Target tracking switching control method based on omnidirectional wheel vehicle

Abstract

The invention discloses a target tracking switching control method based on an omni-directional wheel vehicle, relates to the technical field of target tracking switching control, and aims to solve the problem that in the prior art, due to the fact that obtained target information is discontinuous, a traditional controller is prone to failing or even target tracking fails. The method is characterized by comprising the steps of establishing a target tracking system kinematics model; designing a switching control strategy; giving a motion range of the target when the target pose information is lost; deriving the maximum increment of the course angle deviation between the omnidirectional wheel vehicle and the target along with time and the maximum increment of the position deviation between the omnidirectional wheel vehicle and the target along with time in the target pose information loss mode; and obtaining the minimum duration of the mode in which the target pose information is not lost, wherein the minimum duration enables the tracking system to be stable. According to the invention, when the omnidirectional wheel vehicle is faced with intermittent loss of the target pose information, the structure and gain of the control system are adjusted through switching control, the overall tracking effect is improved, and the global asymptotic stability of the tracking system is realized under the constraint of the residence time condition.

Description

Technical Field

[0001] The present invention relates to the technical field of switching control for target tracking, and particularly to a switching control method for target tracking based on an omnidirectional wheel vehicle. Background Art

[0002] In the target tracking task of a mobile platform, target tracking based on a vision sensor is widely used in practice. An unavoidable problem encountered when obtaining target information through a vision sensor is the loss of target information caused by occlusion of the target or the camera, failure of target feature matching due to light changes, camera failure, etc. There are also problems with discontinuous acquisition of target information based on other types of sensors. Discontinuous acquisition of target information easily causes traditional control strategies to fail and even leads to target tracking failure. In the target tracking task of an omnidirectional wheel vehicle, the modeling of the tracking system, the design method of the switching control strategy, and the stability criterion of the tracking system are all crucial. There is little detailed elaboration in the prior art.

[0003] Reference [1] uses robust adaptive control to improve the path tracking accuracy and response speed of a mecanum wheel robot in the presence of disturbances. Its disadvantage is that it does not consider the problem of discontinuous acquisition of target position information brought by sensors, especially vision sensors, and the design of the controller uses the target and mecanum wheel robot information in the global coordinate system.

[0004] Reference [2] focuses on the stability conditions of switching systems with unstable subsystems, but their research is based on the basic assumption that the control target is an equilibrium point. In the tracking problem, when target information is lost, the state variables of the tracking system are non-equilibrium and uncontrollable.

[0005] [1] Alakshendra V, Chiddarwar S S. Arobust adaptive control of mecanumwheel mobile robot: Simulation and experimental validation[C]. 2016IEEE / RSJInternational Conference on Intelligent Robots and Systems (IROS)..[S.l.]:[s.n.], 2016:5606-5611.

[0006] [2]Zhai G,Hu B,Yasuda K,et al.Stability analysis of switched systemswith stable and unstable subsystems:An average dwell time approach[J].International Journal ofSystems Science,2001,32(8):1055-1061. Summary of the Invention

[0007] The technical problem to be solved by the present invention is as follows:

[0008] In order to solve the problem that in the prior art, due to the discontinuous acquisition of target information, traditional controllers are likely to fail and even cause target tracking failure, a switching control method for target tracking based on an omnidirectional wheel vehicle is proposed. The present invention will be described from aspects such as the modeling of the tracking system, the design method of the switching control strategy, and the stability criterion of the tracking system.

[0009] The technical solution adopted by the present invention to solve the above technical problem is as follows:

[0010] A switching control method for target tracking based on an omnidirectional wheel vehicle, and the implementation process of the method is as follows:

[0011] Step 1: Establish a kinematic model of an omnidirectional wheel vehicle-based vision target tracking system;

[0012] Step 2: Design a switching control strategy;

[0013] Step 3: Give the motion range of the target when the target pose information is lost;

[0014] Step 4: Deduce the maximum increment of the heading angle deviation between the omnidirectional wheel vehicle and the target with time in the mode of lost target pose information;

[0015] Step 5: Deduce the maximum increment of the position deviation between the omnidirectional wheel vehicle and the target with time in the mode of lost target pose information;

[0016] Step 6: Obtain the minimum duration of the mode without lost target pose information for the tracking system to be stable.

[0017] Furthermore, in Step 1, the process of establishing a kinematic model of an omnidirectional wheel vehicle-based vision target tracking system is as follows:

[0018] Define three coordinate systems, namely the global coordinate system fixed in the environment The body coordinate system fixed to the body The target coordinate system fixed to the target

[0019] The goal of tracking the problem is to make the omnidirectional wheel vehicle track a moving object, and the specific motion information of the object is unpredictable. The omnidirectional wheel vehicle obtains the target information in real time through its own sensors (such as cameras, radars, etc.); the state of the tracking system is defined as e = [e x e y e φ , where e x represents the difference between the position of the omnidirectional wheel vehicle and the position of the target on the x q axis; e y represents the difference between the position of the omnidirectional wheel vehicle and the position of the target on the y q axis; e φ represents the difference between the heading angle of the omnidirectional wheel vehicle and the heading angle of the target on the z q axis;

[0020] When ‖e‖ is less than a threshold ε, the target will be clear enough relative to the omnidirectional wheel vehicle and it is difficult to lose information due to external interference. The selection of ε can be determined according to the actual needs in engineering; assume that the target cannot move omnidirectionally and cannot reverse during the movement. Let the maximum acceleration of the target in the forward direction be a max , the maximum adjustment speed of the direction angle be ω max , and let the maximum time for the target pose information to be lost be T max ;

[0021] To obtain the dynamic equation of the state e, first transform the coordinates in the global coordinate system into the coordinates in the body coordinate system :

[0022] e = J(φ(t))[x d (t) - x(t) y d (t) - y(t) φ d (t) - φ(t)] T (1)

[0023] where

[0024]

[0025] is the Jacobian matrix of the global coordinate system relative to the body coordinate system ; t represents time; [x d (t) y d (t) φ d (t)] T is the pose of the target in the global coordinate system ; [x(t) y(t) φ(t)] Tis the pose of the omnidirectional wheel vehicle in the global coordinate system ;

[0026] Taking the derivative of Equation (1) with respect to time, the system model can be obtained

[0027]

[0028] where v xd , v yd , ω d are the velocity of the target relative to the x-axis q , y q and the angular velocity around the z-axis q ; u x , u y , u φ are the control inputs of the omnidirectional wheel vehicle, representing the velocity of the omnidirectional wheel vehicle along the x-axis q , y-axis q and the angular velocity around the z-axis q .

[0029] Furthermore, in Step 2, the process of designing the switching control strategy is as follows:

[0030] The tracking process includes two modes: the target pose information not lost mode, denoted as mode m, and the target pose information lost mode, denoted as mode u;

[0031] When the target pose information is not lost, based on the feedback linearization technique, the form of the controller is:

[0032]

[0033] where k xm , k ym , k φm are the controller gains, and the subscript m represents the image not lost mode; u x , u y , u φ are the control inputs of the omnidirectional wheel vehicle. By substituting Equation (4) into (3), the equation of the closed-loop system is obtained:

[0034]

[0035] At this time, in the target pose not lost mode, the system closed-loop is exponentially stable;

[0036] In the target pose information lost mode, e x , e y , e φ and v xd , v yd , ω dis not available, so a predictor needs to be designed to provide the controller with the estimated target position and attitude. Assume that the target pose information is lost starting from time t0. The predictor assumes that the target maintains a constant velocity v in the global coordinate system before the image loss, x0 v y0 and the attitude angle φ0; denote as v0, and let where represents the differences between the position of the omnidirectional wheel vehicle and the target position estimated by the predictor on the x q axis and the y q axis respectively; represents the difference between the heading angle of the omnidirectional wheel vehicle and the estimated target heading angle on the z q axis. Then the predictor and the controller for the predictor output can be derived in the following form:

[0037]

[0038] and

[0039]

[0040] In equations (6)-(10), e x0 , e y0 , e φ0 are respectively the initial values of . Together with v0, v x0 , v y0 , φ0, they can all be measured at the moment before the target is lost; u x , u y , u φ are the control inputs; are respectively the velocities of the target estimated by the predictor along the x-axis, y-axis, and around the z-axis under . According to the structure of the predictor, should be 0; is the position and attitude of the target estimated by the predictor under ; [x y φ] T is the representation of the pose of coordinate system relative to coordinate system under . x, y, φ can be measured by the IMU or obtained by integrating the control inputs; The form of J(φ) is the same as equation (2); k xu , k yu , k φu are the controller gains, and the subscript m represents the mode of target information loss.

[0041] Substitute Equation (10) into Equation (7) to obtain the closed-loop dynamics of the estimated state:

[0042]

[0043] Substitute Equation (10) into Equation (3) to obtain the closed-loop dynamics of the true state:

[0044]

[0045] By deriving the upper bound of the increment of the state quantity in the target information loss mode, prepare for the stability criterion of the tracking system to cope with the problem that the true state change over time cannot be calculated by Equation (3) due to the inability to obtain the target position information.

[0046] Furthermore, Steps 3, 4, and 5 derive the upper bound of the increment of the state quantity in the target information loss mode to prepare for the stability criterion of the tracking system. Specifically:

[0047] In Step 3, give the motion range of the target when the target pose information is lost:

[0048] Denote the maximum acceleration of the target as a max , and the maximum angular velocity of the target as ω max . Let T = t - t0. At time t in mode u, all possible positions of the target are included in the region described by Equation (13),

[0049] x d = Rsin(δ), y d = Rcos(δ) (13)

[0050] where δ ∈ [-ω max T, ω max T], R ∈ [0, (v0 + 0.5a max T)T];

[0051] In Step 4, derive the maximum increment of the heading angle deviation between the omnidirectional wheel vehicle and the target over time in the target pose information loss mode. Specifically:

[0052] First, derive the upper bound of .

[0053]

[0054] where is the actual angle turned by the target during the information loss process. Based on symmetry, without loss of generality, let and denote as The initial values of different variables at the initial moment of mode m are the same, i.e., e φb (0) = eφ e(0) = e φ0 , The growth of is related to two elements, e φ (0) and T. First, find the derivative of e φ (0):

[0055]

[0056] Set the derivative equal to 0 to obtain the extreme point:

[0057]

[0058] When the derivative value is positive, otherwise it is negative; therefore, if the time length T is known, when e φ (0) is taken as the extreme point (16), the upper bound of increases with the time increment e φb and reaches the maximum value;

[0059] Next, find the derivative with respect to time T:

[0060]

[0061] is monotonically increasing. If is satisfied, then is the maximum increment of within T ∈ [0, T max . in this range.

[0062] In step five, derive the maximum increment of the position deviation between the omnidirectional wheel vehicle and the target over time in the target pose information loss mode, specifically:

[0063] Derive the upper bound of and its change over time: In the global coordinate system at time t0 denoted as to calculate the upper bound of,

[0064] The coordinates of the omnidirectional wheel vehicle in the new coordinate system are

[0065]

[0066] The tracking error can be written as

[0067]

[0068] where x d and y dbelongs to the area described by equation (13); to derive the maximum value of equation (19), combine (18) and (11) and Denoted as ψ, Recorded as

[0069]

[0070] Recorded as Will Recorded as From formula (11), we can know Therefore, we can get Formula (20) becomes

[0071]

[0072] The equal sign can be obtained when T is 0, and the right side of equation (21) is recorded as variable The growth of is related to three elements: T, R and e xy (0); Obviously, given the time T and the initial value of the relative position error e xy (0), when R takes its upper bound (v0+0.5a max T)T, the right side of formula (20) reaches the maximum value;

[0073] Calculate now For the initial value The derivative of k xyu =min(k xu ,k yu ),get

[0074]

[0075] Let the partial derivative be 0, and we get

[0076]

[0077] The extreme point (23) is positive when When , the partial derivative value is positive, otherwise it is negative; therefore, if e xy (0) can take the value of the extreme point (23), The increment in time T will reach a maximum value; because T max is used to calculate the maximum increment. T in formula (23) can be taken as T max ; v0 in formula (23) can be taken as a max T max To derive a stability condition that is easy to calculate and verify;

[0078] According to the variable The variation with time T will be divided into two parts: and 2Rv0T. For the latter, it is easy to know that its second-order time derivative is positive; for the former, taking the second-order time derivative of it, we get

[0079]

[0080] Since

[0081]

[0082] Taking the first and second derivatives of yields

[0083]

[0084] Since R, are all positive, the second derivative can be further simplified

[0085]

[0086] From equation (26), it can be seen that the second derivative of is also a positive number. Therefore, either strictly monotonically increases or first decreases and then increases; within a finite time, will definitely monotonically increase; thus, if can be satisfied, then is the maximum increment of max within T ∈ [0, T .

[0087] Furthermore, in step six, the minimum duration of the non-loss mode of the target pose information that makes the tracking system stable is derived, specifically:

[0088] Based on the upper bound of the tracking error after a finite time will necessarily monotonically increase. To derive the stability criterion of the tracking system, a Lyapunov function in the following form is defined:

[0089]

[0090] The Lyapunov functions in mode m and u can be denoted as V m (e), V u (e);

[0091] Using ΔV max to represent the maximum increment of the Lyapunov function V u (e) in the target image loss mode:

[0092] ΔV max (e) = ΔV1 + ΔV2 (27)

[0093] where

[0094]

[0095] e φ (0), e xy (0) can be obtained from equations (6) and (13) respectively;

[0096] The decrease and its lower bound of the Lyapunov function V(e) when the target image is not lost:

[0097]

[0098] where τ represents the duration of mode m, k m = min(k xm , k ym , k φm ), V m0 denotes the initial value when mode m is activated;

[0099] Finally, based on the maximum increase (27) of the Lyapunov function under mode u and the minimum decrease (29) of the Lyapunov function under mode m, the stability criterion of the tracking system is given.

[0100] Furthermore, the process of stability judgment based on the stability criterion of the tracking system is as follows:

[0101] For the switched system described by equation (3), if the duration of mode m satisfies equation (30), the system is asymptotically stable, where ΔV max is obtained from equation (27), and τ represents the duration of mode m.

[0102] τ > τ * = ln(ε / (ε + ΔV max )) / (-k m ) (30)

[0103] Suppose mode u is activated at time t0, and at this time V(e) just reaches the threshold ε; the increment of the Lyapunov function V u (e) in mode u and the dwell time of mode u are denoted as ΔV max and T max respectively; at time t0 + T max , the system switches to mode m, and the error starts to decrease. According to equation (29):

[0104]

[0105] Then when Equation (32) is satisfied, the condition V m (e) < ε can be guaranteed,

[0106] (ε + ΔV max )exp(-2k m ) < ε (32)

[0107] Equation (32) can be written as

[0108] τ > ln(ε / (ε + ΔV max )) / (-k m ).

[0109] Now consider another case: when V(e) satisfies

[0110] V(e) = ε′ > ε

[0111] the mode u is activated, and the system transfers to mode m after time t0 + T max and V m (e) decreases to the value ε′ at time t1′.

[0112] Then at time t0 + T max it can be obtained that

[0113] ε′ + ΔV max > ε + ΔV max

[0114] Since the decay rate of V m (e) is the same in both cases, it is easy to prove that t1 > t1′. Therefore, after τ * V m (e) will be strictly smaller than ε′, meaning that V(e) has a decaying trend; when V(e) decreases to the threshold ε, the system returns to the situation of Case 1; thus, if Equation (30) can be satisfied, V(e) < ε can be achieved in finite time, and then the switching will not occur again, and the system will remain in m with dynamics (5), and thereafter the system will converge exponentially to the equilibrium point. Therefore, the system is asymptotically stable.

[0115] The present invention has the following beneficial technical effects:

[0116] In the target tracking task of a mobile platform, target tracking based on a vision sensor is widely used in practice. An unavoidable problem encountered when obtaining target information through a vision sensor is the loss of target information caused by the occlusion of the target or the camera, the failure of target feature matching due to light changes, camera failures, etc. There are also problems with discontinuous acquisition of target information based on other types of sensors. Discontinuous acquisition of target information easily causes traditional controllers to fail and even leads to target tracking failure. The technical means adopted in the present invention completely solves the above technical problems. A switching control for target tracking based on an omnidirectional wheel vehicle proposed in the present invention includes the modeling of a tracking system, a method for designing a switching control strategy, and a stability criterion for the tracking system. When the omnidirectional wheel vehicle faces intermittent loss of target pose information, the control system structure and gain can be adjusted through switching control to improve the overall tracking effect, and global asymptotic stability of the tracking system can be achieved under the constraint of the dwell time condition. The present invention is suitable for the switching control of target tracking of intelligent unmanned vehicles.

[0117] Figure 5 and Figure 6 show the effects of tracking a moving target in the switching framework of the invention, which are respectively the trajectory diagrams of the target and the omnidirectional wheel vehicle, and the change curve of the Lyapunov function during the tracking process. It can be seen that under the dwell time condition calculated according to the invention, when target information is lost during the tracking process, the sum of the squares of the tracking error e, that is, the Lyapunov function, gradually tends to 0, indicating that the omnidirectional wheel vehicle can successfully track the target. It can be seen from Fig. 5 that within a short period of time when target information is lost, the omnidirectional wheel vehicle can track the target in a roughly accurate direction. In addition, through Figure 6 it can be seen that after using the switching controller, the error growth in mode m is slower compared to the non-switched controller, further confirming the rationality and effectiveness of the design. Brief Description of the Drawings

[0118] Figure 1 is a diagram showing the relationship between three defined coordinate systems, namely the global coordinate system fixed in the environment the body coordinate system fixedly connected to the body the target coordinate system fixedly connected to the target

[0119] Figure 2 is a schematic diagram assuming that the target can reach point s, Figure 3 is a schematic diagram assuming that the target can reach point s on the boundary ab;

[0120] Figure 4 show the calculation of the upper bound requires a schematic diagram of the coordinate system, where the English annotations from left to right are: taking the pose of the target at the moment as Estimated target;

[0121] Figure 5 and Figure 6 show the effects of the switching framework in the invention for tracking a moving target, which are respectively the trajectory diagrams of the target and the omnidirectional wheel vehicle, and the curve of the Lyapunov function varying with time during the tracking process; Figure 5 In, the solid line represents the motion trajectory of the MWMR (i.e., the omnidirectional wheel robot), and the dashed line represents the motion trajectory of the target; Figure 6 In the main figure, the solid line represents the curve of the Lyapunov function under the switching control gain, the dashed line represents the curve of the Lyapunov function under the constant control gain, and the rectangular wave in the upper box describes the variation of the mode with time. The value of the rectangular wave being 1 indicates that the current moment is the mode in which the target information can be obtained, and vice versa is the mode in which the target information is lost. Detailed implementation manners

[0122] Combined with the attached Figures 1 to 6 to illustrate this implementation manner. The switching control method for target tracking based on an omnidirectional wheel vehicle described in this implementation manner includes the modeling of the tracking system, the design method of the switching control strategy, and the stability criterion of the tracking system. The switching control framework (i.e., the control method) for the target tracking task based on an omnidirectional wheel vehicle includes the following steps:

[0123] Step 1: Establish the kinematic model of the vision-based target tracking system for the omnidirectional wheel vehicle:

[0124] In the target tracking problem, the robot (abbreviated as the body) implementing the tracking needs to detect a target with a certain initial distance from the body, and then continuously shorten the distance and pose gap between itself and the target by adjusting its own motion, and finally maintain a certain relative pose with the target. During the tracking process, the loss of target pose information may occur. This may be caused by factors such as the target being blocked by obstacles, unfavorable light conditions, the failure of the image matching algorithm, and the damage of the camera. As Figure 1 shown, three coordinate systems are defined, namely the global coordinate system fixed in the environment the body coordinate system fixedly connected to the body the target coordinate system fixedly connected to the target The goal of the tracking problem solved by the present invention is to enable the omnidirectional wheel vehicle to track a moving object, and the specific motion information of this object is unpredictable. The omnidirectional wheel vehicle can only obtain target information in real time through its own sensors, such as cameras, radars, etc. The state of the tracking system is defined as e = [e x e y e φ , where e x represents the position of the omnidirectional wheel vehicle and the position of the target in x qDifference on the axis; e y Indicates the difference in the y-axis between the position of the omnidirectional wheel vehicle and the position of the target q Difference on the axis; e φ Indicates the difference in the z-axis between the heading angle of the omnidirectional wheel vehicle and the heading angle of the target q Difference on the axis.

[0125] This invention assumes that when ‖e‖ is less than a threshold ε, the target will be clear enough relative to the omnidirectional wheel vehicle so that it is difficult to lose information due to external interference. The selection of ε can be determined according to the actual requirements in engineering. Assume that the target cannot move omnidirectionally and cannot reverse during movement. Let the maximum acceleration of the target in the forward direction be a max , and the maximum adjustment speed of the direction angle be ω max . Let the maximum time for the target pose information to be lost be T max .

[0126] To obtain the dynamic equation of state e, we should first transform the coordinates in the global coordinate system into the coordinates in the body coordinate system :

[0127] e = J(φ(t))[x d (t) - x(t) y d (t) - y(t) φ d (t) - φ(t)] T (1)

[0128] Where

[0129]

[0130] is the Jacobian matrix of the global coordinate system relative to the body coordinate system ; t represents time; [x d (t) y d (t) φ d (t)] T is the pose of the target in the global coordinate system ; [x(t) y(t) φ(t)] T is the pose of the omnidirectional wheel vehicle in the global coordinate system .

[0131] Taking the derivative of equation (1) with respect to time, the system model can be obtained

[0132]

[0133] Where v xd , v yd , ω d is the velocity of the target relative to the x-axis q , yq The speed and the angular velocity around the z q axis; u x , u y , u φ are the control inputs of the omnidirectional wheel vehicle, and they represent the speed of the omnidirectional wheel vehicle along the x q axis, the y q axis and the angular velocity around the z q axis.

[0134] Step 2: Switching control strategy design:

[0135] The tracking process includes two modes: the target pose information non-loss mode, denoted as mode m, and the target pose information loss mode, denoted as mode u.

[0136] When the target pose information is not lost, based on the feedback linearization technique, the form of the controller is:

[0137]

[0138] where k xm , k ym , k φm are the controller gains, and the subscript m represents the image non-loss mode; u x , u y , u φ are the control inputs of the omnidirectional wheel vehicle. By substituting Equation (4)

[0139] into (3), we can obtain the equation of the closed-loop system:

[0140]

[0141] At this time, in the target pose non-loss mode, the closed-loop system is exponentially stable.

[0142] In the target pose information loss mode, e x , e y , e φ and v xd , v yd , ω d are not available. Therefore, a design predictor is needed to provide the estimated target position and pose for the controller. Assume that the target pose information is lost since time t0. The predictor assumes that the target maintains a constant speed v in the global coordinate system x0 , v y0 and the attitude angle φ0 before the image loss. Denote as v0. Let The predictor and the controller for the predictor output can be derived in the following form:

[0143]

[0144] and

[0145]

[0146] In equations (6) - (10), represents the projection of the position error on the x-axis in , represents the projection of the position error on the y-axis in , represents the magnitude of the heading angle error with respect to the z-axis in ; e x0 , e y0 , e φ0 are respectively 's initial values, and together with v0, v x0 , v y0 , φ0 can all be measured at the moment immediately before target loss; u x , u y , u φ are control inputs; are respectively the velocities of the target estimated by the predictor along the x-axis, y-axis, and around the z-axis under . According to the predicted design structure should be 0; is the position and attitude of the target estimated by the predictor under ; [x y φ] T is the representation of the pose of coordinate system relative to coordinate system under . x, y, and φ can be measured by an IMU or obtained by integrating the control inputs; The form of J(φ) is the same as that of equation (2).

[0147] Substituting equation (10) into equation (7), we can obtain the closed-loop dynamics of the estimated state:

[0148]

[0149] Substituting equation (10) into equation (3), we can obtain the closed-loop dynamics of the true state:

[0150]

[0151] It should be noted that since the target position information cannot be obtained, the change of the true state over time cannot be calculated by equation (3). To address this issue, in steps three, four, and five, the upper bounds of the increments of the state variables in the target information loss mode are derived, preparing for the stability criterion of the tracking system.

[0152] Step 3: Give the motion range of the target when the target pose information is lost:

[0153] We denote the maximum acceleration of the target as a max , and the maximum speed of the target as ω max . Let T = t - t0. The following lemma gives the motion range of the target under mode u.

[0154] Lemma 1: All possible positions of the target at time t are included in the region described by Equation (13).

[0155] x d = Rsin(δ), y d = Rcos(δ) (13)

[0156] where δ ∈ [-ω max T, ω max T], R ∈ [0, (v0 + 0.5a max T)T].

[0157] Proof: The proof is divided into two parts:

[0158] (I) Assume that the target can reach point s, as Figure 2 shown, which is on the line segment . According to Assumption 1, the target can only change the moving direction by changing the body orientation. Therefore, at time t, the moving direction of the target coincides with the tangent of the trajectory. Thus, the angle difference between the tangent of the trajectory and the initial direction of the target is equal to the angle that the target body has turned within [t0, t], that is, φ d (t) - φ d (t0). According to the Lagrange mean value theorem, there exists a point on the arc os, where the slope of the tangent is equal to the slope of the line . Therefore, there exists a time such that can be satisfied, and thus a contradiction can be deduced: ω max is not the maximum angular velocity. The first part is proven.

[0159] (II) Now consider the case of Figure 3 . Assume that the target can reach point s on the boundary ab. Since the speed of the target is v0 and the maximum acceleration is a max , the maximum distance that the target can move is v0T + 0.5a max T 2 . Obviously, in the figure, the actual distance of the target movement, that is, the curve os, is greater than the outer diameter of the region: v0T + 0.5a max T 2(Indicated by the dashed line). Therefore, a contradiction can be deduced. Therefore, the target cannot move out of the outer diameter of the area. Q.E.D.

[0160] Step 4: Deduce the maximum increment of the heading angle deviation between the omnidirectional wheel vehicle and the target over time in the mode of target pose information loss:

[0161] First, deduce the upper bound of

[0162]

[0163] Due to symmetry, without loss of generality, let and denote as The initial values of different variables at the initial moment of mode m are the same, i.e., e φb (0) = e φ (0) = e φ0 . The growth of φ is related to two elements, e For the derivative of e φ (0):

[0164]

[0165] Let the derivative be equal to 0, and the extreme point can be obtained:

[0166]

[0167] When , the derivative value is positive, otherwise it is negative. For a determined time length T, when e φ (0) is taken as the extreme point (), the upper bound of φb obtains the maximum increment over time, e

[0168] Next, find the derivative of with respect to time T:

[0169]

[0170] It is not difficult to find that is positive. Therefore, may increase monotonically with T, or first decrease monotonically and then increase monotonically. In short, will eventually increase monotonically. Therefore, if can be satisfied, then is the maximum increment of max within T ∈ [0, T .

[0171] Step 5: Deduce the maximum increment of the position deviation between the omnidirectional wheel vehicle and the target over time in the mode of target pose information loss:

[0172] This step focuses on deducing the upper bound of and its change over time. Since rotating and translating coordinate systems do not change the magnitude of a vector, is denoted as to calculate the upper bound of Figure 4 Figure shows the coordinate systems required to calculate the upper bound of

[0173] The coordinates of the omnidirectional wheel vehicle in the new coordinate system are

[0174]

[0175] The tracking error can be written as

[0176]

[0177] where x d and y d belong to the region described by Equation (13). To deduce the maximum value of Equation (19), combine (18) and (11), and define

[0178]

[0179] Let and Since we can obtain Therefore, Equation (20) becomes

[0180]

[0181] The equal sign can be achieved when T is 0. Denote the right end of Equation (21) as The variable grows related to three elements: T, R, and e xy (0). Obviously, given the time T and the initial value of the relative position error e xy (0), when R takes its upper bound (v0 + 0.5a max T)T, the right end of Equation (20) reaches the maximum value.

[0182] Now calculate For the initial value of the derivative. Let k xyu = min(kxu ,k yu ), we can get

[0183]

[0184] Setting the partial derivative to 0, we can get

[0185]

[0186] It is easy to find that the extreme point (23) is positive. When , the partial derivative value is positive, otherwise it is negative. Therefore, if e xy (0) can take the value of the extreme point (23), The increment in time T will reach a maximum value. max is used to calculate the maximum increment. T in formula (23) can be taken as T max Similarly, v0 in equation (23) can be taken as a max T max Used to derive a stability condition that is easy to calculate and verify.

[0187] Now consider the variable With the change of time T. Divided into 2 parts: and 2Rv0T. For the latter, it is easy to know that its second-order time derivative is positive. For the former, taking its second-order time derivative, we can get

[0188]

[0189] because

[0190]

[0191] right Taking the first and second order derivatives we can find

[0192]

[0193] In addition, due to R, are all positive, and the second-order derivative can be further simplified

[0194]

[0195] Formula (26) Explanation The second derivative of is also a positive number. Either strictly monotonically increasing or decreasing first and then increasing. In short, within a finite time, will increase monotonically. So if Can satisfy, then That is, the maximum increment within T ∈ [0, T max . Step 6: Deduce the minimum duration of the non-loss mode of the target pose information for stabilizing the tracking system:

[0196] According to the foregoing deduction, we know that

[0197] the second derivative of and the second derivative of are both positive. This means that the upper bound of the total tracking error the second derivative of is positive, and this upper bound either monotonically increases with time T or first monotonically decreases and then monotonically increases. In short, after a finite time, the upper bound of the tracking error will necessarily monotonically increase.

[0198] To deduce the stability criterion of the tracking system, define a Lyapunov function in the following form:

[0199]

[0200] The Lyapunov functions in modes m and u can be denoted as V m (e) and V u (e), respectively.

[0201] Use ΔV max to represent the maximum increment of the Lyapunov function V u (e) in the target image loss mode:

[0202] ΔV max (e) = ΔV1 + ΔV2 (27)

[0203] where

[0204]

[0205] e φ (0) and e xy (0) can be obtained from Eqs. (6) and (13), respectively.

[0206] The following gives the decrease and its lower bound of the Lyapunov function V(e) when the target image is not lost.

[0207]

[0208] where τ represents the duration of mode m, and k m = min(k xm , k ym , k φm ), and V m0 represents The initial value when mode m is activated.

[0209] Finally, based on the maximum increase (27) of the Lyapunov function in mode u and the minimum decrease (29) of the Lyapunov function in mode m, the stability criterion of the tracking system is given.

[0210] Theorem 1: Consider the switched system described by Equation (3). If the duration of mode m satisfies

[0211] τ > τ * = ln(ε / (ε + ΔV max )) / (-k m ) (30)

[0212] where ΔV max is obtained from Equation (27), the system is asymptotically stable.

[0213] Proof: First, consider a case where mode u is activated at time t0 when V(e) just reaches the threshold ε. Denote the increment of the Lyapunov function V u (e) in mode u and the dwell time of mode u as ΔV max and T max . respectively. At time t0 + T max , the system switches to mode m and the error starts to decrease. According to

[0214]

[0215] Then the condition V m (e) < ε can be guaranteed if the following equation is satisfied

[0216] (ε + ΔV max ) exp(-2k m τ) < ε (32)

[0217] Therefore, (32) can be written as

[0218] τ > ln(ε / (ε + ΔV max )) / (-k m )

[0219] Now consider another case: mode u is activated when V(e) satisfies

[0220] V(e) = ε′ > ε

[0221] The system transfers to mode m after time t0 + T max , and V m (e) decreases to ε′ at time t1′. Obviously, at time t0 + T max , we can obtain

[0222] ε′ + ΔV max >ε + ΔV max

[0223] Since V m (e) The decay rates are the same in both cases, and it is easy to prove that t1 > t1'. Therefore, at τ * after which V m (e) will be strictly smaller than ε′, meaning that V(e) has a tendency to decay. When V(e) decreases to the threshold ε, the system returns to the situation of case 1. Therefore, if (30) can be satisfied, V(e) < ε can be achieved in finite time. Furthermore, the switching will not occur again, and the system will remain in m with dynamics (5). After that, the system will converge exponentially to the equilibrium point. Therefore, the system is asymptotically stable. Proven.

Claims

1. A switching control method for target tracking of an omnidirectional wheel vehicle, characterized in that The implementation process of the method is as follows: Step 1: Establish the kinematic model of the vision-based target tracking system for an omnidirectional wheel vehicle; Step 2: Design a switching control strategy; Step 3: Give the motion range of the target when the target pose information is lost; Step 4: Deduce the maximum increment of the heading angle deviation between the omnidirectional wheel vehicle and the target over time in the target pose information loss mode; Step 5: Deduce the maximum increment of the position deviation between the omnidirectional wheel vehicle and the target over time in the target pose information loss mode; Step 6: Obtain the minimum duration of the target pose information non-loss mode for the tracking system to be stable.

2. The switching control method for target tracking of an omnidirectional wheel vehicle according to claim 1, wherein In Step 1, the process of establishing the kinematic model of the vision-based target tracking system for an omnidirectional wheel vehicle is as follows: Define three coordinate systems, namely the global coordinate system fixed in the environment the body coordinate system fixedly connected to the body the target coordinate system fixedly connected to the target The goal of tracking the problem is to enable an omnidirectional wheel vehicle to track a moving object, and the specific motion information of the object is unpredictable. The omnidirectional wheel vehicle obtains target information in real time through its own sensors (such as cameras, radars, etc.); the state of the tracking system is defined as e = [e x e y e φ , where e x represents the difference between the position of the omnidirectional wheel vehicle and the position of the target on the x q axis; e y represents the difference between the position of the omnidirectional wheel vehicle and the position of the target on the y q axis; e φ represents the difference between the heading angle of the omnidirectional wheel vehicle and the heading angle of the target on the z q axis; When ‖e‖ is less than a threshold value ε, the target will be clear enough relative to the omnidirectional wheel vehicle so that it is difficult to lose information due to external interference, and the selection of ε can be determined according to the actual requirements in the project; assume that the target cannot move omnidirectionally and cannot reverse during the movement, and assume that the maximum acceleration of the target in the forward direction is a max , the maximum adjustment speed of the direction angle is ω max , and assume that the maximum time for the target pose information to be lost is T max ; To obtain the dynamic equation of state e, first transform the coordinates in the global coordinate system into the coordinates in the body coordinate system : e = J(φ(t))[x d (t) - x(t) y d (t) - y(t)φ d (t) - φ(t)] T (1) Where is the global coordinate system relative to the body coordinate system Jacobian matrix; t represents time; [x d (t)y d (t)φ d (t)] T is the pose of the target in the global coordinate system [x(t) y(t) φ(t)] T is the pose of the omnidirectional wheel vehicle in the global coordinate system underneath; Taking the derivative of Equation (1) with respect to time, the system model can be obtained where v xd , v yd , ω d is the velocity of the target relative to the x q , y q axis and the angular velocity around the z q axis; u x , u y , u φ is the control input of the omnidirectional wheel vehicle, representing respectively the velocity of the omnidirectional wheel vehicle along the x q axis, the y q axis and the angular velocity around the z q axis.

3. A switching control method for target tracking of an omnidirectional wheel vehicle according to claim 1 or 2, characterized in that In Step 2, the process of designing the switching control strategy is as follows: The tracking process includes two modes: the target pose information non-loss mode, denoted as mode m, and the target pose information loss mode, denoted as mode u; When the target pose information is not lost, based on the feedback linearization technique, the form of the controller is: where k xm ,k ym ,k φm are controller gains, and the subscript m represents the image non-loss mode; u x ,u y ,u φ is the control input of the omnidirectional wheel vehicle. By substituting Equation (4) into (3), the equation of the closed-loop system is obtained: At this time, in the target pose non-loss mode, the system closed-loop is exponentially stable; In the target pose information loss mode, e x , e y , e φ and v xd , v yd , ω d are not available. Therefore, a predictor needs to be designed to provide the controller with the estimated target position and pose. Assume that the target pose information is lost starting from time t0. The predictor assumes that the target maintains a constant velocity v in the global coordinate system before the image loss, x0 , v y0 and the attitude angle φ0; Denote as v0, and let where represents the differences between the position of the omnidirectional wheel vehicle and the estimated target position of the predictor on the x q axis and the y q axis respectively; represents the difference between the heading angle of the omnidirectional wheel vehicle and the estimated target heading angle on the z q axis; Then the predictor and the controller for the predictor output can be derived in the following form: And In equations (6)-(10), e x0 , e y0 , e φ0 are respectively 's initial values, and together with v0, v x0 , v y0 , φ0 can all be measured at the moment immediately before the target is lost; u x , u y , u φ are control inputs; are respectively the velocities of the target estimated by the predictor along the x-axis, y-axis, and around the z-axis under . According to the structure of the predictor, should be 0; is the position and attitude of the target estimated by the predictor under . [x y φ] T is a coordinate system relative to the coordinate system pose at The representation under, x, y, φ can be measured by the IMU or obtained by integrating the control input; The form of J(φ) is consistent with Equation (2); k xu , k yu , k φu are controller gains, and the subscript m represents the mode of target information loss; Substituting Equation (10) into Equation (7), the closed-loop dynamics of the estimated state are obtained: Substituting Equation (10) into Equation (3), the closed-loop dynamics of the true state are obtained: By deriving the upper bound of the increment of the state quantity in the target information loss mode, it prepares for the stability criterion of the tracking system to cope with the problem that the true state change over time cannot be calculated by Equation (3) due to the inability to obtain the target position information.

4. A switching control method for target tracking of an omnidirectional wheel vehicle according to claim 3, characterized in that In Steps 3, 4, and 5, the upper bounds of the increments of the state quantities in the target information loss mode are deduced to prepare for the stability criterion of the tracking system. Specifically: In Step 3, give the motion range of the target when the target pose information is lost: Denote the maximum acceleration of the target as a max , and denote the maximum angular velocity of the target as ω max , let T = t - t0. At time t in mode u, all possible positions of the target are included in the region described by Equation (13). x d = Rsin(δ), y d = Rcos(δ) (13) where δ ∈ [-ω max T, ω max T], R ∈ [0, (v0 + 0.5a max T)T]; In Step 4, deduce the maximum increment of the heading angle deviation between the omnidirectional wheel vehicle and the target over time in the target pose information loss mode. Specifically: First, derive the upper bound of, Among them is the actual angle that the target has turned during the process of information loss; Based on symmetry, without loss of generality, let and denote as The initial values of different variables at the initial moment of mode m are the same, that is: e φb (0) = e φ (0) = e φ0 , The growth of is related to two elements e φ (0) and T. First, obtain The derivative of e φ (0): Let the derivative be equal to 0, and the extreme point can be obtained: When the derivative value is positive, otherwise it is negative; therefore, if the time length T is known, when e φ (0) is taken as the extreme point (16), the upper bound of increases with the time increment e φb to obtain the maximum value; Next, find the derivative with respect to time T: is monotonically increasing. If can be satisfied, then is the maximum increment within T ∈ [0, T max ;​ In Step 5, deduce the maximum increment of the position deviation between the omnidirectional wheel vehicle and the target over time in the target pose information loss mode. Specifically: Derivation of the upper bound and its variation over time: the global coordinate system at time t0 is denoted as to calculate the upper bound of The coordinates of the omnidirectional wheel vehicle in the new coordinate system are The tracking error can be written as where x d and d belongs to the area described by equation (13); to derive the maximum value of equation (19), combine (18) and (11) and Denoted as ψ, Recorded as Denote as Let Denote as As can be seen from Equation (11) Therefore, it can be obtained that Equation (20) becomes The equal sign can be obtained when T is 0. Denote the right - hand side of Equation (21) as The variable growth is related to three elements: T, R, and e xy (0); Obviously, given the time T and the initial value of the relative position error e xy (0), when R takes its upper bound (v0 + 0.5a max T)T, the right - hand side of Equation (20) reaches its maximum value; Now calculate For the initial value of the derivative, let k xyu = min(k xu , k yu ), and obtain Let the partial derivative be 0, and we get The extreme point (23) is positive. When , the partial derivative value is positive; otherwise it is negative. Therefore, if e xy (0) can take the value of the extreme point (23), the increment within time T will reach a maximum value; since T max is used to calculate the maximum increment, T in equation (23) can be taken as T max ; v0 in equation (23) can be taken as a max T max to derive a stability condition that is easy to calculate and verify; According to the variation of the variable with time T, divide it into two parts: and 2Rv0T. It is easy to know that the second-order time derivative of the latter is positive; for the former, take the second-order time derivative of it to obtain Since Pair Taking the first and second derivatives gives Since R, are all positive, the second derivative can be further simplified As can be seen from Equation (26) The second derivative of is also a positive number. Therefore either strictly monotonically increases or first decreases and then increases; within a finite time will definitely increase monotonically; thus if can be satisfied, then is the maximum increment of max within T ∈ [0, T .

5. The switching control method for target tracking based on an omnidirectional wheel vehicle according to claim 4, characterized in that In Step 6, deduce the minimum duration of the target pose information non-loss mode for the tracking system to be stable. Specifically: Based on the upper bound of the tracking error after a finite time will necessarily increase monotonically. To derive the stability criterion of the tracking system, a Lyapunov function in the following form is defined: The Lyapunov functions under modes m and u can be denoted as V m (e) and V u (e), respectively; Using ΔV max to represent the maximum increment of the Lyapunov function V u (e) in the target image loss mode: ΔV max (e) = ΔV1 + ΔV2 (27) Where e φ (0), e xy (0) can be obtained from Equations (6) and (13) respectively; The decrease amount and its lower bound of the Lyapunov function V(e) when the target image is not lost: where τ represents the duration of mode m, k m = min(k xm , k ym , k φm ), V m0 represents the initial value when mode m is activated; Finally, based on the maximum rise amount (27) of the Lyapunov function in mode u and the minimum decrease amount (29) of the Lyapunov function in mode m, the stability criterion of the tracking system is given.

6. The switching control method for target tracking based on an omnidirectional wheel vehicle according to claim 5, characterized in that The process of performing stability judgment based on the stability criterion of the tracking system is as follows: For the switched system described by Equation (3), if the duration of mode m satisfies Equation (30), the system is asymptotically stable, where ΔV max is obtained from Equation (27), and τ represents the duration of mode m; τ > τ * = ln(ε / (ε + ΔV max )) / (-k m ) (30) Suppose the mode u is activated at time t0, and at this time V(e) just reaches the threshold ε; the increment of the Lyapunov function V u (e) in the mode u and the dwell time of the mode u are respectively denoted as ΔV max and T max ; at time t0 + T max , the system switches to mode m, and the error begins to decrease. According to Equation (29): Then when Equation (32) is satisfied, the condition V m (e) < ε can be guaranteed, (ε + ΔV max ) exp(-2k m τ) < ε (32) Equation (32) can be written as τ > ln(ε / (ε + ΔV max )) / (-k m ) Now consider another case: when V(e) satisfies V(e) = ε′ > ε When the time mode u is activated, and the system transfers to mode m at time t0 + T max after that, and V m (e) decreases to the value ε′ at time t1′; then at time t0 + T max it can be obtained ε′ + ΔV max > ε + ΔV max Since V m (e) The decay rates are the same in both cases. It is easy to prove that t1 > t′1. Therefore, at τ * later, V m (e) will be strictly smaller than ε′, meaning that V(e) has a tendency to decay. When V(e) decreases to the threshold ε, the system returns to the situation of case one. Therefore, if equation (30) can be satisfied, V(e) < ε can be achieved within a finite time, and then the switching will no longer occur. The system will remain in m with dynamics (5). After that, the system will converge exponentially to the equilibrium point. Therefore, the system is asymptotically stable.

7. A switching control method and system for target tracking based on an omnidirectional wheel vehicle, characterized in that: This system has program modules corresponding to the steps of any one of claims 1-6, and executes the steps in the switching control method for target tracking based on an omnidirectional wheel vehicle when running.

8. A computer-readable storage medium, characterized in that: The computer-readable storage medium stores a computer program, and the computer program is configured to implement the steps of a switching control method for target tracking of an omnidirectional wheel vehicle according to any one of claims 1-6 when called by a processor.

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