IROS2019国际学术会议论文集0510

Adaptive Neural Admittance Control for Collision Avoidance in Human-Robot Collaborative Tasks Xinbo Yu1, Student Member, IEEE, Wei He1, Senior Member, IEEE, Chengqian Xue1, Bin Li1, Long Cheng2, Senior Member, IEEE and Chenguang Yang3, Senior Member, IEEE AbstractThis paper proposed an adaptive neural admit- tance control strategy for collision avoidance in human-robot collaborative tasks. In order to ensure that the robot end- effector can avoid collisions with surroundings, robot should be operated compliantly by human within a constrained task space. An impedance model and a soft saturation function are employed to generate a differentiable reference trajectory. Then, adaptive neural network control with position constraint, based on integral barrier Lyapunov function (IBLF), is designed to achieve precise tracking while guaranteeing constrained satisfaction. Utilizing Lyapunov stability principles, we prove that semi-globally uniformly bounded stability is guaranteed for all states of the closed-loop system. At last, the effectiveness of the proposed algorithm is verifi ed on a Baxter robot experimental platform. Collisions with surroundings can be avoided in human-robot collaborative tasks. I. INTRODUCTION There exists a vast interest in scenarios where human and robot perform collaborative tasks 1. Human-in-loop control strategies are much more complicated than conventional control strategies for only robots. Typical applications in human-robot interaction (HRI) include rehabilitation robots which are used in patient recovery 2. They should not only guide the motion of patients but also comply with forces exerted by patients. Impedance control is widely used to regulate interactive forces in HRI. It expresses relationships between inter- action forces and state errors in the form of prescribed impedance model. There are two common ways of imple- menting impedance control, which are impedance control and admittance control in literatures 34. In 5, an impedance control method is proposed to enhance the performance in 1X. Yu, W. He, C. Xue and B. Li are with the School of Automation and Electrical Engineering, Institute of Artifi cial Intelligence, University of Science and Technology Beijing, Beijing 100083, China. The corresponding author is W. He, Email: 2L. Cheng is with the State Key Laboratory of Management and Con- trol for Complex Systems, Institute of Automation, Chinese Academy of Sciences, Beijing 100190, China, and also with the School of Artifi cial Intelligence, University of the Chinese Academy of Sciences, Beijing 100049, China. 3C. Yang is with the Bristol Robotics Laboratory, University of the West of England, Bristol BS16 1QY, U.K. This work was supported by the National Natural Science Foundation of China under Grant No. 61873298, the Beijing Natural Science Foundation under Grant No. 417204, Engineering and Physical Sciences Research Council (EPSRC) under Grant EP/S001913 and the Innovation Talents Foundation of University of Science and Technology Beijing. HRI by combining Cartesian impedance modulation and redundancy resolution. In following years, they propose a suitable modulation strategy for variable impedance param- eter tuning 6. In 7, uncertainties in robotic dynamics are stressed in adaptive impedance controller design with input saturation, neural networks (NNs) are used to estimate system unknown parameters. Various adaptive learning meth- ods are proposed to solve uncertainties or disturbances in interactive control design 89. Although impedance control can improve interactive performances of HRI notably, it can not guarantee safety and avoid collisions with surroundings. Recent years, barrier Lyapunov function (BLF) is proposed to solve issues on constraints in the view of control 1011. Many forms of BLF are proposed in different situations. Different from other BLFs, integral barrier Lyapunov func- tion (IBLF) can directly constrain system states instead of constraining error signals indirectly, and avoid the violation of states without the requirement of initial values 12. How- ever, they are not straightforward to extend existing methods in HRI. On the other hand, undesired robot trajectory can lead to collisions of the robot with environment. The main contribution of this paper is a framework in HRI for avoiding collisions in the view of both trajectory shaping and controller design. A reference trajectory is shaped fi rstly and adaptive neural admittance control is proposed for im- proving tracking accuracy and interactive compliance. IBLF is involved in controller design to constrain the position of robot end-effector in a constrained task space which leads to collision avoidance with surroundings. The remainder of the paper is structured as follows: In Sec. II, problem is formulated, Sec. III presents a collision avoidance method involving trajectory shaping and control design, Sec. IV evaluates our proposed approach, Sec. V concludes our work and considers our future work. II. PROBLEMFORMULATION We consider a human-robot collaborative scenario shown in Fig. 1. The motion of the robot end-effector needs to comply with human in a constrained task space and avoid collisions with environmental obstacles. Fistly we consider robots dynamic model in task space as follow: Mx(x) x + Cx(x, x) x + Gx(x) = f fe(1) 2019 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS) Macau, China, November 4-8, 2019 978-1-7281-4003-2/19/$31.00 2019 IEEE7568 Constrained space HumanRobot Interaction force Obstacle Collision avoidance Fig. 1: A human-robot collaborative scenario in a constrained task space. where x, x, x Rndenote the position, velocity and acceleration vectors in task space, respectively; Mx(x) Rnn,Cx(x, x) Rnnand Gx(x) Rndenote the inertia matrix, Coriolis and Centripetal matrix and gravity vector of the robots dynamic model in task space, respectively; fe Rndenotes interactive forces measured by force sensors, when they come to zero it means no contact between robot and human or environment, f Rndenotes the control input vector to robot. III. COLLISIONAVOIDANCE A. Constrained Trajectory Shaping Firstly we shape the reference trajectory to ensure robot end-effector within the constrained space subjectively. To compute reference trajectory xr , we fi rst consider the desired impedance model in task space as follows: Md x + Dd x + Kd x = fe(2) where x = xr xd, and xris an intermediate variable vector, xdis the desired trajectory vector. Md,Dd,Kdare the desired stiffness, damper and inertia matrices of the desired impedance model, respectively. xrcan be obtained when Kd,Dd,Mdand xdare available and fecan be online measured or transformed by torque sensory information. For simplicity, we decompose the impedance model into each dimension in task space and xrican be obtained from the impedance model equation Kmi xi+ Kdi xi+ Kki xi= feii = 1,2,.,n(3) where Kmi, Kdiand Kkiare positive constants to guarantee the desired impedance at the end-effector and xi= xrixdi. We obtain xriby a soft saturation function as follows: xri= xriif | xri| kci i(1 e( xri+kci)/i) kciif xri kci (4) where i = 1,2,.,n and i= (1 )kci, 0 1 is a constant selected to satisfy |xdi(t)| 0, the control parameters kiand the positive gain matrix K2 should be satisfi ed min(ki) 0,min(K2) 0 Hence z1and z2will converge to zero and x1can remain in the constrained task space. To address uncertainties in robots dynamic model Mx(x1), Cx(x1,x2) and Gx(x1), the control input f based on dynamic model cannot be designed in real systems for uncertainties. To solve this issue, NNs are utilized to approximate in robot. An adaptive neural network control input is proposed as follows: f = z11k2 c1 k2 c1x211 z12k2 c2 k2 c2x212 . . . z1nk2 cn k2 cnx21n K2z2+ fe+ WTS(Z)(19) where W are the actual weights of NNs and S(Z) = s1(Z),s2(Z),.,sl(Z) is the regressor vector and si(Z) is the Gaussian radial basis functions as follows: si(Z) = exp(Z oi) T(Z oi) 2 i (20) where oi= oi1,oi2,.,oipTis the center of the receptive fi eld and i= i1,i2,.,ipTis the Gaussian functions width. l is the number of NN nodes and p is the dimension of Z. Z = xT 1,xT2,T, TT are the input variables of the NNs. The adaptive updating laws is designed as follows: Wi= i ( Si(Z)z2i+ iWi ) (21) where i are positive defi nite symmetric matrices and i are small positive constants. WTS(Z) is used to estimate WTS(Z) and WT S(Z) is defi ned as follows: WTS(Z) = Gx(x1) + Cx(x1,x2) + Mx(x1) (22) where is the approximation error and Ware optimal weights of NNs. To prove the stability of the close-loop system, we choose a new IBLF candidate as follows: V3= V2+ 1 2 n i=1 Wi T 1 i Wi(23) where W= W Wis the error of weights, Then differentiating V3as follows: V3= n i=1 kiz2 1ik2ci k2 ci x21i + n i=1 z1iz2ik2 ci k2 ci x21i + zT 2(f fe Gx Cxx2) + n i=1 Wi T 1 i Wi(24) Substituting (19) into V3, we obtain V3= n i=1 kiz2 1ik2ci k2 ci x21i zT 2K2z2+ z T 2( WTS(Z) WTS(Z) ) + n i=1 Wi T (Si(Z)z2i+ iWi) (25) 7570 since inequality relations: z2T 1 2z2 Tz2 + 1 2 2 i Wi T Wi i 2 (Wi2 Wi 2) where is the upper limit of error. We further have V3 n i=1 z1i 0 kik2 ci k2 ci ( + x1i)2 d zT 2(K2 1 2I)z2 i 2 n i=1 Wi 2 + i 2 n i=1 Wi2+ 1 2 2 3V3+ C3(26) where 3= min ( min i=1,2,.,n(ki), 2(min(K2 1 2I) max(Mx(x1) , min i=1,2,.,n( i max(1 i ) ) ) C3= i 2 n i=1 Wi2+ 1 2 2 (27) To ensure 3 0, the gain parameters ki, the positive gain matrix K2and ishould be chosen to satisfy: min(ki) 0, min(K2 1 2I) 0, min(i) 0 So z1, z2and Wiare semiglobally uniformly bounded and x1 can remain in the predefi ned constrained space. The closed-loop error signals will remain within the compact sets z1, z2and W , respectively and defi ned by z1= z1 Rn| |z1i| H,i = 1,2,.,n (28) z2= z2 Rn| z2 H min(Mx(x1) (29) W = W Rn| W H min(1) (30) where H = 2(V3(0) + C3/3) with C3and 3are give in (27). IV. EXPERIMENTAL EVALUATION A. Experiment Setup The proposed method is evaluated in a HRI collaborative task. Baxter robot is employed to cooperate with human under our proposed algorithm. Robot end-effector carries the manipulated object and human interacts with robot arm to guide it to a target position. Baxter robot has two arms, each of them has 7 fl exible joints with advanced sensors, including position, velocity and torque sensors. The experimental plat- form is operated based on robotic operating system (ROS). In this part, we evaluate our proposed method through two cases. Firstly we consider constraining the position of end- effector in a predefi ned 3-dimension task space in HRI; in next case, we consider a scenario that robot avoids collisions with construct surroundings in one dimension. B. Case 1: Constrained and Tracking Performance in HRI Reference trajectory Desired trajectory Constrained space Fig. 3: Case 1: constraining the position of end-effector in a predefi ned 3-dimension In this part, we apply our proposed controller on Bax- ter robot, and the scenario is shown in Fig. 3. Ini- tially, robot end-effector keeps at the origin x(0)= 0.13(m),0.4(m),0.74(m). The control gains are de- signed as k1= 17.7,k2= 15,k3= 22 and K2= diag5.1,12,4.5. The original desired trajectory in task space is described by xdx(t) = (0.15sin(50/t) 0.1)(m) xdy(t) = (0.2cos(50/t) 0.6)(m) xdz(t) = (0.2sin(50/t) + 0.75)(m)(31) Then, the reference trajectory xrcan be obtained by desired impedance model and soft saturation function. Parameters of impedance model are design as kmi= 1, kdi= 10 and kki= 30,i = 1,2,3. The parameters of soft saturation function is design as = 0.95 and it is obvious that kdi= max|xdi(t)|. Position constraints are set as kc1= 0.3, kc2= 1.2 and kc3= 1, respectively. The centers of NN nodes are designed between the upper and lower bounds of the position and speed limits evenly, the number of NN node is set as 28, and the initial value of NN weight is set as 0. iare selected as 100I, and i=0.002. The tracking performances in X-axis, Y-axis and Z-axis are shown in Fig. 4, Fig. 6 and Fig. 8 where the green, red, blue and black lines represent the actual, reference, desired trajectories and position constraint, respectively. We can see that tracking errors in three axes converge to zero indicated from Fig. 5, Fig. 7 and Fig. 9, correspondingly. The position tracking performance in task space is shown as Fig. 10. It is obvious that the reference trajectory xrvaries with interaction force. Above results express that our proposed controller ensures robot end-effector tracking the reference trajectory in real time within the constrained task space. As shown in Fig. 11, interaction forces in three axes are in proper values which will not bring uncomfortable feelings to human operator. On the basis of results, we can give a summary that the proposed controller can not only ensure the end-effector of Baxter robot tracking the reference trajectory 7571 in good performance but also complying with human and within the constrained task space. Fig. 4: Tracking trajectory and constraint in X-axis. Fig. 5: Tracking error in X-axis. Fig. 6: Tracking trajectory and constraint in Y-axis. C. Case 2: Collision Avoidance In this part, object is moved towards bounds by robot guided by human in one dimension, there exists obstacle located in the bound shown in Fig. 12. We employ three human subjects (A, B, C) to test popularity of our proposed method. Each of them performs the same task in a similar condition. X A, X B and X C in Fig. 13 denote positions of robot end-effector operated by human subjects A, B and C. We can see that collisions can be avoided under our pro- posed method. We also compared our proposed method with controller design without position constraints and without trajectory shaping in same situations. Seen from Fig. 14, we Fig. 7: Tracking error in Y-axis. Fig. 8: Tracking trajectory and constraint in Z-axis. Fig. 9: Tracking error in Z-axis. Fig. 10: Tracking trajectory in task space. 7572 Fig. 11: Interaction forces. Fig. 12: Case 2: collision avoidance. found that collisions with obstacle are generated when robot moves towards bounds no matter without position constraints or without trajectory shaping. A video of the experiment are available in attachment supplement. V. CONCLUSIONS AND FUTURE WORK In this paper, a neural admittance control strategy has been developed to avoid collisions in HRI. Robot under our proposed controller has shown great tracking performance considering unknown robotic dynamics. An impedance mod- el and a soft saturation function have been utilized to shape reference trajectory in the constrained task space. IBLF has been involved in controller to ensure position constraining within the constrained task space. The validity of the pro- posed strategy method has been illustrated through human- robot collaborative tasks. Our future work will consider more complex human-robot collaborative tasks13, such as co- carrying task, sawing task and so on. and we will also focus Fig. 13: Collision avoidance tests in human subjects A, B and C. Fig. 14: Comparative controllers with our proposed method, without position constraints and without trajectory shaping. on controller design involving velocity constraints to ensure safe velocity in HRI tasks. REFERENCES 1 W. He, Z. Li, and C. P. Chen, “A survey of human-centered intelligent robots: issues and challenges,” IEEE/CAA Journal of Automatica Sinica, vol. 4, no. 4, pp. 602609, 2017. 2 Z. Li, B. Huang, A. Ajoudani, C. Yang, C.-Y. Su, and A. 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