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 Abstract This 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 3 4 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 weihe ieee org 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 8 9 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 10 11 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 robot s 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 Rn n Cx x x Rn nand Gx x Rndenote the inertia matrix Coriolis and Centripetal matrix and gravity vector of the robot s 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 xri xdi 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 kci t 0 5 xri 1 5 1 0 500 511 5 xri 1 5 1 0 5 0 0 5 1 1 5 Fig 2 Soft saturation function As shown in Fig 2 where kci 1 and 0 9 it is obvious that the soft saturation ensures xriis twice differ entiable and constrained in task space The soft saturation function ensures the subjective mobile intention of robot xri never beyond the constrained boundary and the constraint is fi rstly implemented in path planing B Control Design with Position Constraint Based on shaped trajectory we consider constrained method in the view of control Undesired tracking perfor mance can make robot end effector out of constrained region and generate collisions with surroundings In our controller IBLF is involved to ensure position of end effector in a constrained task space For facilitating control design we defi ne x1 x x2 x The robot s dynamic model 1 can be rewritten as state space forms x1 x2 x2 Mx x1 1 f fe Gx x1 Cx x1 x2 x2 6 we defi ne error variables as follows z1 x1 xr z2 x2 7 where z1 z11 z12 z1n T z2 z21 z22 z2n T and 1 2 n Tare virtual control variable vectors One of control objective is to maintain position of robot end effector x1constrained in a limited region namely x1i 0 Substituting 12 and 16 into 15 we can get V2 n i 1 kiz2 1ik2ci k2 ci x21i zT 2K2z2 n i 1 z1i 0 kik2 ci k2 ci xri 2 d zT 2K2z2 2V2 17 where 2 is a constant defi ned as 2 min min i 1 2 n ki 2 min K2 max Mx x1 18 To ensure 2 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 robot s 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 c1 x211 z12k2 c2 k2 c2 x212 z1nk2 cn k2 cn x21n 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 oip Tis the center of the receptive fi eld and i i1 i2 ip Tis the Gaussian functions width l is the number of NN nodes and p is the dimension of Z Z xT 1 xT2 T T T are the input variables of the NNs The adaptive updating laws is designed as follows Wi i Si Z z2i i Wi 21 where i are positive defi nite symmetric matrices and i are small positive constants WTS Z is used to estimate W TS Z and W T S Z is defi ned as follows W TS Z Gx x1 Cx x1 x2 Mx x1 22 where is the approximation error and W are 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 W is 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 W TS Z n i 1 Wi T Si Z z2i i Wi 25 7570 since inequality relations z2T 1 2z2 Tz2 1 2 2 i Wi T Wi i 2 Wi 2 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 Wi 2 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 Wi 2 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 diag 5 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 tasks 13 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 602 609 2017 2 Z Li B Huang A Ajoudani C Yang C Y Su and A Bicchi Asymmetric bimanual control of dual arm exoskeletons for human cooperative manipulations IEEE Transactions on Robotics vol 34 no 1 pp 264 271 2018 3 C Ott R Mukherjee and Y Nakamura Unifi ed impedance and admittance control in Robotics and Automation ICRA 2010 IEEE International Conference on pp 554 561 IEEE 2010 4 K Hashtrudi Zaad and S E Salcudean Analysis of control architec tures for teleoperation systems with impedance admittance master and slave manipulators The International Journal of Robotics Research vol 20 no 6 pp 419 445 2001 5 F Ficuciel