Adaptive fuzzy impedance control of human-robot interaction modular robot manipulators based on human motion intention estimation

Authors: bo  dong
tianjiao  an
bing  ma
chen  li
Venue: IEEE_org_ICIST_2024_Conference
Published: 2024-08-12 10:15:31

Abstract: For modular robot manipulators (MRMs) with physical human-robot interaction (pHRI) tasks, an adaptive fuzzy impedance control method based on the estimation of human motion intention is proposed in this paper. Dynamic subsystem of MRM is built based on joint torque feedback (JTF) technique. Processing unknown human limb models using fuzzy logic systems (FLSs), the obtained intention of the human
is considered as the desired trajectory for impedance control, enabling the robot to actively follow a target impedance model. Adaptive fuzzy impedance control is utilized to compensate for model uncertainty and accomplish tracking goals. The uniformly ultimately bounded (UUB) of the tracking error is verified through Lyapunov theory. Eventually, the validity of the proposed adaptive fuzzy impedance control method is experimentally verified.

Main paper: 
 i. introduction: 
 Compared with traditional robots, modular robot manipulators (MRMs) are reconfigurable and have good flexibility and versatility, which have an increasing influence in robotics. Since the first industrial MRM systems were designed and developed in the world, MRMs have rapidly developed andThe work is supported by the National Natural Science Foundation of China (62173047), the Scientific Technological Development Plan Project in Jilin Province of China (20220201038GX), Key Laboratory of Advanced Structural Materials (Changchun University of Technology), Ministry of Education, China (ASM-202202).been applied [1] . Today, MRMs play a crucial role in areas such as post-disaster rescue, aerospace and physical humanrobot interaction (pHRI).In daily life, there are inevitably some tasks that require a minimum of two people to complete, such as moving larger objects can't be done by one person, and collaboration robot can assist human in accomplishing tasks. Robot can ensure the safety of the collaborator in human-robot collaboration tasks by obtaining the intention of the collaborator [2] . If the robot can acquire the intention of the human, it can use the result as its desired trajectory, then pHRI is realized [3] . Therefore, the robot recognition of human motion intention is the key to pHRI [4] . Using an electromyography-based method, Bednarczyk et al. [5] distinguished interactive forces from forces generated by interacting with the environment to capture the operator's motion intention. Due to the complexity of the human body, methods based on human biological signals for intention recognition have significant flaws. Compared to using human biological signals for intention recognition, utilizing robot's own sensor signals overcome human body uncertainties [6] . Li et al. [7] used the position and force information obtained from the sensors to apply a neural network for intention recognition. An et al. [8] proposed a harmonic drive compliance model-based intention recognition, which only required the position measurement of the robot.In pHRI tasks, applying appropriate control strategies can ensure system stability. Impedance control is widely used in the pHRI due to its good robustness [9] . Fuzzy logic systems (FLSs) are considered to have ability to approximate nonlinear systems [10] . Zhang et al. [11] solved the target tracking control challenges in nonlinear pure-feedback systems by FLSs. Zhao et al. [12] used FLSs to accomplish the trajectory tracking control for a category of low triangular nonlinear systems with uncertainty. Wang et al. [13] used FLSs approximation of unknown nonlinear functions and ensured the trajectory tracking tasks are accomplished.As a result of the above discussion, an adaptive fuzzy impedance control method for pHRI oriented MRM systems based on human motion intention estimation is proposed in this paper. First, the joint torque feedback (JTF) technique is used to establish the MRM system dynamic model. Then, an FLS is introduced, which is applied to recognize the human motion intention, and the recognized result is treated as the expected trajectory in the impedance model. An adaptive fuzzy impedance controller is used to compensate for model uncertainty so that the robot can successfully accomplish the position tracking tasks. Finally, Lyapunov theory demonstrates the stability of the MRM system, and the results of the experiment verify the effectiveness of the proposed method.In this paper, an n degrees of freedom MRM has considered and the expression of the dynamic model for the ith joint subsystem in the MRM is given by:I mi β i αi + f li (α i , αi ) + L i (α, α, α) + τ ci β i = τ i + τ jf i (1)where α, α and α are the position, velocity and acceleration vector of the ith joint of the modular robot. τ i is the control torque. τ jf i is pHRI torque. τ ci represents the joint torque detected by the sensor. I mi means the rotor's moment of inertia about the axis of rotation. β i indicates the reduction ratio of the motor. L i (α, α, α) denotes the interconnected dynamic coupling (IDC) terms. f li (α i , αi ) is the joint friction torque.1) The IDC items:EQUATIONThe IDC items can be reexpressed as follows:L i (α, α, α) = i-1 n=1 U i n Q i n + i-1 n=2 n-1 s=1 S i sn R i sn = Q i z + R i z (3)where h mi is the unit vector around the ith motor rotation axis, h qn and h ls are the unit vectors in the direction of the axis of rotation of the nth joint and the sth joint.A i n = h T mi h qn means dot product of h T mi , h qn . Ãi n represents the alignment error of A i n , Ãi n + Âi n = A i n . B i sn = h T mi (h ls × h qn ) denotes dot product of h T mi , (h ls × h qn ). Bi sn means the alignment error of B i sn , Bi sn + Bi sn = B i sn .2) The joint friction torque:EQUATIONwhere f αi (α i , αi ) is the position-dependent friction parameter, f bi denotes the viscous friction parameters, f ci is the coulomb friction parameters, f si is the static friction, f ti is the Stribeck effect parameter. According to the proposed linearization strategy, one can obtain:EQUATIONSubstituting ( 5) into (4) yields:EQUATIONwhere Fi = -fbi + f bi , -fci + f ci , -fsi + f si , -fti + f ti T denotes the uncertaint friction parameters, Z ( αi ) is denoted as follows:EQUATIONSubstituting ( 3) and ( 6) into (1), one has:EQUATIONwhereN i = (I mi β i ) -1 , define state variables as x i = [x i1 x i2 ] T = [α i αi ] T ∈ R 2×1 , u i = τ i ∈ R 1×1 is the controlinput of the systems. The MRM subsystem state space can be represented as:     ẋi1 = x i2 ẋi2 = C i (x i ) + N i u i + N i τ jf i + T i (x)EQUATIONThe precise modeling item and measurable part of the subsystem dynamic model is denoted as:EQUATIONwhereT i (x) = -N i Q i z + R i z + f αi (α i , αi ) + Z ( αi )Fi represents the uncertainty component of the subsystem.FLSs have strong approximation capabilities and are often used as approximation nonlinear functions. The IF-THEN rules in FLSs can be defined as follows:EQUATIONwhere x ij denotes the input of FLSs, y i denotes the output of FLSs, F k ij and H k i represent the fuzzy sets. One can obtain:EQUATIONwhereψ k = max ζ H k i .Define the fuzzy basis function as follows:EQUATIONEquation ( 12) can be redescribed as follows:EQUATIONwhereW = [W 1 , . . . , W N ] T = [ψ 1 , . . . , ψ N ]T . Lemma 1 [14] : For a given continuous function y i , there is an FLS which satisfies sup xi y i -W T i ζ ≤ η i , η i denotes an arbitrarily positive constant.In pHRI, a human limb model in the Cartesian space is defined as:-C H ẋ + G H (x Hd -x) = f (15)where C H is the human's damper matrix, G H is the human's spring matrix, x Hd denotes the desired trajectory of the human, f represents interaction force, the motion intention x Hd is expressed as:EQUATIONwhere Y (•) represents an unknown function, since Y (•) is an unknown nonlinear function, approximating it by fuzzy logic. The desired trajectory of the human and its estimation are denoted by:EQUATIONwhereb i = f i T , x i T , ẋT i Trepresents the input of FLSs. Using the steepest descent method, one can obtain:EQUATIONThen,Ẇ 1i (t) = -a ′ i ∂E i ∂ Ŵ1i = -a ′ i ∂E i ∂f i ∂f i ∂x Hd,i ∂x Hd,i ∂ Ŵ1i (19)where ∂fi ∂x Hd,i , ∂x Hd,i ∂ Ŵ1i are obtained by:EQUATIONThe update adaptive rate can be designed as follows:EQUATIONwhere a i = a i ′ G H,i , a i ′ is a small positive scalar, a i ′ and G H,i can be absorbed by a i . Eventually, the method to derive the update law of Ŵ1i is:EQUATION)The estimation of human motion intention xHd can be obtained by substituting ( 22) into (17).The target impedance model of the MRM can be represented as follows:M di (α di -αi ) + C di ( αdi -αi ) + G di (α di -α i ) = J T i f (23)where M di , C di and G di are the desired matrices of inertia, damper and stiffness.Since the human expected trajectory obtained earlier is in Cartesian space, in this section, it is transformed into joint space as:EQUATIONwhere x, ẋ, ẍ ∈ R m represent position, velocity, acceleration vectors in the Cartesian space, χ ( • ) represents the robot kinematics. Motion intention estimation αi is defined as the expected trajectory α di and constructs error signal as follows:EQUATION)Define the error signal as follows:EQUATION)To facilitate analysis, define another error signal as follows:EQUATION)whereK ai = M di -1 , K bi = M di -1 C di , K ci = M di -1 G di .Select two positive definite matrices g i and h i as follows:EQUATION)Defining K ai τ jf i = τjfli + τ jf li h i yields:d = ëi + (g i + h i ) e i + ( ġi + h i g i ) e i -τjfi -τ jf i h i . (29)Define an auxiliary variable z as:EQUATION)One can obtain:EQUATION)Suppose that the existence of lim t→∞ z(t) = 0 will make lim t→∞ ż(t) = 0, lim t→∞ d (t) = 0, then the control objective lim t→∞ z(t) = 0 is achieved.Differentiating equation (30) yields:EQUATION)Substituting ( 26) and ( 32) into (7) leads to:EQUATIONBy defining H (Φ) = I mi β i (α di -T i (x) + ġi e i + g i ėi + g i ëi -τjfli ), one can obtain:EQUATIONAdaptive fuzzy impedance controller can be designed as:EQUATIONwhere K g1 is the positive-definite matrix, u i1 = Ŵ T 2i S 1 (Φ) = Ĥ (Φ) -ε 2i . The adaptive law is as follows:EQUATIONSubstituting ( 35) into (33), one has:EQUATIONwhere W2i denotes the weight error, W2i = Ŵ2i -W 2i . Theorem 1. Considering the dynamic model of the MRM system in (1) and its state space representation in (9), the trajectory tracking error under the pHRI task is uniformly ultimately bounded (UUB) via the proposed control method in (35).Proof: Choose the following Lyapunov candidate functions as bellow:EQUATIONDerivation for V with respect to time, one can obtain:EQUATIONSubstituting ( 36) and (37) into (39) leads to:EQUATIONSubstituting the adaptive law (36) into (40), one can obtain:EQUATIONThen, we have:EQUATIONwhereEQUATION43) where ζ is matrix eigenvalue. In order to make ρ > 0, it is necessary to make ζ min (K g1 -1 2 I) > 0,EQUATIONwhere K e = 2 (C + V (0)) /ρ.The effectiveness of the proposed method is validated on a two degrees of freedom MRM experimental platform in this part. For the proposed adaptive fuzzy impedance control method, the inputs to the fuzzy logic are position error e i and velocity error ėi , the output to the fuzzy logic is u i1 . Then, the rule base consists of 5 m rules, as shown in Table 1 . Fig. 1 and Fig. 2 represent the position tracking curves. Fig. 3 represents the tracking error curves for the two joints, and it shows that the robot can accomplish the tracking tasks. Fig. 4 represents the control torque curves. Fig. 5 represents the fuzzy logic weights in the proposed adaptive fuzzy impedance control method. Fig. 6 shows the fuzzy membership functions. From the above experiments, it can be summarized that the interaction tasks can be successfully accomplished by using the proposed method. V. CONCLUSION This paper introduces an adaptive fuzzy impedance control approach based on intent recognition. Based on the establishment of the MRM dynamic model, we use FLSs for intent recognition, and let the obtained result as the desired trajectory for impedance control. Then, an adaptive fuzzy impedance controller to compensate for the model uncertainty while completing the tracking of the target is designed. MRM system is demonstrated to be UUB via Lyapunov theory. Verification of the validity of the proposed adaptive fuzzy impedance control method is accomplished by experiment. 
 
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Reviews: review: title: title: This article is very interesting and a good one
main_review: main_review: In this paper, an adaptive fuzzy impedance control method based on the estimation of human motion intention was proposed for MRMs with pHRI tasks. The obtained result is valuable and can be accepted if the following problems can be clarified. 
(1) In the introduction, the shortages of those relevant studies are suggested to be further summarized. 
(2) In the end of Section 1, the organization of this study is suggested to be summarized.
 (3) There exist several spelling and grammar errors. Please check carefully and further polish 
(4) In the simulation section, more analysis can be added to better explain the main results of this paper, that's not enough. 
(5) The future work is missing in the Conclusion.
title: title: Accept
main_review: main_review: In this paper, " Adaptive fuzzy impedance control of human-robot interaction modular robot manipulators based on human motion intention estimation", an adaptive fuzzy impedance control method based on human motion intention estimation is proposed. Firstly, the dynamic subsystem of MRM is established based on joint torque feedback (JTF) technology. Then, the fuzzy logic system (FLSs) is used to process the unknown human limb model. The article has clear logic and organization, but there are still some problems. My specific feedback is as follows :1) In the introduction part, the author's analysis of fuzzy impedance control is insufficient. 2) What are the advantages of the PHRI-based adaptive fuzzy impedance control method for MRM system compared with the traditional method?
title: title: accept
main_review: main_review: Comment: This paper proposes an adaptive fuzzy impedance control method based on the estimation of human motion intention for modular robot manipulators (MRMs) with physical human-robot interaction (pHRI) tasks. The theory is correct and can be accepted after responding the following comments.
(1) More comprehensive literature review is needed to clarify the research gap and research motivation.
(2) In the simulation section, more analysis can be added to better explain the main results of this paper, that's not enough.
(3) In the end of the conclusions, some research directions are suggested to be added.

Comments: title: This article is very interesting and a good one
comment: In this paper, an adaptive fuzzy impedance control method based on the estimation of human motion intention was proposed for MRMs with pHRI tasks. The obtained result is valuable and can be accepted if the following problems can be clarified.
(1)	In the introduction, the shortages of those relevant studies are suggested to be further summarized.
(2)	In the end of Section 1, the organization of this study is suggested to be summarized. 
(3)	There exist several spelling and grammar errors. Please check carefully and further polish
(4)	In the simulation section, more analysis can be added to better explain the main results of this paper, that's not enough.
(5)	The future work is missing in the Conclusion.