A mechanical arm collision detection method based on inner feedback super-helix outer torque observation

Abstract

The application discloses a mechanical arm collision detection method based on inner feedback super-helical outer torque observation, belongs to the field of mechanical arm collision detection, and establishes a multi-joint industrial mechanical arm dynamics model for the mechanical arm configuration; for the problem that the outer torque is unobservable, an improved inner feedback super-helical algorithm is used to design an observer to perform observation; for the false detection phenomenon caused by the fixed threshold value, a time-varying threshold value model is constructed by using a least square method in combination with the mechanical arm model characteristics, so as to judge whether a collision occurs; simulation experiments show that the collision detection method has good accuracy and sensitivity, and can timely and accurately monitor the collision event.

Description

Technical Field

[0001] This invention relates to robotic arm collision detection technology, specifically to a robotic arm collision detection method based on internal feedback superhelical external torque observation. Background Technology

[0002] With the advent of the intelligent era, the application of robotic arms is steadily increasing in various fields. They are not only used in completely enclosed industrial environments, but the demand for human-machine collaborative work is also constantly rising. Due to the complexity of the robotic arm system and the uncertainty of the working environment, collisions are commonplace. Therefore, accurate and timely detection of collisions between the robotic arm and the external environment, and ensuring the safety of both humans and machines, is crucial.

[0003] Currently, there are two main methods for collision detection: one is based on external sensors, which integrates vision sensors and torque sensors into the design of the robotic arm. By collecting environmental information from these sensors, it determines whether a collision has occurred. For multi-degree-of-freedom robotic arms, multiple sensors are needed to accurately perceive the external environment, leading to a sharp increase in the production and design costs, hindering widespread market adoption. Furthermore, the introduction of sensors increases the complexity of the robotic arm structure and reduces its rigidity, posing new challenges to its motion control. The other method is collision detection without external sensors. It accurately estimates the external torque of the robotic arm by analyzing control variables, state variables, and the robotic arm model during motion control. However, collision detection without external sensors is prone to problems such as untimely collision estimation and false detections. Summary of the Invention

[0004] The purpose of this invention is to provide an external torque observation method based on the internal feedback supersonic algorithm (IF-STA) to solve the problem of untimely external torque estimation; and to design a time-varying collision threshold to reduce false detection phenomena caused by collision detection.

[0005] The technical solution to achieve the purpose of this invention is as follows: a collision detection method based on the observation of external torque using an internal feedback superspiral algorithm, which is determined based on the designed external torque observer and the time-varying threshold model established by the least squares method. The specific steps are as follows:

[0006] Step 1: Construct a dynamic model of a multi-joint industrial robotic arm.

[0007] Step 2: As the various joints of the multi-joint industrial robotic arm move normally, the joint control quantity τ is obtained by combining the dynamic model of the multi-joint industrial robotic arm. u Joint position q, joint velocity

[0008] Step 3: Based on the dynamic model of the multi-joint industrial robotic arm and the joint control quantity τ u Joint position q, joint velocity An external torque observer is designed based on an improved internal feedback superhelical algorithm to estimate the external torque.

[0009] Step 4: Apply Lyapunov's stability theorem to prove the stability of the designed external torque observer.

[0010] Step 5: Construct a time-varying threshold model. In a collision-free scenario, the observation results of the external torque observer are used as input. The upper and lower bounds of the time-varying threshold are established by the least squares method to detect whether a collision has occurred.

[0011] The significant advantages of this invention compared to existing technologies are:

[0012] (1) This invention introduces an improved superspiral algorithm with internal feedback, which suppresses overshoot and improves convergence speed through damping generated by internal feedback. Based on the improved superspiral algorithm, and taking advantage of the convergence characteristics of the superspiral algorithm itself, it is possible to accurately estimate the external torque within a finite time.

[0013] (2) In view of the false detection phenomenon that occurs when the fixed threshold is used, the present invention designs a time-varying threshold based on the state information of the robotic arm to detect whether a collision has occurred. The design of the time-varying threshold takes into account the influence of model uncertainty and robotic arm friction. In the non-collision scenario, the observation results of the external torque observer are used as input, and the least squares method is used to identify the coefficients of the time-varying threshold model, which can accurately determine whether a collision has occurred. Attached Figure Description

[0014] Figure 1 This is a schematic diagram of the robotic arm control method of the present invention.

[0015] Figure 2 This is a flowchart of the collision detection process for the robotic arm of this invention.

[0016] Figure 3 This is the estimation diagram of the step signal of the external torque of the first joint of the robotic arm of the present invention.

[0017] Figure 4 This is the estimation diagram of the sinusoidal signal of the external torque of the second joint of the robotic arm of this invention.

[0018] Figure 5 This is a diagram showing the estimation error of the external torque of the first joint of the robotic arm of this invention.

[0019] Figure 6 This is a diagram showing the estimation error of the external torque of the second joint of the robotic arm in this invention.

[0020] Figure 7 This is the time-varying threshold applied external torque diagram of the present invention.

[0021] Figure 8 This is a diagram showing the observation of external torque and collision conditions under the fixed threshold of the first joint of the robotic arm of this invention.

[0022] Figure 9 This is a diagram showing the observation of external torque and collision conditions at the fixed threshold of the second joint of the robotic arm of this invention.

[0023] Figure 10 This is a diagram showing the observation of external torque and collision conditions at the time-varying threshold of the first joint of the robotic arm of this invention.

[0024] Figure 11 This is a diagram showing the observation of external torque and collision conditions at the time-varying threshold of the second joint of the robotic arm of this invention. Detailed Implementation

[0025] This invention discloses a collision detection method for robotic arms based on internal feedback superhelical external torque observation, combined with... Figure 1 and Figure 2 The specific steps are as follows:

[0026] Step 1: Construct a dynamic model of a multi-joint industrial robotic arm. The specific steps are as follows:

[0027] For a multi-joint industrial robotic arm, whose mechanical structure consists of a series of rotary joints, the dynamic model with n degrees of freedom is represented by the Lagrangian method:

[0028]

[0029] Among them: q, Representing the position, velocity, and acceleration of the robotic arm link, respectively, q, Denotes the first derivative; Represents the second derivative; Let M(q) represent a vector of dimension n; M(q) represents the inertia matrix of the robotic arm links. Represents an n×n two-dimensional matrix; This represents the centrifugal torque and Coriolis torque vector of the robotic arm linkage. G(q) represents the gravitational torque. τ f τ represents frictional torque. u It is the output torque of the motor; τ ext The external torque generated when the robotic arm comes into contact with the external environment, i.e., the collision torque, is calculated as follows:

[0030] τ ext =J T F c (2)

[0031] Here, J represents the Jacobian matrix of the force; * T Indicates transpose; F c This represents the external collision force of the robotic arm. Equation (2) converts the collision force in Cartesian coordinates into the external torque of each joint.

[0032] Property 1: Matrices For an antisymmetric matrix, its equivalent expression is:

[0033]

[0034] The generalized momentum p of the robotic arm is defined as:

[0035]

[0036] Combining equations (1), (3), and (4), the following first-order dynamic model is obtained.

[0037]

[0038] Assumption 1: When the robotic arm collides, the external torque τ at each joint is... ext The derivative of the external torque Both are bounded.

[0039] Step 2: As the various joints of the multi-joint industrial robotic arm move normally, the joint control quantity τ is obtained by combining the dynamic model of the multi-joint industrial robotic arm. u Joint position q, joint velocity The specific steps are as follows:

[0040] Assumption 2: The nominal values ​​of the robotic arm's dynamic parameters have been accurately obtained through identification methods, i.e., M(q). G(q), τ f It concerns joint position q and joint velocity. The known quantities.

[0041] pass Figure 1 It can be seen that by using a PD controller to control a multi-joint industrial robotic arm, each joint tracks the desired position q. d Motion and angle sensors acquire the real-time joint positions 'q' of the robotic arm. The joint position differences are then processed to obtain the joint motion velocity of the robotic arm. Based on the dynamic model of the multi-joint industrial robotic arm, its control torque is expressed as:

[0042]

[0043] Wherein, the position tracking error during the movement of the robotic arm is e = qq d Speed ​​tracking error during robotic arm movement Kkp K kd These are the proportional and derivative adjustment parameters of PD control, which are adjustable constants; This represents an estimated value of the external torque.

[0044] Step 3: Based on the dynamic model of the multi-joint industrial robotic arm and the joint control quantity τ u Joint position q, joint velocity An external torque observer is designed based on an improved internal feedback superhelical algorithm to estimate the external torque. The specific steps are as follows:

[0045] Step 3.1: Design an improved internal feedback superspiral algorithm:

[0046] For common superhelical algorithms:

[0047]

[0048] In the formula, x and y are state variables, α and β are adjustable constant coefficients, s(t) is a time-varying disturbance, and sgn(*) represents the standard symbolic function. Under the condition that s(t) is bounded, by adjusting α and β, the state variable (x,y) can be made to converge to (0,0) in a finite time. and By introducing different internal feedback terms, the convergence speed of the algorithm is improved, resulting in the improved internal feedback superspiral algorithm:

[0049]

[0050] In the formula, γ, κ, and η are adjustable constant coefficients. An improved superspiral algorithm is used to design the external torque observer, enabling accurate estimation of the external torque.

[0051] Step 3.2: Design an external torque observer based on the improved internal feedback superhelical algorithm:

[0052] For the generalized momentum p, its corresponding estimated value is expressed as: Then the estimation error of generalized momentum Represented as:

[0053]

[0054] Estimation error based on generalized momentum The constructed observer is as follows:

[0055]

[0056] In the formula, K1, K2, K3, K4, and K5 are all gain coefficients, and all are adjustable constants that are greater than zero; Let represent the first derivative of the generalized momentum estimate; σ is an intermediate variable. Based on equations (5) and (10), the error dynamics equation of the observer is obtained as follows:

[0057]

[0058] In the formula, The first derivative represents the error in the generalized momentum estimation; the intermediate variable z = σ - τ ext Intermediate variables Where τ ext and If the algorithm is bounded, then h(t) is guaranteed to be bounded. Equation (11) and the improved superspiral algorithm (8) are consistent. By adjusting the values ​​of K1, K2, K3, K4, and K5, within a finite time... If it converges to (0,0), then σ is the time interval τ. ext The estimated value.

[0059] Step 4: Apply Lyapunov's stability theorem to prove the stability of the designed external torque observer. The specific steps are as follows:

[0060] Lemma 1: For a nonlinear control system, if there exists a positive definite Lyapunov function V(t) with coefficients ζ1 > 0, coefficients ζ2 > 0, and coefficient a satisfying 0 < a < 1, and satisfies the inequality... The system state of the nonlinear control system can converge to the origin in a finite time, and its convergence time t s satisfy:

[0061]

[0062] Design the Lyapunov function as follows:

[0063]

[0064] Rewrite equation (12) in quadratic form:

[0065] V = ξ T Pξ (13)

[0066] Among them, intermediate variables Matrix P is shown below:

[0067]

[0068] Differentiating equation (13), we get:

[0069]

[0070] Substituting equation (11) and simplifying, we get:

[0071]

[0072] Where Ω1 and Ω2 both represent intermediate variables:

[0073]

[0074] In the formula, intermediate variables but The constant ψ > 0 is an upper bound of h(t).

[0075]

[0076] λ min {*} denotes the smallest eigenvalue of the matrix, λ max {*} represents the largest eigenvalue of the matrix. Then, through equation (16), we obtain:

[0077]

[0078] According to equation (13), we obtain the Rayleigh-Ritz theorem:

[0079]

[0080] so

[0081]

[0082] Where ξ1 is the first term in ξ, obtained from equations (19), (20), and (21):

[0083]

[0084] In the formula, the positive constant term normal numbers According to equation (22), the requirements of Lemma 1 are satisfied, thus yielding the convergence time. The designed observer is able to t s Then accurately estimate the magnitude of the external torque.

[0085] At this point, it is necessary to ensure that matrices P, Ω1, and Ω2 are all positive definite matrices. Since |θ|≤ψ, the calculated ranges of values ​​for K1, K2, K3, K4, and K5 are as follows:

[0086]

[0087]

[0088]

[0089] Step 5: Construct a time-varying threshold model. In a collision-free scenario, use the observation results of the external torque observer as input, and establish upper and lower bounds of the time-varying threshold using the least squares method to detect whether a collision has occurred. The specific steps are as follows:

[0090] The designed observer can obtain an estimate of the external torque in real time. However, in the absence of a collision, the observer's estimate will vary due to modeling errors, frictional variations, and the influence of the external working environment. The collision threshold fluctuates around zero. The threshold needs to be sufficiently large to avoid false alarms, but an excessively large threshold can reduce detection sensitivity. Considering the different model errors of the robotic arm under different states, a time-varying threshold collision detection method is adopted.

[0091] Considering the impact of modeling errors, the main characteristics are the correlation quantities of the robot arm's joint position, velocity, and acceleration. These are linearized and combined, then incorporated into the time-varying threshold. Regarding the influence of friction, since the Coulomb-viscous friction model can effectively identify the friction of the robot arm, its friction force model f is expressed as:

[0092]

[0093] Where F o Let F be the Coulomb friction parameter. v Let ε be the viscous friction parameter, ε be the velocity exponent, and B be the friction bias term. Considering the small frictional fluctuations during the robot arm's reversal, we also introduce... If the term is specified, then the time-varying threshold model χ for the i-th joint is... i Represented as:

[0094]

[0095] In the formula, i b0、 i b1、 i b2, i b3, ib4, and ib5 are all threshold model coefficients for the i-th joint; q i It is the joint position of the i-th joint; φ i It is the constant coefficient of the i-th joint, 0 < φ i <1; ε i Let be the velocity index of the i-th joint.

[0096] Identification using the least squares method yields the following linear form of the corresponding regression matrix:

[0097]

[0098] Where, Θ i This represents the coefficient matrix for the i-th joint. (Regression matrix) for:

[0099]

[0100] χ i Corresponding estimated value Represented as:

[0101]

[0102] Where, Θ i Corresponding estimated value υ i Let represent the zero-mean vector of the estimation error of the i-th joint.

[0103] The estimated value of the i-th joint coefficient matrix is ​​then obtained by using the least squares algorithm. for:

[0104]

[0105] When the robotic arm does not collide, the estimated external torque obtained by the external torque observer using least squares identification is... This reflects the uncertainty of the corresponding model and the related terms of friction error, therefore the estimated external torque value of the i-th joint is... Replace χ i ,but The identification results differ for different joints i.

[0106] Based on the identification results, the upper bound of the time-varying threshold χ is obtained. Ui and lower bound χ Li The expression form is:

[0107]

[0108] In the formula, i μ1、 i μ2 is the constant coefficient diagonal matrix of the i-th joint. This is a normal value for the i-th joint. Based on the upper and lower bounds of the time-varying threshold, it can be determined whether a collision has occurred, using the estimated external torque of the i-th joint. Each is compared with the upper bound of the time-varying threshold χ of the i-th joint. Ui Lower bound χ Li Compare and return the collision result of the i-th joint as a boolean.

[0109]

[0110] Therefore, the entire collision detection process is as follows: Figure 2As shown, in the motion control process of the robotic arm, when the external torque estimated by the external torque observer reaches or exceeds the upper or lower bound of the time-varying threshold, it is determined that a collision has occurred, and the robotic arm then activates the corresponding response strategy.

[0111] Simulation experiment examples:

[0112] To demonstrate the effectiveness of the collision detection method described above, a two-degree-of-freedom robotic arm model was used for simulation verification. For a two-degree-of-freedom robotic arm, the matrices in its dynamic equations are as follows:

[0113]

[0114] In the formula, q1 and q2 represent the positions of the first and second joints of the robotic arm, respectively. The mass of the first robotic arm is selected as m1 = 1 kg; the mass of the second robotic arm is selected as m2 = 1 kg; the length of the first robotic arm is selected as l1 = 1 m; the length of the second robotic arm is selected as l2 = 1 m; and the acceleration due to gravity is selected as g = 9.8 m / s². 2 To construct a two-degree-of-freedom robotic arm.

[0115] Design the frictional torque of the i-th joint of the robotic arm. i τ f for:

[0116]

[0117] In the formula, q i This indicates the joint position of the i-th joint.

[0118] The design aims to track and control the joint trajectory of the robotic arm by using a slowly varying sinusoidal signal.

[0119]

[0120] In the formula, q 1d Let q be the desired position of the first joint of the robotic arm; 2d This represents the desired position of the second joint of the robotic arm. To verify the effectiveness of the external torque observation method designed in this invention, two external torque signals are set: a step torque for the first joint and a sinusoidal torque for the second joint, to simulate actual collision situations, as follows:

[0121]

[0122] In the formula, 1d τ ext The external torque given to the first joint of the robotic arm; 2d τ ext An external torque is applied to the second joint of the robotic arm. A torque observation method based on GMOs is compared with the superhelical observation method with internal feedback designed in this invention. The parameters of the two observers are selected as follows:

[0123] GMO observer: Gain coefficient K1 = 100 for the first joint and gain coefficient K2 = 80 for the second joint.

[0124] IF-STA observer: the gain coefficient corresponding to the first joint in equation (10) 1 K1, 1 K2, 1 K3 1 K4 1 K5 is as follows: 1 K1 = 4, 1 K2 = 25, 1 K3 = 3, 1 K4 = 2, 1 K5 = 0.2; the gain coefficient corresponding to the second joint in equation (10) 2 K1, 2 K2, 2 K3 2 K4 2 K5 is as follows: 2 K1 = 5, 2 K2 = 20, 2 K3 = 3, 2 K4 = 1, 2 K5 = 0.1.

[0125] Observation results as follows Figures 3 to 6 As shown, this demonstrates the effectiveness of the proposed internal feedback superspiral observation method. Given external torques from both step and sinusoidal signals, within a bounded time period where the derivative of the external torque is continuous, the IF-STA algorithm exhibits faster convergence speed and smaller convergence error compared to the GMO algorithm, resulting in better observation performance.

[0126] The dynamic model of the robotic arm and the friction error are set to 10% of its parameters. To simulate the effects of model uncertainty and friction identification error, time-varying threshold simulation is performed, with parameters ε1=ε2=3 and φ1=φ2=0.3. 1 μ1 = 0.9, 1 μ2 = 0.85, 2 μ1 = 0.8, 2 μ2 = 0.9, Set the external torque of the two joints as follows: Figure 7 As shown, to simulate actual collision scenarios, both GMO and IF-STA observers are used to estimate the torque. Using the IF-STA observations in a collision-free scenario as input, the least squares method is applied to identify the following results:

[0127]

[0128] Figures 8 to 11 The results show that both observers can detect collisions using the time-varying threshold method. However, when there is model uncertainty, the fixed threshold is set too high because it uses the maximum and minimum values ​​of the identification results as the upper and lower bounds. This makes it difficult to detect collisions with small external torques. In contrast, the time-varying threshold method proposed in this invention can monitor collisions to the maximum extent.

[0129] In summary, this invention addresses collision detection in robotic arms by estimating the external torque of each joint using a designed internal feedback superspiral external torque observation method, and then determining whether a collision has occurred based on a time-varying threshold model designed using the least squares method. This method exhibits excellent detection accuracy and sensitivity, enabling accurate and timely monitoring of collision events.

Claims

1. A collision detection method for a robotic arm based on internal feedback superhelical external torque observation, characterized in that, The specific steps are as follows: Step 1: Construct a dynamic model of a multi-joint industrial robotic arm; Step 2: As each joint of the multi-joint industrial robotic arm moves normally, the joint control quantities are obtained by combining the dynamic model of the multi-joint industrial robotic arm. Joint position Joint velocity ; Step 3: Based on the dynamic model of the multi-joint industrial robotic arm and the joint control parameters Joint position Joint velocity An external torque observer is designed based on an improved internal feedback superhelical algorithm to estimate the external torque; Step 4: Apply Lyapunov's stability theorem to prove the stability of the designed external torque observer; Step 5: Construct a time-varying threshold model. In a collision-free scenario, the observation results of the external torque observer are used as input. The upper and lower bounds of the time-varying threshold are established by the least squares method to detect whether a collision has occurred. In step 1, a dynamic model of a multi-joint industrial robotic arm is constructed. The specific steps are as follows: For a multi-joint industrial robotic arm, whose mechanical structure consists of a series of rotary joints, the dynamic model with n degrees of freedom is represented by the Lagrangian method: （1）， in: , , These represent the position, velocity, and acceleration of the robotic arm links, respectively. , , ; Denotes the first derivative; Represents the second derivative; Represents a vector of dimension n; This represents the inertia matrix of the robotic arm links. ; express A two-dimensional matrix; This represents the centrifugal torque and Coriolis torque vector of the robotic arm linkage. ; Represents gravitational torque. ; Indicates frictional torque; It is the output torque of the motor; The external torque generated when the robotic arm comes into contact with the external environment, i.e., the collision torque, is calculated as follows: （2）， Here The Jacobian matrix represents the force; Indicates transpose; The external collision force of the robotic arm is represented by equation (2); the collision force in Cartesian coordinates is converted into the external torque of each joint by equation (2); Property 1: Matrices For an antisymmetric matrix, its equivalent expression is: （3）， Generalized momentum of the robotic arm Defined as: （4）， Combining equations (1), (3), and (4), the following first-order dynamic model is obtained. : （5）， Assumption 1: When the robotic arm collides, the external torques of its various joints... The derivative of the external torque Both are bounded; In step 2, each joint of the multi-joint industrial robot moves normally, and the joint control quantities are obtained by combining the dynamic model of the multi-joint industrial robot. Joint position Joint velocity The details are as follows: Assumption 2: The nominal values ​​of the robotic arm's dynamic parameters have been accurately obtained through identification methods, that is: , , , It's about joint position. Joint velocity The known quantities; A PD controller is used to control a multi-joint industrial robotic arm, with each joint tracking the desired position. Motion and angle sensors acquire the joint positions of the robotic arm in real time. The joint position difference is processed to obtain the joint motion velocity of the robotic arm. Based on the dynamic model of a multi-joint industrial robotic arm, its control torque is expressed as: （6）， Among them, the position tracking error during the movement of the robotic arm Speed ​​tracking error during robotic arm movement ; , These are the proportional and derivative adjustment parameters of PD control, which are adjustable constants; This represents an estimated value of the external torque; In step 3, based on the dynamic model of the multi-joint industrial robotic arm and the joint control parameters... Joint position Joint velocity An external torque observer is designed based on an improved internal feedback superhelical algorithm to estimate the external torque, as detailed below: Step 3.1: Design an improved internal feedback superspiral algorithm: set up , For state variables, , , , , It is an adjustable constant coefficient. For time-varying interference, Represents standard symbolic functions; while ensuring Under bounded conditions, by adjusting , , , , This enables the state variables Converges to within a finite time. ;exist and By introducing different internal feedback terms, the convergence speed of the algorithm is improved, resulting in the improved internal feedback superspiral algorithm: （8）， An improved superhelical algorithm is used to design an external torque observer, which enables the estimated external torque to be accurately estimated. Step 3.2: Design an external torque observer based on the improved internal feedback superhelical algorithm: For generalized momentum The corresponding estimated value is expressed as The estimation error of generalized momentum is... Represented as: （9）， Estimation error based on generalized momentum The constructed observer is as follows: （10）， In the formula, , , , , All of these are gain coefficients, and all are adjustable constants greater than zero; The first derivative of the generalized momentum estimate; As an intermediate variable; according to equations (5) and (10), the error dynamics equation of the observer is obtained as follows: （11）， In the formula, The first derivative of the error in the generalized momentum estimation; intermediate variable Intermediate variables ,in and If it is bounded, then it can guarantee Bounded; Equation (11) and the improved superspiral algorithm (8) are consistent; by adjusting , , , , The value, within a finite time Able to converge to ,but Within a limited time The estimated value.

2. The robotic arm collision detection method based on internal feedback superhelical external torque observation according to claim 1, characterized in that: In step 4, the stability of the designed external torque observer is proven using Lyapunov's stability theorem: Lemma 1: For a nonlinear control system, if there exists a positive definite Lyapunov function... ,coefficient ,coefficient ,coefficient satisfy And satisfy the inequality If the system state of the nonlinear control system can converge to the origin in a finite time, then the convergence time is... satisfy: ; Design the Lyapunov function as follows: （12）， Rewrite equation (12) in quadratic form: （13）， Among them, intermediate variables ,matrix As shown below: （14）， Differentiating equation (13), we get: （15）， Substituting equation (11) and simplifying, we get: （16）， in, , Both represent intermediate variables; （17）， In the formula, intermediate variables ,but , where constant ,yes The upper bound; （18）， Represents the smallest eigenvalue of the matrix. Let represent the largest eigenvalue of the matrix; then, through equation (16), we obtain: （19）， According to equation (13), we can obtain the Rayleigh-Ritz theorem: （20）， so （21）， in, for The first term in the equation is obtained from equations (19), (20), and (21): （22） In the formula, the positive constant term normal numbers According to equation (22), the requirements of Lemma 1 are satisfied, thus yielding the convergence time. The designed observer is able to Then accurately estimate the magnitude of the external torque; At this point, it is necessary to ensure the matrix , , Both are positive definite matrices, because Then the calculation yields , , , , The range of values ​​for is as follows: （23）。 3. The robotic arm collision detection method based on internal feedback superspiral external torque observation according to claim 2, characterized in that, In step 5, a time-varying threshold model is constructed. In a collision-free scenario, the observation results from the external torque observer are used as input. The upper and lower bounds of the time-varying threshold are established using the least squares method to detect whether a collision has occurred, as detailed below: The designed observer can obtain an estimate of the external torque in real time. However, in the absence of a collision, the observer's estimate will vary due to modeling errors, frictional variations, and the influence of the external working environment. This phenomenon exhibits fluctuations around the zero value; The collision threshold needs to be large enough to avoid false alarms, but an excessively large threshold will also reduce the detection sensitivity. Considering that the model error of the robotic arm is different in different states, a time-varying threshold collision detection method is adopted. Considering the impact of modeling errors, the main characteristics are the correlation quantities of the robot arm's joint position, velocity, and acceleration. These are linearized and combined, then incorporated into the time-varying threshold. Regarding the influence of friction, the Coulomb-viscous friction model effectively identifies the friction of the robot arm, and its friction force model... Represented as: ； in Here are the Coulomb friction parameters. These are viscous friction parameters. Let B be the speed exponent and B be the friction bias term; considering the small fluctuations in friction during the robot arm's reversal, we also introduce... The term then represents the time-varying threshold model for the i-th joint. Represented as: （24）， In the formula, , , , , , All are threshold model coefficients for the i-th joint; It is the joint position of the i-th joint; It is the adjustable constant coefficient of the i-th joint. ; The velocity index of the i-th joint; Identification using the least squares method yields the following linear form of the corresponding regression matrix: （25）， in, The coefficient matrix represents the i-th joint; the regression matrix represents the coefficient matrix. for: ， Corresponding estimated value Represented as: （26）， in, Corresponding estimated value , Let represent the zero-mean vector of the estimation error for the i-th joint; The estimated value of the i-th joint coefficient matrix is ​​then obtained by using the least squares algorithm. for: （27）， When the robotic arm does not collide, the estimated external torque obtained by the external torque observer using least squares identification is... This reflects the uncertainty of the corresponding model and the related terms of friction error, therefore the estimated external torque value of the i-th joint is... replace ,but The identification results differ for different joints i. Based on the identification results, the upper bound of the time-varying threshold is obtained. and the lower realm The expression form is: （28）， In the formula, , Let be the diagonal matrix with constant coefficients for the i-th joint. , Let be the normal value of the i-th joint; based on the upper and lower bounds of the time-varying threshold, it can be determined whether a collision has occurred, using the estimated value of the external torque of the i-th joint. Each is compared with the upper bound of the time-varying threshold of the i-th joint. Lower Boundary Compare and return the collision result of the i-th joint as a boolean. : （29）。

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