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英文原文 A simple approach to the control of locomotion in self-reconfigurable robots K. Sty a, , W.-M. Shen b, P.M. Will b a The Adaptronics Group, The Maersk Institute, University of Southern Denmark, Campusvej 55, DK-5230 Odense M, Denmark b USC Information Sciences Institute and Computer Science Department, 4676 Admiralty Way, Marina del Rey, CA 90292, USA Abstract In this paper we present role-based control which is a general bottom-up approach to the control of locomotion in self-reconfigurable robots. We use role-based control to implement a caterpillar, a sidewinder, and a rolling track gait in the CONRO self-reconfigurable robot consisting of eight modules. Based on our experiments and discussion we con-clude that control systems based on role-based control are minimal, robust to communication errors, and robust to recon-figuration. 2003 Elsevier Science B.V. All rights reserved. Keywords: Self-reconfigurable robots; Locomotion; Role-based control 1. Introduction Reconfigurable robots are robots made from a pos-sibly large number of independent modules connected to form a robot. If the modules from which the re-configurable robot is built are able to connect and disconnect without human intervention the robot is a self-reconfigurable robot. Refer to Fig. 1 for an exam-ple of a module of a self-reconfigurable robot or refer to one of the other physical realized systems described in 7,8,1015,17,21,23 . Several potential advantages of self-reconfigurable robots over traditional robots have been pointed out in literature: Versatility. The modules can be combined in differ-ent ways making the same robotic system able to perform a wide range of tasks. Adaptability. While the self-reconfigurable robot performs its task it can change its physical shape to adapt to changes in the environment. Robustness. Self-reconfigurable robots consist of many identical modules and therefore if a module fails it can be replaced by another. Cheap production. When the final design for the basic module has been obtained it can be mass pro-duced. Therefore, the cost of the individual module can be kept relatively low in spite of its complexity. Self-reconfigurable robots can solve the same tasks as traditional robots, but as Yim et al. 23 point out; in applications where the task and environment are given a priori it is often cheaper to build a special purpose robot. Therefore, applications best suited for self-reconfigurable robots are applications where some leverage can be gained from the special abilities of self-reconfigurable robots. The versatility of these Fig. 1. A CONRO module. The three male connectors are located in the lower right corner. The female connector is partly hidden from view in the upper left corner. robots make them suitable in scenarios where the robots have to handle a range of tasks. The robots can also handle tasks in unknown or dynamic environ-ments, because they are able to adapt to these envi-ronments. In tasks where robustness is of importance it might be desirable to use self-reconfigurable robots. Even though real applications for self-reconfigurable robots still are to be seen, a number of applications have been envisioned 17,23: fire fighting, search and rescue after an earthquake, battlefield reconnais-sance, planetary exploration, undersea mining, and space structure building. Other possible applications include entertainment and service robotics. The potential of self-reconfigurable robots can be realized if several challenges in terms of hardware and software can be met. In this work we focus on one of the challenges in software: how do we make a large number of connected modules perform a coor-dinated global behavior? Specifically we address howto design algorithms that will make it possible for self-reconfigurable robots to locomote efficiently. In order for a locomotion algorithm to be useful it has to preserve the special properties of these robots. From the advantages and applications mentioned above we can extract a number of guidelines for the design of such a control algorithm. The algorithm should be dis-tributed to avoid having a single point of failure. Also the performance of the algorithm should scale with an increased number of modules. It has to be rob ust to re-configuration, because reconfiguration is a fundamen-tal capability of self-reconfigurable robots. Finally, it is desirable to have homogeneous software running on all the modules, because it makes it possible for any module to take over if another one fails. It is an open question if a top-down or a bottom-up approach gives the best result. We find that it is diffi-cult to design the system at the global level and then later try to make an implementation at the local level,because often properties of the hardware are ignored and a slow robotic system might be the result. There-fore, we use a bottom-up approach where the single module is the basic unit of design. That is, we move from a global design perspective to a bottom-up one where the important design element is the individual module and its interactions with its neighbors. The global behavior of the system then emerges from the local interaction between individual modules. A sim-ilar approach is also used by Bojinov et al. 1,2 and Butler et al. 4. 2. Related work In the related work presented here we focus on con-trol algorithms for locomotion of self-reconfigurable robots. Yim et al. 22,23 demonstrate caterpillar-like loco-motion and a rolling track. Their system is controlled based on a gait control table. Each column in this table represents the actions performed by one module. Mo-tion is then obtain by having a master synchronizing the transition from one row to the next. The problem with this approach is that the amount of communica-tion needed between the master and the modules will limit its scalability. Another problem is the need for a central controller, since it gives the system a single point of failure. If there is no master it is suggested that the modules can be assumed to be synchronized in time and each module can execute its column of actions open-loop. However, since all the modules are autonomous it is a questionable assumption to assume that all the modules are and can stay synchronized. In order to use the gait control table each module needs to know what column it has to execute. This means that the modules need IDs. Furthermore, if the con-figuration changes or the number of modules changes the table has to be rewritten. Shen et al. 17 propose to use artificial hormones to synchronize the modules to achieve consistent global locomotion. In earlier versions of the system a hor-mone is propagated through the self-reconfigurable system to achieve synchronization. In later work the hormone is also propagated backward making all modules synchronized before a new action is initiated 16,18. This synchronization takes time O(n), where n is the number of modules. This slows down the system considerably, because it has to be done before each action. Also, the entire system stops working if one hormone is lost. This is a significant problem, because a hormone can easily be lost due to unreli-able communication, a module disconnecting itself before a response can be given, or a module failure. In fact, the system has n points of failure which is not desirable. The earlier version is better in this sense, but still performance remains low because a synchronization hormone is sent before each action. Butler et al. 4 propose a method inspired by cel-lular automata. In their approach modules respond to state changes of neighbor modules. Their approach is a bottom-up approach related to ours, but in cellular automata there is no concept of time only of sequence. Timing is important in locomotion, because it is the key to produce smooth and life-like locomotion and avoid jerky locomotion. In our system all modules repeatedly go through a cyclic sequence of joint angles describing a motion. This sequence could come from a column in a gait con-trol table, but in our implementation the joint angles are calculated using a cyclic function with period T . Every time a module has completed a specified frac-tion d of the period a message is sent through the child connectors. If the signal is received the child module resets its action sequence making it delayed d com-pared to the parent. This way the actions of the indi-vidual module are decoupled from the synchronization mechanism resulting in a faster and more reliable sys-tem. Furthermore, there is no need to make changes to the algorithm if the number of modules changes. 3. Role-based control We assume that the modules are connected to form a tree structure, that a parent connector is specified, and that this connector is the only one that can connect to child connectors of other modules. Furthermore, we assume that the modules can communicate with the modules to which they are connected. The algorithm is instantiated by specifying three components. The first component is a cyclic action sequence A(t), where t 0 : T . T is the second component that needs to be specified and is the pe-riod of the action sequence. A(t) describes the ac-tions that each module repeats cycle after cycle. In our implementation A(t) returns joint angles to control the two degrees of freedom of the CONRO module, but the action sequence could also be used to trigger dif-ferent behaviors at different times during a cycle. The third component is a delay d. This delay specifies the fraction of a period the childrens action sequences are delayed compared to their parents. The skeleton algorithm looks like this: t=0 while(true) if(t=d)then if then t=0 t=(t+1) modulus T Ignoring the first two lines of the loop, the module repeatedly goes through a sequence of actions param-eterized by the cyclic counter t. This part of the al-gorithm alone can make a single module repeatedly perform the specified sequence of actions. In order to coordinate the actions of the individual modules to produce the desired global behavior the modules need to be synchronized. Therefore, at step t = d a signal is sent through all child connectors. If a child receives a signal it knows that the parent is at t = d and there-fore sets its own step counter to t = 0. This enforces that the child is delayed d compared to its parent. From the time the modules are connected it takes time proportional to d times the height of the con-figuration tree for all the modules to synchronize. To avoid problems with uncoordinated modules initially we make sure the modules do not start moving until they receive the first synchronization signal. After the start-up phase the modules stay synchronized using only constant time. 4. Experimental setup To evaluate our algorithm we conducted several ex-periments using the CONRO (CONfigurable RObot) modules of which one is shown in Fig. 1. The CONRO modules have been developed at USC/ISI 5,9. The modules are roughly shaped as rectangular boxes mea-suring 10 cm 4.5 cm 4.5 cm and weigh 100 g. The modules have a female connector at one end and three male connectors located at the other. Each connectorhas a infra-red transmitter and receiver used for local communication and sensing. The modules have two controllable degrees of freedom: pitch (up and down) and yaw (side to side). Processing is taken care of by an onboard Basic Stamp 2 processor. The modules have onboard batteries, but these do not supply enough power for the experiments reported here and there -fore the modules are powered through cables. Refer to /conro for more details and videos of the experiments reported later. 5. Experiments In this section we describe three different locomo-tion gaits implemented using role-based control. For each gait we have chosen to report the length of our programs as a measure of the complexity of the control algorithm. These results are used to support our claim that the implemented control systems are minimal. We also report the speed of the locomotion patterns, but this should only be considered an example, the reason being that in our system the limiting factors are how robust the modules physically are, how powerful the motors are, and how much power we can pull from the power source. To report a top speed is not meaningful before we run the robot autonomously on batteries. 5.1. Caterpillar locomotion We connect eight of our modules in a chain and designate the male opposite the female connector to be the parent connector. We then implement the algorithm described above with the following parameters. T = 180, _ pitch(t) = 50 sin 2 t , T yaw(t) = 0, d = 51 T. (1) Pitch and yaw is measured in a coordinate system where a yaw and a pitch of zero mean that the joints are straight. The motor control of our modules makes the joint go to the desired angle as fast as possible. This means that way-points have to be specified to avoid jerky motion. The period T can be used to control the number of way-points and therefore the smoothness and speed of the motion. The action sequence is an oscillation around 0 with an amplitude of 50 for the pitch angle and the yaw joint is kept straight. Each module is delayed one-fifth of a period compared to its parent. The modules are connected and after they synchro-nize a sine wave is traveling along the length of the robot. Refer to Fig. 2. This produces caterpillar-like locomotion at a speed of 4 cm/s. Note that it is easy to adjust the parameters of this motion. For instance, the length of the wave can be controlled using the de-lay. The program is simple. The main loop contains 13 lines of code excluding comments and labels (shown in Fig. 2). The initialization including variable and constant declaration amounts to 18 lines of code. Fig. 3. A snapshot of sidewinder-like locomotion. lines of code. The parameters for the eight module rolling track are: T = 180, 2 60 21 T, pitch(t) 1 sin t if t _ _ T _ = 60 if t 1 yaw(t) 2 T, = 0, d = 41 T. (3) Unlike the controller for the sidewinder gait and the caterpillar gait this controller only works with eight modules, because of the physical constraint. It might be possible to make a more general solution by mak-ing pitch(t) and d a function of the number of mod-ules. The number of modules in the loop could be ob-tained by the leader by including a hop count in the signal. 6. Handling a general configuration We saw in the previous section that we had to in-troduce IDs to find a unique leader in a configuration that contains loops. Introducing the ID mechanism un-fortunately ruins the opportunity to use the synchro-nization algorithm to automatically find a leader in a tree structure, because synchronization signals are only propagated down in the configuration tree. In fact, the loop algorithm will fail in this situation unless the module with the highest ID also happens to be the root. In order to make a general algorithm the syn-chronization signal has to be propagated both upward and downward in the tree. 7. Discussion An important issue in the design of control algo-rithms for self-reconfigurable robots is that the algo-rithms should still be efficient in systems consisting of many modules. Role -based control is only initially dependent on the number of modules, because it de-cides how long it takes for the synchronization sig-nal to be propagated through the system. After this start-up phase it takes constant time to keep the mod-ules synchronized implying that the algorithm scales. In role-based control all modules run identical pro-grams and there is no representation of a modules po-sition in the configuration. Therefore, the system is highly robust to reconfiguration. In fact, the caterpil-lar can be divided in two and both parts still work. If they are reconnected in a different order they will quickly synchronize to behave as one caterpillar again. This also implies that the system is robust to module failure. If a module is defect and it can be detected this module can be ejected from the system and the remaining modules when reconnected can continue to perform. Finally, if a synchronization signal is lost it is not crucial for the survival of the system. If a signal is lost it just means that the receiving module and its children will be synchronized a period later. In role-based control the synchronization signal is only sent once per period. This means that in order for the modules to stay synchronized the time to complete a period has to be the same for all modules. In the experiments presented here the cycles take the same amount of time, but in more complex control systems where other parts of the control system use random amounts of computat ion time this cannot be assumed to be true. This problem can easily be handled by using timers. Even though timers are not precise enough to keep modules synchronized over a long period of time they can be used for this purpose. In the work presented here we have shown what can be achieved using as simple a control algorithm as possible. In related work we have investigated how we can extend the algorithm to handle more complex locomotion gaits. We have shown how to implement a hexapod walking gait in the CONRO system in 19. Another issue is that if the self-reconfigurable robot is to locomote autonomously in a real complex envi-ronment the control algorithm has to be able to take feedback from the environment into account. We have done some initial work on how sensor feedback can be included in role-based control in 20. 8. Summary We have presented role-based control a general control algorithm for controlling locomotion in self-reconfigurable robots. The algorithm has the follow-ing properties: distributed, scalable, homogeneous, and minimal. We have shown how the algorithm easily can be used to implement a caterpillar- and sidewinder-like locomotion pattern. Furthermore, we have seen that by giving modules IDs it is possible to handle loop configurations. We have demonstrated this using the rolling track as an example. Acknowledgements This work is supported under the DARPA contract DAAN02-98-C-4032, the EU contract IST-20001-33060, and the Danish Technical Research Council contract 26-01-0088. References 1 H. Bojinov, A. Casal, T. 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Will, Hormones for self-reconfigurable robots, in: Proceedings of the International Conference on Intelligent Autonomous Systems (IAS-6), Venice, Italy, 2000, pp. 918925. 19 K. Sty, W.-M. Shen, P. W ill, How to make a self-reconfigurable robot run, in: Proceedings of the First International Joint Conference on Autonomous Agents and Multiagent Systems (AAMAS02), Bologna, Italy, 2002, pp. 813820. 20 K. Sty, W.-M. Shen, P. Will, On the use of sensors in self-reconfigurable robots, in: Proceedings of the Seventh International Conference on the Simulation of Adaptive behavior (SAB02), Edinburgh, UK, 2002, pp. 4857. 21 C. nsal, P.K. Khosla, Mechatronic design of a modular self-reconfiguring robotic system, in: Proceedings of the IEEE International Conference on Robotics and Automation (ICRA00), San Francisco, CA, 2000, pp. 17421747. 22 M. Yim, Locomotion with a unit-modular reconfigurable robot, Ph.D. Thesis, Department of Mechanical Engineering, Stanford University, 1994. 23 M. Yim, D.G. Duff, K.D. Roufas, Polybot: a modular reconfigurable robot, in: Proceedings of the IEEE International Conference on Robotics and Automation (ICRA00), San Francisco, CA, 2000, pp. 514-520. 中文譯文 一個簡單的方法來控制運動中的自重構(gòu)機器人 K. Sty a, W.-M. Shen b, P.M. Will b 摘要 在本文中,我們提出了基于角色的控制,這是一般的自下而上的方法,在自重構(gòu)機器人的運動控制。我們使用基于角色的控制,實施毛蟲,響尾蛇,并滾動軌道中的 CONRO 8 個模塊組成的自我重構(gòu)機器人步態(tài)。我們的實驗和討論的基礎(chǔ)上,我們 CON 包括控制系統(tǒng),基于角色的控制的基礎(chǔ)是最小的,健壯的通信錯誤,和強大的偵察配置。 關(guān)鍵詞:自重構(gòu)機器人 ;步態(tài) ;基于角色的控制 介紹 可重構(gòu)機器人是由一個獨立的模塊連接在一起,形成一個機器人的 POS 大量的機器人。如果重新配置機器人內(nèi)置的模塊可以連接和斷開,無需人工干預(yù),機器人是自重構(gòu)機器人。參考圖 1的自重構(gòu)機器人的模塊或參考其他物理實現(xiàn)描述的系統(tǒng)之一 7,8,10-15,17,21,231。 幾個潛在的自重構(gòu)機器人,比傳統(tǒng)文學(xué)上指出的更有優(yōu)點。 多功能性。模塊可以在相同的機器人系統(tǒng),能夠執(zhí)行各種任務(wù)的不同方式相結(jié)合。 適應(yīng)性。雖然自重構(gòu)機器人執(zhí)行其 任務(wù),它可以改變其物理形狀以適應(yīng)環(huán)境的變化。 健壯性。自重構(gòu)機器人由許多相同的模塊,因此,如果一個模塊發(fā)生故障,它可以被另一個取代。 廉價生產(chǎn)。當(dāng)已獲得最終設(shè)計為基本模塊,它可以產(chǎn)生的質(zhì)量。因此,單個模塊的成本可以保持比較低的,盡管它的復(fù)雜性。 自重構(gòu)機器人,可以解決傳統(tǒng)機器人相同的任務(wù),但圖 23機器人表明任務(wù)和環(huán)境先驗往往是便宜,以建立一個專用機器人的應(yīng)用程序。因此,最適合自重構(gòu)機器人的應(yīng)用程序都可以從自重構(gòu)機器人的特殊能力取得一些杠桿的應(yīng)用。這些多功能機器人讓他們在合適的情況下,機器人必須 處理的任務(wù)范圍。該機器人還可以處理未知或動態(tài)的環(huán)境中使用的任務(wù),因為他們能夠適應(yīng)這些 ENVI 環(huán)境。在其中魯棒性的重要性的任務(wù),它可能是最好使用自重構(gòu)機器人。自重構(gòu)機器人的實際應(yīng)用中,即使仍然可以看到,大量的應(yīng)用程序已經(jīng)設(shè)想 17,23:地震發(fā)生后,消防,搜尋和救援的戰(zhàn)場,行星探測,海底采礦,空間結(jié)構(gòu)建設(shè)。其他可能的應(yīng)用包括娛樂和服務(wù)機器人。 如果在硬件和軟件方面的一些挑戰(zhàn)可以得到滿足,可實現(xiàn)自重構(gòu)機器人的潛力。在這項工作中,我們專注于軟件的挑戰(zhàn)之一:我們?nèi)绾问勾罅康倪B接模塊執(zhí)行協(xié)調(diào) dinated 的全局行為 ?具體來說,我們解決了如何設(shè)計,這將使自重構(gòu)機器人有可能 locomote 有效的算法。為了一個運動算法是有用的,它具有維護這些機器人的特殊性質(zhì)。從上述的優(yōu)勢和應(yīng)用,我們可以提取了這種控制算法的設(shè)計準(zhǔn)則。該算法應(yīng)該是分布式的,以避免單一故障點。算法的性能也應(yīng)該擴展模塊的數(shù)量增加。它具有強勁的重新配置,重新配置,因為是 TAL 的自重構(gòu)機器人的基本能力。最后,這是可取的,有均勻的軟件運行在所有的模塊,因為它可以使任何模塊接管另一個失敗。 它是一個開放的問題,如果一個自上而下或自下而上的方法提供了最好的結(jié)果。我們發(fā)現(xiàn), 這是很難邪教組織在全球范圍內(nèi)設(shè)計系統(tǒng),再后來嘗試在地方一級執(zhí)行,因為經(jīng)常硬件的屬性被忽略,一個緩慢的機器人系統(tǒng),可能的結(jié)果。因此,我們使用一種自下而上的方法,其中單個模塊是設(shè)計的基本單元。也就是說,我們從全球設(shè)計的角度來看,從下往上的一個重要的設(shè)計元素是單個模塊和與鄰國的互動。然后,該系統(tǒng)的全球行為出現(xiàn)從當(dāng)?shù)馗鱾€模塊之間的互動。 SIM 卡類似的方法也可用于由博季諾夫等 1,2和巴特勒等人 4。 相關(guān)工作 相關(guān)工作在這里提出,我們集中的自重構(gòu)機器人的運動控制算法。 Yim 等 22,23表明毛 蟲般的局部運動和一個滾動的軌道。步態(tài)控制表的基礎(chǔ)上,他們的系統(tǒng)控制。本表中的每一列代表一個模塊執(zhí)行的動作。鉬然后獲得主同步從一行到下一過渡。這種方法的問題是,需要主機和模塊之間的通信量將限制它的可擴展性。另一個問題是需要一個中央控制器,因為它給出了系統(tǒng)的單點故障。如果沒有掌握它建議模塊可以假定時間同步,每個模塊可以執(zhí)行其行動開環(huán)列。然而,由于所有的模塊都是自治的,它是一個可疑的假設(shè),假設(shè)所有的模塊,并能保持同步。為了使用的步態(tài)控制表,每個模塊需要知道哪些列執(zhí)行。這意味著該模塊需要的 ID。此外,如果組態(tài)中變更 或模塊數(shù)量改變表被改寫。 Shen 等 17提出使用人工激素,同步模塊,以實現(xiàn)全球一致的運動。在系統(tǒng)的早期版本 1性激素傳播通過自重構(gòu)系統(tǒng)實現(xiàn)同步。激素,在以后的工作也落后傳播同步之前,一個新的行動啟動 16,18的所有模塊。這種同步需要時間為 O( n),其中 n為模塊的數(shù)目。這會減慢系統(tǒng)很大,因為它有每個動作之前完成。此外,整個系統(tǒng)停止工作,如果失去一種激素。這是一個重大的問題,因為激素可以很容易丟失,由于不可靠的通信,可以一個模塊斷開響應(yīng)之前,或一個模塊失敗。事實上,該系統(tǒng)有 n 個故障點,這是不可取的。 早期版本的比較好,在這個意義上說,但仍表現(xiàn)仍然很低,因為每個動作之前發(fā)送一個同步激素。 巴特勒等人 4提出啟發(fā) CEL-lular 的自動方法。在他們的做法模塊鄰居模塊狀態(tài)的變化作出反應(yīng)。他們的做法是一種自下而上的方法,涉及到我們,但在細胞自動機有沒有,只有時間序列的概念。時機是在運動的重要,因為它是生產(chǎn)順利和生活類的運動,避免干運動的關(guān)鍵。 在我們所有的系統(tǒng)模塊反復(fù)關(guān)節(jié)的角度,描述了一個議案通過循環(huán)序列。這個序列可能來自步態(tài)控制表列,但在我們實施的關(guān)節(jié)角度計算使用一個循環(huán)周期T功能。通過子連接器 的每一個模塊已經(jīng)完成了指定的分?jǐn)?shù) 期間消息的時間發(fā)送。如果信號接收子模塊復(fù)位的動作序列,使得它推遲 相比父。這樣的單個模塊的行動是從同步機制,更快和更可靠的 SYS-TEM 脫鉤。此外,也沒有必要進行修

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