Self Resonance Cancellation for Joint Torque Control Using Torque Sensor

Transcription

1 IEEJ International Workhop on ening, Actuation, Motion Control, and Optimization elf onance Cancellation for Joint Torque Control Uing Torque enor Akiyuki Haegawa tudent Member, Hirohi Fujimoto enior Member Taro Takahahi Member Demand for indutrial robot in collaboration with people and nuring robot i increaing. In order to realize afe contact between robot and people, force control i required. We previouly propoed elf onance Cancellation (RC), poition control method for two-inertial ytem. In thi paper, we applied RC to joint torque control by uing torque enor. Conventional RC ue motor-ide and load-ide encoder. Propoed RC ue torque enor on haft between motor-ide and load-ide. Propoed controller can be deigned without plant parameter. The relationhip between the two control parameter and the control performance i clear. imulation and experimental reult how the effectivene of the propoed method. eyword: two-inertial ytem, vibration uppreion control, torque enor, elf reonance cancellation, humanoid robot, joint torque. Introduction Along with the development of robotic engineering, indutrial robot that collaborate with human being are required (), in the welfare field, nuring care robot are being put into practical ue (). Robot that work in coexitence with uch people are required to control force o a not to harm people. In thi paper, torque tranmitted by the tranmiion mechanim from the drive motor to the load ide i called joint torque. A joint of a humanoid robot uing an electric motor i not directly connected to a load by a motor, but i connected to a load via a timing belt or a gear. The belt drive improve the degree of freedom of the motor arrangement and the gear make it poible to obtain a large output torque with a mall motor. Although both are general mechanim, the rigidity of belt and gear i low. In order to improve the control performance of the entire leg, it i neceary to control a ingle joint in a high frequency region. However, an elatic body uch a a belt and a gear in a joint caue reonance vibration and retrict the control band, therefore reonance uppreion ha become a ubject of robot joint control. In order to control the joint torque, it i neceary to etimate the joint torque with a reaction force oberver or meaure it with a torque enor. In the pat, ince the rigidity of the torque enor itelf and the enor band were low and it wa difficult to ue it for feedback control, tudy uing a reaction force oberver ha been conducted. In the cae of uing The Univerity of Tokyo 5--5, ahiwanoha, ahiwa, Chiba, Japan Phone: haegawa6@hflab.k.u-tokyo.ac.jp Advanced Technology Engineering Department,Partner Robot Diviion, Toyota Motor Corporation --8, oraku, Bunkyo-ku, Tokyo -87, Japan taro takahahi@mail.toyota.co.jp the reaction force oberver, ince the etimated external force include diturbance uch a friction, much tudy on friction compenation ha been done (). However, in recent year, enor with high rigidity and high reolution have been developed, making it poible to ue enor value for feedback control, (5) (6). In the future, it i expected that the number of device having enor for force control will increae. In thi paper, we deign the propoed method baed on elf onance Cancellation control (RC) () which ha been tudied a a poition control of two-inertial ytem in thi laboratory. RC ha the advantage of implifying the deign of the control parameter and i compatible with the advantage of the torque enor which enable imple joint torque feedback. Combining RC and torque enor make it poible to deign a imple joint torque control ytem leaving the advantage of mutual implicity, and deigned a highly practical control ytem in indutry. The propoed method for joint torque control make it poible to intuitively adjut the control performance by tuning two parameter.. Experiment etup A ingle joint of a robot can be modeled a a low dimenional model into two-inertial ytem. Therefore, a twoinertial motor bench wa ued a an experimental machine for baic experiment. The Meaured frequency characteritic of the two-inertial motor bench are hown in Fig.. Meaurement of frequency characteritic wa carried out with a method uing multi-ine wave (7). The parameter obtained by fitting the model from the meaurement reult i hown in Tab... Propoed Joint torque control by elf reonance cancellation control uing torque enor Demand for joint torque control in dometic robot and indutrial robot i increaing o that joint torque control enc 7 The Intitute of Electrical Engineer of Japan.

2 elf onance Cancellation for Joint Torque Control Uing Torque enor (Akiyuki Haegawa et al.) T L Plant J L L J L J RC T RC J M M J M J RC Fig.. Block diagram of RC () Fig.. Photo of two-inertial ytem motor bench ha no reonance, therefore feedback of θ RC make higher control frequency. Phae [deg] Motor-ide - Fig.. bench Phae [deg] Load-ide -5 Meaured frequency characteritic of motor Table. Fitting parameter of two-inertial motor benche J M Motor-ide moment of inertia.9 kgm D M Motor-ide vicoity friction coefficient.8 Nm/rad Torional rigidity coefficient 9.67 N/m J L Load-ide moment of inertia.57 kgm D L Load-ide vicoity friction coefficient.86 Nm/rad able advanced work and afe collaboration work with human. In conideration of uch background, in thi chapter, we propoe joint torque control with reference to Frequency eparation elf-onant Cancellation Control (F-RC) (8) which i one of the two-inertial poition control method uing RC Propoe a ytem.. Principle of elf onance Cancellation (RC) () In order to explain F-RC, the principle of RC will be decribed firt. Block diagram of RC i hown in Fig.. RC calculate virtual angle θ RC from driving ide angle and load ide angle. θ RC i denoted by (), and θ RC i the center of gravity of the driving ide angle and the load ide angle. θ RC θ RC = J Mθ M J Lθ L. () J M J L J M J L θ RC i denoted by (), becaue the equation of motion on the driving ide and the load ide in the inertial ytem i denoted by (), (). J M θ M = (θ M θ L ), () J L θ L = (θ M θ L ), () θ RC = J M θ M J L θ L J M J L J L J L =. () J M J L The tranfer function from input torque to θ RC i hown in (5). ince it i a rigid body model without reonance, the deign of the controller become very imple. θ RC = (J M J L ) =. (5) J RC However, even if θ RC i controlled, the load ide angle deviate from the command value. Alo, ince θ RC neglect the reonance component, there i a problem that vibration uppreion performance can not be improved.. Principle of Frequency eparation RC (F-RC) (8) F-RC i a control method that made it poible to intuitively adjut the Nyquit diagram utilizing the fact that RC can create virtual angle which ha no reonance. The control ytem of F-RC i hown in Fig.5. The virtual angle θ L i denoted in (6). θ L = ω c ω c θ L = ω c ω c θ L θ α ω c {αθ L ( α)θ M }. (6) ω c ω c i a firt order Low Pa FiIter(LPF) i a ω c ω c firt order High Pa FiIter(HPF). ω c i the cut-off frequency. (6) how that θ L i almot equal to θ L in a ufficiently low

3 elf onance Cancellation for Joint Torque Control Uing Torque enor (Akiyuki Haegawa et al.) Phae [deg] Fig.. Comparion of frequency characteritic of θ M and θ L and θ RC ref L C() TL TM P LANT JL DL JM DM L M!c!c LP F!c HPF Fig. 5. Block Diagram of F-RC (8) frequency region and almot equal to θ α in a ufficiently high frequency region. When (7) i atified, the reonance component diappear from θ α in the ame way a RC. L Fig. 6. lation between parameter and Nyquit diagram in F-RC f c = α : cutoff frequency[hz] α : ( α) = J L : J M (7) Here, in F-RC, rather than completely eliminating the reonance component, adjut α to create a virtual angle θ α with a little reonance component. Leaving a little reonance component make it poible to have reonance uppreion function by feedback of θ α. After all, in the low frequency region without reonance, it i poible to control directly feedbacking θ L, and in the high frequency region affected by the reonance, feedback θ α with a little reonance component. Therefore, ince θ L ha no reonance component in the low frequency region and ha only a mall reonance component even in the high frequency region, jut deign the controller C() for the rigid body i ufficient. In other word, ince the tranfer function of the plant i, pole aignment i poible with PI controller. J RC D RC lation between parameter and Nyquit diagram in F- RC are hown in Fig.6 and Fig.7. In F-RC adjut the degree of reonance uppreion with α and adjut phae compenation with ω c. By adjuting α and cutoff frequency ω c, we realize a enitivity function that i balanced between reonance frequency and other frequencie.. Propoal of RC uing torque enor(trc) F-RC wa a method baed on RC. In deigning joint torque F-RC(F-TRC), firtly, RC uing a torque en Fig. 7. lation between parameter and Nyquit diagram in F-RC f c : α: or (TRC) wa deigned. RC add the equation of motion on the motor-ide and the load-ide of two-inertial ytem, and cancel T = (θ M θ L ). () () how that the motoride value in the RC i T, lord-ide value in the RC J RC T i J RC. Therefore, they can be obtained by meauring T uing a torque enor. Fig.8 how block diagram of TRC. gardle of the plant parameter, TRC will be rigidified if T and T are added. However, when rigidification i made, the virtual torque T RC become the input value, therefore effective control can not be performed a it i.. Propoal of joint torque control F-RC (F-TRC) Torque dimenion F-RC (F-TRC) wa deigned uing torque enor. The control ytem of F- TRC i hown in Fig.9. The virtual torque T i denoted in (8). T = ω c T T α, ω c ω c

4 elf onance Cancellation for Joint Torque Control Uing Torque enor (Akiyuki Haegawa et al.) T L T Plant J L J M L M T RC T ref T C() T L Fig. 8. Block Diagram of TRC P LANT J L D L J M D M L M! c! c LP F! c HPF T Fig.. lation between parameter and Nyquit diagram in F-RC f c = Hz α : 5 Fig. 9. = ω c ω c T = ω c ω c T Block Diagram of F-TRC {αt ( α)( T )}, ω c {(α )T ( α) }.(8) ω c (8) how that T i almot equal to T in a ufficiently low frequency region and almot equal to T α in a ufficiently high frequency region. According to the ame principle a F-RC, in the low frequency region without reonance, it i poible to control directly feedbacking T, and in the high frequency region affected by the reonance, feedback T α with a little reonance component. Where T α i rigidified when α =.5. In other word, unlike F-RC, even if we do not know the moment of inertia on the driving ide and the load ide, we can adjut the parameter a a guide that α =.5 i made rigid. Alo, the controller C() can be deigned for a rigid body like F-RC. That i, conidering the cae of α =.5, you can deign for the tranfer function T α =.5, therefore jut a ingle integrator i enough to eliminate teady-tate deviation. Therefore, you can eaily adjut the characteritic imply by adjuting two parameter, α and ω c. lation between parameter and Nyquit diagram in F- TRC are hown in Fig. and Fig... imulation Frequency repone of F-TRC wa evaluated by imulation. Parameter in the imulation were performed in three cae hown in Tab..When uing a controller C(), an integrator controller with a gain of wa ued. T A comparion of Nyquit diagram of without a controller i hown in Fig.. A the cutoff frequency f c rie, Fig.. lation between parameter and Nyquit diagram in F-TRC f c : Hz α : Table. Parameter of F-TRC α f LPF [Hz] Cae. 5 Cae. Cae. 5 the phae advance, and a α approache.5, the reonance component decreae and the rotation decreae. A comparion of the frequency characteritic of the enitivity function T i hown in Fig.. It can be een that there i a tradeoff between diturbance uppreion performance at low frequencie and diturbance uppreion performance around reonance frequency. A comparion of tep repone of T i hown in Fig.. It alo how that there i a tradeoff between diturbance uppreion performance at low frequencie and diturbance uppreion performance around reonance frequency. cutoff frequency[hz]

5 elf onance Cancellation for Joint Torque Control Uing Torque enor (Akiyuki Haegawa et al.) Fig Comparion of Nyquit diagram of T (imulation) Toque[Nm] econd [] Fig.. tep repone of T (imulation) - - Phae [deg] Fig.. Comparion of frequency characteritic of T (imulation) 5. Experiment The frequency repone of F-TRC wa evaluated by experiment. Unipule torque enor wa ued (6). Parameter were performed in the three cae hown in Tab. a in imulation. When uing a controller C(), an integrator controller with a gain of wa ued. T A comparion of Nyquit diagram of without a controller i hown in Fig.5. A comparion of the frequency characteritic of the enitivity function T i hown in Fig.6. A comparion of tep repone of T i hown in Fig.7. ult very imilar to imulation were obtained. The reaon why the peak of the enitivity function i lowered in the experiment i conidered to be the limit of frequency reolution and the exitence of nonlinear friction that can not be modeled by identifying by frequency characteritic meaurement Fig Comparion of Nyquit diagram of T (Experiment) It i conidered that the vibration decreae with tep repone alo due to the exitence of nonlinear friction. 6. Concluion In the background that joint torque control enable ophiticated work and afe collaboration work with human, the cae of mounting torque enor on dometic robot and indutrial robot i increaing. In thi paper, we propoed F- TRC, an joint torque control method uing a torque enor baed on the poition control method called F-RC. The performance of the controller of the propoed method wa evaluated by imulation and experiment. In the propoed method, the controller i the integrator only, and it i a method that can intuitively tune the control performance by uing the remaining two parameter. Becaue tuning can be done very eaily, it i expected to be ued in the indutry. The propoed method can be applied not only to joint of robot, however alo to other application that can be modeled into two-inertial ytem. 5

6 elf onance Cancellation for Joint Torque Control Uing Torque enor (Akiyuki Haegawa et al.) - - ytem and It Application to a Large-cale tage. IEEJ Journal of Indutry Application, Vol., No. 6, pp. 55 6,. 5-5 Phae [deg] Fig. 6. Comparion of frequency characteritic of θ re f L θ L (Experiment) θ re f L.5 Torque[Nm] econd [] Fig. 7. tep repone of T (Experiment) ference ( ) oichi akata, azuaki aiki, and Hirohi Fujimoto. elf onance Cancellation uing Multiple enor for Ballcrew Driven tage. In I EE-Japan Indutry Application ociety Conference (IEEJ JIAC ), No., pp. 5 56,. ( ) Yakawa. Development of human-coexitent robot MOTOMAN-HC - Pioneering a new era of production equipment -(in Japanee). http: // ( ) TOYOTA. Partner Robot Family (Human upport Robot). toyota-global.com/innovation/partner_robot/family_.html. ( ) Emre ariyildiz and ouhei Ohnihi. An Adaptive action Force Oberver Deign. IEEE/AME Tranaction on MechatronicTRONIC, Vol., No., pp , 5. ( 5 ) Taro Takahahi, Yohihiro uroki, Yuuke oaka, Eiji Niwa, Hirohi aminaga, and Yohihiko Nakamura. Development of flexible joint technology for human-coexiting robot on Cr-N thin film type torque enor(in Japanee). Toyota technical review, pp. 8, 5. ( 6 ) UNIPULE. Product information rotational torque meter (in japanee). ( 7 ) Johan Pitelon, Rik chouken. ytem Identification: A Frequency Domain Approach, nd Editon. Wiley-IEEE Pre,. ( 8 ) oichi akata, Hiroyohi Aaumi, azuyuki Hirachi, azuaki aiki, and Hirohi Fujimoto. elf onance Cancellation Technique for a Two-Ma 6