An adaptive control method for rail-mounted robot based on motion planning

Abstract

The present invention discloses an adaptive control method for a rail-hanging robot based on motion planning, which belongs to the technical field of automatic control of nonlinear under-actuated systems. The method comprises: establishing a dynamic model of the rail-hanging robot system, initializing the state and control parameters of the system; formulating a motion plan, designing a desired motion position time curve for the rail-hanging robot, so that the rail-hanging robot can quickly reach the target position along the curve, and the load swing angle is controlled within a smaller range; designing an adaptive tracking controller, which guides the actuator of the rail-hanging robot to provide a corresponding output force through a control signal, thereby driving the rail-hanging robot to complete tracking according to the target motion trajectory. The present invention realizes the rapid positioning of the rail-hanging robot, suppresses the residual swing of the load of the rail-hanging robot, and ensures the smoothness of the control input when different parameters change.

Description

Technical Field

[0001] The invention belongs to the technical field of automatic control of nonlinear under-actuated systems, and in particular relates to an adaptive control method of a rail-hanging robot based on motion planning. Background Art

[0002] Rail-mounted inspection robots are specially designed for inspection and maintenance tasks on rail-mounted systems. Currently, rail-mounted inspection robots are widely used in industrial automation and production lines, power and distribution systems, nuclear power plants, and high-risk areas.

[0003] Rail-mounted robots can cause their loads to oscillate during operation. When the robot reaches a designated position and stops, the load suspended by the robot will experience significant residual oscillation, posing a significant safety hazard and significantly impacting the robot's operating efficiency.

[0004] Although numerous researchers in the field of automation, both domestically and internationally, have conducted extensive research on rail-mounted robotic systems and proposed various control methods for these underactuated systems, striving to achieve safe and efficient transportation. However, a convenient and reliable automatic control system or method for rail-mounted robots has yet to be developed. Furthermore, existing control algorithms lack the ability to adapt to unknown parameters. These unknown parameters, which vary with task and state, significantly impact various control algorithms, significantly limiting the functionality and practical application of the controllers.

[0005] Therefore, reducing the impact of parameters that may change with the task, working environment, etc. (such as rope length, load and robot mass, friction level of corresponding parts, etc.) on the robot's anti-sway positioning, while allowing the robot to quickly reach a stable state and have good robustness, is an urgent problem to be solved in this field. Summary of the Invention

[0006] In view of the deficiencies in the prior art, the object of the present invention is to provide an adaptive control method for a rail-hanging robot based on motion planning.

[0007] The object of the present invention is achieved through the following technical solution: a motion planning-based adaptive control method for a rail-hanging robot, comprising the following steps:

[0008] Establishing a dynamic model of the rail-hanging robot and initializing the state and control parameters of the model;

[0009] Develop a motion plan to design a desired motion position-time curve for the rail-mounted robot, so that the rail-mounted robot can reach the target position within 6 seconds along the curve, and the load swing angle is controlled within 2 degrees;

[0010] When the experimental parameters of the rail-mounted robot are unknown during its movement, an adaptive tracking controller is designed to improve the robot's ability to track a preset curve. The adaptive tracking controller instructs the robot's actuator to provide corresponding output force through a control signal to drive the robot to complete tracking along the target motion trajectory. The experimental parameters include load mass, telescopic rod length, friction resistance, and internal damping of the system.

[0011] Furthermore, the step of establishing a dynamic model of the rail-hanging robot and initializing the state and control parameters of the model includes:

[0012] The dynamic model of the rail-hanging robot is expressed by dynamics as follows:

[0013]

[0014] q(t)=[x θ] T (2)

[0015]

[0016] G(q)=[0 -mglsinθ] T (5)

[0017]

[0018] U(t)=[f x 0] T (7)

[0019] Where q(t) = [xθ] T is the system state vector, including the robot position x and the load swing angle θ; is the speed of the robot, is the angular velocity of the load, ε is the unknown parameter of the system; U(t) is the control input force vector, where f x is the driving force of the robot; M(q) is the inertia matrix of the system, m x is the weight of the robot, m is the weight of the load, and l is the length of the telescopic rod; and G(q) are the Coriolis-centripetal force matrix and gravity vector respectively; represents the internal damping vector of the system, k c and k b are the different friction coefficients of the system, k θ is the damping parameter of the system.

[0020] Furthermore, the motion planning is to design a desired motion position time curve for the rail-hanging robot as follows:

[0021] The displacement time curve of the rail-hanging robot is designed to be a unidirectional smooth S-shaped curve, and the desired trajectory is designed:

[0022]

[0023]

[0024]

[0025] Among them, p d ∈R + is the target position that the robot wants to reach; k a 、k v ∈R + Respectively represent the maximum allowable acceleration and speed of the robot; ∈∈R + To adjust and optimize the parameters of initial acceleration; x d (t), and They represent the displacement, velocity and acceleration of the rail-hanging robot respectively, and t represents time;

[0026] The displacement x of the rail-hanging robot on the curve d (t), speed acceleration They are all smooth continuous curves.

[0027] Furthermore, when the experimental parameters of the rail-hanging robot are unknown during its movement, the tracking capability of the rail-hanging robot for a preset curve is improved by designing an adaptive tracking controller, which includes:

[0028] The specific form of the tracking controller is:

[0029]

[0030] in, is the error derivative, is the control item of PD in the controller, is the parameter adaptation term; f x is the driving force of the robot; k p and k d is the driving parameter in the controller; k e and k h Assign PD and adaptive coefficients to the controller;

[0031] r(t) is the current position of the robot x(t) and the trajectory position x in the motion position time curve in the motion planning at the same moment d The error between (t) is specifically:

[0032] r(t)=x(t)-x d(t) (12)

[0033] β is the unknown parameter vector:

[0034] β=[k c k b ml mk θ / l] T (13)

[0035] Y(t) is the unknown adaptation coefficient:

[0036]

[0037] n(t) is the unknown parameter that needs to be adapted when designing the controller:

[0038] n(t)=Y T β (15)

[0039]

[0040] The unknown parameter term β is estimated, and the parameter update rate is:

[0041]

[0042] in, is the speed of the robot, is the angular velocity of the load, ε is the unknown parameter of the system; k c and k b are the different friction coefficients of the system, k θ is the damping parameter of the system; m x is the weight of the robot, m is the weight of the load, l is the length of the telescopic rod; τ is a positive definite symmetric matrix. Perform online integration to obtain an estimate The estimated value Substitute into the controller.

[0043] The beneficial effects of this invention lie in its application to the horizontal transport control of a load on a rail-mounted robot, based on practical engineering needs. This method adapts to parameters that may vary with the task and working environment (such as rope length, load and robot mass, and the friction level of various components). This overcomes the influence of these unknown parameters, transports the load to the target position, and converges the swing angle to zero. The designed algorithm has been theoretically proven to be stable, demonstrating the reliability of the controller.

[0044] The present invention realizes rapid positioning of the rail-hanging robot, suppresses residual load swing of the rail-hanging robot, and ensures smooth control input when different parameters change. BRIEF DESCRIPTION OF THE DRAWINGS

[0045] Figure 1 It is a simplified system diagram of the present invention;

[0046] Figure 2 This is the experimental result diagram of the present invention when the load weight is 2kg and the rod length is 0.6m;

[0047] Figure 3 This is the experimental result diagram of the present invention when the load weight is 2kg and the rod length is 0.8m;

[0048] Figure 4 This is the experimental result diagram of the present invention when the load weight is 4kg and the rod length is 0.6m;

[0049] Figure 5 This is the experimental result diagram of the present invention when the load weight is 4kg and the rod length is 0.8m. DETAILED DESCRIPTION

[0050] The present invention will be described in detail below with reference to the accompanying drawings. Unless there is any conflict, the features of the following embodiments and implementations may be combined with each other.

[0051] An embodiment of the present invention provides a method for adaptive control of a rail-hanging robot based on motion planning, comprising the following steps:

[0052] Step 1: Develop a motion plan. Design a desired motion position-time curve for the robot, along which the robot can reach the target position relatively quickly while keeping the load swing angle within a small, acceptable range. The robot's displacement-time curve is designed to be a unidirectional, smooth S-shaped curve. The process is as follows:

[0053] Design expected trajectory:

[0054]

[0055]

[0056]

[0057] Among them, p d ∈R + is the target position that the robot wants to reach; k a 、k v ∈R + Respectively represent the maximum allowable acceleration and speed of the robot; ∈∈R + To adjust and optimize the parameters of initial acceleration; x d (t), and They represent the displacement, velocity and acceleration of the rail-mounted robot respectively, and t represents time.

[0058] Step 2: Establish a dynamic model of the rail-hanging robot system and initialize the system state and control parameters. The process is as follows:

[0059] The dynamics of the rail-mounted robot is expressed as:

[0060]

[0061] q(t)=[x θ] T (5)

[0062]

[0063] G(q)=[0 -mglsinθ] T (8)

[0064]

[0065] U(t)=[f x 0] T (10)

[0066] Where q(t) = [xθ] T is the system state vector, including the robot position x and the load swing angle θ; is the speed of the robot, is the angular velocity of the load, ε is the unknown parameter of the system; U(t) is the control input force vector, where f x is the driving force of the robot; M(q) is the inertia matrix of the system, m x is the weight of the robot, m is the weight of the load, and l is the length of the telescopic rod; and G(q) are the Coriolis-centripetal force matrix and gravity vector respectively; represents the internal damping vector of the system, k c and k b are the different friction coefficients of the system, k θ is the damping parameter of the system.

[0067] Step 3: Design an adaptive tracking controller. When certain experimental parameters (such as load mass, telescopic rod length, frictional resistance, and internal system damping) are unknown, an adaptive tracking controller is designed to enable the robot to better track the predetermined design curve. This controller dynamically calculates the control output by measuring the robot's position and speed, as well as the load's swing angle and angular velocity, in real time. The control signal instructs the motor and other actuators to provide the corresponding output force, thereby driving the robot to accurately track the target motion trajectory. The specific form of this controller is:

[0068]

[0069] Where ir is the error derivative, is the control item of PD in the controller, is the parameter adaptation term; f x is the driving force of the robot; k p and k d is the driving parameter in the controller; k e and k h Assign PD and adaptive coefficients to the controller.

[0070] r(t) is the current position of the robot x(t) and the trajectory position x in the motion position time curve in the motion planning at the same moment d The error between (t) is specifically:

[0071] r(t)=x(t)-x d (t) (12)

[0072] β is the unknown parameter vector:

[0073] β=[k c k b ml mk θ / l] T (13)

[0074] Y(t) is the unknown adaptation coefficient:

[0075]

[0076] n(t) is the unknown parameter that needs to be adapted when designing the controller:

[0077] n(t)=Y T β (15)

[0078]

[0079] The unknown parameters are estimated and the parameter update rate is:

[0080]

[0081] in, is the speed of the robot, is the angular velocity of the load, ε is the unknown parameter of the system; k c and k b are the different friction coefficients of the system, k θ is the damping parameter of the system; m x is the weight of the robot, m is the weight of the load, l is the length of the telescopic rod; τ is a positive definite symmetric matrix. Perform online integration to obtain an estimate The estimated value Substitute into the controller.

[0082] Step 4: Prove the stability of the adaptive tracking controller. This section theoretically explains the role of the controller and its parameter adaptation function. That is, when there are unknown parameters, the robot position error and the load swing angle error can approach zero over time under the control of the controller:

[0083]

[0084] After performing corresponding mathematical processing on the robot model, it can be divided into the following two subsystems:

[0085]

[0086] Where h(θ) represents the following auxiliary function:

[0087] h(θ)=m x +msin 2 θ>0 (20)

[0088] For the rail-mounted robot represented by formula (1), considering the mechanical energy of the system

[0089]

[0090] Among them, the first term is the kinetic energy of the system, and the second term represents the potential energy of the system. is a semi-positive definite function. Taking the derivative of both sides of equation (21) and simplifying it, we get:

[0091]

[0092] Integrate both sides of equation (22) with respect to time:

[0093]

[0094] The projection function is defined as follows:

[0095]

[0096] Construct non-negative functions V1, V2∈R:

[0097]

[0098] The derivative of the function with respect to time is

[0099]

[0100]

[0101] For the function proj defined therein i(u),i=1,2,3,4,5, it can be proved that:

[0102]

[0103] so It can be seen that the system can remain stable.

[0104] In order to verify the effectiveness of the above controller, the present invention conducts a simulation experiment on the control effect of the adaptive controller shown in formula (11).

[0105] Its controller and system parameters are:

[0106] k e =0.9, k h =0.1,ε=2,k p =20,k d =50

[0107] p d =1,k v =0.4, k a =0.2,τ=20,∈=2

[0108] The four sets of experimental parameters are:

[0109] Experiment 1.m x =25kg, m=2kg, l=0.6m

[0110] Experiment 2.m x =25kg, m=2kg, l=0.8m

[0111] Experiment 3.m x =25kg, m=4kg, l=0.6m

[0112] Experiment 4.m x =25kg, m=4kg, l=0.8m

[0113] The experimental results are as follows Figures 2 to 5 As shown:

[0114] Figure 2 This is the result of Experiment 1, which shows that the controller is under condition m x =25kg, m=2kg, l=0.6m, the robot position curve tracking situation and the load swing angle change relationship, as well as the force command curve output by the controller, all have good performance; Figure 3 This is the result of Experiment 2. When the telescopic rod length is increased by 33%, the robot's position curve tracking and the relationship between the load swing angle and the force command curve output by the controller all have good performance. Figure 4This is the result of Experiment 3. When the load increases by 100%, the robot's position curve tracking and the relationship between the load swing angle and the force command curve output by the controller all have good performance. Figure 5 This is the result of Experiment 4. When the load increases by 100% and the telescopic rod length increases by 33%, the robot's position curve tracking and the relationship between the load swing angle and the force command curve output by the controller all have good performance.

[0115] The above descriptions represent simulation and comparative experiments presented in this invention, demonstrating the superiority of the proposed method. Clearly, the present invention is not limited to the aforementioned examples and is amenable to various modifications without departing from the basic spirit or exceeding the scope of the present invention. The proposed control method effectively addresses the uncertainty of system parameters, ensuring efficient and stable operation of the robot in complex environments.

Claims

1. A motion planning-based adaptive control method for a rail-hanging robot, characterized in that: The steps include: Establishing a dynamic model of the rail-hanging robot and initializing the state and control parameters of the model; Develop a motion plan to design a desired motion position-time curve for the rail-mounted robot, so that the rail-mounted robot can reach the target position within 6 seconds along the curve, and the load swing angle is controlled within 2 degrees; When the experimental parameters of the rail-hanging robot are unknown during its movement, an adaptive tracking controller is designed to improve the tracking capability of the rail-hanging robot for a preset curve, including: the specific form of the tracking controller is: ； in, is the error derivative, is the control item of PD in the controller, is the parameter adaptation term; It is the driving force of the robot; and is the driving parameter in the controller; and Assign PD and adaptive coefficients to the controller; The current position of the robot The trajectory position in the motion position time curve in the motion planning at the same moment The error between them is: ； is the unknown parameter vector: ； is the unknown adaptation coefficient: ； The unknown parameters that need to be adapted when designing the controller are: ； ； To estimate the unknown parameter term β, we have the parameter update rate: ； in, is the speed of the robot, is the angular velocity of the load, ε is the unknown parameter of the system; are the different friction coefficients of the system, is the damping parameter of the system; is the weight of the robot, m is the weight of the load, l is the length of the telescopic rod; g represents the acceleration of gravity, τ is a positive definite symmetric matrix, Perform online integration to obtain an estimate , the estimated value Substitute into the controller; The adaptive tracking controller instructs the actuator of the rail-mounted robot to provide corresponding output force through a control signal to drive the rail-mounted robot to complete tracking according to the target motion trajectory; the experimental parameters include load mass, telescopic rod length, friction resistance, and internal damping of the system.

2. The adaptive control method of a rail-hanging robot based on motion planning according to claim 1, characterized in that: The step of establishing a dynamic model of the rail-hanging robot and initializing the state and control parameters of the model includes: The dynamic model of the rail-hanging robot is expressed by dynamics as follows: ； ； ； ； ； ； ； in, is the system state vector, including the robot position x and the load swing angle θ; is the speed of the robot, is the angular velocity of the load, ε is the unknown parameter of the system; is the control input force vector, where As the driving force for the robot; is the inertia matrix of the system, is the weight of the robot, m is the weight of the load, and l is the length of the telescopic rod; are the Coriolis-centripetal force matrix and gravity vector respectively; represents the internal damping vector of the system, are the different friction coefficients of the system, is the damping parameter of the system.

3. The adaptive control method of a rail-hanging robot based on motion planning according to claim 1, characterized in that: The motion planning is to design a desired motion position time curve for the rail-hanging robot as follows: The displacement time curve of the rail-hanging robot is designed to be a unidirectional smooth S-shaped curve, and the desired trajectory is designed: ； ； ； in, is the target position that the robot wants to reach; 、 Respectively represent the maximum allowable acceleration and speed of the robot; To adjust and optimize the parameters of initial acceleration; 、 and They represent the displacement, velocity and acceleration of the rail-hanging robot respectively, and t represents time; The displacement of the rail-hanging robot on the curve ,speed , acceleration They are all smooth continuous curves.

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