Leg motion control method and system of flying type double-wheel-leg robot based on active-disturbance-rejection control

Abstract

The invention discloses a leg motion control method and system for a flying type double-wheel-leg robot based on active-disturbance-rejection control, and the method comprises the following steps: S1, solving a five-connecting-rod kinematics calculation formula of the legs of the robot based on the geometrical relationship of a five-connecting-rod mechanism; s2, on the basis of the five-connecting-rod kinematics solution formula, virtual model control is utilized, and the mapping relation between the force of the working space and the joint torque is obtained; s3, solving a kinetic equation of a leg mechanism of the robot by utilizing a Lagrange equation; s4, constructing an active-disturbance-rejection control model based on the kinetic equation, and dynamically optimizing the active-disturbance-rejection control model by using an RBF neural network to obtain a robot leg control model; and S5, regulating and controlling the leg movement of the robot by using the robot leg control model.

Description

Technical Field

[0001] The present invention belongs to the technical field of robot control, and particularly relates to a leg motion control method and system for a flyable two-wheeled leg robot based on active disturbance rejection control. Background Art

[0002] In the field of intelligent unmanned equipment where technology is developing rapidly today, electronic technology and modern control technology are developing at a high speed. With the increasing diversification and difficulty of emergency rescue scenarios, single-function mobile robots are gradually showing their limitations and can no longer meet the growing application needs of people. People have an increasing demand for the working area of robots. Compared with single-function mobile robots, multi-modal robots are more flexible and can quickly adjust their own states and action modes under different environmental conditions. At the same time, it also has strong environmental adaptability and can better cope with complex terrains, changing climate conditions, or environments with different media. Therefore, designing and researching amphibious robots that can switch between land and air modes, changing the single motion mode and single working environment, to meet people's needs for extensive space scientific research and exploration has important academic and practical engineering significance.

[0003] The parallel two-wheeled leg mechanism has two symmetric legs on the left and right. Each leg is driven by two joint motors, and there is a driving wheel at the end of the leg. Overall, the leg is a five-link structure with two degrees of freedom. This structure has the advantages of strong load-bearing capacity, high maintainability, and multiple degrees of freedom, which can make the robot more flexible. Summary of the Invention

[0004] The present invention aims to solve the deficiencies of the prior art and provides the following solutions:

[0005] A leg motion control method for a flyable two-wheeled leg robot based on active disturbance rejection control, comprising the following steps:

[0006] S1. Based on the geometric relationship of the five-link mechanism, solve the five-link kinematic calculation formula of the robot leg;

[0007] S2. Based on the five-link kinematic calculation formula, use virtual model control to obtain the mapping relationship from the force in the working space to the joint torque;

[0008] S3. Use the Lagrangian equation to solve the dynamic equation of the robot leg mechanism;

[0009] S4. Based on the dynamic equation, construct an active disturbance rejection control model, and use an RBF neural network to dynamically optimize the active disturbance rejection control model to obtain a robot leg control model;

[0010] S5. Regulate the leg movement of the robot by using the robot leg control model.

[0011] Preferably, the five-bar kinematic solution formula includes:

[0012] Cartesian coordinates:

[0013]

[0014] Polar coordinates:

[0015]

[0016] Among them, x C represents the abscissa of the end point C of the five-bar linkage, y C represents the ordinate of the end point C of the five-bar linkage, l2 represents the length of the second link, φ1 represents the angle between the first link and the horizontal plane, φ2 represents the angle between the second link and the horizontal plane, L0 represents the robot leg length, φ0 represents the polar angle of the end point C of the five-bar linkage, and l5 represents the length of the fifth link.

[0017] Preferably, the method for obtaining the mapping relationship from the force in the workspace to the joint torque includes:

[0018] Construct a first formula according to the geometric relationship of the five-bar linkage mechanism:

[0019]

[0020] Among them, x B represents the abscissa of the intersection point B of the first link and the second link, y B represents the ordinate of the intersection point B of the first link and the second link, x D represents the abscissa of the intersection point D of the third link and the fourth link, y D represents the ordinate of the intersection point D of the third link and the fourth link, l3 represents the length of the third link, and φ3 represents the angle between the third link and the horizontal plane;

[0021] Derive the first formula to obtain a second formula:

[0022]

[0023] Among them, represents the velocity component of the intersection point B in the x direction, represents the velocity component of the intersection point B in the y direction, represents the angular velocity of the angle φ2, represents the velocity component of the intersection point D in the x direction, represents the velocity component of the intersection point D in the y direction, represents the angular velocity of the angle φ3;

[0024] Derive the derivative of the rectangular coordinates to obtain the third formula:

[0025]

[0026] wherein, represents the velocity component of the intersection point C in the x direction, represents the velocity component of the intersection point C in the y direction, represents the angular velocity of the angle φ1;

[0027] Eliminate in the second formula to obtain the fourth formula;

[0028]

[0029] wherein, l4 represents the length of the fourth connecting rod, φ4 represents the angle between the fourth connecting rod and the horizontal plane, represents the angular velocity of the angle φ4;

[0030] Combine the third formula and the fourth formula to obtain the fifth formula:

[0031]

[0032] Based on the fifth formula and the robot leg length, obtain the mapping relationship:

[0033]

[0034] wherein, τ1 represents the torque of the driving motor at the intersection point A of the first connecting rod and the fifth connecting rod, τ4 represents the torque of the driving motor at the intersection point E of the fourth connecting rod and the fifth connecting rod, F represents the thrust along the leg at the end point C of the five-link mechanism that needs to be controlled, and T P represents the torque along the central axis at the end point C of the five-link mechanism that needs to be controlled.

[0035] Preferably, the method for solving the dynamic equation includes:

[0036] Calculate the generalized active force of the five-link mechanism:

[0037]

[0038] wherein, F1 represents the generalized active force, F represents the resistance at the end point C of the five-link mechanism, v C1 represents the partial velocity of the velocity at the intersection point C with respect to the generalized velocity u1, ω 11 represents the partial angular velocity of φ1 with respect to the generalized velocity u1, ω 41 represents the partial angular velocity of φ4 with respect to the generalized velocity u1, v C2It represents the partial velocity of the velocity at the intersection point C with respect to the generalized velocity u2, ω 12 Denotes the angular velocity of φ1 with respect to the generalized rate u2, ω 42 represents the angular velocity of φ4 with respect to the generalized rate u2;

[0039] Based on the generalized active force, solve the equation corresponding to u r The generalized inertial force of

[0040]

[0041] in, represents the generalized inertial force, represents the inertia force of connecting rod j, represents the inertia moment of connecting rod j, v jr Denotes the velocity at the center of mass j with respect to the generalized rate u r The partial velocity, ω jr Denotes the velocity at the center of mass j with respect to the generalized rate u r Angular velocity, m j represents the mass of connecting rod j, a j represents the acceleration vector at the center of mass j, represents the acceleration at the center of mass j, e n Represents the unit vector in the n direction of space, I j represents the moment of inertia of connecting rod j around the center of mass, ω j represents the angular velocity of the connecting rod j, represents the angular acceleration of the connecting rod j;

[0042] Substituting the generalized active force and the generalized inertia force into the Kane equation, the sixth formula is obtained:

[0043]

[0044] Among them, v j1 represents the partial velocity of the velocity at the center of mass j with respect to the generalized velocity u1, v j2 represents the partial velocity of the velocity at the center of mass j with respect to the generalized velocity u2, ω j1 Represents φ j For the angular velocity of the generalized rate u1, ω j2 Represents φ j For the deflection velocity of the generalized rate u2;

[0045] Combining the sixth formula, we obtain the dynamic equation.

[0046] Preferably, the active disturbance rejection control model is composed of a linear tracking differentiator, an extended state observer and a nonlinear state error feedback control law;

[0047] The transfer function of the linear tracking differentiator is as follows:

[0048]

[0049] where Y represents the output of the linear tracking differentiator, U represents the step input, r represents the convergence rate of the system, and s represents the Laplace variable;

[0050] The extended state observer is as follows:

[0051]

[0052] where z1, z2, and z3 represent state variables, represents the estimated value of the previous moment of the state variable z2, represents the estimated value of the previous moment of the state variable z3, β1, β2, and β3 represent the feedback gains of the system state error, u represents the output of the controller, b represents the compensation coefficient of the disturbance, represents the estimated value of the system output L, J represents the system output matrix, represents the estimated value of the system state vector;

[0053] The non-linear state error feedback control law is as follows:

[0054]

[0055] where r1 represents the error of the leg length, r2 represents the error of the leg length telescopic speed, k1 and k2 represent the error feedback coefficients, L M represents the set leg length, represents the leg length telescopic speed.

[0056] Preferably, the method for dynamically optimizing the active disturbance rejection control model using an RBF neural network includes:

[0057] Dynamically updating and adjusting the feedback gains β1, β2, and β3 of the system state error of the extended state observer using an RBF neural network. The update formula is as follows:

[0058]

[0059] where Δβ1(k) represents the increment of β1, Δβ2(k) represents the increment of β2, and Δβ3(k) represents the increment of β3.

[0060] The present invention also provides a leg motion control system for a flyable two-wheeled leg robot based on active disturbance rejection control. The control system applies the method described in any one of the above, and includes: a kinematic solution module, a mapping relationship construction module, a dynamic equation solution module, a control model construction module, and a regulation module;

[0061] The kinematic solution module solves the kinematic solution formula of the five-link mechanism of the robot leg based on the geometric relationship of the five-link mechanism;

[0062] The mapping relationship construction module obtains the mapping relationship from the force in the workspace to the joint torque based on the kinematic solution formula of the five-link mechanism and using virtual model control;

[0063] The dynamic equation solving module solves the dynamic equation of the robot leg mechanism using the Lagrange equation;

[0064] The control model construction module constructs an active disturbance rejection control model based on the dynamic equation, and dynamically optimizes the active disturbance rejection control model using an RBF neural network to obtain a robot leg control model;

[0065] The regulation module regulates the leg movement of the robot using the robot leg control model.

[0066] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0067] The present invention improves the anti-disturbance ability of the leg movement of the flyable two-wheeled leg robot, effectively improves the movement performance of the flyable two-wheeled leg robot under complex road conditions, and broadens the application scenarios and task execution capabilities of the robot. And the parameters of the active disturbance rejection control system are dynamically optimized using an RBF neural network, solving the problem of complex and difficult parameter modulation of the active disturbance rejection control system. BRIEF DESCRIPTION OF THE DRAWINGS

[0068] In order to more clearly illustrate the technical solutions of the present invention, the drawings required for use in the embodiments will be briefly introduced below. Obviously, the drawings in the following description are only some embodiments of the present invention. For those of ordinary skill in the art, other drawings can be obtained based on these drawings without creative efforts.

[0069] Figure 1 It is a schematic flowchart of the method of the embodiment of the present invention;

[0070] Figure 2 It is a schematic diagram of the robot structure of the embodiment of the present invention;

[0071] Figure 3 It is a schematic diagram of the five-link structure of the robot leg of the embodiment of the present invention;

[0072] Figure 4 It is a schematic diagram of the dynamics of the robot leg of the embodiment of the present invention;

[0073] Figure 5 It is a control block diagram of the active disturbance rejection control model of the embodiment of the present invention;

[0074] Figure 6 This is the structure diagram of the RBF neural network according to the embodiment of the present invention. Specific embodiments

[0075] Next, the technical solutions in the embodiments of the present invention will be clearly and completely described in conjunction with the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts shall fall within the protection scope of the present invention.

[0076] To make the above objects, features, and advantages of the present invention more obvious and understandable, the present invention will be further described in detail below in conjunction with the accompanying drawings and specific embodiments.

[0077] Embodiment 1

[0078] In this embodiment, as Figure 2 shown is the overall structure diagram of the flyable two-wheeled leg robot. The main body of the robot is mainly composed of a quadrotor and a parallel two-wheeled leg chassis. The quadrotor structure has the advantages of high mobility, simple and compact structure, stable flight altitude, and vertical takeoff and landing ability. Since its four rotors can independently control the rotation speed, the UAV can perform rapid translational, rotational, and lifting movements in three-dimensional space. It is very advantageous when performing tasks that require rapid direction change, such as tracking dynamic targets or avoiding obstacles. However, it can only perform large-area inspection work in open and obstacle-free scenarios and is difficult to perform tasks in indoor and jungle environments with many obstacles and small spaces. The parallel wheel-leg mechanism combines wheels and legs, improving the comprehensive performance of the amphibious robot in walking on land. The parallel wheel-leg mechanism has obvious advantages. It has a simple structure, a small volume, a small footprint, and a zero turning radius, and is suitable for a variety of application scenarios. It can not only move quickly on conventional flat roads, but also show good adaptability and powerful obstacle-crossing functions when facing complex and variable rough roads, greatly expanding the application scenarios and task execution capabilities of the robot. The quadrotor structure and the parallel wheel-leg structure are complementary in functional characteristics and can effectively make up for each other's deficiencies. With its flight ability, the quadrotor can quickly reach the task location and carry out preliminary inspection work first. After completing the preliminary inspection, the system can quickly switch to the parallel wheel-leg structure and use the advantages of this structure in terrain adaptation and fine detection to carry out more detailed detection operations, thereby optimizing the task execution process and more efficiently and accurately completing the established target tasks.

[0079] As Figure 3 shown, it is the structure diagram of the planar five-link mechanism. Figure 2 The leg structure ofFigure 3 Schematic diagram of the planar five-link structure shown Figure 2 A, B, C, D, and E in Figure 3 correspond to the hinge points of each connecting rod and the rod Figure 3 In Figure 3 l1, l2, l3, l4, and l5 are the lengths of the connecting rods. φ1, φ2, φ3, and φ4 are the angles between the connecting rods and the horizontal plane, and φ0 is the polar angle of the polar coordinates of point C. Using the mathematical calculation of the planar five-link, the leg length L0 of the robot can be calculated by the angles φ1 and φ4 of the two joint motors Figure 3 The dotted line with an arrow in C is the rectangular coordinate axis, and the direction indicated by the arrow is the positive direction C ).

[0080] A leg motion control method for a flyable two-wheeled leg robot based on active disturbance rejection control, comprising the following steps

[0081] S1. Based on the geometric relationship of the five-link mechanism, solve the five-link kinematic calculation formula of the robot leg

[0082] The five-link kinematic calculation formula includes

[0083] From Figure 3 it can be obtained that

[0084]

[0085] Among them, x B represents the abscissa of point B, the intersection of the first connecting rod and the second connecting rod, and y B represents the ordinate of point B, the intersection of the first connecting rod and the second connecting rod, x D represents the abscissa of point D, the intersection of the third connecting rod and the fourth connecting rod, and y D represents the ordinate of point D, the intersection of the third connecting rod and the fourth connecting rod, l2 represents the length of the second connecting rod, l3 represents the length of the third connecting rod, and φ3 represents the angle between the third connecting rod and the horizontal plane

[0086] Eliminating φ3 gives

[0087] A0cosφ2 + B0sinφ2 - C0 = 0 (2)

[0088] Among them, there are

[0089] A0 = 2l2(x D - xB )

[0090] B0 = 2l2(y D - y B )

[0091]

[0092] For the convenience of simplifying the subsequent formula derivation, in the formula, A0, B0, and C0 only represent the symbol substitutions of the expressions on the right side of the equal sign and have no actual physical meaning. l BD represents the distance between points B and D;

[0093] Solving Equation (2) gives:

[0094]

[0095] Substituting φ2 into Equation (1) gives:

[0096] φ3 = arctan(y C - y D / x C - x D ) (4)

[0097] Then the rectangular coordinates are:

[0098]

[0099] The polar coordinates are:

[0100]

[0101] where x C represents the abscissa of the end point C of the five-link mechanism, y C represents the ordinate of the end point C of the five-link mechanism, φ1 represents the angle between the first link and the horizontal plane, φ2 represents the angle between the second link and the horizontal plane, L0 represents the leg length of the robot, φ0 represents the polar angle of the end point C of the five-link mechanism, and l5 represents the length of the fifth link.

[0102] S2. Based on the five-link kinematic solution formula, using virtual model control, obtain the mapping relationship from the force in the workspace to the joint torque.

[0103] In this embodiment, the core idea of Virtual Model Control (VMC) is to generate desired control instructions by constructing a virtual physical model, enabling the behavior of the controlled object to mimic the dynamic characteristics of the virtual model. According to the control objective and the characteristics of the controlled object, a virtual mechanical model is designed. A virtual spring-damper model is constructed to describe the desired interaction force between the end effector of the robot and the target object. Here, the virtual model control is to map the force or torque in the workspace into the joint torque in the joint space. In this five-link problem, it is necessary to obtain the mapping relationship between the thrust F along the leg and the torque T along the central axis at the end of the five-link mechanism through virtual model control. P They respectively correspond to the mapping relationships between the polar coordinates (L0, φ0) and the driving motor torques τ1 and τ4 of the two rotating pairs at A and E.

[0104] The methods for obtaining the mapping relationship from the force in the workspace to the joint torque include:

[0105] Taking the derivative of Equation (5), we can obtain:

[0106]

[0107] Among them, represents the velocity component of the intersection point C in the x direction, represents the velocity component of the intersection point C in the y direction, represents the angular velocity of the angle φ1;

[0108] Taking the derivative of Equation (1), we can obtain:

[0109]

[0110] Among them, represents the velocity component of the intersection point B in the x direction, represents the velocity component of the intersection point B in the y direction, represents the angular velocity of the angle φ2, represents the velocity component of the intersection point D in the x direction, represents the velocity component of the intersection point D in the y direction, represents the angular velocity of the angle φ3;

[0111] Eliminating from it, we can obtain:

[0112]

[0113] Among them:

[0114]

[0115] In the formula, l4 represents the length of the fourth link, Denote the angular velocity of angle φ4, where φ4 represents the angle between the fourth link and the horizontal plane;

[0116] By combining equations (7), (9), and (10), we can obtain:

[0117]

[0118] Among them, l1 represents the length of the first link; J0

[0119] Briefly recorded as:

[0120]

[0121] Then there is:

[0122]

[0123] Based on the fifth formula and the leg length of the robot, the mapping relationship is obtained:

[0124]

[0125] Among them, τ1 represents the torque of the driving motor at point A, the intersection of the first link and the fifth link, τ4 represents the torque of the driving motor at point E, the intersection of the fourth link and the fifth link, F represents the thrust along the leg at the end point C of the five-link, and T P represents the torque along the central axis at the end point C of the five-link that needs to be controlled and obtained.

[0126] In this embodiment, the thrust F along the leg and the torque T along the central axis at the end of the mechanism P are virtual forces and do not actually exist. They are the forces produced by the combined action of τ1 and τ4. The output result of the ADRC (Active Disturbance Rejection Control) controller is F. Through this mapping relationship, τ1 and τ4 are obtained, and then the motor outputs.

[0127] S3. Use the Lagrangian equation to solve the dynamic equation of the robot leg mechanism.

[0128] As Figure 4 shown is the dynamic modeling sketch of the parallel five-link leg structure. e1, e2, and e3 are unit vectors in three directions of space. Given that the lengths of the five-link legs are l1, l2, l3, l4, and l5, and the corresponding centroid positions 1, 2, 3, 4, and 5 are at the midpoints of the first link, the second link, the third link, the fourth link, and the fifth link respectively. The resistance F at the end point C of the five-link fActing at point C with a constant magnitude and a direction opposite to the velocity direction of point C. In the five-bar linkage, the first link and the fourth link are the driving links (connected to the motor), the second link and the third link are the driven links, and the fifth link is the fixed link. Given the motion laws of the driving members, the first link and the fourth link, the masses of the components, and the moments of inertia about the mass centers, the equilibrium torques acting on the driving members can be obtained by formulating the dynamic equations, providing a basis for the establishment of the control model and the parameter calibration of ADRC.

[0129] The methods for solving the dynamic equations include:

[0130] Taking the angles φ1 and φ4 between l1, l4 and the horizontal as independent variables, a complete Kane equation of the multi-rigid-body system can be formed using the generalized velocities to describe the system, where ω1 and ω4 are the angular velocities of φ1 and φ4, and the partial angular velocities are solved as follows:

[0131] From we get:

[0132]

[0133] From we get:

[0134]

[0135] where ω 11 represents the partial angular velocity of φ1 with respect to the generalized velocity u1, ω 41 represents the partial angular velocity of φ4 with respect to the generalized velocity u1, ω 12 represents the partial angular velocity of φ1 with respect to the generalized velocity u2, and ω 42 represents the partial angular velocity of φ4 with respect to the generalized velocity u2;

[0136] From the velocity at the center of mass 1 [[ID=3)] the partial velocities are obtained as:

[0137]

[0138] where v 11 represents the partial velocity of the velocity at the center of mass 1 with respect to the generalized velocity u1, and v 12 [[ID=5)]represents the partial velocity of the velocity at the center of mass 1 with respect to the generalized velocity u2;

[0139] From the velocity at the center of mass 4 the partial velocities are obtained as:

[0140]

[0141] where v 41 represents the partial velocity of the velocity at the center of mass 4 with respect to the generalized velocity u1, and v 42Denote the partial velocity of the velocity at the centroid 4 with respect to the generalized velocity u2;

[0142] The partial velocities and partial angular velocities of the third link and the fourth link can be obtained from the constraint conditions:

[0143]

[0144] Differentiate both sides of Equation (21) to obtain:

[0145]

[0146] where, ω2 represents the angular velocity of φ2;

[0147] Then there is:

[0148]

[0149]

[0150] Because:

[0151]

[0152] v B = l1ω1(e2cosφ1 - e1sinφ1) (29)

[0153] where, v B represents the linear velocity of the intersection point B;

[0154] Then there is:

[0155]

[0156] where, v 21 represents the partial velocity of the velocity at the centroid 2 with respect to the generalized velocity u1, and v 22 represents the partial velocity of the velocity at the centroid 4 with respect to the generalized velocity u2;

[0157] Similarly, it can be obtained:

[0158] v C1 = (l1cosφ1 + l1ω 21 cosφ2)e2 - (l1sinφ1 + l2ω 21 sinφ2)e1 (32)

[0159] v C2 = l2ω 22 (e2cosφ2 - e1sinφ2) (33)

[0160]

[0161] where, v C1Denotes the partial velocity of the velocity at the intersection point C with respect to the generalized rate u1, v C2 Denotes the partial velocity of the velocity at the intersection point C with respect to the generalized rate u2, v 31 Denotes the partial velocity of the velocity at the center of mass 3 with respect to the generalized rate u1;

[0162] In Kane's equations, the generalized active force corresponding to the ideal constraint force is equal to zero. The constraints in the motion of the five-bar mechanism are ideal constraints, that is, smooth surfaces without considering the frictional force at the contact. Therefore, when calculating the generalized active force, the ideal constraint force can be excluded.

[0163] The forces acting on the end of the five-link are the resistance force F f , the two driving torques τ1 and τ4. Calculate the generalized active force of the five-link mechanism:

[0164]

[0165] Among them, F1 represents the generalized active force, F f represents the resistance force at the end point C of the five-link, τ1 represents the driving torque at the intersection point A of the first link and the fifth link, and τ4 represents the driving torque at the intersection point E of the fourth link and the fifth link;

[0166] Based on the generalized active force, solve the generalized inertia force corresponding to u r :

[0167]

[0168] Among them, represents the generalized inertia force, represents the inertia force of link j, represents the inertia torque of link j;

[0169] Assume that the rods in the five-link mechanism have uniform mass, and the mass of the rod is m j (j = 1, 2, 3, 4), and the moment of inertia about the center of mass is I j (j = 1, 2, 3, 4), then:

[0170]

[0171] Among them, v jr represents the partial velocity of the velocity at the center of mass j with respect to the generalized rate u r , ω jr represents the partial angular velocity of the velocity at the center of mass j with respect to the generalized rate u r , m j represents the mass of link j, a j represents the acceleration vector at the center of mass j, represents the acceleration at the center of mass j, e nDenote the unit vector in the spatial n direction, I j Denote the moment of inertia of link j about its centroid, ω j Denote the angular velocity of link j, Denote the angular acceleration of link j;

[0172] Substitute the generalized active force and generalized inertial force into Kane's equation F r +F r * =0, (r = 1, 2), and we can obtain:

[0173]

[0174] where, v j1 Denote the partial velocity of the velocity at the centroid j with respect to the generalized velocity u1, v j2 Denote the partial velocity of the velocity at the centroid j with respect to the generalized velocity u2, ω j1 Denote φ j The partial angular velocity with respect to the generalized velocity u1, ω j2 Denote φ j The partial angular velocity with respect to the generalized velocity u2;

[0175] By combining Equation (39), the expressions of τ1 and τ4 can be obtained, and the dynamic equation is obtained. In this embodiment, to dynamically optimize the parameters of the ADRC controller using the RBF neural network, an initial parameter needs to be estimated and then dynamically optimized. The role of the dynamic equation is to estimate the initial parameters of the ADRC controller.

[0176] S4. Based on the dynamic equation, construct an active disturbance rejection control model and dynamically optimize the active disturbance rejection control model using the RBF neural network to obtain the robot leg control model.

[0177] To improve the walking ability of the robot on rough roads, the leg telescopic control is carried out using an active disturbance rejection controller (ADRC). In the actual operating environment of the wheel-legged robot, there are various interference factors, such as uneven ground, load changes, etc. As Figure 5 shown in the control block diagram of the ADRC, where L0 in the figure is the robot leg length feedback by the system, L M is the target leg length. The extended state observer can estimate and compensate these interferences in real time, making the leg telescopic control more stable. When the robot walks on rough terrain, the roughness of the ground will interfere with the leg telescopic control, and the ESO can estimate this interference and compensate it in the control law. The ADRC controller is designed as follows: The active disturbance rejection control model consists of a linear tracking differentiator, an extended state observer, and a nonlinear state error feedback control law.

[0178] Linear Tracking Differentiator (TD): Its function is to smooth the step input of the system, reduce the overshoot of the system, and give the estimated values of the desired input signal of the system and its first derivative. For the leg length control of a two-wheeled leg robot, according to the desired leg length change trajectory, a smooth transition trajectory is generated by TD to avoid sudden changes in the control signal. The linear tracking differentiator is obtained from the standard form of the transfer function of a typical second-order system:

[0179]

[0180] where s represents the Laplace variable, ξ represents the damping ratio, and ω n is the undamped natural oscillation frequency. When ξ = 1, the system will not have overshoot and the response time is short. Therefore, ξ is set to 1, and ω n = r. At this time:

[0181]

[0182] where r represents the convergence speed of the system. The larger r is, the faster the convergence speed. The transfer function of the linear tracking differentiator is:

[0183]

[0184] where Y represents the output of the linear tracking differentiator and U represents the step input.

[0185] Extended State Observer (ESO): It is used to estimate the state of the system and external disturbances in real time. In a two-wheeled leg robot, ESO can estimate the actual length, speed of the leg length, and the influence of factors such as possible external disturbance forces on leg length control. By accurately estimating the system state and external disturbance factors, it provides accurate feedback information for subsequent control and cancels the interference. ESO can estimate in real time the interference to leg length control caused by uneven ground or inertial forces generated by the robot's own movement. The extended state observer is designed as follows:

[0186]

[0187] where z1, z2, z3 represent state variables, represents the estimated value of the state variable z2 at the previous moment, represents the estimated value of the state variable z3 at the previous moment, β1, β2, and β3 represent the feedback gains of the system state error, u represents the output of the controller, b represents the compensation coefficient of the disturbance, represents the estimated value of the system output L, J represents the system output matrix, represents the estimated value of the system state vector.

[0188] Nonlinear State Error Feedback Control Law (NLSEF): It is used to calculate the control input based on the desired trajectory given by TD and the actual state estimated by ESO. Through the feedback control of the state error by a nonlinear function, the system can quickly and accurately track the desired trajectory. According to the error between the desired leg length and the actual leg length and the change rate of the error, the control torque of the motor is calculated through the state error feedback control law to drive the leg mechanism to adjust the leg length. The nonlinear state error feedback control law is designed as follows:

[0189]

[0190] Among them, r1 represents the error of the leg length, r2 represents the error of the leg length telescopic speed, k1 and k2 represent the error feedback coefficients, and L M represents the set leg length, and represents the leg length telescopic speed.

[0191] The method for dynamically optimizing the active disturbance rejection control model using an RBF neural network includes:

[0192] The selection of the three parameters β1, β2, and β3 plays a crucial role in the performance of the controller. Using an RBF neural network to optimize the setting of these parameters can improve the anti-interference ability and tracking performance of the ADRC controller. The RBF neural network is a three-layer feedforward network structure including an input layer, a hidden layer, and an output layer. In the hidden layer, each neuron corresponds to a radial basis function, and these functions are connected to the output layer through weights. The neurons in the hidden layer use the radial basis function as the activation function, and this function calculates the output based on the distance between the input vector and the neuron center.

[0193] Its network structure is as Figure 6 shown. The input layer of the RBF neural network only undertakes the task of signal transmission and does not perform any processing on the input vector. The hidden layer uses the radial basis function as its activation function to achieve the nonlinear mapping from the input layer to the hidden layer. The output layer generates the final output result through the linear combination of the output of the hidden layer. This process not only improves the learning efficiency but also helps to avoid the problem of falling into local minima.

[0194] Let the input variable be X = [x1, x2,..., x n T , the radial basis vector be H = [h1, h2,..., h m T , and the weight vector be W = [w1, w2,..., w m T , then there is:

[0195] ​​​

[0196] Among them, P q = [p q1 , p q2 ,..., p qn T represents the center vector of the q-th node in the hidden layer, and b q represents the width of the q-th basis function.

[0197] The output of the RBF neural network is:

[0198] y m (k) = h1w1 + h2w2 +... + h m w m (46)

[0199] Among them, k represents the discrete time step.

[0200] The feedback gains β1, β2, and β3 of the system state error of the extended state observer are dynamically updated and adjusted using the RBF neural network. Define the loss function required for updating the controller parameters as:

[0201] E c = 0.5(y in - y out ) 2 (47)

[0202] Among them, y[[ID=*46]] in = L M represents the input state variable of the system, and y out = L0 represents the output state variable of the system.

[0203] The incremental expressions for the parameters β1, β2, and β3 to be updated by the ESO are:

[0204]

[0205] Among them, ξ1, ξ2, and ξ3 represent the parameter update coefficients, and e eso represents the observation error, and the expression of the fal(x, α, δ) filtering function is:

[0206]

[0207] Among them, δ represents the piecewise parameter. Then the update formula for the extended state observer of the final active disturbance rejection control model is:

[0208]

[0209] Among them, Δβ1(k) represents the increment of β1, Δβ2(k) represents the increment of β2, and Δβ3(k) represents the increment of β3.

[0210] It should be noted that there seems to be a small error in the original text where "y in = L M " is likely an incomplete or incorrect expression. This might need to be further clarified in the original source for a more accurate translation.S5. Use the robot leg control model to regulate the leg movement of the robot.

[0211] Embodiment 2

[0212] In this embodiment, a leg movement control system for a flyable two-wheeled leg robot based on active disturbance rejection control includes: a kinematic solution module, a mapping relationship construction module, a dynamic equation solution module, a control model construction module, and a regulation module.

[0213] The kinematic solution module solves the five-link kinematic calculation formula of the robot leg based on the geometric relationship of the five-link mechanism.

[0214] The mapping relationship construction module uses virtual model control based on the five-link kinematic calculation formula to obtain the mapping relationship from the force in the workspace to the joint torque.

[0215] The dynamic equation solution module uses the Lagrangian equation to solve the dynamic equation of the robot leg mechanism.

[0216] The control model construction module constructs an active disturbance rejection control model based on the dynamic equation, and dynamically optimizes the active disturbance rejection control model using an RBF neural network to obtain the robot leg control model.

[0217] The regulation module uses the robot leg control model to regulate the leg movement of the robot.

[0218] The above-described embodiments are only descriptions of the preferred embodiments of the present invention, and do not limit the scope of the present invention. Without departing from the design spirit of the present invention, various deformations and improvements made by those of ordinary skill in the art to the technical solution of the present invention shall fall within the protection scope determined by the claims of the present invention.

Claims

1. A leg motion control method for a flyable two-wheeled leg robot based on active disturbance rejection control, characterized in that, It includes the following steps: S1. Based on the geometric relationship of the five-bar linkage mechanism, solve the kinematic solution formula of the five-bar linkage of the robot leg; S2. Based on the kinematic solution formula of the five-bar linkage, use virtual model control to obtain the mapping relationship from the force in the workspace to the joint torque; S3. Use the Lagrangian equation to solve the dynamic equation of the robot leg mechanism; S4. Based on the dynamic equation, construct an active disturbance rejection control model, and use the RBF neural network to dynamically optimize the active disturbance rejection control model to obtain the robot leg control model; S5. Use the robot leg control model to regulate the leg movement of the robot.

2. The leg motion control method of a flyable two-wheeled leg robot based on active disturbance rejection control according to claim 1, wherein, The kinematic solution formula of the five-bar linkage includes: Rectangular coordinates: Polar coordinates: where x C represents the abscissa of the end point C of the five-link mechanism, y C represents the ordinate of the end point C of the five-link mechanism, l2 represents the length of the second link, φ1 represents the angle between the first link and the horizontal plane, φ2 represents the angle between the second link and the horizontal plane, L0 represents the leg length of the robot, φ0 represents the polar angle of the end point C of the five-link mechanism, and l5 represents the length of the fifth link.

3. The leg motion control method of a flyable two-wheeled legged robot based on active disturbance rejection control according to claim 2, characterized in that, The method for obtaining the mapping relationship from the force in the workspace to the joint torque includes: According to the geometric relationship of the five-bar linkage mechanism, construct the first formula: Among them, x B represents the abscissa of the intersection point B of the first link and the second link, y B represents the ordinate of the intersection point B of the first link and the second link, x D represents the abscissa of the intersection point D of the third link and the fourth link, y D represents the ordinate of the intersection point D of the third link and the fourth link, l3 represents the length of the third link, and φ3 represents the angle between the third link and the horizontal plane; Derive the first formula to obtain the second formula: Among them, represents the velocity component of the intersection point B in the x direction, represents the velocity component of the intersection point B in the y direction, represents the angular velocity of the angle φ2, represents the velocity component of the intersection point D in the x direction, represents the velocity component of the intersection point D in the y direction, represents the angular velocity of the angle φ3; Derive the rectangular coordinates to obtain the third formula: Among them, represents the velocity component of the intersection point C in the x direction, represents the velocity component of the intersection point C in the y direction, represents the angular velocity of the angle φ1; Eliminate the in the second formula to obtain a fourth formula; where, l4 represents the length of the fourth link, and φ4 represents the angle between the fourth link and the horizontal plane, represents the angular velocity of the angle φ4; Combine the third formula and the fourth formula to obtain the fifth formula: Based on the fifth formula and the robot leg length, obtain the mapping relationship: Among them, τ1 represents the torque of the driving motor at point A, the intersection of the first link and the fifth link, τ4 represents the torque of the driving motor at point E, the intersection of the fourth link and the fifth link, F represents the thrust along the leg at point C, the end point of the five-link mechanism that needs to be controlled, and T P represents the torque along the central axis at point C, the end point of the five-link mechanism that needs to be controlled.

4. The leg motion control method of a flyable two-wheeled leg robot based on active disturbance rejection control according to claim 3, characterized in that The method for solving the dynamic equation includes: Calculate the generalized active force of the five-bar linkage mechanism: Among them, F1 represents the generalized active force, F f represents the resistance at point C, the end point of the five-link mechanism, v C1 represents the partial velocity of the velocity at point C of the intersection with respect to the generalized velocity u1, ω 11 represents the partial angular velocity of φ1 with respect to the generalized velocity u1, ω 41 represents the partial angular velocity of φ4 with respect to the generalized velocity u1, v C2 represents the partial velocity of the velocity at point C of the intersection with respect to the generalized velocity u2, ω 12 represents the partial angular velocity of φ1 with respect to the generalized velocity u2, ω 42 represents the partial angular velocity of φ4 with respect to the generalized velocity u2; Based on the generalized active force, solve for the generalized inertia force corresponding to u r : Among them, represents the generalized inertial force, represents the inertial force of link j, represents the inertial moment of link j, v jr represents the partial velocity of the velocity at the centroid j with respect to the generalized velocity u r ω jr represents the partial angular velocity of the velocity at the centroid j with respect to the generalized velocity u r ω j represents the mass of link j, a j represents the acceleration vector at the centroid j, represents the acceleration at the centroid j, e n represents the unit vector in the spatial n direction, I j represents the moment of inertia of link j about the centroid, ω j represents the angular velocity of link j, represents the angular acceleration of link j; Substitute the generalized active force and the generalized inertial force into the Kane equation to obtain the sixth formula: where, v j1 represents the partial velocity of the velocity at the centroid j with respect to the generalized velocity u1, v j2 represents the partial velocity of the velocity at the centroid j with respect to the generalized velocity u2, ω j1 represents φ j the partial angular velocity of φ with respect to the generalized velocity u1, ω j2 represents φ j the partial angular velocity of φ with respect to the generalized velocity u2; Combine the sixth formula to obtain the dynamic equation.

5. The leg motion control method of a flyable two-wheeled legged robot based on active disturbance rejection control according to claim 1, wherein, The active disturbance rejection control model consists of a linear tracking differentiator, an extended state observer, and a nonlinear state error feedback control law; The transfer function of the linear tracking differentiator is: Where, Y represents the output of the linear tracking differentiator, U represents the step input, r represents the convergence speed of the system, and s represents the Laplace variable; The extended state observer is: where z1, z2, and z3 represent state variables, represents the estimated value of the state variable z2 at the previous moment, represents the estimated value of the state variable z3 at the previous moment, β1, β2, and β3 represent the feedback gains of the system state error, u represents the output of the controller, b represents the compensation coefficient of the disturbance, represents the estimated value of the system output L, J represents the system output matrix, represents the estimated value of the system state vector; The nonlinear state error feedback control law is: Among them, r1 represents the error of the leg length, r2 represents the error of the leg length telescoping speed, k1 and k2 represent the error feedback coefficients, and L M represents the set leg length, and represents the leg length telescoping speed.

6. The leg motion control method of a flyable two-wheeled leg robot based on active disturbance rejection control according to claim 5, characterized in that, The method for dynamically optimizing the active disturbance rejection control model using the RBF neural network includes: Use the RBF neural network to dynamically update and adjust the feedback gains β1, β2, and β3 of the system state error of the extended state observer. The update formula is: Where, Δβ1(k) represents the increment of β1, Δβ2(k) represents the increment of β2, and Δβ3(k) represents the increment of β3.

7. A leg motion control system for a flyable two-wheeled legged robot based on active disturbance rejection control, the control system applying the method according to any one of claims 1-6, characterized in that, It includes: A kinematic solution module, a mapping relationship construction module, a dynamic equation solution module, a control model construction module, and a regulation module; The kinematic solution module, based on the geometric relationship of the five-bar linkage mechanism, solves the kinematic solution formula of the five-bar linkage of the robot leg; The mapping relationship construction module, based on the kinematic solution formula of the five-bar linkage, uses virtual model control to obtain the mapping relationship from the force in the workspace to the joint torque; The dynamic equation solution module uses the Lagrangian equation to solve the dynamic equation of the robot leg mechanism; The control model construction module, based on the dynamic equation, constructs an active disturbance rejection control model, and uses the RBF neural network to dynamically optimize the active disturbance rejection control model to obtain the robot leg control model; The regulation module uses the robot leg control model to regulate the leg movement of the robot.

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