Stiffness Control of a Robotic Arm Using Robust Fixed Point Transformations

Transcription

1 Proc. 14th Int. Conf. on Global Reearch an Eucation, Inter-Acaemia 2015 JJAP Conf. Proc. 4 (2016) The Japan Society of Applie Phyic Stiffne Control of a Robotic Arm Uing Robut Fixe Point Tranformation Teréz A. Várkonyi 1 *, Józef K. Tar 1, an Imre J. Rua 2 1 Antal Bejczy Center for Intelligent Robotic, Óbua Univerity, Buapet H-1032 Hungary 2 Univerity Reearch an Innovation Center, Óbua Univerity, Buapet H-1032 Hungary varkonyi.teri@nik.uni-obua.hu, tar.jozef@nik.uni-obua.hu, rua@uni-obua.hu (Receive September 27, 2015) Nowaay, energy conumption of electronic ytem i a very important quetion. Much money an time can be ave with a well-eigne ytem, where the epletion i minimal. In thi paper, the power uage of the arm of a NAO Next Gen robot i optimize by controlling ynamically the tiffne of it motor. The control trategy i bae on Robut Fixe Point Tranformation (RFPT). The reult how that the propoe control metho can reuce the power uage ignificantly, an a a urprie, it can reuce the inaccuracy of the tracking caue by the unpunctual enor of the robot. 1. Introuction In thee ay, energy conumption of electronic tool i a central quetion. Many prouct are eigne to be a effective a it can with le energy uage. Saving energy mean better utilization plu time an money aving. Thi quetion, in cae of robot working on battery, for example a NAO robot (ee Fig.1 an Ref. 1), i alo crucial. It i not the ame how long a robot can operate before the battery get empty. NAO itelf i a robot that can go ea an can overheat eaily which mean energy optimization woul be important for it. Since it ha everal enor (e.g. tactile enor, ultraonic enor, gyrometer, accelerometer, force enor, infrare enor, HD camera, an microphone), it ha everal feature (like autonomy, walking, ancing, peech, face- an voice recognition), it can be ue by chilren with the help of a rag an rop interface, an it can be programme in everal language (for example Python, Java, C#, Matlab, an C++), it i applicable for everal tak an reearche. Thu, it i very popular an ue in many area: at chool for eucation, at performance for entertainment, in hopital for patient with pecial nee, an at RoboCup occer competition, Ref. 2. One of the main ifficultie in all of thee ituation i alway the ame: the battery of the robot quickly goe ea an ha to be charge often. It woul make le eman an it woul increae the lifetime of the battery if the power uage of the motor coul be optimize. The energy conumption of the NAO robot can be influence by moifying the tiffne value of the joint motor. Several ucceful application have been mae o far, e.g. in Ref. 3, a control trategy for the tiffne value i given to reuce the energy uage of the robot uring walking, in Ref. 4, the tanup proceure i optimize through tiffne control to ave energy, an in Ref. 5, a new walking trategy i preente for energy aving. In thi paper, a Robut Fixe Point Tranformation-bae (ee Ref. 6) control cheme i propoe for the tiffne of the houler joint of the NAO robot. In aition, a rough moel i given for the ufficient tiffne value calculation that i enough for moving to the arm in a eire poition. Thi

2 Fig. 1. NAO robot (got from Ref. 7) i the firt real application of RFPT. It i ue becaue it can hanle moel oximation. The reult how that the propoe control metho can reuce the power uage of the robotic arm ignificantly, an a a urprie, the tracking error can alo be cut own a little bit. The paper i organize a follow: in Sect. 2 the main iea of Robut Fixe Point Tranformation i preente. In Sect. 3, the control of the tiffne of the NAO robot i explaine. Section 4 how ome repreentative tet reult. Finally, in Sect. 5, concluion are ummarize. 2. Baic of the RFPT-bae control trategy RFPT-bae control, a een in Fig.2, work a follow: A nominal poition i precribe for the ytem to be controlle. Bae on thi, the controller calculate a eire repone for the ytem, which can be either velocity or acceleration, or other, epening on the control tak, o that it get to the nominal poition (uually, the higher orer ifferentiation, the more accurate control can be achieve). After that, bae on a rough moel of the ytem, a control ignal u i generate to force the ytem to eire repone. Then, thi control ignal i given to the ytem which reult in a real repone r r. Since the moel i not exact (it i very ifficult to moel a ytem that e.g. i not built for precie work) an r r will iffer from each other. They can iffer lightly or ignificantly, epening on the accuracy of the moel. For uch inaccuracy, RFPT might give a olution. In thi oach, RFPT i ue to tranform the output of the controller, o that the given moel calculate with a moifie controller value. RFPT i eigne to locally converge it input cloer to u, where enote the rough moel, u tan for the control value that force the ytem to give the eire repone, an etail, ee Ref Stiffne control of the arm of the NAO robot f 1. For further The power uage of a motor can be calculate a it voltage multiplie by it current. The current level of a joint motor can be calculate a (foetail, ee Ref. 4) I I K, (1) where I i the upplie current to the motor wining an K mark the eire tiffne function K 0,1 ). Thi mean that by controlling tiffne, the power uage of the motor can for the joint ( be influence. The voltage can be given a V I L t RI kbw, (2)

3 where L i the motor inuctance, R enote the motor wining reitance, I tan for the current, k b i the motor back emf contant, an w mark the rotor angular velocity. In our oach, the control tak i to et a proper tiffne value K o that the robotic arm, hown in Fig. 3, can get to a precribe poition. If the tiffne value i not enough, the arm i not able to move, ince it oe not get enough current. If the tiffne value i too high, more than neceary power might be ue for the movement. In the control cheme, tiffne can be coniere a the control ignal u. In the olution, the tiffne an the poition of the arm can be get an et with acceptable accuracy, o the moel ha to fin connection between thee value. The bet olution woul be controlling the acceleration of the ytem, but it can be only oximate from poition an velocitie which woul give u a lot of fale value. The enor of the NAO robot are not accurate enough for that. It mean that ytem repone r r an can be coniere a poition an in the control cheme, the eire repone i equivalent with the nominal poition. In the next tep, accoring to RFPT, the following tranformation i applie on the eire poition of the arm of the robot : r = r K1 B tanh A f r r K G r,, (3) Fig. 2. Block cheme of the RFPT-bae control trategy. where A, B, an K are control parameter (fur furtheetail, ee Ref. 6), r i the previou output of RFPT, an f r tan for the output of the ytem in the previou control cycle. After RFPT, the tranforme poition i given to a rough invere moel of the robotic arm o that i calculate an opriate tiffne value for the rotating motor. The proper tiffne calculation i got a follow: a meaurement howe, tiffne value 0.4 i enough to keep the robotic arm in the ame poition no matter in which angle it i. If the poition of the arm i 0 (traight ownwar), then at leat 0.4 tiffne i neee to move it. In the wort cae, when the poition of the arm i π/2, at leat 0.7 tiffne i neee to move it. Gravity ignificantly influence the movement, thu when the robotic arm ha to be move, two cae occur: when it ha to be move upwar an ownwar. Bae on thi, the following equation can be given a the rough moel:

4 if r r K if the arm move upwar (4) r r, r * in r * it r, r r * in r 0.3 * it r, r where it a, b min 4 * a b /,1. A the lat tep, tiffne value r r poition. 4. Tet reult otherwie, K, i et for the NAO which move towar the eire To illutrate the effectivene of the propoe metho, in the following, ome ample tet reult are preente. In the tet, the right houler of a NAO Next Gen wa controlle (for the technical etail of the robot, ee Ref. 7); it ha to follow the movement of the left houler. An automatic motion wa given to the left arm: it went up to ¾ π an came own to ¼ π quickly (in oximately 2 econ) an then went up an own lowly (in oximately 6 econ). Thi motion kept going until it wa terminate by han. In the tet, three ifferent cae were inpecte: in the firt cae, the control tak wa one on full tiffne. Fig. 3 how the reult of that. In the econ cae, a hown in Fig. 4, the moel-bae tiffne control wa applie without RFPT. The peak in the error mean that the motoi not get enough current to go to the given poition, becaue the tiffne value wa too low for that, thu the power uage increae ignificantly. In the lat cae, RFPT wa witche on for the ynamic tiffne control (ee Fig. 5). The characteritic of the power uage an the error were very imilar in thi cae to that with full tiffne, but the error wa lightly relaxe, epecially aroun the 9 th econ. For checking the capabilitie of RFPT, other tet were mae where the moel output wa ecreae by 0.1, to ee how RFPT can hanle uch ifficultie (ee Fig. 6 an 7). A it can be een, without RFPT, the power uage ecreae thank to the ynamic tiffne control, but the error increae ignificantly, ince the moel oximate the real ytem quite roughly. On the other han, RFPT coul hanle the worene moel without remarkable increae in the power uage or in the tracking error. RFPT coul till ecreae lightly the inaccuracy compare to the cae with full tiffne. For more clear comparion, in Table I, the umme up error an power value are hown for each cae. 5. Concluion In thi paper, a ynamic, RFPT-bae tiffne control for a NAO robot i propoe. A rough moel for the tiffne calculation i given an the control i tete. The reult how that the control trategy can reuce the power uage of the robotic arm ignificantly an can hanle the inaccuracy caue by the enor of the robot. Table I. Summe up power uage an error of the ifferent cae. All tiffne Normal moel, without RFPT Normal moel, with RFPT Worene moel, without RFPT Worene moel, with RFPT Power (W) Error (ra)

5 Fig. 3. Power uage an tracking error in cae of all tiffne. Fig. 4. Power uage an tracking error in cae of normal moel, without RFPT. Fig. 5. Power uage an tracking error in cae of normal moel, with RFPT.

6 Fig. 6. Power uage an tracking error in cae of worene moel, without RFPT. Fig. 7. Power uage an tracking error in cae of worene moel, with RFPT. Reference [1] Dataheet for the NAO Next Gen robot [2] NAO robot for eucation an reearch [3] E. Elibol, J. Caleron, an A. Weitzenfel, Optimizing Energy Uage through Variable Joint Stiffne Control uring Humanoi Robot Walking, RoboCup 2013: Robot Worl Cup XVII (Springer Berlin Heielberg, 2014) p [4] J. M. Caleron, E Elibol, W. Moreno, an A. Weitzenfel, Current Uage Reuction Through Stiffne Control in Humanoi Robot: Proc. 8 th Workhop on Human Soccer Robot, 13 th IEEE_RAS International Conference on Humanoi Robot, Atlanta, GA, [5] N. Shafii, N. Lau, an L. P. Rei, Generalize Learning to Create an Energy Efficient ZMP-Bae Walking, RoboCup 2014: Robot Worl Cup XVIII (Springer International Publihing, 2015) p [6] J. K. Tar, J F. Bitó, L. Náai, an J. A. Tenreiro Machao, Robut Fixe Point Tranformation in Aaptive Control Uing Local Bain of Attraction, Acta Polytechnica Hungarica, 6, 21 (2009). [7]