IROS2019国际学术会议论文集 2564

A Mechanical Approach to Suppress the Oscillation of a Long Continuum Robot Flying with Water Jets Tomoka Yamaguchi1 Yuichi Ambe2 Hisato Ando1 Masashi Konyo1 Kenjiro Tadakuma1 Shigenao Maruyama3and Satoshi Tadokoro1 Abstract Flexible continuum robots exhibit a strong poten tial for approaching narrow and intricate spaces However such long fl exible bodies often experience oscillations making them unstable To enhance their performance in order to realize rapid and precise movements unnecessary vibrations should be suppressed The authors have proposed a new type of continuum robot aimed for fi refi ghting this robot Dragon Firefi ghter DFF can fl y using water jets The DFF suffers from the same problem of body oscillation In particular a more challenging issue for the DFF is the use of limited number of actuators owing to the constraints of weight and water fl ow Discrete locations of the actuators on the long body of a robot can generate uncontrollable resonant modes This paper proposes a mechanical approach to suppress the oscillation passively without actuation control The proposed mechanism is composed of wires threaded along the body and connected to rotary dampers to restrict the deformation of the body First a numerical model to simulate the oscillation and damping behavior was reported A basic experiment with a 1 m long fl exible tube shows that the damping mechanism suppresses the vibration appropriately which also corresponds well with the simulation Second a stability analysis of the simulation of the fl ying motion shows that the passive damping mechanism can improve the stability with the convergence time becoming approximately 2 4 times shorter than that in the case without the mechanism Finally we apply the damping mechanism to a 3 6 m long fl ying robot The demonstration shows that the robot can fl oat stably and that the damping mechanism works correctly I INTRODUCTION Flexible continuum robots have a strong potential for exploring intricate spaces by changing their body shapes In recent years several types of continuum robots have been studied Tendon based robots that deform through a fl exible backbone by pulling wires from the end of their body were developed by OC Robotics 1 NASA 2 and others 3 Many types of backbone structures have been recently developed such as those that use extensible sections 4 gravity compensation 5 and stiffening capa bility with a layer jamming method 6 A continuum robot composed of fl exible concentric tubes which can rotate and This research was partially supported by Japan Science and Technology Agency Impulsing Paradigm Change Through Disruptive Technologies Program ImPACT Tough Robotics Challenge and by JSPS KAKENHI Grant Number JP19H00748 1The authors are with the Graduate School of Information Sciences Tohoku University Japanyamaguchi tomoka ando hisato konyo tadakuma tadokoro rm is tohoku ac jp 2Y Ambe is with the Graduate School of Engineering Tohoku University Japanambe rm is tohoku ac jp 3S Maruyama is with the National Institute of Technology Hachinohe College Japanmaruyama ifs tohoku ac jp x y z Fig 1 A prototype of the Dragon Firefi ghter translate with respect to each other was also developed for minimally invasive surgery 7 A continuum robot actuated by distributed pneumatic actuators has also been widely developed 8 9 A multi link fl ying robot incorporating a self weight compensation mechanism has also been recently developed 10 11 The body vibration of continuum robots must be sup pressed for a rapid and precise movement Because con tinuum robots have long and fl exible bodies the vibration easily occurs Thus studies on dynamic modelling and controls of continuum robots constitute a hot topic these days As examples of dynamic controls a model based dy namic controller is proposed for the Festo s Bionic Handling Assistant actuated by several pneumatic chambers 12 A planar soft robot with pneumatic actuators is controlled by dynamic feedback controllers derived from the strategy used in multi link robots 13 Nonlinear control strategies for extensible continuum manipulators pneumatically actuated are also proposed 14 15 For a tendon based robot a closed loop dynamic control by using learning method is proposed 16 Gravagne et al 17 applied a damping effect on the wire displacement by using a motor at the base to suppress the body vibration The continuum robot Dragon Firefi ghter DFF 18 em ployed in this work has been developed by the authors This robot is actuated by water jets and here the vibration also needs to be suppressed The DFF has several nozzles on its fl exible body inside which pressurized water fl ows this is different from conventional continuum robots The nozzles release water jets and control their direction to generate a translational net force for fl ying The goal of our robot is to fl y directly into the fi re sources inside buildings for extinguishing fi re Thus this robot needs to move rapidly and the body vibration must be suppressed There are some other continuum robots actuated by fl uid jets A long continuum robot whose head is controlled by three water jets is proposed for inspections of nuclear power plants 19 A concept of long fl ying hose for fi refi ghting is proposed with a IEEE Robotics and Automation Letters RAL paper presented at the 2019 IEEE RSJ International Conference on Intelligent Robots and Systems IROS Macau China November 4 8 2019 Copyright 2019 IEEE nozzle design 20 We have also developed an active scope camera whose head is controlled by direction control of an air jet 21 We believe that vibration suppression is also required for these robots A challenging issue in suppressing the body vibration is the use of a limited number of actuators owing to the constraints of the weight and water fl ow Discrete positioning of the nozzles on the long body can generate uncontrollable resonant modes However the number of nozzles should be minimized because the nozzle that installs motors is heavy and the pump ability is limited The purpose of this study is to develop a mechanical approach to suppress the oscillation of a continuum robot driven by water jets Specifi cally in this study we fi rst propose a passive tendon mechanism for the robot The mechanism is simple and light weight because only wires and fi xations are installed on the robot body For numer ical simulation a robot model is developed and a 1 m long prototype of a fl exible tube with the above mentioned mechanism is designed We conduct basic experiments to validate that the developed mechanism can suppress the vibration of the tube and that the model can extract the tendency of the experiments Additionally by performing linear stability analysis by simulation we confi rm that the mechanism can improve the stability of the fl ying motion Finally we implement the mechanism in the newly developed DFF 3 6 m in length and demonstrate that the mechanism works appropriately with the actual fl ying DFF The contributions of this work are described as follows 1 We propose a simple passive vibration damping mechanism for a robot actuated by the reaction forces of jets The mech anism is very light weight because only wires and fi xations are installed on the robot body The basic experiment with the 1 m long prototype tube shows that the mechanism works appropriately and suppresses the vibration 2 We validate the effectiveness of the proposed damping mechanism for a jet driven fl ying continuum robot by using a dynamic simulation The simulation model is designed by adding the proposed mechanism based on 18 22 The validity of the model is examined by basic experiments The stability analysis performed with the simulation of the fl ying motion confi rms that the mechanism can improve the stability of the fl ying motion the time to convergence is nearly 2 4 times shorter than that of the case without the mechanism Finally we demonstrate that the mechanism also works suitably with the newly developed DFF 3 6 m length It exemplifi es the effectiveness of the vibration damping mechanism Although the mechanism itself is a hardware implementa tion of the controller proposed in 17 the targeted robot is totally different It is actuated by thrust forces rather than cables To the best of our knowledge this is the fi rst study validating the effectiveness of the proposed passive damping mechanism for jet driven fl ying continuum robots In addition our passive mechanism has some advantages explained in Section III A Fig 2 Body oscillation observed in the prototype robot The body vibrates whereas the head position is practically unchanged Head position m Head pose deg Time s Time s x y z x y z AB Fig 3 Time response of the A head position and B head posture II PROBLEM FORMULATION The prototype of the DFF is composed of a nozzle module on the head and a 1 8 m long fl exible body as shown in Fig 1 18 High pressurized water fl ows from the base to the nozzle module through a hose inside the body The nozzle module ejects four water jets to generate a net force for fl ying Note that each water jet generates a reaction force QU where Q and U denote the density fl ow rate and velocity of water jet at the nozzle outlet respectively The net force of the nozzle module can be controlled by adjusting the direction of the water jets Inertial measurement units IMU are distributed on the body to estimate the shape of the robot on line The detailed information can be found in our previous work 18 To make the robot fl y stably we previously proposed a control method for the net force and confi rmed that the robot could fl y stably 18 The control method controls net force f f f R3as f f f F F F Dd r r r 1 where F F F R3 r r r R3are the constant force vector and head velocity respectively In this study the matrix Dd R3 3is defi ned as Dd diag s s s and the element s 0 represents the coeffi cient of derivative term All the vectors are defi ned in the inertial frame as displayed in Fig 1 The fi rst term F F F determines the equilibrium shape of the robot The second term is a derivative term for the head velocity to achieve better stability With this controller we confi rmed that the robot could fl y stably 18 However because the system was underactuated the method did not well suppress the body oscillation in which the head position remained unchanged such as the oscillation in which the head and base were the nodes In this case the feedback term of 1 does not function at all Thus the oscillation converges gradually by dissipating the energy with viscous damping of the body Fig 4 Proposed mechanism to damp the vibration A wire is threaded through the guides along both the body sides to the head module At the base of the robot the wire is turned back by a pulley which transmits the rotation to a rotary damper and potentiometer Such an oscillation is also observed in the prototype robot Figures 2 and 3A and B show snapshots of the oscillation time response of the head position and head posture respectively In this oscillation the head and base are the nodes as displayed in Fig 2 The head position does not change signifi cantly but the head posture particularly pitch angle oscillates periodically as shown in Fig 3 Further worsening the scenario the oscillation does not seem to converge in this case because the net force is affected by the periodic noise from the water pump III PASSIVE DAMPING MECHANISM AND THE MODEL A Passive damping mechanism A passive damping mechanism is proposed which is shown in Fig 4 Figure 4 shows the side view of the prototype robot with a single nozzle module on the head A wire is threaded through the guides along both the body sides and both ends of the wire are connected to the head module At the base of the robot the wire is turned back by a pulley which transmits the rotation to a rotary damper and potentiometer As the robot undergoes a change in the shape the lengths of both the body sides vary Because the wire is threaded along the body sides the wire rotates the rotary damper by the pulley which damps the body oscillation The same mechanism acts on the robot rotating 90 deg to damp the horizontal oscillation The proposed mechanism has two advantages First the mechanism is very simple and easy to implement Because the robot is actuated by jets the mechanism can be passive Compared with the damping mechanism actuated by motors described in 17 a passive mechanism omits the requirement of a powerful motor against the heavy body and complex controls Second the mechanism applied to the body is very lightweight Only wires and wire guides are installed on it Although it would be possible to suppress the oscillation by adding nozzle modules or numerous nozzles for control the weight of the robot would increase and a large amount of water would be required to fl oat the body B Model To evaluate the damping ability of the mechanism we model the robot and mechanism Based on the previous model 18 we model the robot by multiple links connected by elastic joints To focus on the pitch oscillation as depicted in Fig 3 we design the model in a two dimensional space as shown in Fig 5 The net force of the nozzle module is modelled as an external force applied on the center of mass COM of the link A wire is threaded through the guides Fig 5 Model of the Dragon Firefi ghter with the proposed mechanism located on the middle of the links and is folded back at the base We assume that the wire is suffi ciently tensed to not slack Because the robot does not deform signifi cantly we ignore the friction force between the wire and wire guides for simplicity Under the above assumptions the model consists of N rigid links mass mi 0 inertia moment Ii 0 length l 0 connected by elastic joints spring constant k damper constant d in the O xy plane The head link is link 1 For link i we denote the pitch angle by i generalized coordinates in this model joint angle by i COM position the center of the link by xi yi and external force on the COM by fxi fyi Because the body has a bending tendency we set the neutral joint angle for the joint spring as oi The gravity acceleration width of the wire guides and radius rotation angle and damper coeffi cient of the rotary damper are set as g 2rg rp and c respectively From here for simplifi cation of the derivation we defi ne the vectors x x x y y y m m m o f f fx and f f fy RN 1whose elements are xi yi i mi i oi fxi and fyi i 1 N respectively We derive the equation of motion with reference to 22 The kinetic energy can be written as the summation of the translational kinetic energies x and y directions and rotational kinetic energy of all links T 1 2 x x x TM x x x y y yTM y y y TJ 2 where x x x lAS y y y lAC A 1 21 1 01 2 1 00 1 2 S diag sin 1 sin N M diag m m m C diag cos 1 cos N J diag I I I Potential energy V can be written as the summation of elastic and gravitational potential energies V 1 2k R o T R o lgm m mTAsin 3 where sin sin 1 sin N Tand R is an N N matrix that satisfi es R Then Lagrangian L T V can be derived Because the wire is suffi ciently tensed not to slack rotation angle of the rotary damper is equal to half of the length difference between the parts of the wire on both sides 2rg rp sin N 2 sin N 1 2 sin 1 2 4 The rotational velocity of the rotary damper is derived by differentiating 4 rg rp Tb b b 5 where b b b cos 1 2 2 cos 2 3 2 cos 1 2 2 cos N 2 cos N 1 N 2 A dissipation function can be derived as the summation of dissipations induced by joint dampers coeffi cient c and the rotary damper at the root coeffi cient d U 1 2d T 1 2 c 2 6 1 2d TRTR 1 2c rg rp 2 Tb b bb b bT 7 Virtual work W that is done by external force f f fx f f fycan be described by using virtual displacement W l f f fT xAS l f f f T yAC 8 Then the Euler Lagrangian equation can be derived as d dt L L U l f f fT xAS l f f f T yAC 9 By solving 9 the equation of motion is derived as H D kRT R o dRTR c rg rp 2B B BB B BT lgC ATm m m 10 lS ATf f fx lC ATf f fy where H S MS C MC J D ml2 S ATAC C ATAS diag M l2ATMA 11 Note that the matrix H is positive defi nite because the kinetic energy fulfi ls the relation 2T TH which means that the matrix is invertible C Dimensionless model To reduce the parameters to investigate m l and l g are used as the characteristic mass length and time scale of the model respectively The variables are made dimensionless as m i mi m I i Ii ml2 k k lmg d d lm lg f x y fx y mg l g o o t t g l r g rg l r p rp l c c lm lg Then the dimensionless equation of motion is derived by dividing 10 by lmg TABLE I Physical parameters for the preliminary experiments ElementValueElementValueElementValue l m 0 200m 1 5 1 0 o1 0 179 m kg 0 0420k 50 4 o2 0 166 g m s2 9 80d 16 0 o3 0 00980 I 1 5 0 0858r g 0 188 o4 0 0231 N5r p0 175 o5 0 00 0102030 0 6 0 4 0 2 0 0 2 AB Wire Damper Wire guide Wire 1 m IMU1 Peg IMU2 IMU3 IMU4 IMU5 Fig 6 A Test bed for the preliminary experiments B Time response of 1in the experiment and simulation using the estimated parameters IV PRELIMINARY EXPERIMENTS To evaluate the mechanism and model a fl exible tube with the mechanism is developed The damping performance is evaluated by experiments and simulations A Test bed The test bed developed is shown in Fig 6A The body is composed of a 1 m long fl exible corrugate tube with a diameter of 48 mm NGN 40B AVC Corporation of Japan The wire guides are located on the body at intervals of 100 mm Five IMU sensors MPU 9250 InvenSense are located on the body at intervals of 200 mm from the tip and are sensed with 2 kHz At the base of the body a pulley transmits the rotation to a rotary damper and potentiometer RV30YN20S B101 Tokyo Cosmos Electric Corporation A wire threads from the upside head through the guides and pulley to the downside head To adjust the tension of the wire tuning pegs are installed on the head To constrain the body movement mainly on the sagittal plane the left and right axial lengths between the guides are constrained to be the same by using b