Self-adaptive trajectory tracking control method for dynamical model of wheeled mobile robot

Abstract

The invention relates to a self-adaptive trajectory tracking control method for a wheeled mobile robot (WMR) kinetic model, which comprises the following steps of: firstly, designing a kinematics expected control signal for a WMR kinematics model; secondly, aiming at the WMR kinetic model, designing a hierarchical adaptive control strategy: introducing a correction function into a parameter estimation layer, realizing accurate estimation of uncertainty in a kinetic control loop, and ensuring that parameter estimation is quickly converged to a true value; in a controller design layer, a self-adaptive control signal is designed, accurate tracking of an expected control signal in a kinematics control loop and online compensation of system uncertainty are achieved, meanwhile, the fluctuation phenomenon of a pose error in a steady state is eliminated, and it is ensured that the pose error is accurately converged to zero. The method has good control performance and is more suitable for high-speed and high-precision scenes; accurate tracking of the time-varying trajectory is achieved, and it can be ensured that the pose error is asymptotically converged to zero while it is ensured that the parameter estimation error index is converged to zero. And the tracking precision and the convergence speed of the system are greatly improved.

Description

Technical Field

[0001] This invention belongs to the technical field of underactuated system control, trajectory tracking control and accurate parameter estimation, and specifically relates to an adaptive trajectory tracking control method for a dynamic model of a wheeled mobile robot. Background Technology

[0002] Tracking control of wheeled mobile robots (WMRs) is a core issue in the field of intelligent automation, and its theoretical research and engineering applications have received widespread attention in recent years. Existing research largely focuses on controller design at the kinematic level, as it can directly establish the mapping between pose and velocity through geometric relationships, offering advantages such as simple modeling and high computational efficiency. However, kinematic models only describe geometric relationships and cannot characterize dynamic characteristics such as inertial forces and friction effects. This leads to limited control performance in high-speed, high-precision scenarios, increased tracking errors, and even system instability. In contrast, dynamic models, by analyzing energy conversion and nonlinear coupling effects, can more comprehensively describe system behavior. As nonlinear differential equations containing the relationship between torque and motion state, dynamic models face three fundamental challenges in control design: First, as a typical underactuated system, the dynamic equations of WMRs contain nonlinear coupling terms and nonholonomic constraints, making it difficult to directly use traditional methods for control; second, the inherent non-minimum phase characteristic of the system makes it internally unstable, and classical control theories such as backstepping and sliding mode control are mainly designed for minimum-phase systems, and their direct use cannot ensure the stability of the system's internal state.

[0003] For the control challenges of WMR underactuated models, adaptive control based on the Sontag general formula and traditional adaptive control based on Lyapunov theory have emerged as feasible solutions. While the Sontag general controller can construct a stable control law by controlling the Lyapunov function, its denominator approaches zero, leading to drastic changes in the control input and inducing high-frequency oscillations. If the control Lyapunov function itself has a non-smooth region in the state space, it may also cause high-frequency oscillations in the control input during state transitions. Research indicates that these oscillations stem from multiple factors, including the discontinuity of the control law during state transitions, the interaction between parasitic parameters and the controller dynamics, high gain due to improper parameter selection, and the mismatch between the sampling rate and the system's high-frequency characteristics. Furthermore, while Lyapunov-based adaptive control methods can compensate for model uncertainties through parameter estimation—for example, the adaptive estimation method mentioned in the literature [Ma Shuhua et al., Adaptive Trajectory Tracking Control of Mobile Robots. Firepower and Command Control, 2022, 47(8), 13-24.] directly uses parameter estimates to precisely cancel uncertainties and obtain the adaptive law—its theoretical framework has inherent flaws. In mainstream Lyapunov-based adaptive control methods, the parameter adaptive law is designed to cancel the cross-terms in Lyapunov stability analysis. The parameter estimates are directly obtained through the update value of the adaptive law, and the design of the adaptive law and the controller are coupled and interrelated. Although this method can guarantee the stability of the closed-loop system, due to the inherent flaws in its theoretical framework, it cannot guarantee the convergence of parameter estimation unless the strict continuous excitation (PE) condition is met. The reason is that the parameter convergence of Lyapunov-based adaptive control requires the system input to always contain rich excitation information, i.e., continuous excitation. However, this condition is very strict and difficult to meet and verify in actual working conditions. However, in the process of tracking time-varying trajectories, insufficient excitation characteristics of the reference input cause parameter estimation to lag behind trajectory changes. Furthermore, model parameter uncertainties (such as unmodeled dynamics, friction, etc.) and external disturbances can also induce parameter drift. To address the problems of mainstream Lyapunov-based adaptive control when the PE condition is not met, existing improvement schemes, such as σ... - While the modified method ensures that the parameter estimation error converges exponentially and that the parameter estimation is bounded, it introduces a quadratic term in the Lyapunov stability analysis, causing the closed-loop system to asymptotically degenerate into a uniformly eventually bounded state. This improvement comes at the cost of sacrificing steady-state accuracy. The challenge lies in achieving precise convergence of parameter estimation while maintaining tracking accuracy.

[0004] More notably, in the adaptive tracking control problem of WMR, most existing studies can only achieve accurate tracking of time-invariant trajectories (such as straight trajectories). However, when facing time-varying trajectories, although current research can theoretically ensure the asymptotic stability of the system, in practice, under the combined influence of various factors, the pose error does not converge to zero, but exhibits periodic or random fluctuations. For example, the robust adaptive tracking control method for mobile robots mentioned in the literature [Shen Zhida et al., Robust Adaptive Tracking Control of Uncertain Mobile Robots Based on Neural Networks. Journal of Dynamics and Control, 2023, 21(7), 89-96.] uses traditional adaptive methods to estimate uncertainties, which means that when tracking circular trajectories, the tracking error does not converge asymptotically to zero, but rather has a bounded error. The common reasons for this phenomenon are: first, there are nonlinear couplings and nonholonomic constraints in the dynamic model of underactuated systems, and parameter uncertainties amplify this coupling effect; second, in traditional adaptive control, parameter estimation errors lead to control force deviations and parameter estimation lags. Time-varying trajectories may continuously excite nonlinear coupling terms in underactuated systems, while parameter estimation in adaptive controllers struggles to compensate for these time-varying terms in real time. Third, the WMR system is a non-minimum-phase system. For minimum-phase systems, their internal dynamics possess self-stability, thus requiring only the design of a tracking controller for the external state. However, for non-minimum-phase systems, their internal dynamics lack self-stability. Classical nonlinear tracking control theories, such as feedback linearization, dynamic inversion, backstepping, and sliding mode control, are primarily developed based on minimum-phase systems. These methods typically only consider output tracking, neglecting internal dynamic stability. Therefore, even if the tracking error is controlled to zero, the system's internal state may still diverge due to uncompensated zero dynamics, causing position errors to fluctuate in steady state. Thus, although traditional adaptive control methods theoretically guarantee asymptotic stability, the combined effects of nonlinear coupling, parameter estimation lag, non-minimum-phase characteristics, and non-ideal system factors in underactuated systems mean that pose errors cannot completely converge to zero in practice, instead exhibiting periodic or random fluctuations.

[0005] In summary, for the dynamic model of WMR, providing an adaptive trajectory tracking control method that can solve the control problem of underactuated systems and ensure accurate convergence of parameter estimation and pose error is a technical problem that urgently needs to be solved. Summary of the Invention

[0006] This invention provides an adaptive trajectory tracking control method for a dynamic model of a wheeled mobile robot, which overcomes the problems of existing technologies, such as the inability of pose error to converge completely to zero in practice, the existence of wave phenomenon in pose error under steady state, and the difficulty in ensuring the accurate convergence of parameter estimation error and pose error.

[0007] To achieve the objectives of this invention, the technical solution adopted is as follows: An adaptive trajectory tracking control method for a wheeled mobile robot dynamics model, comprising the following steps:

[0008] Step 1: Establish the dynamic model of WMR;

[0009] Step 2: Establish the kinematic model of WMR, and based on the kinematic model, establish a reference model and generate a reference trajectory;

[0010] Step 3: Based on the kinematic model, reference model, and geometric relationships of WMR motion, establish the pose error signal and its dynamic system in the WMR body coordinate system;

[0011] Step 4: Based on the dynamic system of pose error, construct the desired velocity signal and desired angular velocity signal under the kinematic control loop to achieve accurate tracking of time-varying trajectories;

[0012] Step 5: Based on the dynamic model of WMR, in the parameter estimation layer under the dynamic control loop, construct the parameter adaptive law for the unknown parameters in the model to ensure accurate convergence of parameter estimation;

[0013] Step 6: Based on the WMR dynamic model, in the controller design layer under the dynamic control loop, construct a torque signal to achieve accurate tracking of the desired velocity signal and desired angular velocity signal in the kinematic control loop.

[0014] Furthermore, the parameter adaptive law described in step five above is constructed as follows:

[0015]

[0016] in and Representing the unknown parameter τ d1 and τ d2 The actual estimated value; and σ1α1(θ,v) and σ2α2(ω) represent the parameter estimation nominal values; σ1, σ2 > 0 are the design parameters; the design of the adjustment functions α1(θ,v) and α2(ω) must satisfy:

[0017] ▽ v α1(θ,v)=ρ1φ1,

[0018] ▽ ω α2(ω)=ρ2φ2,

[0019] in ρ1,ρ2>0 are design parameters.

[0020] Furthermore, in step six above, the torque signal in the dynamic control loop is constructed as follows:

[0021]

[0022] Where v e =v d -v,ω e =ω d -ω; k4, k5 > 0 are design parameters.

[0023] Furthermore, in step four above, the desired velocity signal and desired angular velocity signal in the kinematic control loop are constructed as follows:

[0024] v d =k1x e +v r cosθ e ,

[0025] ω d =ω r +k3y e v r +k2sinθ e ,

[0026] Where k1, k2, k3 > 0 are design parameters.

[0027] Furthermore, the WMR dynamic model mentioned in step one above is as follows:

[0028]

[0029] Where x and y represent the coordinates of the x-axis and y-axis, respectively; θ represents the rotation angle of WMR relative to the geodetic coordinate system; v and ω represent the linear velocity and angular velocity, respectively; τ1 and τ2 represent the input torques of the two rear wheels; and These are known physical parameters, where m is the mass, J is the moment of inertia, r is the radius of the driving wheel, and 2R represents the rear wheelbase; d1 and d2 represent the lumped uncertainty, including unmodeled dynamics and friction, which can be parameterized as follows: and Where τ d1 and τ d2 It is an unknown parameter.

[0030] Furthermore, the WMR kinematic model mentioned in step two above is as follows:

[0031]

[0032] Where v d and ω dThese represent the desired linear velocity and desired angular velocity, respectively, required to achieve time-varying trajectory tracking under the kinematic control loop.

[0033] Furthermore, the reference model described in step two above is as follows:

[0034]

[0035] Where v r and ω r It is the input to the reference model, (x) r ,y r ,θ r ) represents the reference trajectory generated by the reference model.

[0036] Furthermore, in step three above, the pose error signal in the WMR body coordinate system is established as follows:

[0037] x e =cosθ(x r -x)+sinθ(y r -y),

[0038] y e =-sinθ(x) r -x)+cosθ(y r -y),

[0039] θ e =ω r -ω,

[0040] Where (x) e ,y e ) represents the position error in the body coordinate system; θ e This represents the angular error in the body coordinate system.

[0041] Furthermore, in step three above, the error dynamic system is established as follows:

[0042]

[0043] Compared with the prior art, the beneficial effects of the present invention are:

[0044] 1. To address the control challenges of underactuated characteristics in WMR dynamic models, this invention provides a dual-loop hierarchical adaptive control method that divides the control loop into a kinematic control loop and a dynamic control loop. Specifically, the method first constructs desired control signals (desired velocity and angular velocity signals) capable of tracking a time-varying reference trajectory within the kinematic control loop, achieving accurate tracking of the trajectory and asymptotically converging the pose error to zero. Secondly, a parameter adaptive law and controller are constructed within the dynamic control loop, enabling accurate estimation of unknown parameters, online compensation for uncertainties, and precise tracking of the desired control signals. Because this invention achieves control over the dynamic model, it can characterize dynamic characteristics such as inertial forces and friction effects, and exhibits excellent control performance. Therefore, it can more comprehensively describe the system's behavior and is more suitable for high-speed, high-precision scenarios compared to kinematic control.

[0045] 2. The dual-loop hierarchical adaptive control method provided by this invention divides the adaptive control strategy into a parameter estimation layer and a controller design layer within the dynamic control loop. Specifically, in the parameter estimation layer, a correction function is introduced to design the adaptive law, ensuring that the parameter estimation error converges exponentially to zero and avoiding the PE condition. In the controller design layer, a control torque signal is designed to achieve online compensation for uncertainties and precise tracking of the desired control signal. In the hierarchical adaptive control strategy provided by this invention, the parameter estimate is not entirely obtained through the adaptive law, but rather consists of the updated value of the adaptive law and a correction term. This correction term is obtained by solving a partial differential equation. By using this correction term to correct the updated value of the adaptive law, the control objective of precisely converging the parameter estimation error to zero can be achieved, thus avoiding the PE condition. The hierarchical adaptive control strategy completely separates the design of the adaptive law and the controller, making them independent and unaffected by each other. This breaks through the limitations of the deterministic equivalence principle of traditional adaptive control and provides more design freedom. The dual-loop hierarchical adaptive control method provided by this invention ensures that the parameter estimation error converges exponentially to zero while also ensuring that the pose error asymptotically converges to zero. That is, ensuring parameter convergence no longer comes at the expense of steady-state accuracy, and can simultaneously guarantee parameter convergence and steady-state tracking accuracy.

[0046] 3. The hierarchical dual-loop adaptive control method provided by this invention overcomes the control challenges of underactuation, nonholonomic constraints, and minimum phase characteristics of the WMR model by introducing a dual-loop hierarchical control mechanism. Precise and rapid parameter convergence avoids control force deviation and parameter estimation lag, and can compensate for nonlinear coupling terms and uncertainties in underactuated systems in real time. This effectively eliminates periodic or random fluctuations in pose error under steady state, even when facing time-varying reference trajectories. Theoretically and practically, it ensures that pose error converges precisely to zero, greatly improving the system's tracking accuracy. Simultaneously, the exponential convergence characteristic of parameter estimation error accelerates the system's response speed. Furthermore, the adaptive control signal provided by this invention changes smoothly over time, avoiding the high-frequency oscillation phenomenon of the Sontag universal controller, which is more beneficial for practical applications. Attached Figure Description

[0047] Figure 1 This is a control block diagram of an adaptive trajectory tracking control method for a WMR dynamic model according to the present invention;

[0048] Figure 2 This is a diagram of the WMR structure and pose error;

[0049] Figure 3 These are the tracking effect diagrams of the method proposed in this invention for different trajectories: (a) tracking a straight line trajectory, (b) tracking a trigonometric function trajectory, (c) tracking a circular trajectory, and (d) tracking a spiral trajectory.

[0050] Figure 4 These are pose errors from different methods: (a) compares x-axis tracking errors, (b) compares y-axis tracking errors, and (c) compares angle-selection tracking errors.

[0051] Figure 5 The tracking errors of the desired control signal are compared using different methods. (a) is a comparison of the tracking errors of the desired velocity, and (b) is a comparison of the tracking errors of the desired angular velocity.

[0052] Figure 6 These are parameter estimates using different methods, (a) is the parameter τ d1 Comparison of estimation errors, (b) is the parameter τ d2 Comparison of estimation errors;

[0053] Figure 7 These are control input signals from different methods. (a) is a comparison of torque signal τ1, and (b) is a comparison of torque signal τ2. Detailed Implementation

[0054] The embodiments of the present invention are described in detail below. To facilitate understanding of the present invention, specific examples are provided below in conjunction with the accompanying drawings for further explanation and illustration.

[0055] The design concept of this invention is as follows: First, for the WMR kinematic model, a desired kinematic control signal is designed to achieve accurate tracking of the time-varying reference trajectory. Second, for the WMR dynamic model, breaking through the limitation of the deterministic equivalence principle, a hierarchical adaptive control strategy is designed: a correction function is introduced in the parameter estimation layer to achieve accurate estimation of uncertainties in the dynamic control loop, ensuring the convergence of parameter estimation; in the controller design layer, accurate tracking of the desired control signal in the kinematic control loop is achieved, eliminating the fluctuation of pose error in steady state.

[0056] See Figure 1 The present invention provides an adaptive trajectory tracking control method for a WMR dynamic model, comprising the following steps:

[0057] Step 1: Establish the dynamic model of WMR, as follows:

[0058]

[0059] Where x and y represent the coordinates of the x-axis and y-axis, respectively; θ represents the rotation angle of WMR relative to the geodetic coordinate system; v and ω represent the linear velocity and angular velocity, respectively; τ1 and τ2 represent the input torques of the two rear wheels; and These are known physical parameters, where m is the mass, J is the moment of inertia, r is the radius of the driving wheel, and 2R represents the rear wheelbase; d1 and d2 represent the lumped uncertainty, including unmodeled dynamics and friction, which can be parameterized as follows: and Where τ d1 and τ d2 It is an unknown parameter.

[0060] Step 2: Establish the kinematic model of WMR, as follows:

[0061]

[0062] Where v d and ω d These represent the desired linear velocity and desired angular velocity, respectively, that enable time-varying trajectory tracking under the kinematic control loop.

[0063] Furthermore, based on the above kinematic model, a reference model is established as follows:

[0064]

[0065] Where v r and ω r It is the input to the reference model, (x) r ,y r ,θr ) represents the reference trajectory generated by the reference model.

[0066] Step 3: Based on the kinematic model, reference model, and geometric relationships of WMR motion, establish the pose error signal in the WMR body coordinate system as follows:

[0067] x e =cosθ(x r -x)+sinθ(y r -y),

[0068] y e =-sinθ(x) r -x)+cosθ(y r -y),

[0069] θ e =ω r -ω,

[0070] Where (x) e ,y e ) represents the position error in the body coordinate system; θ e This represents the angular error in the body coordinate system;

[0071] Furthermore, based on the above pose error signals, the pose error dynamic system is established as follows:

[0072]

[0073] Step 4: Based on the pose error dynamic system, construct the desired velocity signal and desired angular velocity signal under the kinematic control loop;

[0074] To ensure pose tracking error x e ,y e ,θ e Converging to zero, the alternative Lyapunov function is constructed as follows:

[0075]

[0076] Differentiating the above alternative Lyapunov functions along the trajectory of the dynamic system solution of the pose error, we can obtain:

[0077]

[0078] Based on the above formula, the desired velocity signal and the desired angular velocity signal are constructed as follows:

[0079] v d =k1x e +v r cosθ e ,

[0080] ωd =ω r +k3y e v r +k2 sinθ e ,

[0081] Where k1, k2, k3 > 0 are design parameters; the constructed v d ,ω d Substitute From this, we can obtain:

[0082]

[0083] First, let's analyze x. e ,θ e Convergence: From the above equation, we know that convergence is achieved if and only if x e =0 and θ e When = 0, the following set is given.

[0084]

[0085] It is an invariant set; therefore, the pose error x e ,θ e It will converge to set I over time. K In the middle, that is, converges to zero;

[0086] Next, we will analyze y. e Convergence: when When all signals in the closed-loop system reach steady state, then there is Since θ in steady state e =0, so y e =0, therefore y e It will also converge to zero over time.

[0087] Step 5: Based on the WMR dynamic model, in the parameter estimation layer under the dynamic control loop, construct the parameter adaptive law for the unknown parameters in the model:

[0088] The parameter estimates are defined as follows:

[0089]

[0090] in and Representing the unknown parameter τ d1 and τ d2 The actual estimated value; and σ1α1(θ,v) and σ2α2(ω) represent the nominal estimated values; σ1,σ2>0 are the correction values;

[0091] The parameter estimation error signal is defined as follows:

[0092]

[0093] Taking the derivative of the above parameter estimation error signal, we can obtain the following dynamic system of parameter estimation error:

[0094]

[0095] To ensure that the parameter estimation error signal ξ2 converges to zero, an alternative Lyapunov function is constructed as follows:

[0096]

[0097] Along the parameter estimation error dynamic system pair Differentiation yields:

[0098]

[0099] Based on the above formula, construct The adaptive law is as follows:

[0100]

[0101] Will Bring into From this, we can obtain:

[0102]

[0103] To ensure the convergence of ξ², the design of the adjustment function α²(ω) must satisfy the following conditions:

[0104] ▽ ω α2(ω)=ρ2φ2,

[0105] in ρ2>0 is a design parameter; therefore, we can obtain:

[0106]

[0107] From the above equation, we can see that the following set exists if and only if ξ2=0.

[0108]

[0109] It is an invariant set; therefore, the parameter estimation error signal ξ2 will converge to the set as time evolves. In this case, it converges to zero exponentially;

[0110] To ensure that the parameter estimation error signal ξ1 converges to zero, an alternative Lyapunov function is constructed as follows:

[0111]

[0112] Along the parameter estimation error dynamic system pair Differentiation yields:

[0113]

[0114] Based on the above formula, construct The adaptive law is as follows:

[0115]

[0116] Will Bring into From this, we can obtain:

[0117]

[0118] To ensure the convergence of ξ1, the design of the adjustment function α1(θ,v) must satisfy the following conditions:

[0119] ▽ v α1(θ,v)=ρ1φ1,

[0120] in ρ1 > 0 is a design parameter; therefore, we can obtain:

[0121]

[0122] From the above equation, we can see that the following set exists if and only if ξ1cosθ=0.

[0123]

[0124] It is an invariant set; therefore, ξ1cosθ will converge to zero over time; the integral achievable

[0125]

[0126] in

[0127] like but When cosθ = 0 at certain times, we have and At this point, ξ1 stops converging; when cosθ≠0, μ1>0, at which point ξ1 converges exponentially; since cosθ(t) is not always zero, therefore, in summary, ξ1 will converge to zero exponentially with time.

[0128] Strict PE conditions are essential for traditional adaptive control to ensure parameter convergence, but they are not easy to meet and verify in practice. Most adaptive laws cannot be accurately estimated when PE conditions are not met. The adaptive law designed in this step can estimate the true value of the unknown parameter without strict PE conditions.

[0129] Step 6: Based on the WMR dynamic model, in the controller design layer under the dynamic control loop, construct torque signals to achieve accurate tracking of the desired velocity and angular velocity signals in the kinematic control loop;

[0130] Based on the adaptive law designed in step five, a new controller was designed in this step. Compared with the existing method controller, this controller can ensure that the pose error converges precisely to zero when tracking a time-varying reference trajectory.

[0131] The tracking error signals for the desired velocity and desired angular velocity are defined as follows:

[0132] v e =v d -v,

[0133] ω e =ω d -ω,

[0134] To ensure tracking error v e ,ω e Converging to zero, the global candidate Lyapunov function is constructed as follows:

[0135]

[0136] Along the dynamic model and pose error dynamic system for V D Differentiation yields:

[0137]

[0138] For the cross term v in the above formula e φ1ξ1 and ω e Taking the absolute value of φ2ξ2 and scaling it, then transforming it using Young's inequality, we get:

[0139]

[0140] Where ∈1, ∈2>0 are design parameters;

[0141] based on Based on the above transformations, the torque signal is constructed as follows:

[0142]

[0143] Input the constructed torque signal From this, we can obtain:

[0144]

[0145] Case 1: When cosθ is not zero and does not approach zero, and the selection of design parameters satisfies the following conditions.

[0146]

[0147] There always Therefore, the closed-loop system is asymptotically stable;

[0148] Case 2: When cosθ is zero or approaches zero at certain times, there is no condition that satisfies the condition. The parameters σ1 and ρ1;

[0149] Define at these moments Consider the worst-case scenario, where cosθ = 0. The derivative of η is calculated as follows:

[0150]

[0151] From the above equation, we know that when cosθ=0, the rate of change of η is zero. From the definition of η, we know that the rate of change of ξ1 is also zero. Therefore, the evolution of ξ1 over time can be summarized as follows:

[0152]

[0153] Therefore when have ξ1 will converge exponentially to zero over time;

[0154] Therefore, when the selection of design parameters meets the following conditions...

[0155]

[0156] There always As time approaches infinity, η converges to zero, therefore the closed-loop system is asymptotically stable.

[0157] Combining Case 1 and Case 2, under the control of the aforementioned adaptive law and torque signal, as time approaches infinity, the pose tracking error x... e ,y e ,θ e Tracking error v of desired velocity and desired angular velocity e ,ω e The parameter estimation errors ξ1 and ξ2 both converge to zero.

[0158] To verify the effectiveness of the adaptive trajectory tracking control method for a WMR dynamic model proposed in this invention, the method is applied to the WMR dynamic model, and MATLAB simulation experiments are conducted. The details are as follows:

[0159] The structure and pose error diagram of the WMR involved in this invention are shown below. Figure 2 As shown, where (x r ,y r ,θ r (x, y, θ) represents the reference trajectory, and (x, y, θ) represents the real-time pose of the WMR. e ,y e ,θ e ) indicates pose error.

[0160] The parameters of the WMR kinetic model are shown in Table 1.

[0161] Table 1 WMR kinetic model parameters

[0162]

[0163] To verify the effectiveness of the control method proposed in this invention in tracking different types of reference trajectories, the simulation provided the following four reference trajectories:

[0164] (a) Straight-line trajectory: v r =1m / s, ω r =0 rad / s;

[0165] (b) Trigonometric function locus: v r =1m / s, ω r = sin(t) rad / s;

[0166] (c) Circular trajectory: v r =1m / s, ω r = 2 rad / s;

[0167] (d) Spiral trajectory:

[0168] The method provided by this invention is used to design an adaptive tracking controller for the above four time-varying reference trajectories. The selection of the initial values ​​of the model and the controller is shown in Table 2, and the selection of the controller parameters is shown in Table 3.

[0169] Table 2 Initial values ​​of the model and controller

[0170]

[0171] Table 3 Controller Parameters

[0172]

[0173] The controller's tracking performance on four time-varying trajectories is as follows: Figure 3 As shown. From Figure 3 As can be seen from (a), (b), (c) and (d) in the figure, the control method proposed in this invention can achieve accurate tracking of different types of time-varying trajectories.

[0174] To verify the superiority of the method proposed in this invention, the following uses a circular trajectory as an example to compare the tracking performance of the method proposed in this invention, the traditional Lyapunov adaptive method, and the Sontag general method. Figure 4 These are pose errors from different methods, from Figure 4 As can be seen from (a), (b), and (c) in the figure, neither the traditional Lyapunov adaptive method nor the Sontag general method can ensure that the pose error converges precisely to zero, and they exhibit fluctuations in steady state. However, the method proposed in this invention can ensure that the pose error converges to zero quickly and accurately. Figure 5 It refers to the tracking error of the desired control signal by different methods, from Figure 5 As can be seen from (a) and (b), the traditional Lyapunov adaptive method and the Sontag general method have poor tracking performance of the desired control signal. Furthermore, the tracking curve of the Sontag general method also exhibits high-frequency oscillation, which deteriorates the control performance. In contrast, the method proposed in this invention can accurately track the desired control signal, and the tracking error can converge to zero quickly and accurately. Figure 6 These are parameter estimation methods from... Figure 6 As can be seen from (a) and (b), only the method proposed in this invention can achieve accurate estimation of unknown parameters among the three methods. The other two methods cannot achieve accurate convergence of parameter estimation errors because the regression vector of the model does not satisfy the PE condition. Figure 7 These are control input signals from different methods, from Figure 7 As can be seen from (a) and (b), the control input of the Sontag general method exhibits high-frequency oscillation, which will cause significant wear and tear on the actuator in practical applications. In contrast, the control input of the method proposed in this invention is smoother.

[0175] In summary, the adaptive trajectory tracking control method for a wheeled mobile robot dynamic model proposed in this invention can not only achieve accurate tracking of various time-varying trajectories and accurate estimation of unknown parameters, but also has significantly better control performance than other existing methods in terms of tracking accuracy, convergence speed, and smoothness of closed-loop signals.

Claims

1. An adaptive trajectory tracking control method for a dynamic model of a wheeled mobile robot, characterized in that: Includes the following steps: Step 1: Establish the dynamic model of WMR; Step 2: Establish the kinematic model of WMR, and based on the kinematic model, establish a reference model and generate a reference trajectory; Step 3: Based on the kinematic model, reference model, and geometric relationships of WMR motion, establish the pose error signal and its dynamic system in the WMR body coordinate system; Step 4: Based on the dynamic system of pose error, construct the desired velocity signal and desired angular velocity signal under the kinematic control loop to achieve accurate tracking of time-varying trajectories; Step 5: Based on the dynamic model of WMR, in the parameter estimation layer under the dynamic control loop, construct the parameter adaptive law for the unknown parameters in the model to ensure accurate convergence of parameter estimation; Step 6: Based on the WMR dynamic model, in the controller design layer under the dynamic control loop, construct a torque signal to achieve accurate tracking of the desired velocity and angular velocity signals in the kinematic control loop, as well as online compensation for uncertainties.

2. The adaptive trajectory tracking control method for a wheeled mobile robot dynamics model according to claim 1, characterized in that: The parameter adaptive law described in step five is constructed as follows: in and Representing the unknown parameter τ d1 and τ d2 The actual estimated value; and σ1α1(θ,v) and σ2α2(ω) represent the parameter estimation nominal values; σ1, σ2 > 0 are the design parameters; the design of the adjustment functions α1(θ,v) and α2(ω) must satisfy: in ρ1,ρ2>0 are design parameters.

3. The adaptive trajectory tracking control method for a wheeled mobile robot dynamics model according to claim 2, characterized in that: In step six, the torque signal in the dynamic control loop is constructed as follows: Where v e =v d -v,ω e =ω d -ω; k4, k5 > 0 are design parameters.

4. The adaptive trajectory tracking control method for a wheeled mobile robot dynamics model according to claim 3, characterized in that: In step four, the desired velocity signal and desired angular velocity signal in the kinematic control loop are constructed as follows: in d =k1x e +v r cosθ e , oh d =ω r +k3y e v r +k2sinθ e , Where k1, k2, k3 > 0 are design parameters.

5. The adaptive trajectory tracking control method for a wheeled mobile robot dynamics model according to claim 4, characterized in that: In step one, the WMR dynamic model is as follows: Where x and y represent the coordinates of the x-axis and y-axis, respectively; θ represents the rotation angle of WMR relative to the geodetic coordinate system; v and ω represent the linear velocity and angular velocity, respectively; τ1 and τ2 represent the input torques of the two rear wheels; and These are known physical parameters, where m is the mass, J is the moment of inertia, r is the radius of the driving wheel, and 2R represents the rear wheelbase; d1 and d2 represent the lumped uncertainty, including unmodeled dynamics and friction, which can be parameterized as follows: and Where τ d1 and τ d2 It is an unknown parameter.

6. The adaptive trajectory tracking control method for a wheeled mobile robot dynamics model according to claim 5, characterized in that: In step two, the WMR kinematic model is as follows: Where v d and ω d These represent the desired linear velocity and desired angular velocity, respectively, that enable time-varying trajectory tracking under the kinematic control loop.

7. The adaptive trajectory tracking control method for a wheeled mobile robot dynamics model according to claim 6, characterized in that: The reference model mentioned in step two is as follows: Where v r and ω r It is the input to the reference model, (x) r ,y r ,θ r ) represents the reference trajectory generated by the reference model.

8. The adaptive trajectory tracking control method for a wheeled mobile robot dynamics model according to claim 7, characterized in that: In step three, the pose error signal in the WMR body coordinate system is established as follows: x e =cosθ(x r -x)+sinθ(y r -y), and e =-sinθ(x r -x)+cosθ(y r -and), i e =ω r -oh, Where (x) e ,y e ) represents the position error in the body coordinate system; θ e This represents the angular error in the body coordinate system.

9. The adaptive trajectory tracking control method for a wheeled mobile robot dynamics model according to claim 8, characterized in that: In step three, the error dynamic system is established as follows:

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