A redundancy degree continuous arm control method based on MRAC and PID

Abstract

The application discloses a kind of redundancy degree of freedom continuous arm control method based on MRAC and PID, comprising: S1: according to the structure and joint parameters of pneumatic continuous arm, the kinematics, statics and dynamics modeling of pneumatic continuous arm is carried out;Pneumatic continuous arm is divided into multiple sections, each section includes rigid skeleton and pneumatic muscle;S2: the joint angle of pneumatic continuous arm is zero, and the air passage of pneumatic muscle and control parameter are initialized, and target angle is set;S3: according to target angle, joint angle trajectory planning is carried out, and angle decoupling is carried out;S4: according to the joint angle data of pneumatic continuous arm, the difference between current angle and target angle is calculated, and control scheme optimization adjustment is carried out in combination with load, and pneumatic continuous arm reaches target position.The application reduces the accuracy requirement of model, reasonably selects control scheme according to different conditions, reduces operation amount, improves real-time performance, and has flexibility and robustness.

Description

Technical Field

[0001] This invention relates to the field of automatic control technology, and in particular to a redundant degree-of-freedom continuous arm control method based on MRAC and PID. Background Technology

[0002] Traditional rigid robotic arms, due to their structural and material properties, possess high precision and maneuverability. However, as the application environments of robots become increasingly complex, expanding from industry to various sectors such as healthcare, exploration, and services, the poor human-robot interaction safety, low degrees of freedom, and poor adaptability to complex environments exposed by traditional rigid robotic arms limit their application scenarios. In contrast, soft robotic arms, fabricated using soft or flexible materials, possess flexibility, greater agility, non-destructive operation, and improved human-robot interaction safety—qualities that traditional rigid robots lack. Furthermore, they maintain relatively good performance even under certain stretching or compression conditions, making them more suitable for service robots. Based on this phenomenon, existing technologies have proposed rigid-flexible coupled continuous arms that integrate the characteristics of both rigid and soft arms.

[0003] For robot modeling and control algorithms, the pose of a traditional rigid robot at any point in the workspace can be determined by the link length and joint angles, establishing a relatively accurate kinematic and dynamic model. Based on this, fast, accurate, and stable control is achieved, with most studies employing conventional PID control methods. However, conventional PID control alone is unsuitable for rigid-flexible coupled continuous arms with a large number of degrees of freedom. Furthermore, the large elastic deformation of flexible materials leads to strong nonlinearity, resulting in low modeling accuracy and difficulties in vibration suppression. The time-varying nature of the end-effector load and soft material parameters also places high demands on the robustness of the control system. In addition, the strong coupling of the continuous arm makes it difficult to achieve good overall control results. These reasons make it difficult for traditional control algorithms to adapt to the motion control requirements of nonlinear systems; therefore, further improvements are needed in the research of control methods for continuous robots. Summary of the Invention

[0004] To address the shortcomings of existing technologies, this invention proposes a redundant degree-of-freedom continuous arm control method based on MRAC and PID. This method can effectively reduce the coupling effect between different segments of the continuous arm and the vibration after reaching the target position while satisfying the real-time performance and rapid motion of the continuous arm. It can also reduce the accuracy requirements of the model and eliminate the need to establish a complete dynamic model of the multi-degree-of-freedom continuous arm. It features good real-time performance, fast response time, high motion accuracy, and good robustness.

[0005] The specific technical solution is as follows:

[0006] A redundant degree-of-freedom continuous arm control method based on MRAC and PID includes the following steps:

[0007] S1: Based on the structure and joint parameters of the pneumatic continuous arm, kinematic, static and dynamic models of the pneumatic continuous arm are performed; the pneumatic continuous arm is divided into multiple segments, each segment has two degrees of freedom, and each segment includes a rigid frame using a universal joint structure and pneumatic muscles controlled by air pressure.

[0008] S2: Set the joint angle of the pneumatic continuous arm to zero, initialize the airways and control parameters of the pneumatic muscle, and set the target angle;

[0009] S3: Based on the target angle, perform joint angle trajectory planning, and obtain the target angle corresponding to each PID control through angle decoupling;

[0010] S4: Based on the real-time joint angle data of the pneumatic continuous boom, calculate the difference between the current angle and the target angle, and optimize and adjust the control scheme in conjunction with the load of the pneumatic continuous boom, and control the pneumatic continuous boom to reach the target position; the optimization and adjustment of the control scheme is as follows: if the difference between the current angle and the target angle is less than the minimum threshold, then perform PID control on the pneumatic continuous boom; if the difference between the current angle and the target angle is greater than the maximum threshold, or if the difference between the current angle and the target angle is between the minimum threshold and the maximum threshold but the load is greater than the self-weight of a single pneumatic continuous boom segment, then perform MRAC and PID joint control on the pneumatic continuous boom; if the difference between the current angle and the target angle is between the minimum threshold and the maximum threshold, and the load is less than the self-weight of a single pneumatic continuous boom segment, then perform PID control on the pneumatic continuous boom based on the initial static values ​​obtained from the static model.

[0011] Furthermore, in S1, a kinematic model of the pneumatic continuous arm is established using a segmented analysis method, specifically as follows:

[0012] The pneumatic continuous arm can be represented as n interconnected cuboid structures, with the pneumatic continuous arm furthest from the object being the head and the pneumatic continuous arm closest to the object being the tail. The center point of each cuboid structure is the universal joint center, which is designated as point O. The universal joint center can rotate in two directions with rotation angles α and α' respectively. i and β i , i = 1, 2, ..., n; the side of the cuboid closest to the object is the upper surface, point O is mapped to point G2 on the upper surface of the cuboid, and the four vertices of the upper surface are b1, b2, b3, b4 respectively; point O is mapped to point G1 on the lower surface of the cuboid, and the four vertices of the lower surface are a1, a2, a3, a4 respectively.

[0013] The kinematic model of the i-th segment of the pneumatic continuous arm is established, and its expression is as follows:

[0014]

[0015] In the formula, T i Let be the homogeneous transformation matrix of the i-th pneumatic continuous arm segment, and h be the length of each pneumatic continuous arm segment;

[0016] Thus, the expression for the position l of the midpoint of the plane near the object at the end of the pneumatic continuous arm is obtained as follows:

[0017]

[0018] Taking the positional accuracy of the pneumatic continuous boom end effector as the primary consideration, the objective function is designed as follows:

[0019] f(r,p,Θ)=λf(r,p)+(1-k)g(Θ)

[0020] λ=0.5e -f(r，p) +0.5

[0021] f(r, p) = min(ω) r r+ω p p)

[0022]

[0023] θ i =[α i ,β i ] T

[0024] Θ = [θ1, θ2] T

[0025] In the formula, k is a coefficient for considering the positional accuracy of the pneumatic continuous boom's end effector; r is the end effector attitude error; p is the end effector position error; Θ is the joint angle vector of the entire pneumatic continuous boom; θ is the joint angle vector of a single section; θ1 is the joint angle vector of the first section of the pneumatic continuous boom; and θ2 is the joint angle vector of the second section of the pneumatic continuous boom. r ω is the normalization coefficient for the end-effector attitude error. p This is the normalization coefficient for the end position error; Let be the initial joint angle vector of the i-th segment of the pneumatic continuous arm. ω is the joint angle vector of the i-th segment of the pneumatic continuous arm during the genetic algorithm solution process. i Let be the weight of the i-th segment of the pneumatic continuous arm;

[0026] The fitness function expression is established as follows:

[0027]

[0028] Given the target point, a genetic algorithm is used to obtain the inverse solution, and then the desired angle α of each joint is obtained. d β d .

[0029] Furthermore, in step S1, a static model is established, and the required air pressure values ​​for each pneumatic muscle are obtained through the target angle. The specific operation is as follows:

[0030] The expression for taking the moment about the center of the universal joint is as follows:

[0031]

[0032]

[0033]

[0034]

[0035]

[0036] In the formula, M x M represents the x-component of spatial torque. y M represents the y-component of spatial torque. z The z-component represents the spatial torque; This represents the force acting on point b1, where Fs1 is the air pressure value of the muscle at point b1, and L1 is the muscle length at point b1. This represents the force acting on point b2, where Fs2 is the air pressure value of the muscle at point b2, and L2 is the muscle length at point b2. This represents the force acting on point b3, where Fs3 is the air pressure value of the muscle at point b3, and L3 is the muscle length at point b3. This represents the force acting on point b4, where Fs4 is the air pressure value of the muscle at point b4, and L4 is the muscle length at point b4.

[0037] Because in the static equilibrium state, we have

[0038] ∑M x =0

[0039] ∑M y =0

[0040] Thus, the two air pressure values ​​P1 and P2 on the inflation side can be obtained.

[0041] Furthermore, in S1, a dynamic model is established by setting the relationship between the angular acceleration of each joint and the air pressure value of the pneumatic muscle. The specific operation is as follows:

[0042] The dynamic models are divided into dynamic models of rigid skeletons and equivalent torque models of pneumatic muscles.

[0043] The dynamic model of the rigid skeleton is expressed as follows:

[0044]

[0045] Θ = [θ1, θ2] T

[0046] In the formula, τ is the torque required for the joint. c To represent the contact force in the joint space, the M matrix is ​​the mass matrix, V is the centrifugal force and Coriolis force vector, and G is the gravity vector; Θ is the joint angle vector of the entire pneumatic continuous arm, θ1 is the joint angle vector of the first pneumatic continuous arm, and θ2 is the joint angle vector of the second pneumatic continuous arm. The first derivative of Θ, The second derivative of Θ;

[0047] The expression for the equivalent torque model of the pneumatic muscle is as follows:

[0048] P = Fp(τ,Θ)

[0049] In the formula, P is the air pressure vector of the pneumatic muscle;

[0050] By combining the dynamic model of the rigid skeleton with the equivalent torque model of the pneumatic muscle, the relationship between the angular acceleration of each joint and the air pressure of the pneumatic muscle can be obtained, and can be simplified into a state-space equation:

[0051]

[0052]

[0053] y r =[P,τ c ] T

[0054] In the formula, x m This is the state vector of the pneumatic continuous boom reference model. For x m The first derivative, y r A is the reference input vector; m B m It is a constant matrix.

[0055] Furthermore, step S3 specifically includes the following sub-steps:

[0056] (3.1) Perform joint angle trajectory planning, the expression of which is as follows:

[0057] θ(t)=a0+a1t+a2t 2 +a3t 3 +a4t4 +a5t 5

[0058] In the formula, a0 to a5 are all undetermined coefficients, and t is time;

[0059] Given that the joint space parameters of the pneumatic continuous arm at time zero are θ S , endpoint t f The joint space parameter at time θ f With the angular velocity and angular acceleration at both the starting and ending points being 0, the following constraints are obtained:

[0060] θ(0)=θ S

[0061]

[0062]

[0063] θ(t f )=θ f

[0064]

[0065]

[0066] Thus, the expressions for the undetermined coefficients a0 to a5 are obtained as follows:

[0067] a0=θ S

[0068] a1 = a2 = 0

[0069]

[0070]

[0071]

[0072] (3.2) Perform angle decoupling, so that the pneumatic muscles are offset from the center of the universal joint by 45°, as shown in the following expression:

[0073]

[0074]

[0075] Where, α i β i Let α be the actual joint rotation angle in two directions of the i-th segment of the pneumatic continuous arm; i ′、β i ′ represents the joint rotation angles in the two directions obtained after decoupling.

[0076] Furthermore, in S4, the pneumatic continuous boom is subjected to joint MRAC and PID control, specifically as follows:

[0077] The pneumatic continuous arm at the head or both ends, which is far from the object, is subjected to angular acceleration control based on a dynamic model, so that when the pneumatic continuous arm at the head or both ends reaches the target position, the angular velocity and angular acceleration are zero. This process is achieved through a dynamic feedforward PD control module and a dynamic model-based MRAC control module. The pneumatic muscles in the remaining sections of the pneumatic continuous arm gradually increase the air pressure to the initial static value, and then PID control is applied when they approach the target position. The initial static value is the air pressure value of the pneumatic muscles obtained by establishing the relationship between the joint angle and the air pressure value of each pneumatic muscle through a static model.

[0078] The MRAC control module based on the dynamic model employs state-variable-based Lyapunov-MRAC control, using an adaptive law to adjust the state feedback controller F and the feedforward controller K online; the selected Lyapunov function is:

[0079]

[0080] In the formula, Q and P F P K All are symmetric positive definite matrices; E is the augmented error vector; This represents the parameter error vector of the state feedback controller. This is the parameter error vector of the feedforward controller;

[0081] The adaptive law used to adjust the error between the output of the controlled object and the output of the reference model, so that the dynamic characteristics of the controlled object are consistent with the reference model, is expressed as follows:

[0082]

[0083]

[0084] In the formula, Both are gain matrices; B m R1 and R2 are the ideal constant matrices in the reference model; x p Let y be the state vector of the continuous arm. r The reference input vector;

[0085] A dynamic feedforward PD control module is added above the dynamic model-based MRAC control module. The dynamic feedforward method considers the influence of inertial, centrifugal, Coriolis, and gravitational terms on the system in the continuous arm dynamics. The air pressure value is obtained through the joint torque equivalent module P=Fp(τ,Θ), and is used as the reference input of the dynamic model-based MRAC control module. The expression of the dynamic feedforward PD control law is as follows:

[0086]

[0087] P = Fp(τ,Θ)

[0088] Θ = [θ1, θ2] T

[0089] θ i =[α i ,β i ] T

[0090] In the formula, τ is the torque required for the joint, and K p K d All are constant matrices, τ c To represent the contact force in the joint space, the M matrix is ​​the mass matrix, V is the centrifugal force and Coriolis force vector, and G is the gravity vector; Θ is the joint angle vector of the entire pneumatic continuous arm, θ1 is the joint angle vector of the first segment of the pneumatic continuous arm, and θ2 is the joint angle vector of the second segment of the pneumatic continuous arm. For the desired angular acceleration, Θ e For angular error; α i β i Let be the actual joint rotation angles in two directions of the i-th segment of the pneumatic continuous arm.

[0091] Furthermore, in S4, the minimum threshold for the difference between the current angle and the target angle is 5°, and the maximum threshold is 15°.

[0092] A rigid-flexible coupled continuous arm, used to implement the redundant degree-of-freedom continuous arm control method based on MRAC and PID, includes: a multi-segment pneumatic continuous arm, a fixed support, a controller, and a valve device; one end of the multi-segment pneumatic continuous arm is fixedly connected to the fixed support, and a pressure sensor is installed at the connection point to measure the load change of the pneumatic continuous arm, this segment of the pneumatic continuous arm being the first continuous arm; the other end of the multi-segment pneumatic continuous arm is fixedly connected to a vacuum suction cup, this segment of the pneumatic continuous arm being the last continuous arm;

[0093] Each segment of the pneumatic continuous arm consists of pneumatic muscles and a rigid frame. The rigid frame uses a universal joint structure and is evenly distributed circumferentially along the axis of the pneumatic continuous arm, enabling each segment to rotate in two directions, i.e., each segment has two degrees of freedom. Hall sensors are installed at the rotation axis of the rigid frame to measure joint angles. The pneumatic muscles are made of flexible material and are arranged on the outer periphery of the rigid frame.

[0094] The controller is used to calculate the air pressure required for each pneumatic muscle after the target position is determined; the air valve device is used to achieve precise control of the air pressure based on the controller's calculation results, so that the pneumatic continuous arm can bend and reach the target position.

[0095] The beneficial effects of this invention are:

[0096] (1) The present invention introduces MRAC control to realize the motion control of the rigid-flexible coupled continuous arm, which can reduce the accuracy requirements of the model, overcome the shortcomings of traditional control methods in terms of model uncertainty, and complete the control without the need for an accurate mathematical model.

[0097] (2) This invention designs a fusion control method of MRAC and PID based on dynamic model and static model. The control scheme is reasonably selected according to different situations, which reduces the amount of computation, improves real-time performance, and has both flexibility and robustness. Attached Figure Description

[0098] Figure 1 This is a schematic diagram of the rigid-flexible coupling continuous arm structure used in this invention.

[0099] Figure 2 This is a flowchart of the redundant degree-of-freedom continuous arm control method based on MRAC and PID of the present invention.

[0100] Figure 3 Here are simplified diagrams of the structure and force analysis of the pneumatic continuous arm of the present invention, wherein (a) is an equivalent model diagram of the pneumatic continuous arm, and (b) is a simplified diagram of the force analysis of a single segment of the pneumatic continuous arm.

[0101] Figure 4 This is a flowchart of the control mode selection based on the state of the pneumatic continuous boom according to the present invention.

[0102] Figure 5 This is a structural diagram of the dynamic feedforward PD control module and the MRAC control module based on the dynamic model of the present invention.

[0103] In the diagram, 1 is pneumatic muscle, 2 is rigid frame, 3 is Hall sensor, 4 is pressure sensor, 5 is vacuum suction cup, 6 is controller, and 7 is air valve device. Detailed Implementation

[0104] The present invention will be described in detail below with reference to the accompanying drawings and preferred embodiments. The objectives and effects of the present invention will become clearer as a result. The present invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention.

[0105] like Figure 1 As shown, this invention designs a rigid-flexible coupling continuous arm, comprising: a four-segment pneumatic continuous arm, a fixed support, a controller 6, and a valve device 7. One end of the four-segment pneumatic continuous arm is fixedly connected to the fixed support, and a pressure sensor 4 is installed at the connection point to measure the load change of the pneumatic continuous arm; this segment of the pneumatic continuous arm is the first continuous arm. The other end is fixedly connected to a vacuum suction cup 5; this segment of the pneumatic continuous arm is the last continuous arm.

[0106] Each segment of the pneumatic continuous arm includes pneumatic muscles 1 and a rigid frame 2. The rigid frame 2 employs a universal joint structure and is evenly distributed circumferentially along the axis of the pneumatic continuous arm, allowing each segment to rotate in two directions, i.e., each segment has two degrees of freedom, and the entire pneumatic continuous arm has eight degrees of freedom. Hall sensors 3 are installed at the rotation axis of the rigid frame 2 to measure joint angles. The pneumatic muscles 1 are arranged on the outer periphery of the rigid frame 2. In this embodiment, to enhance the bending effect of the joint, the pneumatic muscles 1 and the Hall sensors 3 are offset by 45°.

[0107] The controller 6 is used to calculate the air pressure value required for each pneumatic muscle 1 after the target position is determined. The air valve device 7 is used to achieve precise control of the air pressure according to the calculation result of the controller 6, so that the four-segment pneumatic continuous arm can bend and reach the target position.

[0108] Because the pneumatic continuous boom is driven by pneumatic muscles 1, which are made of silicone, its actual physical model is very complex due to factors such as material elasticity and friction from the woven mesh sleeve. If model-free control, such as PID, is used, the effects of inertia, centrifugal force, Coriolis force, and gravity on the system in the continuous boom dynamics are not considered, resulting in severe joint coupling effects and poor control performance. If only a simplified model is used, the modeling difficulty leads to significant differences between the simplified and real models, thus affecting the control effect. Furthermore, MRAC control of the entire boom requires establishing an 8-DOF dynamic model of the pneumatic continuous boom, which is extremely complex. In actual performance characterization experiments, it was found that the two ends of the pneumatic continuous boom are the main sources of vibration. Therefore, this invention proposes a redundant-DOF continuous boom control method based on MRAC and PID, such as... Figure 2 As shown, the specific steps are as follows:

[0109] S1: Based on the specific structure and joint parameters of the pneumatic continuous boom, perform kinematic, static, and dynamic modeling of the pneumatic continuous boom, which includes the following sub-steps:

[0110] (1.1) Based on the type, specific size and connection method of each joint of the pneumatic continuous arm, the kinematic model of the pneumatic continuous arm is established by segmented analysis.

[0111] Since the pneumatic continuous boom is a four-segment design, its equivalent model diagram is shown below. Figure 3 As shown in (a), each segment of the pneumatic continuous arm can be equivalent to four cuboids, where plane 0 is close to the fixed support and plane 4 is close to the vacuum suction cup 5. Figure 3 As shown in (b), for a single-segment pneumatic continuous arm, its center point is the center of the universal joint. Let this center point be point O. Point O is mapped to the upper surface of the cuboid as point G2, and the four vertices of the upper surface are b1, b2, b3, and b4, respectively. Point O is mapped to the lower surface of the cuboid as point G1, and the four vertices of the lower surface are a1, a2, a3, and a4, respectively.

[0112] The kinematic model of the i-th segment of the pneumatic continuous arm is established, and its expression is as follows:

[0113]

[0114] In the formula, T i Let be the homogeneous transformation matrix of the i-th segment of the pneumatic continuous arm, h be the length of each segment of the pneumatic continuous arm, and α be the length of each segment. i Let β be the actual joint rotation angle in one direction measured by Hall sensor 3 in the i-th segment of the pneumatic continuous arm. i The actual joint rotation angle in another direction is measured by Hall sensor 3 in the i-th segment of the pneumatic continuous arm.

[0115] Since the structures of each segment of the pneumatic continuous arm are identical, the position of the end point, i.e., the midpoint of plane 4, is easily determined. This position can be represented by the position vector l in the base coordinate system as follows:

[0116]

[0117] In the forward kinematics equations, there are 12 equations, of which only 6 are independent. Due to redundant degrees of freedom, the robotic arm has infinitely many sets of inverse kinematic solutions. To obtain a unique inverse solution, additional constraints are needed. By adding appropriate constraints, an optimal solution that satisfies the constraints can be obtained.

[0118] For solving the inverse kinematics problem of a super-redundant robotic arm, the positional accuracy of the pneumatic continuous arm's end effector should be the primary consideration. It is necessary to minimize the error when it reaches the expected position and attitude. Therefore, the objective function is established as follows:

[0119] f(r, p) = min(ω) r r+ω p p)

[0120] In the formula, r is the end-effector attitude error, p is the end-effector position error, and ω r ω is the normalization coefficient for the end-effector attitude error. p This is the normalization coefficient for the end position error.

[0121] Meanwhile, the fitness function is established using the "motion compliance" principle, meaning that the change in joint angles of the pneumatic continuous arm from its current pose point to the desired target point is minimized. Furthermore, considering energy and motion stability, the principle of "more lower arm movement, less upper arm movement" should be adopted. Based on the principles of "motion compliance" and "more lower arm movement, less upper arm movement," the objective function is established as follows:

[0122]

[0123] θ i =[α i ,β i ] T

[0124] Θ = [θ1, θ2] T

[0125] In the formula, E is the joint angle vector of the entire pneumatic continuous arm, θ is the joint angle vector of a single section, θ1 is the joint angle vector of the first section of the pneumatic continuous arm, and θ2 is the joint angle vector of the second section of the pneumatic continuous arm. Let be the initial joint angle vector of the i-th segment of the pneumatic continuous arm. ω is the joint angle vector of the i-th segment of the pneumatic continuous arm during the genetic algorithm solution process. i Let ω1 = 1, ω2 = 0.6, ω3 = 0.2, and ω4 = 0.1 be the weights of the i-th segment of the pneumatic continuous arm. In this embodiment, we take ω1 = 1, ω2 = 0.6, ω3 = 0.2, and ω4 = 0.1.

[0126] Taking into account the above two considerations, and with the positional accuracy of the pneumatic continuous boom end being the primary consideration, the objective function is designed as follows:

[0127] f(r,p,Θ)=λf(r,p)+(1-k)g(Θ)

[0128] λ=0.5e -f(r，p) +0.5

[0129] In the formula, k is a coefficient that considers the positional accuracy of the end of the pneumatic continuous arm.

[0130] By using the coefficient λ, when the end-effector pose error is large in the early stage of the solution, the positional accuracy of the pneumatic continuous arm end-effector and the principle of "motion compliance" are considered at the same time. As the end-effector pose error decreases, λ tends to 1, and the end-effector pose error is considered in particular.

[0131] In summary, the fitness function is established as follows:

[0132]

[0133] Given the target point, the inverse solution can be obtained through a genetic algorithm, yielding the desired angle α for each joint. d β d .

[0134] (1.2) Establish a static model. The purpose of establishing this model is to obtain the air pressure value required for each pneumatic muscle 1 through the target angle.

[0135] Taking moments about the center of the universal joint, and neglecting gravity, the expression is as follows:

[0136]

[0137] In the formula, M x M represents the x-component of spatial torque. y M represents the y-component of spatial torque. z The z-component represents the spatial torque; This represents the force acting on point b1. This represents the force acting on point b2. This represents the force acting on point b3. This represents the force acting on point b4.

[0138] The muscle contraction force of each pneumatic muscle 1 in the inflated state is Fs = Fs(P,L), where P is the muscle air pressure value, L is the muscle length, and the muscle length is the expected angle α of each joint obtained from the kinematic model. d β d We obtain the following expressions for the forces acting on each corner point:

[0139]

[0140]

[0141]

[0142]

[0143] Because in the static equilibrium state, we have

[0144] ∑M x =0

[0145] ∑M y =0

[0146] Thus, the two air pressure values ​​P1 and P2 on the inflation side can be obtained.

[0147] (1.3) Establish a dynamic model. The purpose of establishing this model is to establish the relationship between the angular acceleration of each joint and the air pressure value of the pneumatic muscle 1.

[0148] As mentioned earlier, the first two sections of the pneumatic continuous arm are the main source of vibration, and dynamic modeling of the entire arm would be very complex. Therefore, the Newton-Euler method is used to model the dynamics of the first two sections of the continuous arm. The influence of the last two sections of the continuous arm on the first two sections of the continuous arm is regarded as a contact force. To simplify the calculation, it is divided into dynamic modeling of the rigid frame 2 and equivalent torque modeling of the pneumatic muscle 1.

[0149] After rearranging the dynamic equations, the expression for the dynamic model of the rigid skeleton 2 with contact is as follows:

[0150]

[0151] In the formula, τ is the torque required for the joint, and σ c The expression of contact force in joint space (fitted from experimentally measured data) is given by the following matrix: M is the mass matrix, V is the vector of centrifugal force and Coriolis force, and G is the vector of gravity. The first derivative of Θ, It is the second derivative of Θ.

[0152] Based on the dynamic modeling expression of rigid frame 2, the expression for the torque τ required by the joint and time is calculated. Then, by taking the moment around the center of the universal joint during the static modeling process, the relationship between τ and the air pressure P of pneumatic muscle 1 is obtained, thus completing the equivalent torque modeling of pneumatic muscle 1.

[0153] σ(P,θ)=σ

[0154] Simplifying the equation, we get:

[0155] P = Fp(τ,Θ)

[0156] In the formula, P is the air pressure vector of pneumatic muscle 1.

[0157] By combining the dynamic model of the rigid skeleton with the equivalent torque model of the pneumatic muscle, the angular acceleration of each joint and the air pressure and contact force τ of the pneumatic muscle 1 can be obtained. c The relationship can be simplified into a state-space equation:

[0158]

[0159] In the formula, x mThis is the state vector of the pneumatic continuous boom reference model. Its first derivative is defined as follows: y r Let y be the reference input vector. r =[P,τ c ] T A m B m It is an 8x8 constant matrix.

[0160] S2: On the host computer, the joint angles of the rigid-flexible coupled continuous arm are zeroed, and the airways and control parameters of the pneumatic muscle 1 are initialized. Then, the target position is set, and the target angles of each joint are obtained from the end pose of the pneumatic continuous arm through inverse kinematics.

[0161] S3: Plan the joint angle trajectory based on the target angle, and obtain the decoupling angle corresponding to each PID control through angle decoupling. This includes the following sub-steps:

[0162] (3.1) For the vibration suppression problem of continuous arms, planning joint angular acceleration is a direct and effective method. This invention adopts joint angle trajectory planning based on fifth-order polynomial interpolation. The fifth-order polynomial has the following form:

[0163] θ(t)=a0+a1t+a2t 2 +a3t 3 +a4t 4 +a5t 5

[0164] In the formula, a0 to a5 are all undetermined coefficients, and t is time.

[0165] If the joint space parameters of the pneumatic continuous boom at time zero are known as θ S , endpoint t f The joint space parameter at time θ f Given that the angular velocity and angular acceleration at the starting and ending points are both 0, the following constraints can be obtained:

[0166] θ(0)=θ S

[0167]

[0168]

[0169] θ(t f )=θ f

[0170]

[0171]

[0172] Thus, the expressions for the undetermined coefficients a0 to a5 are obtained as follows:

[0173] a0=θ S

[0174] a1 = a2 = 0

[0175]

[0176]

[0177]

[0178] (3.2) From a structural perspective, to enhance the bending effect of the joint, the pneumatic muscle 1 and the Hall sensor 3 are staggered by 45°. To ensure that the control of a pair of pneumatic muscles 1 has a one-to-one corresponding angle, angle decoupling is required. That is, the angle after rotating 45° around the z-axis by the angle actually measured by the Hall sensor 3 is calculated. The expression is as follows:

[0179]

[0180]

[0181] Where, α i ′、β i ′ represents the joint rotation angles in the two directions obtained after decoupling.

[0182] S4: Based on the load weight information read by pressure sensor 4 and the joint angle data collected in real time using Hall sensor 3, the control scheme is optimized and adjusted by the difference between the current angle and the target angle, and the pneumatic continuous boom is controlled to reach the target position. This is specifically achieved through the following operations:

[0183] Performance tests on the pneumatic continuous boom revealed that when the swing angle and speed of the pneumatic continuous boom are larger, the vibration of the upper two sections (i.e., the two sections starting from the first continuous boom) due to inertia is the root cause of the overall boom vibration. Under these circumstances, using only PID control will result in significant motion coupling between the sections of the pneumatic continuous boom, as well as noticeable and persistent oscillations.

[0184] Adopting such Figure 4 The control strategy shown considers the distance between the target position and the current position, as well as the load weight, when selecting the control mode. The distance between the target position and the current position is categorized based on the difference between the current angle and the target angle, as shown in Table 1: a difference less than 5° is considered "closer," a difference between 5° and 15° is considered "medium," and a difference greater than 15° is considered "farther." Load weights less than the weight of a single joint are considered "smaller," and load weights greater than the weight of a single joint are considered "larger."

[0185] Table 1

[0186]

[0187] When the distance between the target position and the current position is small, the vibration effect caused by inertia is not obvious. Therefore, PID control is used for the entire arm to reduce the amount of calculation and control complexity, and improve the system response and motion real-time performance.

[0188] When the distance between the target position and the current position is moderate and the load is small, the air pressure value of pneumatic muscle 1 obtained by establishing the relationship between the joint angle and the air pressure value of each pneumatic muscle 1 through the static model is used as the initial static value. Subsequently, due to factors such as model error and environmental interference, the pneumatic continuous arm cannot accurately reach the target position, but will be near the target position. After reaching the target position, PID control is then used.

[0189] When the distance between the target position and the current position is large, or when the distance between the target position and the current position is moderate but the load is large, the vibration effect caused by inertia of the pneumatic continuous boom is very obvious, and the vibration is mainly generated by the top two sections. Therefore, by performing angular acceleration control based on the dynamic model on the top section (i.e., the first continuous boom) or the two sections, the angular velocity and angular acceleration of the top section or the two sections of the pneumatic continuous boom are 0 when the pneumatic continuous boom reaches the target position. This process adopts Model Reference Adaptive Control (hereinafter referred to as MRAC). The pneumatic muscles 1 in the remaining sections of the pneumatic continuous boom gradually increase the air pressure to the initial static value, and then perform PID control when approaching the target position. This can effectively reduce the motion coupling effect of the pneumatic continuous boom and effectively suppress the motion vibration of the pneumatic continuous boom.

[0190] As can be seen from the above control strategy, the controller 6 includes the following control sub-modules: a PID control module for a single pair of pneumatic muscles 1, an angle decoupling module, a static initial value calculation module, a trajectory planning module, a dynamic feedforward PD control module, and a MRAC control module based on a dynamic model. The PID control module for a single pair of pneumatic muscles 1 is used to perform PID control on the air pressure value of the pneumatic muscles 1; the angle decoupling module is used to implement the angle decoupling calculation in step (3.2); the static initial value calculation module is used to obtain the air pressure value of the pneumatic muscles 1 by establishing the relationship between the joint angle and the air pressure value of each pneumatic muscle 1 through the static model, and uses it as the static initial value; the trajectory planning module is used to plan the trajectory of the pneumatic continuous arm according to the condition that the joint angular velocity and angular acceleration are 0 when reaching the end point.

[0191] The MRAC control module based on the dynamic model adopts Lyapunov-MRAC control based on state variables. It uses an adaptive law to adjust the state feedback controller F and the feedforward controller K online. Theoretically, it can achieve a complete match between the reference model and the controlled object, so that the motion response process of the continuous arm is consistent with the output of the reference model, thus achieving the desired control performance.

[0192] The Lyapunov function is selected as follows:

[0193]

[0194] In the formula, Q and P F P K All are symmetric positive definite matrices; E is the augmented error vector; This represents the parameter error vector of the state feedback controller. This is the parameter error vector of the feedforward controller.

[0195] The adaptive law can be derived as follows:

[0196]

[0197]

[0198] In the formula, Both are gain matrices; B m R1 and R2 are the ideal constant matrices in the reference model; x p Let y be the state vector of the continuous arm. r The reference input vector is used. Since the augmented error vector E is measurable, the adaptive law can be designed simply by specifying the values ​​of the parameters R1, R2, and Q.

[0199] like Figure 5As shown, the main idea of ​​the MRAC algorithm is to establish an additional adjustment loop consisting of a reference model and an adaptive mechanism outside the closed loop composed of the controller (in this embodiment, a dynamic feedforward PD) and the controlled object. The performance requirements of the MRAC control module based on the dynamic model are entirely expressed through the reference model, that is, the output of the reference model is the ideal output of the module. During operation, if the output of the controlled object cannot track the output of the reference model due to changes in the parameters or characteristics of the controlled object, the error between the output of the controlled object and the output of the reference model is adjusted by the adaptive law, with the aim of making the dynamic characteristics of the controlled object consistent with the reference model. A dynamic feedforward PD control module is added on top of the MRAC control module based on the dynamic model. The dynamic feedforward method considers the influence of inertial terms, centrifugal force, Coriolis force terms, and gravity terms on the system in the dynamics of the continuous arm. The air pressure value is obtained through the joint torque equivalent module P = Fp(τ,Θ) and used as the reference input of the MRAC control module based on the dynamic model. By combining the dynamic feedforward PD algorithm and the MRAC algorithm, the requirements for model accuracy can be effectively reduced, and the control effect can be greatly improved.

[0200] The dynamic feedforward PD control law is expressed as:

[0201]

[0202] P = Fp(τ,Θ)

[0203] In the formula, K p K d All are constant matrices. For the desired angular acceleration, Θ e This represents the angular error.

[0204] This invention designs a redundant degree-of-freedom continuous arm control method based on MRAC and PID to address the motion characteristics of a four-segment, eight-DOF rigid-flexible coupled continuous arm. While satisfying the real-time performance and rapid motion of the continuous arm, this method can effectively reduce the coupling effect between the segments of the continuous arm and the vibration after it reaches the target position.

[0205] It will be understood by those skilled in the art that the above descriptions are merely preferred examples of the invention and are not intended to limit the invention. Although the invention has been described in detail with reference to the foregoing examples, those skilled in the art can still modify the technical solutions described in the foregoing examples or make equivalent substitutions for some of the technical features. All modifications and equivalent substitutions made within the spirit and principles of the invention should be included within the scope of protection of the invention.

Claims

1. A MRAC and PID-based redundant degree of freedom continuous arm control method, characterized by, The method comprises the following steps: S1: kinematics, statics and dynamics modeling of the pneumatic serial arm according to the structure and joint parameters of the pneumatic serial arm; the pneumatic serial arm is divided into multiple segments, each segment has two degrees of freedom, and each segment comprises a rigid skeleton using a universal joint structure and pneumatic muscles controlled by air pressure; S2: setting the joint angles of the pneumatic serial arm to zero, initializing the air passages and control parameters of the pneumatic muscles, and setting a target angle; S3: joint angle trajectory planning according to the target angle, and obtaining a target angle corresponding to each PID control through angle decoupling; S4: calculating the difference between the current angle and the target angle according to the real-time joint angle data of the pneumatic serial arm, combining the load of the pneumatic serial arm, and performing control scheme optimization adjustment to control the pneumatic serial arm to reach the target position; the control scheme optimization adjustment is specifically: if the difference between the current angle and the target angle is less than a minimum threshold, PID control is performed on the pneumatic serial arm; if the difference between the current angle and the target angle is greater than a maximum threshold, or the difference between the current angle and the target angle is between the minimum threshold and the maximum threshold but the load is greater than the self-weight of the single segment pneumatic serial arm, MRAC and PID joint control is performed on the pneumatic serial arm; if the difference between the current angle and the target angle is between the minimum threshold and the maximum threshold, and the load is less than the self-weight of the single segment pneumatic serial arm, PID control is performed on the pneumatic serial arm based on the statics initial value obtained from the statics model; In S4, the MRAC and PID joint control of the pneumatic serial arm is specifically as follows: The first end or the first two ends of the pneumatic serial arm away from the object are controlled based on the angular acceleration of the dynamics model, so that the angular velocity and angular acceleration of the first end or the first two ends of the pneumatic serial arm are 0 when the first end or the first two ends of the pneumatic serial arm reach the target position, and this process is realized through a dynamics feedforward PD control module and an MRAC control module based on the dynamics model; the pneumatic muscles in the remaining joints of the lower part of the pneumatic serial arm are gradually increased in air pressure to the statics initial value, and then PID control is performed near the target position; the statics initial value is the air pressure value of the pneumatic muscle obtained from the relationship between the joint angle and the air pressure value of each pneumatic muscle established by the statics model; The MRAC control module based on the dynamics model adopts Lyapunov-MRAC control based on state variables, and uses an adaptive law to adjust the state feedback controller F and the feedforward controller K online; the Lyapunov function is selected as: ； In the formula, Q, P F , P K are all symmetric positive definite matrices; E is an augmented error vector; is a parameter error vector for the state feedback controller, is a parameter error vector for the feedforward controller; The adaptive law for adjusting the error between the output of the controlled object and the output of the reference model is obtained, so that the dynamic characteristics of the controlled object are consistent with the reference model, and the expression is as follows: ； ； wherein , are gain matrices; B m is an ideal constant matrix in the reference model, R1, R2 are parameter matrices; x p is a continuous arm state vector, y r is a reference input vector; A dynamics feedforward PD control module is added to the upper layer of the MRAC control module based on the dynamics model, the method of dynamics feedforward considers the influence of the inertia term, the centrifugal force and Coriolis force term, and the gravity term in the continuous arm dynamics on the system, and through the joint torque equivalent module The output air pressure value is obtained and taken as the reference input of the MRAC control module based on the dynamics model; the dynamics feedforward PD control law expression is as follows: ； ； ； ； wherein, is the required torque of the joint, , are constant matrices, is the expression of the contact force in the joint space, M is the mass matrix, V is the centrifugal and coriolis force vector, and G is the gravity vector; is the joint angle vector of the whole pneumatic continuum manipulator, is the joint angle vector of the first segment of the pneumatic continuum manipulator, is the joint angle vector of the second segment of the pneumatic continuum manipulator; is the desired angular acceleration, is the angle error; , is the actual joint rotation angle in two directions in the i-th segment of the pneumatic continuum manipulator.

2. The MRAC and PID based redundant degree of freedom continuous arm control method of claim 1, wherein, In S1, the kinematics model of the pneumatic serial arm is established by using the segmented analysis method, and the specific operation is as follows: The pneumatic continuous arm is equivalent to n connected cuboid structures, the pneumatic continuous arm far from the object is the first end, and the pneumatic continuous arm close to the object is the last end; the center point of each cuboid structure is the universal joint center, the center point is O point, the universal joint center can rotate in two directions, the rotation angles are α i and β i , i=1, 2, …, n; the side of the cuboid close to the object is the upper surface, the O point is mapped to the upper surface of the cuboid as G2 point, and the four vertices of the upper surface are b1, b2, b3 and b4 respectively; the O point is mapped to the lower surface of the cuboid as G1 point, and the four vertices of the lower surface are a1, a2, a3 and a4 respectively; The kinematics model of the i-th segment of the pneumatic serial arm is established, and the expression is as follows: ； wherein H is the homogeneous transformation matrix of the i-th segment of the aeromechanical continuum arm, and h is the length of each segment of the aeromechanical continuum arm. Thus the position of the end of the pneumatic continuous arm near the midpoint of the plane of the object is obtained The expression is as follows: ； The position accuracy of the end of the pneumatic serial arm is taken as the main consideration, and the objective function is designed as follows: ； ； ； ； ； ； where k is a coefficient for the position accuracy of the end of the pneumatic serial arm; r is the end attitude error, and p is the end position error, is the joint angle vector of the whole pneumatic serial arm, and θ is the joint angle vector of a single joint, is the joint angle vector of the first section of the pneumatic serial arm, is the joint angle vector of the second section of the pneumatic serial arm; is the normalization coefficient of the end attitude error, is the normalization coefficient of the end position error; is the initial joint angle vector of the i-th section of the pneumatic serial arm, is the joint angle vector of the i-th section of the pneumatic serial arm in the genetic algorithm solving process; is the weight of the i-th section of the pneumatic serial arm; The fitness function expression is established as follows: ； In the case of known target point, inverse solution is obtained by genetic algorithm, and then the desired angle of each joint is obtained , .

3. The MRAC and PID based redundant degree of freedom continuous arm control method of claim 2, wherein, In S1, the statics model is established, and the air pressure value required by each pneumatic muscle is obtained from the target angle, and the specific operation is as follows: The moment of the universal joint center is taken, and the expression is as follows: ； ； ； ； ； In the formula, x component of the spatial moment, y component of the spatial moment, z component of the spatial moment; Fs1 represents the force on the point, Fs1 represents the force on the point, L1 represents the muscle tension value corresponding to the point, L1 represents the muscle length corresponding to the point; Fs2 represents the force on the point, Fs2 represents the force on the point, L2 represents the muscle tension value corresponding to the point, L2 represents the muscle length corresponding to the point; Fs3 represents the force on the point, Fs3 represents the force on the point, L3 represents the muscle tension value corresponding to the point, L3 represents the muscle length corresponding to the point; Fs4 represents the force on the point, Fs4 represents the force on the point, L4 represents the muscle tension value corresponding to the point, L4 represents the muscle length corresponding to the point; Because in static equilibrium state ； ； Thus, the two air pressure values P1, P2 of the inflated side are solved.

4. The MRAC and PID based redundant degree of freedom continuous arm control method of claim 3, wherein, In S1, a dynamic model is established, and the relationship between the joint angle acceleration and the air pressure value of the pneumatic muscle is established by the following specific operation: The dynamic model is divided into a rigid skeleton dynamic model and an equivalent torque model of the pneumatic muscle. The expression of the rigid skeleton dynamic model is as follows: ； ； wherein, is the required torque of the joint, is the expression of the contact force in the joint space, M is the mass matrix, V is the centrifugal and coriolis force vector, and G is the gravity vector; is the joint angle vector of the whole arm of the pneumatic continuum arm, θ is the joint angle vector of the single joint, is the joint angle vector of the first segment of the pneumatic continuum arm, is the joint angle vector of the second segment of the pneumatic continuum arm; is the first derivative of is the second derivative of ;​ The expression of the equivalent torque model of the pneumatic muscle is as follows: ； In the formula, P is the air pressure vector of the pneumatic muscle; The relationship between the joint angle acceleration and the air pressure value of the pneumatic muscle is obtained by combining the rigid skeleton dynamic model and the equivalent torque model of the pneumatic muscle, and can be arranged in the form of a state space equation: ； ； ； wherein is the state vector of the pneumatic continuous arm reference model, is the first derivative of , and is the reference input vector; , is a constant matrix.

5. The MRAC and PID based redundant degree of freedom continuous arm control method of claim 1, wherein, S3 specifically includes the following sub-steps: (3.1) Joint angle trajectory planning is performed, and the expression is as follows: ； In the formula, a0~a5 are all undetermined coefficients, and t is time; The joint space parameter of the starting point of the pneumatic continuous arm at zero time is θ S The joint space parameter of the end point at time t f is θ f The angular velocity and angular acceleration of the starting point and end point are both 0, and the following constraint is obtained: ； ； ； ； ； ； Thus, the expression of the undetermined coefficients a0~a5 is as follows: ； ； ； ； ； (3.2) Angle decoupling is performed, and the expression is as follows: ； ； wherein, , is the actual joint rotation angle in the i-th segment of the aerodynamic continuous arm in two directions; , is the joint rotation angle in two directions obtained by decoupling.

6. The MRAC and PID based redundant degree of freedom continuous arm control method of claim 1, wherein, In S4, the minimum threshold value of the difference between the current angle and the target angle is 5°, and the maximum threshold value is 15°.

7. A rigid-flexible coupled serial arm for implementing the MRAC and PID based redundant degree of freedom serial arm control method of any one of claims 1-6, characterized in that, It comprises: A multi-section pneumatic continuous arm, a fixed support, a controller, and a gas valve device; one end of the multi-section pneumatic continuous arm is fixedly connected to the fixed support, and a pressure sensor is installed at the connection between the two, for measuring the load change of the pneumatic continuous arm; the first end of the pneumatic continuous arm is the first end continuous arm; the other end of the multi-section pneumatic continuous arm is fixedly connected to a vacuum chuck, and the last end of the pneumatic continuous arm is the last end continuous arm; Each section of the pneumatic continuous arm comprises a pneumatic muscle and a rigid skeleton; the rigid skeleton adopts a universal joint structure and is uniformly distributed along the axis of the pneumatic continuous arm, so that each section of the pneumatic continuous arm can rotate in two directions, i.e., each section of the pneumatic continuous arm has two degrees of freedom; a Hall sensor is installed at the rotating shaft of the rigid skeleton, for measuring the joint angle; the pneumatic muscle is made of flexible material and is arranged outside the rigid skeleton; The controller is used to calculate the required air pressure value of each pneumatic muscle after determining the target position; The gas valve device is used to accurately control the air pressure according to the calculation result of the controller, so that the pneumatic continuous arm can make a bending movement and reach the target position.

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