot may be, for example: the length l of the tracked robot is 0.555m, the width w is 0.4m, the radius r of the left driving wheel and the right driving wheel is 0.1m, the distance 2A between the left driving wheel and the right driving wheel is 0.36m, and the white noise interference d (t) is 50 × randn (1, 1). The various parameters of the controller may be, for example: k is a radical ofk1＝kk2＝2，c1＝c2＝2，c3＝c4＝4，kω1＝kω2The sample time is 50ms, 1000.
Verification of left motor and control of motor
The Control method (hereinafter referred to as an ASMTC Control method in the drawings) and the Sliding Mode Control (Sliding Mode Control, hereinafter referred to as an SMC Control method in the drawings) of the conventional exponential approximation law are respectively adopted to perform simulation calculation on the tracked robot, and the tracked robot is controlled to linearly run at a speed at which the linear speed v is 2m/s and the angular speed ω is 0.
Fig. 5 shows a response curve of the angular velocity of the left motor, fig. 6 shows a tracking error curve of the angular velocity of the left motor, and fig. 7 shows a voltage output curve of the left motor. Because the simulation calculation conditions, parameters and models of the left driving wheel and the right driving wheel are completely the same, the simulation result of the right driving wheel is completely the same as that of the left driving wheel under the condition that the crawler robot runs in a straight line. As shown in fig. 5 and 6, when the control method according to the embodiment of the present invention is used to control the left motor and the right motor, the angular velocity response curve of the left motor is smooth and reaches a steady state at 0.375s, the end value of the angular velocity output by the left motor is 20rad/s, and the angular velocity tracking error converges to zero; when the SMC method is adopted for control, the tracked robot needs 0.75s to reach a stable state and has a buffeting phenomenon. As can be seen from fig. 7, compared with the SMC method, the voltage curve output by the ASMTC method of the present invention is smoother, and the buffeting amplitude is not greater than 0.01V. Due to the saturation characteristic of the variable-inclination parameter integral term in the sliding mode switching function, when a crawler robot has a large error, the function of the integral term can be limited, so that the system does not have excessive overshoot; when the error is small, the amplification effect is achieved, and the control precision is improved under the condition that buffeting is not caused.
Tracking control simulation calculation for sliding modes with different tracks
The invention provides an embodiment of simulation calculation for tracking a broken line and a circular track of a crawler robot.
(a) Broken line trajectory sliding mode tracking control
In an embodiment of the invention, the polygonal line path is taken as a simulation calculation path, and the pose instruction of the tracked robot is [0,0, pi/4 ]]TThe initial pose of the crawler robot is [ -2, -2, pi/4 [ -2 [ ]]TThe constant linear velocity is 2m/s, and the time of simulation calculation is 0<t<12s。
Fig. 8 shows a broken line movement locus of the crawler robot, fig. 9 shows a tracking error curve of the broken line movement locus of the crawler robot, and fig. 10 shows angular velocity response curves of the left and right motors. As can be seen from FIGS. 8 and 9, when the crawler robot is started from the initial position, the pose error of the crawler robot can be converged to 0 in a short time, at 8<t<In a time period of 10s, although the curvature of the reference path changes greatly, the controller can still track the reference path quickly, and the pose error after stabilization is as follows: x is the number ofeWithin the interval (-0.08,0.04), yeWithin the interval (-0.07,0.07), thetaeWithin the (-0.02,0.045) interval. As can be seen from fig. 10, the left motor/the right motor has a faster response speed, and can be kept stable after reaching a desired angular speed.
(b) Circular trajectory sliding mode tracking control
In an embodiment of the present invention, a circular path with a radius of 10m is used as a simulation calculation path, and the circular path is tracked at a constant linear speed of 2m/s, where the reference trajectory is: x is 10cos θ, and y is 10sin θ.
The initial pose of the tracked robot is [10,0, pi/2 ]]TThe pose instruction is [7,0, pi/2 ]]TThe angular speeds of the left driving wheel and the right driving wheel are respectively 10rad/s and 30rad/s, the constant linear speed is 2m/s, the left driving wheel and the right driving wheel run in the anticlockwise direction, and the simulation calculation time is 0<t<32s。
Fig. 11 shows a circular motion trajectory of the crawler robot, fig. 12 shows a tracking error curve of the circular motion trajectory of the crawler robot, and fig. 13 shows angular velocity response curves of the left and right motors. As shown in fig. 11 to 13, the control method according to the embodiment of the present invention enables the angular velocities of the left and right motors to respond quickly and to be stable after reaching a desired velocity. The track robot can better track the designed circumferential track, and the pose error tends to be 0. Particularly, when a circular path is tracked, the curvature of the path changes constantly, the output control can be adjusted in time by adopting an ASMTC control method, the output angular velocity curves of the left motor and the right motor are smooth, the tracking is ensured not to be separated from a reference track, and the control precision is high.
Sliding mode tracking control experiment
In an embodiment of the invention, the tracked robot provided by the embodiment of the invention is used for field control experiments, a microcontroller with the model number of S3C2440 is used as a controller of the tracked robot, and the experimental ground condition is a farmland with mixed sandy soil and weeds. The SPAN-CPT combined navigation positioning system is used as a receiving device of state information of the tracked robot, the SPAN-CPT is installed on the tracked robot, the information updating rate is 10hz, the speed precision is 0.01m/s, the angle precision is 0.02rad, the position measurement precision is 0.01m, and the tracking track path of the tracked robot is as follows:
the linear speed of the track robot is 2m/s,
the initial pose is as follows: [ x (0) y (0) θ (0) ]]T＝[0 20 pi/12]T，
The pose instruction is as follows: [ x ] ofr(0) yr(0) θr(0)]T＝[10 40 pi/4]T，
The initial pose error is: [ x ] ofe(0) ye(0) θe(0)]T＝[10 20 pi/6]T。
Fig. 14 shows a movement locus of the crawler robot when the ASMTC control method is adopted, the movement locus is relatively smooth except for an area where the curvature of the initial position and the tracking locus is largely changed. Fig. 15 shows a pose error curve of a motion trajectory of the crawler robot when the ASMTC control method is employed. As can be seen from fig. 15, in the initial stage of the track robot movement, because the initial pose of the track robot is inconsistent with the pose instruction, the initial pose deviation is large, in the time periods of 39-50s and 79-90s, because the change of the path curvature is large, the mechanical steering amplitude is large, the side slip and centrifugal force influence on the track robot is also serious, and serious parameter perturbation and external interference are generated, so that a large pose error is caused, and the error ranges of the generated pose parameters are respectively: -0.03. ltoreq. xe≤0.04m，-0.08≤ye≤0.06m，-0.03≤yeLess than or equal to 0.05 rad. When the tracked robot runs in an area with small curvature change, the tracking track is very smooth, and the deviation between the tracking track and the reference curve is close to zero.
Table 1 shows pose errors generated when the tracked robot tracks the same trajectory under the same experimental conditions and at different running linear speeds. As can be seen from Table 1, when the crawler robot runs along a specified curve under the conditions that the linear speed of the crawler robot is 1m/s,3m/s and 4m/s, the pose error is rapidly reduced and is close to zero, and the requirement of control precision is met.
TABLE 1 trajectory tracking pose error at Low speed
According to the embodiment, the crawler robot is regarded as a cascade system consisting of a motor driving system and a vehicle body motion system, a self-adaptive integral sliding mode switching function with variable inclination parameters is constructed, self-adaptive sliding mode tracking control based on equivalent control and switching control is provided according to the self-adaptive integral sliding mode switching function, the time-varying uncertain parameters of the driving motor obtained through online identification are identified according to the speed of the robot, errors between the driving motor and a target pose obtained in a kinematic model are fed back to a controller of the driving system, then the expected speed of each motor is decomposed according to the kinematic relationship, and stable motion control of the robot is achieved.
The preferred embodiments of the present invention have been described in detail with reference to the accompanying drawings, however, the present invention is not limited to the above embodiments, and various modifications can be made to the technical solution of the present invention within the technical idea of the present invention, and these simple modifications are within the protective scope of the present invention.
It should be noted that the various technical features described in the above embodiments can be combined in any suitable manner without contradiction, and the invention is not described in any way for the possible combinations in order to avoid unnecessary repetition.
In addition, any combination of the various embodiments of the present invention is also possible, and the same should be considered as the disclosure of the present invention as long as it does not depart from the spirit of the present invention.
Claims (2)
1. A control method for a tracked robot, characterized by comprising the steps of:
acquiring the pose of the tracked robot in the current state;
setting a reference track of the tracked robot, wherein the reference track comprises a pose instruction and a speed instruction;
establishing a kinematic model describing a constraint relation between the pose of the tracked robot and the speed of the tracked robot, wherein the speed comprises a linear speed and an angular speed;
establishing a pose error model of the tracked robot according to the pose in the current state and the set reference track;
establishing a pose error differential model of the tracked robot according to the kinematic model and the pose error model;
establishing a driving model of a left motor for driving a left driving wheel and a right motor for driving a right driving wheel of the tracked robot, wherein the driving model comprises a moment driving model and a potential balance model;
obtaining dynamic models of the left motor and the right motor according to the moment driving model and the potential balance model;
establishing a self-adaptive sliding die cutting and changing model which changes along with parameter adjustment;
obtaining the expected speed of the tracked robot according to the pose error differential model and the self-adaptive sliding die cutting model;
the control method further comprises the following steps:
establishing a switching control model for correcting the expected speed of the tracked robot;
correcting the expected speed of the tracked robot by adopting the switching control model and obtaining the corrected expected speed of the tracked robot;
obtaining the expected angular speeds of the left motor and the right motor according to the corrected expected speed;
calculating driving voltages of the left motor and the right motor according to the expected angular velocities of the left motor and the right motor and the dynamic models of the left motor and the right motor;
a kinematic model describing a constraint relationship between the pose of a tracked robot and the velocity of the tracked robot is represented by equation (1):
wherein x and y are respectively the position coordinates of the center of mass of the tracked robot in an XOY coordinate system, and theta is the motion of the tracked robotThe included angle between the direction and the X axis, v and omega are the linear velocity and the angular velocity of the tracked robot respectively, d is the distance between the centroid and the geometric center of the tracked robot,
and
the derivatives of x, y, and θ, respectively, with respect to time;
according to the pose of the tracked robot in the current state and the set reference track, the established pose error model of the tracked robot is represented by a formula (2):
wherein, (x, y, theta)TThe pose of the tracked robot in the current state is represented, X and y are coordinates of the current position of the center of mass of the tracked robot respectively, and theta is an included angle between the motion direction of the tracked robot and an X axis in the current state, (X)r,yr,θr)TFor the pose instruction, xr、yrRespectively, the coordinates of the target position of the center of mass of the tracked robot, thetarIs the included angle between the moving direction of the tracked robot and the X axis when the tracked robot reaches the target position, XeIs the error value of the current position of the center of mass of the tracked robot and the target position along the current movement direction of the tracked robot, yeIs the error value of the current position of the center of mass of the tracked robot and the target position in the direction vertical to the current motion direction of the tracked robot, thetaeIs theta and thetarAn error value therebetween;
the pose error differential model of the tracked robot is established according to the kinematic model and the pose error model:
wherein the content of the first and second substances,
are respectively xe、yeAnd thetaeThe derivatives with respect to time, v and omega are respectively the linear velocity and the angular velocity of the tracked robot in the current state, (v)r,ωr)TFor the speed command, vrAnd ωrRespectively the linear velocity and the angular velocity when the tracked robot reaches a target position, and d is the distance between the centroid and the geometric center of the tracked robot;
the torque balance models of the right motor and the left motor are respectively expressed by an equation (4) and an equation (5):
wherein, Jr(t)、Jl(t) the moment of inertia of the rotating shafts of the right motor and the left motor, respectively, F the viscous friction coefficient on the output shafts of the left motor and the right motor, ktIs the electromagnetic torque coefficient, T, of the left and right motorsdr(t)、Tdl(t) the disturbing moments, ω, experienced by the right and left motors, respectivelydr(t)、ωdl(t) are the angular speeds of rotation of the rotating shafts of the right motor and the left motor respectively,
and
are respectively omegadr(t) and ωdl(t) derivative with time, ir(t)、il(t) are each independentlyArmature currents of the right motor and the left motor;
the potential balance models of the right motor and the left motor are respectively expressed by an equation (6) and an equation (7):
wherein L is armature inductance of the left motor and the right motor, R is armature resistance of the left motor and the right motor, keIs the back electromotive force coefficient of the left motor and the right motor, and ke＝0.10472kt，
And
are respectively ir(t) and il(t) derivative with time, ur(t) and ul(t) a driving voltage of the right motor and a driving voltage of the left motor, respectively;
the dynamic models of the right motor and the left motor obtained from the torque driving model and the potential balance model are expressed by equations (8) and (9):
wherein, Tl(t)＝RJl(t)/(RF+ktke)，Tr(t)＝RJr(t)/(RF+ktke)，
k1＝kt/(RF+ktke)，k2＝R/(RF+ktke)；
The established adaptive sliding die switching model which changes along with parameter adjustment is represented by the formula (10):
wherein alpha is1And alpha2In order to be a parameter of the tilt,
c1、c2、c3、c4、kk1、kk2are all normal numbers, s1And s2Are each with respect to xeAnd thetaeThe switching function of (2);
the expected speed of the tracked robot obtained according to the pose error differential model and the adaptive sliding die switching model is represented by an equation (11):
wherein v isdAnd ωdRespectively a desired linear velocity and a desired angular velocity of the tracked robot,
is v isrA derivative with respect to time;
the switching control model is expressed by equation (12):
wherein, beta1、β2Switching gain greater than zero，β1、β2、Δ1And Δ2Are empirical values, sat is a saturation function;
the corrected desired speed of the crawler robot is represented by equation (13):
wherein, v'dAnd ω'dThe corrected desired linear velocity and the corrected desired angular velocity of the tracked robot are respectively obtained;
the desired angular velocities of the right and left motors are represented by equations (14) and (15), respectively:
ωrd＝(v′d+ω′dA)r-1formula (14)
ωld＝(v′d-ω′dA)r-1Formula (15)
Wherein, ω isrdAnd ωldThe desired angular velocity of the right motor and the desired angular velocity of the left motor are respectively, a is half of the distance between the left driving wheel and the right driving wheel, and r is the radius of the left driving wheel and the right driving wheel.
2. A track robot, comprising:
the left driving wheel is used for driving the left crawler;
a right drive wheel for driving the right track;
a left motor for driving the left drive wheel;
a right motor for driving the right driving wheel;
the sensor is used for detecting the pose of the tracked robot in the current state, and the pose comprises the position and the inclination angle of the tracked robot in a specified coordinate system; and a controller for executing the control method for the tracked robot according to claim 1.
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