Self-adaptive fixed-time motion control method for mobile mechanical arm based on delay observer

Abstract

The invention belongs to the field of robot motion control, and discloses a mobile mechanical arm adaptive fixed time motion controller design method based on a delay observer, which comprises the following steps: 1, establishing an equivalent dynamic model of a mobile mechanical arm, designing the delay observer to realize model-free estimation compensation of generalized dynamic uncertainty, and designing the equivalent dynamic model of the mobile mechanical arm; the calculation execution efficiency of the controller is improved; 2, a fixed-time nonsingular terminal sliding mode controller and a gain parameter self-adaptive law thereof are designed, fixed-time convergence of motion errors of the mobile mechanical arm is achieved, the stability time of the controller is only determined by controller design parameters, the convergence speed of a control algorithm is increased, and the method does not depend on initial conditions of a system state; and 3, the fixed time stability of the whole closed-loop system is observed and controlled through a Lyapunov design method, dependence on priori knowledge such as the upper definite bound of dynamics uncertainty and the upper definite bound of a delay observer is eliminated, and the response speed and precision of motion control of the mobile mechanical arm are improved.

Description

Technical Field

[0001] The invention belongs to the technical field of robot motion control, and in particular relates to an adaptive fixed-time motion control method for a mobile robot arm based on a delay observer. Background Art

[0002] In recent years, the integration of perception, manipulation, and mobility has become a research hotspot and development direction of robotics. The mobile robot composed of an operating arm and a mobile platform has both flexible movement and dexterous manipulation capabilities. It is gradually being used in industries, agriculture, and services, and has broad application prospects. However, the nonlinear strong coupling and complex dynamic factors between the mobile platform and the operating arm directly affect the motion control performance of the mobile robot. How to develop an efficient and advanced autonomous motion controller is still the main challenge to demonstrate its application potential. When a mobile robot performs tasks in an unstructured environment, unknown loads and external disturbances will also cause its dynamics to change in real time. Therefore, designing and studying its motion control method has important engineering significance and practical value.

[0003] At present, there are many advanced control methods used to solve the motion control problems under the influence of uncertain dynamics of robots, such as anti-disturbance controller, sliding mode robust controller and neural network controller, etc. However, most of these control methods only consider the consistent bounded convergence region of motion error, and rarely involve the analysis and design of the convergence speed of motion error. However, in order to effectively solve the problems of time-varying dynamics and external disturbances faced by mobile manipulators, the motion controller design needs to make its motion error converge quickly. Although methods such as terminal sliding mode controller can achieve finite time convergence of motion controller, that is, the controller stability time is bounded and depends on the design parameters and the initial conditions of the system state, such methods cannot be directly applied to complex systems where the initial state is difficult to obtain directly. In addition, most of the above controllers rely on the dynamic model of the robot system or its learning approximation black box model, and the complex computational burden required will also hinder its implementation on mobile manipulators. In order to improve the anti-disturbance ability of the controller, control methods based on disturbance observers have also been gradually applied to complex robot systems, but the observer gain values ​​mostly rely on the disturbance supremum that is difficult to obtain directly, which limits its application in practical engineering. Summary of the invention

[0004] The present invention aims to provide a method for adaptive fixed-time motion control of a mobile robot arm based on a delay observer to solve the above-mentioned technical problems.

[0005] In order to solve the above technical problems, the specific technical solution of the mobile manipulator adaptive fixed-time motion control method based on delay observer of the present invention is as follows:

[0006] A method for adaptive fixed-time motion control of a mobile manipulator based on a time delay observer comprises the following steps:

[0007] Step 1: Establish an equivalent dynamic model of the mobile robot, design a delay observer to achieve model-free estimation compensation of generalized dynamic uncertainty, simplify the calculation amount of the control algorithm and improve the execution efficiency of the controller;

[0008] Step 2: Design a fixed-time non-singular terminal sliding mode controller and its gain parameter adaptive law to achieve fixed-time convergence of the motion error of the mobile robot, so that the controller stabilization time is determined only by the controller design parameters, improving the convergence speed of the control algorithm and not depending on the initial conditions of the system state;

[0009] Step 3: The Lyapunov design method is used to achieve fixed-time stability of the entire closed-loop observation-control system, eliminating the reliance on prior knowledge such as the supremum of dynamic uncertainty and the supremum of the delay observer, and improving the response speed and accuracy of the mobile robot motion control.

[0010] Furthermore, the step 1 includes the following specific steps:

[0011] Step 1.1: Construct the dynamic equations of the Mecanum wheeled mobile manipulator;

[0012] Step 1.2: Derive the equivalent dynamic model of the mobile robot;

[0013] Step 1.3: Design a time-delay observer for the generalized uncertain dynamics of the mobile manipulator.

[0014] Furthermore, the dynamic equation of the Mecanum wheeled mobile manipulator constructed in step 1.1 is as follows:

[0015]

[0016] In formula (1) represents the generalized joint space coordinates of the mobile manipulator, where q b =[x,y,φ] T and q b =[θ1,…,θ n ] T Represent the joint space coordinates of the mobile platform and the robotic arm respectively; represents the inertia matrix, represents the Coriolis moment and centrifugal moment vector, represents the gravity moment vector, represents the unknown torque vector caused by friction, system dynamics uncertainty and external disturbances, is the joint driving torque of the mobile robot, Represents the input transformation matrix.

[0017] Furthermore, the equivalent dynamic model of the mobile robot arm derived in step 1.2 is as follows:

[0018]

[0019] In formula (2) Represents the user-defined positive definite diagonal inertia matrix, τ=E(q)τ * represents the equivalent input torque of the mobile robot, is the generalized uncertain dynamics of the mobile manipulator.

[0020] Furthermore, the time-delay observer of the generalized uncertain dynamics of the mobile manipulator designed in step 1.3 is as follows:

[0021]

[0022] In formula (3) yes The estimated value of L represents the delay time and is often set as the sampling period of the control system; this observer can make the uncertainty dynamics estimation error Converges to a bounded region, that is, there is a constant Make the inequality Established.

[0023] Furthermore, the step 2 includes the following specific steps:

[0024] Step 2.1: Design a fixed-time non-singular terminal sliding mode manifold;

[0025] Step 2.2: Design a fixed-time non-singular terminal sliding mode controller for the mobile manipulator;

[0026] Step 2.3: Design the controller parameter adaptation law.

[0027] Furthermore, the fixed-time non-singular terminal sliding mode manifold designed in step 2.1 is as follows:

[0028]

[0029] e=qq in formula (4) d represents the motion error of the mobile robot, where q d represents the desired motion trajectory; and represents a diagonal positive definite gain matrix, u1, v1, p1 and q1 are positive odd numbers and satisfy inequality 1 <p1 / q1<2、u1 / v1> p1 / q1,

[0030] Define an unknown constant Satisfy at the same time

[0031]

[0032] In formula (5) is a positive definite diagonal matrix, Representative Matrix The minimum eigenvalue of .

[0033] Furthermore, the fixed-time non-singular terminal sliding mode control of the mobile manipulator designed in step 2.2 is

[0034] The device is as follows:

[0035]

[0036] Furthermore, the controller parameter adaptation law designed in step 2.3 is as follows:

[0037]

[0038] τ in formulas (6) and (7) s and τ r represent the sliding control law and the approaching control law respectively, and Positive definite diagonal gain matrix, u2, v2, p2 and q2 are positive odd numbers and satisfy the inequalities u2>v2, p2>q2; represent , σ0>0, σ1>0 and σ2>0 are the constant coefficients of the controller.

[0039] Furthermore, the step 3 includes the following specific steps:

[0040] The dynamic equation of the delay observer is derived from formula (2) and formula (3), as follows:

[0041]

[0042] When the controller delay time L is small enough, the formula (8) Bounded;

[0043] Will Substituting into formula (8), we get

[0044]

[0045] In formula (9) and are bounded; therefore, when the user-defined inertia matrix satisfy When , the solution of the equivalent differential equation corresponding to formula (9) will converge asymptotically to the bounded region, that is, the inequality Established;

[0046] Define the Lyapunov function as Taking the first-order differential of it with respect to time, we get

[0047]

[0048] In formula (10)

[0049]

[0050] It can be seen that the non-singular terminal sliding mode manifold s will converge to the bounded region within a fixed time t, that is,

[0051]

[0052] In formula (11) is a constant that satisfies

[0053] Therefore, it can be seen from formula (4) that the motion error e of the mobile robot will converge to the bounded region within a fixed time, that is, the controller stabilization time is determined only by its design parameters and has nothing to do with the initial conditions of the system state. In addition, it can be seen from the proof process that the stability of the entire observation-control system does not depend on the prior knowledge of the supremum of dynamic uncertainty and the supremum of the delayed observer.

[0054] The adaptive fixed-time motion control method for a mobile robotic arm based on a delay observer of the present invention has the following advantages: the adaptive fixed-time motion control method for a mobile robotic arm of the present invention can achieve fixed-time convergence of its motion error, that is, the stabilization time of the controller is not affected by the initial state of the system which is difficult to obtain in practice, nor does it rely on prior knowledge of system uncertainty; at the same time, the delay observer is designed to estimate the generalized uncertainty of the compensation system dynamics, which greatly simplifies the computational complexity of the control algorithm to optimize the execution efficiency of the controller, and can effectively improve the response speed and accuracy of the motion control of the mobile robotic arm. BRIEF DESCRIPTION OF THE DRAWINGS

[0055] Figure 1 It is a flow chart of the adaptive fixed-time motion control method of a mobile manipulator based on a delay observer of the present invention;

[0056] Figure 2 is a schematic diagram of the expected trajectory of the generalized joint space of the mobile manipulator of the present invention;

[0057] Figure 3It is a schematic diagram of the fixed time convergence effect of the motion control error of the mobile robot arm of the present invention under different initial conditions. DETAILED DESCRIPTION

[0058] In order to better understand the purpose, structure and function of the present invention, the adaptive fixed-time motion control method of a mobile manipulator based on a delay observer of the present invention is further described in detail below with reference to the accompanying drawings.

[0059] The present invention first designs a time-delay observer to compensate for the generalized uncertain dynamics of a mobile robotic arm, and then designs a non-singular terminal sliding mode controller and its gain parameter adaptation law based on the time-delay observer to achieve fixed-time convergence of the motion error, thereby effectively improving the response speed and accuracy of the motion control of the mobile robotic arm.

[0060] like Figure 1 As shown, the specific implementation scheme of the present invention includes the following steps:

[0061] Step 1: Establish an equivalent dynamic model of the mobile robot, design a delay observer to achieve model-free estimation compensation of generalized dynamic uncertainty, simplify the calculation amount of the control algorithm and improve the execution efficiency of the controller;

[0062] Step 1.1: Construct the dynamic equations of the Mecanum wheeled mobile manipulator as follows

[0063]

[0064] In formula (1) represents the generalized joint space coordinates of the mobile manipulator, where q b =[x,y,φ] T and q b =[θ1,…,θ n ] T Represent the joint space coordinates of the mobile platform and the robotic arm respectively; represents the inertia matrix, represents the Coriolis moment and centrifugal moment vector, represents the gravity moment vector, represents the unknown torque vector caused by friction, system dynamics uncertainty and external disturbances, is the joint driving torque of the mobile robot, Represents the input transformation matrix.

[0065] Step 1.2: Based on step 1.1, the equivalent dynamic model of the mobile robot is derived as follows

[0066]

[0067] In formula (2) Represents the user-defined positive definite diagonal inertia matrix, τ=E(q)τ * represents the equivalent input torque of the mobile robot, is the generalized uncertain dynamics of the mobile manipulator.

[0068] Step 1.3: Design a time-delay observer for the generalized uncertain dynamics of the mobile manipulator as follows

[0069]

[0070] In formula (3) yes The estimated value of L represents the delay time and is often set as the sampling period of the control system; this observer can make the uncertainty dynamics estimation error Converges to a bounded region, that is, there is a constant Make the inequality It is established and does not involve the complex calculation of the dynamic matrix of the kinetics, and the algorithm has high execution efficiency.

[0071] S2: Based on the design of fixed-time non-singular terminal sliding mode controller and its gain parameter adaptive law, the fixed-time convergence of the motion error of the mobile robot is achieved, so that the controller stabilization time is only determined by the controller design parameters, which improves the convergence speed of the control algorithm and does not depend on the initial conditions of the system state;

[0072] Step 2.1: In order to make the motion error of the mobile robot converge within a fixed time, a fixed-time non-singular terminal sliding mode manifold is designed as follows

[0073]

[0074] e=qq in formula (4) d represents the motion error of the mobile robot, where q d represents the desired motion trajectory; and represents a diagonal positive definite gain matrix, u1, v1, p1 and q1 are positive odd numbers and satisfy inequality 1 <p1 / q1<2、u1 / v1> p1 / q1.

[0075] Define an unknown constant Satisfy at the same time

[0076]

[0077] In formula (5) is a positive definite diagonal matrix, Representative Matrix The minimum eigenvalue of .

[0078] Step 2.2: Design a fixed-time non-singular terminal sliding mode controller for the mobile manipulator as follows Step 2.3: Design the controller parameter adaptive law as follows

[0079]

[0080] τ in formulas (6) and (7) s and τ r represent the sliding control law and the approaching control law respectively, and Positive definite diagonal gain matrix, u2, v2, p2 and q2 are positive odd numbers and satisfy the inequalities u2>v2, p2>q2; represent The estimated value of σ0>0, σ1>0 and σ2>0 are constant coefficients of the controller. This algorithm makes the motion error of the mobile robot converge to the bounded region within a fixed time, that is, the controller stabilization time is determined only by its design parameters and has nothing to do with the initial conditions of the system state.

[0081] S3: Achieve fixed-time stability of the entire closed-loop observation-control system through Lyapunov design method, eliminate dependence on prior knowledge such as supremum of dynamic uncertainty and supremum of delayed observer, and improve response speed and accuracy of motion control of mobile robot arm.

[0082] The dynamic equation of the delay observer is derived from formula (2) and formula (3), as follows:

[0083]

[0084] When the controller delay time L is small enough, the formula (8) Bounded.

[0085] Will Substituting into formula (8), we can get

[0086]

[0087] In formula (9) and are bounded; therefore, when the user-defined inertia matrix satisfy When , the solution of the equivalent differential equation corresponding to formula (9) will converge asymptotically to the bounded region, that is, the inequality Established.

[0088] In order to further achieve the fixed-time convergence of the designed controller, the Lyapunov function is defined as Taking the first-order differential of it with respect to time, we get

[0089]

[0090] It can be seen that the non-singular terminal sliding mode manifold s will converge to the bounded region within a fixed time t, that is,

[0091]

[0092] In formula (11) is a constant that satisfies

[0093] Therefore, from formula (4), it can be seen that the motion error e of the mobile robot will converge within a fixed time, and from the proof process, it can be seen that the stability of the entire observation-control system does not depend on prior knowledge such as the supremum of dynamic uncertainty and the supremum of the delayed observer.

[0094] Example

[0095] The process of the adaptive fixed-time motion control method of a mobile manipulator based on a delay observer of the present invention is as follows: Figure 1 As shown, the specific implementation object is a mobile robot composed of a Mecanum wheeled mobile platform and a six-degree-of-freedom robot arm, and its kinematic parameters are d b =0.140m, d1=0.140m, a2=0.375m, a3=0.345m, d4=0.122m, d5=0.122m, d6=0.083m, the mass of the connecting rod is m b =76.156kg, m1=4.785kg, m2=5.485kg, m3=3.101kg, m4=2.568kg, m5=2.568kg, m6=0.414kg, the moment of inertia of the connecting rod is I b =9.619kg·m 2 , I1=5.438kg·m 2 , I2=6.251kg·m 2 , I3=4.488kg·m 2 , I4=1.075kg·m 2 , I5=0.130kg·m 2 , I6=0.025kg·m 2 .

[0096] In the implementation process of the present invention, the desired motion trajectory of the end of the mobile robot arm is designed as follows:

[0097] Where ω = 0.1π. Then the expected trajectory of the generalized joint space of the mobile robot can be expressed by the formula Calculated, where is the forward kinematics of the mobile robot, is the pseudo-inverse of the Jacobian matrix of the mobile manipulator, and the gain parameter Λ=1.5; the desired trajectory is obtained as Figure 2 shown.

[0098] The control law of an adaptive fixed-time motion controller for a mobile manipulator based on a delay observer is shown in equations (3), (4), (6), and (7), where the delay time of the delay observer is set to L = 0.001 and the custom inertia matrix is The parameter values ​​of the adaptive motion controller are: u1 / v1=7 / 3, p1 / q1=17 / 9, u2 / v2=9 / 5, q2 / p2=5 / 3, σ0=0.1, σ1=0.6, σ2=0.8, In order to verify that the stabilization time of the designed controller is independent of the initial conditions of the system state, the initial positions of the four groups of mobile robot joint spaces are taken as: q1(0) = 0, q2(0) = [-π / 6, -π / 4, π / 6, π / 4, -T / 12, π / 12, -π / 9, π / 9, -π / 16, T / 16] T , q3(0)=[π / 4,π / 6,-π / 4,-π / 6,π / 20,-π / 20,π / 15,-π / 15,π / 10,-π / 10] T , q4(0)=[π / 3,π / 3,-π / 3,-π / 3,π / 10,-π / 10,π / 8,-π / 8,π / 6,-π / 6] T Based on this, the implementation effect of the mobile robot motion control can be obtained. Figure 3 This shows that the motion errors of the joints of the mobile robot arm can converge quickly, and the convergence time is not affected by the changes in the initial positions of the joints. This shows that the designed controller can effectively improve the response speed and accuracy of the motion control of the mobile robot arm.

[0099] It is to be understood that the present invention is described by some embodiments, and it is known to those skilled in the art that various changes or equivalent substitutions may be made to these features and embodiments without departing from the spirit and scope of the present invention. In addition, under the teachings of the present invention, these features and embodiments may be modified to adapt to specific circumstances and materials without departing from the spirit and scope of the present invention. Therefore, the present invention is not limited by the specific embodiments disclosed herein, and all embodiments falling within the scope of the claims of this application are within the scope of protection of the present invention.

Claims

1. A method for adaptive fixed-time motion control of a mobile manipulator based on a delay observer, characterized in that: The following steps are involved: Step 1: Establish an equivalent dynamic model of the mobile robot, design a time-delay observer to achieve model-free estimation compensation of generalized dynamic uncertainty, simplify the calculation amount of the control algorithm and improve the execution efficiency of the controller; Step 2: Design a fixed-time non-singular terminal sliding mode controller and its gain parameter adaptive law to achieve fixed-time convergence of the motion error of the mobile robot, so that the controller stabilization time is determined only by the controller design parameters, improving the convergence speed of the control algorithm and not depending on the initial conditions of the system state; Step 3: The Lyapunov design method is used to achieve fixed-time stability of the entire closed-loop observation-control system, eliminating the reliance on prior knowledge such as the supremum of dynamic uncertainty and the supremum of the delay observer, and improving the response speed and accuracy of the mobile robot motion control.

2. The method for adaptive fixed-time motion control of a mobile manipulator based on a delay observer according to claim 1, characterized in that: The step 1 comprises the following specific steps: Step 1.1: Construct the dynamic equations of the Mecanum wheeled mobile manipulator; Step 1.2: Derive the equivalent dynamic model of the mobile robot; Step 1.3: Design a time-delay observer for the generalized uncertain dynamics of the mobile manipulator.

3. The method for adaptive fixed-time motion control of a mobile manipulator based on a delay observer according to claim 2, characterized in that: The dynamic equation of the Mecanum wheeled mobile manipulator constructed in step 1.1 is as follows: In formula (1) represents the generalized joint space coordinates of the mobile manipulator, where q b =[x,y,φ] T and q b =[θ1,…,θ n ] T Represent the joint space coordinates of the mobile platform and the robotic arm respectively; represents the inertia matrix, represents the Coriolis moment and centrifugal moment vector, represents the gravity moment vector, represents the unknown torque vector caused by friction, system dynamics uncertainty and external disturbances, is the joint driving torque of the mobile robot, Represents the input transformation matrix.

4. The method for adaptive fixed-time motion control of a mobile manipulator based on a delay observer according to claim 3 is characterized in that: The equivalent dynamic model of the mobile manipulator derived in step 1.2 is as follows: In formula (2) Represents the user-defined positive definite diagonal inertia matrix, τ=E(q)τ * represents the equivalent input torque of the mobile robot, is the generalized uncertain dynamics of the mobile manipulator.

5. The method for adaptive fixed-time motion control of a mobile manipulator based on a delay observer according to claim 4, characterized in that: The time-delay observer of the generalized uncertain dynamics of the mobile manipulator designed in step 1.3 is as follows: In formula (3) yes The estimated value of L represents the delay time and is often set as the sampling period of the control system; this observer can make the uncertainty dynamics estimation error Converges to a bounded region, that is, there is a constant Make the inequality Established.

6. The method for adaptive fixed-time motion control of a mobile manipulator based on a delay observer according to claim 1, characterized in that: The step 2 comprises the following specific steps: Step 2.1: Design a fixed-time non-singular terminal sliding mode manifold; Step 2.2: Design a fixed-time non-singular terminal sliding mode controller for the mobile manipulator; Step 2.3: Design the controller parameter adaptation law.

7. The method for adaptive fixed-time motion control of a mobile manipulator based on a delay observer according to claim 6, characterized in that: The fixed-time non-singular terminal sliding mode manifold designed in step 2.1 is as follows: e=qq in formula (4) d represents the motion error of the mobile robot, where q d represents the desired motion trajectory; and represents a diagonal positive definite gain matrix, u1, v1, p1 and q1 are positive odd numbers and satisfy inequality 1 <p1 / q1<2、u1 / v1> p1 / q1, defines an unknown constant Satisfy at the same time In formula (5) is a positive definite diagonal matrix, Representative Matrix The minimum eigenvalue of .

8. The method for adaptive fixed-time motion control of a mobile manipulator based on a delay observer according to claim 7, characterized in that: The fixed-time non-singular terminal sliding mode controller of the mobile manipulator designed in step 2.2 is as follows:

9. The method for adaptive fixed-time motion control of a mobile manipulator based on a delay observer according to claim 8, characterized in that: The controller parameter adaptive law designed in step 2.3 is as follows: τ in formulas (6) and (7) s and τ r represent the sliding control law and the approaching control law respectively, and Positive definite diagonal gain matrix, u2, v2, p2 and q2 are positive odd numbers and satisfy the inequalities u2>u2, p2>q2; represent , σ0>0, σ1>0 and σ2>0 are the constant coefficients of the controller.

10. The method for adaptive fixed-time motion control of a mobile manipulator based on a delay observer according to claim 5, characterized in that: The step 3 comprises the following specific steps: The dynamic equation of the delay observer is derived from formula (2) and formula (3), as follows: When the controller delay time L is small enough, the formula (8) Bounded; Will Substituting into formula (8), we get In formula (9) and are bounded; therefore, when the user-defined inertia matrix satisfy When , the solution of the equivalent differential equation corresponding to formula (9) will converge asymptotically to the bounded region, that is, the inequality Established; Define the Lyapunov function as Taking the first-order differential of it with respect to time, we get In formula (10) It can be seen that the non-singular terminal sliding mode manifold s will converge to the bounded region within a fixed time t, that is, In formula (11) is a constant that satisfies Therefore, it can be seen from formula (4) that the motion error e of the mobile robot will converge to the bounded region within a fixed time, that is, the controller stabilization time is determined only by its design parameters and has nothing to do with the initial conditions of the system state. In addition, it can be seen from the proof process that the stability of the entire observation-control system does not depend on the prior knowledge of the supremum of dynamic uncertainty and the supremum of the delayed observer.

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