Real-time collision detection based on external torque mutation suppression and time series analysis

Abstract

Purpose

As the demand for human–robot collaboration in manufacturing applications grows, the necessity for collision detection functions in robots becomes increasingly paramount for safety. Hence, this paper aims to improve the existing method to achieve efficient, accurate and sensitive robot collision detection.

Design/methodology/approach

The external torque is estimated by momentum observers based on the robot dynamics model. Because the state of the joints is more accessible to distinguish under the action of the suppression operator proposed in this paper, the mutated external torque caused by joint reversal can be accurately attenuated. Finally, time series analysis (TSA) methods can continuously generate dynamic thresholds based on external torques.

Findings

Compared with the collision detection method based only on TSA, the invalid time of the proposed method is less during joint reversal. Although the soft-collision detection accuracy of this method is lower than that of the symmetric threshold method, it is superior in terms of detection delay and has a higher hard-collision detection accuracy.

Originality/value

Owing to the mutated external torque caused by joint reversal, which seriously affects the stability of time series models, the collision detection method based only on TSA cannot detect continuously. The consequences are disastrous if the robot collides with people or the environment during joint reversal. After multiple experimental verifications, the proposed method still exhibits detection capabilities during joint reversal and can implement real-time collision detection. Therefore, it is suitable for various engineering applications.

Citation

Zhang, T., Luo, H., Liu, N., Min, F., Liang, Z. and Wang, G. (2024), "Real-time collision detection based on external torque mutation suppression and time series analysis", Industrial Robot, Vol. 51 No. 4, pp. 640-657. https://doi.org/10.1108/IR-12-2023-0338

1. Introduction

As the demand for automatic production increases, collaborative robots are being gradually applied to production lines to assist employees in making products. In human–machine interaction scenarios, workers may accidentally collide with collaborative robots. To reduce the degree of damage to all parties after a collision, it is necessary for the robot to detect the collisions in time.

Collisions in robots can be divided into two types according to the intensity of the collision, namely, hard collision and soft collision. The difference between them is the collision duration and characteristics of external torque changes (Park et al., 2020). When a robot is hit by a rigid object, it is usually called a hard collision due to its short duration. When the robot comes into contact with an elastic/flexible/soft object or is subjected to a slowly increasing external force, it is usually called a soft collision due to its long duration. Concerning hard collisions, the external torque shows a trend of rapid increase and is accompanied by a rigid impact. When the object is struck, it undergoes an elastic, undamped impact, rapidly dissipating energy, which may lead to deformation or damage. As for soft collisions, the robot cannot escape the collision state quickly and is subject to continuous resistance. It keeps moving synchronously with the object being hit or absorbs the resistance. At this time, the external torque will slowly increase, and no rigid impact will occur.

By analyzing how the robot obtains information, robot collision detection methods can be divided into two categories: those with external sensors and those without external sensors (Heo et al., 2019). External sensors provide contact information for robots to interact with the outside world, but they also increase structural complexity and introduce data consistency issues (Liu et al., 2021). The external sensors commonly used for implementing robot collision detection are force/torque sensors.

The physical identification method for applying arm surface materials is also limited by the behavioral cognition of the collision subject. In a nonstructurally constrained environment, there is an imbalance between coverage integrity and random collision response.

According to threshold characteristics, conventional robot collision detection methods without external sensors can be divided into two types: static threshold method and dynamic threshold method. Based on these types, further classification can be made according to the dependence on intelligent algorithms, as shown in Table 1. Each method in the table corresponds to a representative literature and will be introduced later.

The static threshold method generally sets a fixed threshold, and its range is larger than the statistical peak value of previous experimental values. For external torque acquisition, besides the direct estimation method (Suita et al., 1995) and the estimation method based on harmonic reducer deformation (Wang et al., 2023), numerous observer-based estimation methods have been proposed (De Luca et al., 2006; Haddadin, 2013; De Luca and Mattone, 2005; Duan et al., 2023; Ren et al., 2018). However, collision detection based on these external torque estimation methods needs to be more sensitive.

For the range limitation problem of static threshold methods, neural networks (NNs) and deep learning can effectively extend the statistical characteristics of time series to the accumulation and prediction of data patterns, and a high collision detection performance can be obtained by using limited and fixed training targets. The deep NN CollisionNet eliminates the cumbersome heuristic decision-making process proposed to detect collisions (Heo et al., 2019). In addition, a multilayer NN is used to fit the robot dynamics data model to supplement or replace the physical model, which plays an important role in collision detection (Sharkawy and Aspragathos, 2018). To set the collision detection threshold closer to the changing trend, using the convolutional NN (CNN) to compensate for the uncertain data characteristics based on the existing dynamic model (Park et al., 2020). After training on the collision data set, the fuzzy system achieved fast and accurate collision detection (Dimeas et al., 2015). Intelligent algorithms can be used to design not only static thresholds but also dynamic thresholds, such as the long short-term memory network, which is used to design high-fit thresholds (Zhang et al., 2023).

However, the training resource consumption of intelligent algorithms and the iterative nested regression of heuristic algorithms all put forward computing power requirements for real-time robot control frameworks. To address this problem, the dynamic threshold method, which usually models the external torque representing the uncertainty of the model and sets the output threshold according to the law, is recommended (Zhang and Hong, 2019; Sotoudehnejad and Kermani, 2014; Li et al., 2021; Indri et al., 2015). Dynamic thresholds generated by methods lacking statistical tools may exceed symmetric static thresholds or be subject to certain application conditions, making them ineffective.

For the above problems of collision detection methods based on dynamic thresholds, time series analysis (TSA) in statistics provides some ideas. Although statistical methods are rarely used in the field of robotics, TSA has shown excellent results in fault detection problems in different fields (Feng et al., 2023; Lin et al., 2019; Liu et al., 2019). Collisions during robot movement can also be regarded as system anomalies. Therefore, applying TSA to robot collision detection is feasible. The sensorless collision-detection method based only on TSA generates dynamic thresholds based on historical information of external torques, conforms to the regular control of data feature statistics, and can achieve more accurate and sensitive collision detection (Zhang et al., 2021). However, there is a blind spot in the detection of joint reversals, which affects collision detection performance.

In this paper, we propose a method that suppresses abnormal external torque estimates to solve the problem of short-term identification failure of collisions when robot joints change their direction. This method is integrated with TSA to build a data model that continuously generates high-fit dynamic thresholds after the initialization conditions are met, and achieves sensitive and real-time collision detection. The new collision detection method improves the short-term identification failure of collisions during joint reversal and reduces the detection delay. When it operates in a robot control system, the block diagram is shown in Figure 1.

The remainder of this paper is organized as follows. Section 2 introduces the external torque estimation based on momentum observers and the problem of the collision-detection method based only on TSA. The proposed method is described in Section 3. Section 4 presents experimental verification and data analysis.

2. Problem description of the collision detection method based only on TSA

2.1 Dynamic model construction

When the robot is running in the position-control mode, the angle difference between the motor and link sides can be ignored. If the robot comes in contact with the external environment under this condition, the dynamic model is given by equation (1):

(1) M(q)q¨+C(q,q˙)q˙+G(q)+f(q˙)=τm+τext

where q, q˙, q¨ are the joint position, joint velocity and joint acceleration, respectively; M(q) is the inertial matrix; C(q,q˙) is a matrix of the centrifugal and Coriolis torques; G(q) is the gravitational torque vector; f(q˙) is the friction torque vector obtained by the Coulomb-viscous friction model; τ_m is the output torque vector of the joint motor; τ_ext is the external torque vector.

2.2 External torque estimation

The dynamic model shown in equation (1) requires the joint acceleration q¨ to calculate the external torque, but the acquisition of q¨ depends on the sensor and cannot be calculated directly from the velocity difference. Therefore, the observer method can be used to obtain the external torque (Haddadin et al., 2017). The generalized momentum observer based on the dynamic model is shown in Figure 2.

Because M˙(q)−2C(q,q˙) is an antisymmetric matrix, matrix M˙(q) can be simplified as shown in equation (2):

(2) M˙(q)=C(q,q˙)+CT(q,q˙)

To facilitate the subsequent derivation of equations, we define the vector Ω(q,q˙) as shown in equation (3):

(3) Ω(q,q˙) :=G(q)+C(q,q˙)q˙+f(q˙)−M˙(q)q˙ =G(q)+f(q˙)−CT(q,q˙)q˙

The obtained generalized momentum p is shown in equation (4):

(4) p=M(q)q˙

Combining equations (1) and (4), the derivative of the generalized momentum p˙ is given by equation (5):

(5) p˙=CT(q,q˙)q˙−G(q)−f(q˙)+τm+τext

The symbol r is replaced with τ_ext and combined with equation (3) to obtain the dynamic response of the momentum observer, as shown in equation (6):

(6) {p^˙=τm−Ω^(q,q˙)+rr˙=KO(p˙−p^˙)            

where K_o is the diagonal gain matrix of the observer; r(t) is the observer output, which can be obtained by integrating r˙, as shown in equation (7):

(7) r=KO(p(t)−∫0tp^˙(s)ds−p(0))

Because p=M^(q)q˙, and under ideal conditions, M^=M and Ω^=Ω, the dynamic relationship between τ_ext and r is given by equation (8):

(8) r˙=KO(τext−r)

The transient response of component r is related to the same component of τ_ext. In the limit case (K_O → ∞), r and τ_ext satisfy the relationship in equation (9):

(9) r≈τext

2.3 Short-term failure during the joint reversal

The collision detection method based only on TSA (Zhang et al., 2021) uses the autoregressive model (AR) as the external torque time-series model. Although collisions can be detected without adjusting the motion trajectory parameters, short-term recognition failure still occurs during the joint reversal. The reason for suspending the method is that the mutated external torque caused by joint reversal causes abnormal statistical information in the time series model, which makes the model unstable. The short-term invalid time of this method is t_pause = t_recover + t_init, where t_recover is the time required for the external torque to return from the abnormal value to the normal value and t_init is the time required to initialize the model coefficients once.

Joint velocity is an important feature for judging joint reversals. To maintain the stability of collision detection, the condition for the judgment of joint reversal is chosen to be q˙≤0.09rad/s in this paper. That is, lower than the velocity of joint creep q˙=0.1rad/s can be regarded as a sign of clockwise/counterclockwise. The external torque of Joint 1 when the robot runs a sinusoidal trajectory and the dynamic threshold generated by this method are shown in Figure 3. Notably, there is an absence of dynamic thresholds within the region highlighted by the arrow in Figure 3. However, this period lasted for 536 ms. If a collision occurred at this time, the method would be invalid.

3. Collision detection based on external torque mutation suppression and TSA

Generally, when a joint changes direction, it goes through three states in sequence: the motion state, transition state between motion and rest and rest state. To solve the problem of the short-term failure of collision detection during joint reversal, it is necessary to handle the mutated external torque during this period.

3.1 Improvement based on external torque mutation suppression

Inspired by the approach that compensates for model uncertainty (Cao et al., 2019), the operator to suppress mutated external torques is constructed using attenuation exponential and cosine functions based on joint velocity characteristics. The suppressed external torque is obtained by multiplying the external torque and the suppression operator. The suppression operator O_sp is given by equation (10):

(10) {Osp=(cos⁡(e−ρ⋅q˙2)))n τsp=τext⋅Osp

where ρ is used to adjust the degree of external torque tracking when the joint does not change its direction; n is used to adjust the suppression effect of the external torque during joint reversal, which directly affects the stability of the timing model; τ_sp is the suppressed external torque.

When the robot runs a sinusoidal trajectory, the results of the external torque of Joint 1 before and after the suppression process under different ρ and n are shown in Figures 4 and 5, respectively. When ρ = 150 and n = 16, the suppressed external torque changed smoothly during joint reversal.

From equation (10), the suppressed external torque is directly affected by the value of the suppression operator. When O_sp = 0, the suppressed external torque is 0. When O_sp ≥ 0.1, the suppressed external torque caused by collisions can still be reflected. When O_sp < 0.1, the suppressed external torque caused by the collision is difficult to reflect, and the method proposed in this paper can be regarded as invalid. The values of the suppression operator for different ρ and n are shown in Figure 6.

O_sp is symmetrical about the vertical line where the joint velocity is 0. As shown in Figure 6, when ρ = 150, n = 16 and O_sp = 0.1, the corresponding joint speed value was approximately ±0.0657 rad/s.

In this paper, we combined external torque mutation suppression and TSA to obtain a novel collision detection method. The process of this method is illustrated in Figure 7, where Processes 1 and 2 are used for offline simulation, and Process 3 is used for online robot control. However, as shown in Figure 3, the collision detection method based only on TSA still needs to wait for the re-initialization, which can resume detection after the completion of joint reversal. According to the above analysis, the short-term failure duration of the method used in this paper is significantly shorter than that of the method based only on TSA.

The pseudocode corresponding to Figure 7 is as follows:

Collision detection method based on external torque mutation suppression and TSA.

Input: Suppression parameters 1, ρ     Suppression parameters 2, n     Model order, u     Prediction length, L     Confidence level, γ     Forgetting factor, λ     Threshold Margin, ψ     The total amount of sample data, N     Number of external torque exceeding the threshold, C      Original external torque, τext      Joint velocity, 

q˙     Running time, run_time

Output: Collision detection result, result1: while t ≤ run_time do2: t ← t + 1;3: 

Osp←(cos(exp(−ρ∗q˙^2)))^n; //Suppression operator initialization.4: τsp ← τext * Osp; //External torque mutation suppression.5: if abs (τext − τsp) ≥ 1e-3 && firstinit = = false //Determine whether the initialization conditions are met.6: continue;7: else if abs (τext − τsp) < 1e-3 && firstinit = = false8: τSP ← [τSP · τsp];9: else10: τSP ← [τSP(2: end) τsp];11: end if12: len ← len + 1;13: if len = = N && firstinit = = false14: θ ← LS_init(τSP); //Using LS algorithm to Initialize model coefficients.15: firstinit ← true;16: continue;17: endif18: if fistinit = = true19: τpd, ηup, ηdown ← TSA_generate_dyth (τSP, ψ, u, γ, θ); //Using TSA to generate dynamic thresholds.20: τPD ← [τPD τpd];21: result ← consecutive_values_out_of_dyth(C, τSP, ηup, ηdown); //Check whether there are C consecutive external torque exceedances22: if result = = false && len % L = = 023:τSP(end−L+1:end)← replace_values_out_of_Dyth τSP (end−L+ 1: end), τPD); //The exceeding limit value among the L actual external torque values is replaced by the predicted value.24: τPD ←[];25: θ ← RLS_update (τSP, λ); //Using RLS algorithm to update model coefficients.26: endif27: if result = = true28: return result;29: endif30: endif31: end while

3.2 Model coefficient identification based on least squares

The u-order autoregressive model AR(u) of the suppressed external torque time series {τ_sp(t)} is expressed in equation (11) (Box et al., 2015):

(11) {τsp(t)=x(t)θ+ε(t) x(t)=[τsp(t−1) τsp(t−2)… τsp(t−u)] θ=[α1  α2… αu]T

where x is the historical external torque vector, θ is the autoregressive coefficient vector and ε(t) is the white noise with a mean of 0 and variance of σε2. The total amount of sample data is assumed to be N. When {t = u + 1, u + 2, …, N}, equation (11) can form the following linear equation (12):

(12) {Y=X⋅θ+ErY=[τsp(u+1)  τsp(u+2)… τsp(N)]TX=[xT(u+1) xT(u+2)… xT(N)]TEr=[ε(u+1) ε(u+2)… ε(N)]T

where Y is the external torque vector, X is the observation matrix of the autoregressive coefficients and E_r is the error vector.

Therefore, the least squares (LS) estimate of θ is given by equation (13):

(13) θ^LS=(XT·X)−1·XT·Y

3.3 Model order determination

After obtaining the parameter identification result θ^LS based on the time series, the prediction error of the model E^r can be expressed as shown in equation (14):

(14) E^r=Y−X⋅θ^LS

An appropriate model order minimizes the error between the prediction results of the model and the actual external torque. The final prediction error (FPE) criterion effectively balances errors arising from an excessive number of parameters or missing parameters. This is achieved by determining model order that minimizes the variance of the one-step prediction error.

In this paper, the one-step prediction error sequence during the offline analysis was assumed to be {τ˜sp(j),j={u+1,u+2,… ,N}}, where τ˜sp(j) is the one-step prediction error of the model, and its expression is given by equation (15):

(15) τ˜sp(j)=τsp(j)−τ^sp(j)

where τ_sp(j) is the true value of the external torque at moment j. τ^sp(j) is the predicted external torque at moment j, and its expression is given by equation (16):

(16) τ^sp(j)=x(j)θ^LS

σ^ε2 is the variance estimate of white noise ε(t), and its expression is shown in equation (17).

(17) σ^ε2=1N−u⋅E^rT⋅E^r

The FPE is the variance of the one-step forecast error sequence, a function of the model order u. Therefore, it can be assumed to be FPE(u), and its expression is shown in equation (18):

(18) FPE(u)=N+uN⋅σ^ε2=N+uN(N−u)⋅E^rT⋅E^r

Therefore, the minimum FPE simplifies the model order and can achieve better prediction. The appropriate model order u₀ is selected according to these conditions, and the initial coefficient θ^LS of the model can be simultaneously obtained.

3.4 Dynamic threshold generation based on prediction results

The different predictive targets cause the different online/offline analysis equation.

During the online analysis, for the time serie {τ_sp(t)}, the value at moment t and before can be used to predict the value of L times in the future. The suppressed external torque τ_sp predicted at moment {j = t + l, l = 1,2, …, L} can be assumed as τ_pd(l), where L is the prediction length. The one-step prediction error ξ_pd(l) of AR(u) is given by equation (19):

(19) ξpd(l)=τsp(t+l)−τ^pd(l)

where τ_pd(l) is the predicted values of AR(u) at moment {j = t + l, l = 1,2, …, L} and L is the prediction length.

After determining the model coefficient θ, the recursive form of the predicted value τ_pd(l) based on AR(u) is given by equation (20):

(20) τpd(l)=α1⋅τpd(l−1)+α2⋅τpd(l−2)+…+αu⋅τpd(l−u)

where{τ_pd(l − 1), τ_pd(l − 2), …, τ_pd(l − u)} represent the predicted values of AR(u) at moment {t + l − 1, t + l − 2, …, t + l − u}, respectively. If l − h < 0(h = 1,2, …, u), then τ_pd(l − h) is replaced by τ_sp(t + l − h).

During the online analysis, the variance of the one-step prediction error Var[ξ_pd(l)] of AR(u) is given by equation (21):

(21) Var[ξpd(l)]=E[(τsp(t+l)−τpd(l))2]

In the TSA, the u-order autoregressive operator α(B) can be defined based on equation (11), as shown in equation (22):

(22) {α(B)=1−α1⋅B−α2⋅B2−…−αu⋅BuBτsp(t)=τsp(t−1)

where B is the delay operator that defines the relationship between the external torque at the current and previous moments. Therefore, AR(u) shown in equation (11) can be rewritten as equation (23):

(23) τsp(t)=α−1(B)ε(t)

The s-order moving average model MA(s) of the external torque time series {τ_sp(t)} is given by equation (24):

(24) τsp(t)=ε(t)+β1⋅ε(t−1)+β2⋅ε(t−2)+…+βs⋅ε(t−s)

where β_i(i = 1,2, …, s) is the moving-average coefficient. β(B) is defined as the s-order moving-average operator, as shown in equation (25):

(25) β(B)=1+β1⋅B+β2⋅B2+…+βs⋅Bs

During a stable motion process, the suppressed external torque fluctuates smoothly around zero, which satisfies the stability requirements of the time series model (Zhang et al., 2021).

Under the condition that the process is stationary, the autoregressive process can be transformed into a moving average process (Chan and Cryer, 2008). Therefore, β(B) = α⁻¹(B) and AR(u) shown in equation (11) is converted into MA(∞). Therefore, MA(∞) shown in equation (24) can be rewritten as equation (26):

(26) τsp(t+l)=β(B)ε(t+l)

where (t + l) is the lth moment in the future.

During the conversion process, the expression for β_i(i = 1,2, …, ∞) can be obtained by combining equations (22) and (25), as shown in equation (27):

(27) {β1= α1β2= α1·β1+ α2⋮βl= α1·βl−1+ α2·βl−2+…+αu·βl−u⋮

ξ_pd(l) of the model can also be expressed as equation (28):

(28) ξpd(l)=ε(t+l)+β1⋅ε(t+l−1)+…+βl−1⋅ε(t+1)

The variance of the one-step prediction error Var[ξ_pd(l)] in equation (21) can be rewritten as in equation (29):

(29) Var[ξpd(l)]=(1+β12+β22+…+βl−12)σε2=(1+∑i=1l−1βi2)σε2

The prediction error is normal white noise with a mean of 0 and variance of Var[ξ_pd(l)]. Consequently, the prediction result of AR(u) at the lth moment in the future should also obey the normal distribution, with a mean of τ_pd(l) and variance of Var[ξ_pd(l)]. Therefore, when the confidence level is γ, the detection threshold at the lth moment in the future is given by equation (30):

(30) η(l)=τpd(l)±(μγ2⋅(1+∑i=1l−1βi2)σ^ε2+ψ)

where μγ2 is the deviation coefficient and the standard normal distribution exceeds μγ2 with a probability of γ2. Parameter ψ was used to adjust the threshold margin.

3.5 Model coefficient update based on recursive least squares

To reduce the computational complexity of generating dynamic thresholds based on prediction results, this paper uses the recursive least squares (RLS) algorithm to update the model coefficients (Song et al., 2019), as shown in equation (31):

(31) {Kw=Pw−1⋅xT(w)[λ+x(w)Pw−1⋅xT(w)]−1Pw=λ−1⋅[I−Kw⋅x(w)]⋅Pw−1θ^w=θ^w−1+Kw⋅[τsp(w)−x(w)θ^w−1]

where K_w is the gain matrix, P_w is the covariance matrix and λ is the forgetting factor.

If no collision is detected in the (w − 1)th detection, L-suppressed external torques obtained in this detection cycle are used to reconstruct τ_sp(w) and x(w). The RLS algorithm is then used to update K_w, P_w and θ^w, which are used for the wth prediction and threshold generation.

4. Experiment validation

4.1 Experiment platform

The 6DOF robot was modeled, and Joint 1 was used as an example to analyze the collision detection data.

The robot controller communicates with a universal collaborative robot based on the EtherCAT protocol, which has a payload of 3 kg and arm span of 0.54 m. The master station control architecture is Igh-EtherCAT +PREEMPT-RT, the control cycle is 1 ms, and the servo slaves are integrated modules. The setup is shown in Figure 8(a).

4.2 Experiment program

In this paper, we designed three trajectories: sinusoidal trajectory in joint space, linear trajectory in Cartesian space and arc trajectory in Cartesian space. The target motion data of Joint 1, when the robot runs these three trajectories, are shown in Figures 9 and 10.

To verify the performance of collision detection methods, two main aspects need to be assessed: accuracy and detection delay. Repeated experiments were conducted to obtain results regarding these two aspects under hard or soft collision conditions, comparing the proposed method with the symmetric threshold method.

4.3 Parameters setting

Setting parameters of the method in this paper according to the process shown in Figure 7. When the robot runs the sinusoidal trajectory for the first time, ρ and n can be determined after performing in Process 1. The suppression effect is shown in Figures 4 and 5. When the robot runs the sinusoidal trajectory for the second time, set the order range of the model AR(u) to u ∈ [1,40]. After executing Process 2, not only N and u can be determined, but also FPE with different orders can be obtained, which are shown in Figure 11. Starting from the third time the robot runs the sinusoidal trajectory, the other parameters in this method except ρ, n, N and u can be determined after executing Process 3 in a loop. For γ, the universal value is 0.05 or 0.01 (Chan and Cryer, 2008). When repeatedly adjusting all the parameters that need to be set, the following two conditions need to be met. First, the method will not cause a false collision alarm. Second, the method can accurately and sensitively detect real collisions.

It can be seen from Figure 11 that starting from the model order u = 12, even if the model order increases, the reduction in FPE is no longer noticeable. Due to the need for selecting the smaller model order under small FPE, u is set to 12.

When the robot runs the sinusoidal trajectory, and no collision occurs, the original external torque of Joint 1 and the dynamic threshold generated by the collision detection method based only on TSA are shown in Figure 3. The suppressed external torque of Joint 1 and the dynamic threshold generated by the method in this paper are shown in Figure 12. When t = 406 ms, the initialization condition shown in Step 2 of Process 3 in Figure 7 is met. Therefore, the external torque when t = 406 ms–615 ms is intercepted to construct the initial sample data. Then, the dynamic thresholds generated by the method in this paper can tightly envelop the external torque, and no false collision alarm occurs during robot motion.

The final parameter values with repeated adjustments are listed in Tables 2 and 3. Method 1 is the collision detection method based only on TSA, and Method 2 is the method proposed in this paper.

To further verify the versatility of the parameters, make the robot run the linear trajectory or the arc trajectory without collision. Multiple tests have found that neither the method in this paper nor the collision detection method based only on TSA has produced any false collision alarm.

4.4 Collision detection experiment

The robot runs the linear trajectory and bears an artificial hard collision when Joint 1 changes direction. The suppressed external torque of Joint 1, the dynamic threshold generated by the method in this paper, and the static threshold set by the symmetric threshold method are shown in Figure 13. Besides, the original external torque of Joint 1 and the dynamic threshold generated by the collision detection method based only on TSA are shown in Figure 14.

Figure 13 shows that the suppressed external torque undergoes a rapid increase starting approximately at t = 5,983 ms, breaking through the lower bound at t = 6,002 ms. By t = 6,005 ms, the method proposed in this paper detects that the lower bound has been exceeded for four consecutive time steps, indicating a collision occurrence. Thus, the detection delay of the method proposed in this paper is approximately 22 ms. However, the symmetric threshold method fails to detect this hard collision.

As shown in Figure 14, when t = 4,522 ms–6,030 ms, |q˙|<0.09rad/s, the collision detection method based only on TSA stops generating dynamic thresholds. Starting from t = 6,031 ms, |q˙|≥0.09rad/s, the external torque for t = 6,031ms–6,240 ms is intercepted to reinitialize the model coefficients and then the collision detection method based only on TSA continues to generate dynamic thresholds. The collision is detected at t = 6,298 ms, and the detection delay of the collision detection method based only on TSA is recorded to be approximately 315 ms.

Therefore, the method in this paper detects this hard collision about 296 ms faster than the collision detection method based only on TSA.

To obtain hard collision statistics, we made the robot run linear and arc trajectories multiple times and then applied 100 hard collisions when the robot ran each trajectory; that is, 200 hard collisions were applied. Then, we collected and analyzed all experiment data. In terms of accuracy, the number of detected collisions divided by the number of real collisions is calculated. In terms of average delay, the sum of collision detection delay divided by the number of successful detections is calculated. The statistical results are shown in Table 4.

When the robot runs the arc trajectory, it comes into contact with the foam board, as shown in Figure 8(b). At this time, the robot has a soft collision. The experiment data is shown in Figure 15.

From Figure 15, we know that the soft collision occurs at approximately t = 2,645 ms and the suppressed external torque breaks through the upper bound at t = 2,680 ms. After 4 ms, the exceeded upper bound leads to the collision alarm of the method in this paper at t = 2,683 ms. However, the symmetric threshold method detects this collision at t = 2,732 ms.

Obviously, in this collision detection, the delay of the method in this paper is about 38 ms, and the delay of the symmetric threshold method is about 87 ms. That is, the method in this paper detects the collision about 49 ms faster than the symmetric threshold method.

To obtain soft collision statistics, we made the robot run linear and arc trajectories multiple times and had 100 soft collisions with the foam board when running each trajectory. That is, 200 soft collisions occurred between the robot and the foam board. The statistical method of repeated experiments, used for hard collision cases, is also used to analyze the results of repeated experiments for soft collisions. The statistical results are shown in Table 5.

5. Conclusion

The method proposed in this paper calculates the external torque using the current/torque data of the servo slave. Then, it performs mutation suppression processing on the external torque. Finally, it uses the TSA method to obtain several steps of predicted response and effectively prevents mutated external torques caused by joint reversals from false collision alarms. Compared with the collision detection method based only on TSA, its invalid time is less. If a collision occurs while the joint changes direction, it saves at least one time required to initialize the model coefficients. Three test trajectories were used to obtain the differences between this method and the symmetric threshold method. The comparison results show that it has higher accuracy and lower detection delay. In addition, it meets the real-time requirements of robot control systems and does not rely on external sensors. Therefore, it is so superior and practical that it can be used to improve the safety of human–machine collaborative production.

Figures

Figure 1

Block diagram of the closed-loop control system

Figure 2

Block diagram of momentum observer

Figure 3

The defect of the collision detection method based only on TSA

Figure 4

The comparison of external torques before and after suppression with different ρ

Figure 5

The comparison of external torques before and after suppression with different n

Figure 6

Suppression operator O_sp under different ρ and n

Figure 7

Flow chart of the method proposed in this paper

Figure 8

Figure 9

The target velocity of Joint 1 when the robot runs the test trajectory

Figure 10

The target acceleration of Joint 1 when the robot runs the test trajectory

Figure 11

FPE with different orders

Figure 12

The suppressed external torque of Joint 1 and the dynamic threshold generated by the method in this paper when the robot runs the sinusoidal trajectory without collision

Figure 13

The suppressed external torque of Joint 1 and the dynamic threshold generated by the method in this paper when the robot runs the linear trajectory and bears a hard collision

Figure 14

The original external torque of Joint 1 and the dynamic threshold generated by the collision detection method based only on TSA when the robot runs the linear trajectory and bears a hard collision

Figure 15

The suppressed external torque of Joint 1 and the dynamic threshold generated by the method in this paper when the robot runs the arc trajectory and collides with the foam board

Figure A1

The target motion data when the robot runs the sinusoidal trajectory

Figure A2

The target motion data when the robot runs the sinusoidal trajectory

Figure A3

The target motion data when the robot runs the linear trajectory

Figure A4

The target motion data when the robot runs the arc trajectory

Figure A5

FPE with different orders

Figure A6

The suppressed external torque of Joint 1 and the dynamic threshold generated by the method in this paper when the robot runs the sinusoidal trajectory without collision

Figure A7

The suppressed external torque of Joint 2 and the dynamic threshold generated by the method in this paper when the robot runs the sinusoidal trajectory without collision

Figure A8

The suppressed external torque of Joint 3 and the dynamic threshold generated by the method in this paper when the robot runs the sinusoidal trajectory without collision

Figure A9

The original external torque of Joint 1 and the dynamic threshold generated by the collision detection method based only on TSA when the robot runs the linear trajectory and bears a hard collision

Figure A10

The original external torque of Joint 2 and the dynamic threshold generated by the collision detection method based only on TSA when the robot runs the linear trajectory and bears a hard collision

Figure A11

The original external torque of Joint 3 and the dynamic threshold generated by the collision detection method based only on TSA when the robot runs the linear trajectory and bears a hard collision

Figure A12

The suppressed external torque of Joint 1 and the dynamic threshold generated by the method in this paper when the robot runs the linear trajectory and bears a hard collision

Figure A13

The suppressed external torque of Joint 2 and the dynamic threshold generated by the method in this paper when the robot runs the linear trajectory and bears a hard collision

Figure A14

The suppressed external torque of Joint 3 and the dynamic threshold generated by the method in this paper when the robot runs the linear trajectory and bears a hard collision

Figure A15

The suppressed external torque of Joint 3 and the dynamic threshold generated by the method in this paper when the robot runs the arc trajectory and collides with the foam board

Table 1

Collision detection method based on the force/torque sensorless

Collision detection method	Advantage	Disadvantage
1. The static threshold method
Based on Nonintelligent algorithms (De Luca and Mattone, 2005)	– Simple threshold	– Limited range – Invalid occasion
Based on intelligent algorithms (Park et al., 2020)	– Detection performance moderate	– Data set need – Much calculation
2. The dynamic threshold method
Based on nonintelligent algorithms (Zhang et al., 2021)	– Detection performance high – Real-time	– Invalid occasion
Based on intelligent algorithms (Zhang et al., 2023)	– Detection performance high	– Data set need – Much calculation

Source: Authors’ own work

Table 2

The values of N, ρ, n and λ in methods 1 and 2

Parameters	N	ρ	n	λ
Method 1	210	–	–	0.999
Method 2	210	150	16	0.999

Source:

Authors’ own work

Table 3

The values of L, C, u, γ and λ in methods 1 and 2

Parameters	L	C	u	γ	ψ
Method 1	15	4	12	0.01	–
Method 2	15	4	12	0.01	0.02

Source:

Authors’ own work

Table 4

The accuracy and average delay of the method in this paper and the symmetric threshold method when the robot bears hard collisions

Detection method	Accuracy (%)	Average delay (ms)
The method in this paper	97.5	10.0
The symmetric threshold method	43.5	71.3

Source:

Authors’ own work

Table 5

The accuracy and average delay of the method in this paper and the symmetric threshold method when the robot collides with the foam board

Detection method	Accuracy (%)	Average delay (ms)
The method in this paper	81.0	33.4
The symmetric threshold method	100.0	84.0

Source:

Authors’ own work

Appendix

When the robot runs the test trajectory, the target motion data of the first three joints are shown in Figures A1–A3.

From Figure A4, the FPE of the three joint timing models at different orders can be seen. For Joint 2, even if the model order continues to increase starting from the model order u = 12, the reduction in FPE is no longer noticeable. For Joint 1 or 3, when the model order u ≥ 12, the FPE decreases as the order increases. The model order should be as small as possible to satisfy the small FPE, and it can make the method in this paper meet the requirements of high real-time and convenient programming.

When the robot runs the sinusoidal trajectory, and no collision occurs, the suppressed external torque of Joints 1 to 3 and the dynamic threshold generated by the method in this paper are shown in Figures A5–A7.

The robot runs the linear trajectory and bears an artificial hard collision when Joint 1 changes direction. However, there was no significant change in the external torques of Joints 2 and 3. The original external torque of Joints 1 to 3 and the dynamic threshold generated by the collision detection method based only on TSA are shown in Figures A8–A10. Besides, the suppressed external torque of Joint 1–3 and the dynamic threshold generated by the method in this paper are shown in Figures A11–A13.

As shown in Figure A8, when t = 4,523 ms–6,024 ms, |q˙|<0.09rad/s, the collision detection method based only on TSA stops generating dynamic thresholds. Starting from t = 6,025 ms, |q˙|≥0.09rad/s, the external torque for t = 6,025 ms–6,234 ms is intercepted to reinitialize the model coefficients and then the collision detection method based only on TSA continues to generate dynamic thresholds. However, the intercepted data is an abnormal external torque caused by collisions, so the predicted values obtained after reidentifying the model coefficients are also considered outliers. Finally, the generated threshold cannot be exceeded by the external torque caused by the collision.

Figure A11 shows that the suppressed external torque rapidly increases approximately from t = 5,894 ms and exceeds the lower bound at t = 5,925 ms. When t = 5,928 ms, the method in this paper detects that the lower bound for four consecutive moments has been exceeded and determines that the collision occurred. However, the static threshold is exceeded by the suppressed external torque at t = 6,145 ms. Obviously, in this collision detection, the delay of the method in this paper is about 34 ms, and the delay of the symmetric threshold method is about 251 ms. This information indicates that the method in this paper detects the collision about 217 ms faster than the symmetric threshold method.

When the robot runs the arc trajectory, it has a soft collision with the foam board, as shown in Figure 8(b). Due to the small velocity of Joint 2, the initialization condition shown in Step (2) of Process 3 in Figure 7 has yet to be satisfied. Therefore, the dynamic threshold related to the suppressed external torque of Joint 2 has not been generated. For Joints 1 and 3, the suppressed external torque and related thresholds are shown in Figures A14 and A15, respectively.

From Figure A15, it can be seen that the suppressed external torque of Joint 3 does not exceed the dynamic threshold generated by the method in this paper and the static threshold set by the symmetric static threshold method. However, Figure A14 shows that the suppressed external torque of Joint 1 exceeds the above two thresholds. For Joint 1, the following details can be obtained from Figure A14. The suppressed external torque slowly increases approximately from t = 2,200 ms and exceeds the upper bound at t = 2,235 ms. After 4 ms, the exceeded upper bound leads to the collision alarm of the method in this paper at t = 2,238 ms. In addition, the static threshold is exceeded by the suppressed external torque at t = 2,264 ms. Therefore, in this collision detection, the delay of the method in this paper is about 38 ms and the delay of the symmetric threshold method is about 64 ms. That is, the method in this paper detects the collision about 26 ms faster than the symmetric threshold method.