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Automated Installation for Modification Surface Properties of Details and Units of the Metallurgical Equipment by the Electron Beam Facing S.I. Belyuk, A.G. Rau, I.V. Osipov*, N.G. Rempe* Institute of Strength Physics and Materials Science, 2/1 Akademicheskii Ave.,Tomsk, Russia *Tomsk State University of Control Systems and Radioelectronics, 40 Lenin Ave., Tomsk, Russia, Abstract : The electron-beam facing installation is designed for the production of coatings on the surface of metal articles. The coatings have protective, wear-resistive,and heat-resistive properties.The installation is capable of creating coatings on large-area surface with high efficiency.The technological process is automated. There are two plasma-cathode e-guns in the facing installation. This makes it possible to increase the facing efficiency and productivity. The guns are placed in a vacuum chamber on a two-rectilinear manipulator and can operate simultaneously. This installation is used in metallurgy for creating wear-resistant coatings on aerial and oxygen lances, on crystallizers of continuous casting of steel, on rolls, etc. 1. Introduction Electron-beam facing in vacuum [1,2] allows coatings with unique properties to be produced. With this method of coating deposition there is no adhesion problem. The materials which can be treated by this method and the coatings which can be produced on their surfaces are widely diversified. The high repeatability of results in combination with the adaptable control of the technological process make it possible to produce coatings of required structure and preassigned properties. We have developed an installation intended for deposition of heat and aerial blast-furnace lances with the purpose of increasing their operational durability and also for restoration of various machine parts and metallurgical equipment. It can also be used for welding various metals and alloys, including high-melting ones. The installation makes it possible to produce mono-and multilayer coatings of various purposes (hardening, wear-resistant, heat-resistant, temperature-resistant, etc.) depending on the composition of the facing powder on the surface of articles made of any metals, steels, and cast iron. With this installation it is possible to deposit coatings on plane surfaces of workpieces of length up to 2100 mm, width up to 900 mm, and thickness up to 200 mm and on bodies of revolution of diameter up to 1200 mm and length up to 2100 mm. The technological process of coating deposition is full-automatic. 2. Electron-beam facing The principle of electron-beam facing is shown in Fig. 1. The electron beam creates a molten metal pool on the surface of the workpiece. The powder whose particles form a coating with required properties on the surface is supplied to the molten metal by a dispenser. The workpiece is moved inside the vacuum chamber relative to the (immobile) e-gun and dispenser or the e-gun with the dispenser are moved relative to the (immobile) workpiece. Fig.1. The technology of multipass electron-beam facing is based on the phenomenon of "freezing" a powder into a melt pool. In every subsequent pass, a new portion of the powder is "frozen" and the previous portion is melted. The powder supplied to the pool speeds up the crystallization of the melt, thus promoting the formation of a fine grain structure and moderating the residual stresses in the deposited coating. The required thickness of the deposited layer is obtained by varying the rate of powder supply or by increasing the number of passes. The process of facing is characterized by the following parameters: the accelerating voltage, the electron beam current, the distance from the focusing system to the surface of the workpiece, the electron beam scanning diameter and length, the velocity of motion of the workpiece, and the rate of powder supply. 3.Electron guns The facing process is accompanied by intense ejection of vapors and gases from the facing zone. The refore, to produce an electron beam, plasma-cathode guns are used [3, 4]. These guns do not contain hot electrodes or components which would be heated in operation, and this makes them insensitive to reactive and high-melting vapors of the materials under treatment. They are capable of operating under the conditions of facing not taking special measures for protection of the emitter. Figure 2 Figure 3 The electron emission in the guns occurs from the plasma of a hollow cathode low-voltage reflected discharge [4]. The electrons outgoing from the plasma get in a high-voltage electric field where they are accelerated, collected in a beam, and focused by the magnetic field of the focusing system. The electron emission current from the plasma is controlled by varying the discharge current. In the design of the guns, metal used whose hermeticity and mechanical strength are provided by electron-beam weding.The gun housings are of in-chamber construction.The design of the housing provides easy and convenient access to the cathode assembly for periodic maintenance. Figure 2 presents the appearance of a gun mounted on the manipulator of the installation. 4. Power supply module The power supply system of the equipment(Fig.3) consists of an accelerating voltage unit (AVU), a discharge power supply unit (DPU), a beam focusing and deflection control unit (BFDU),and a control unit of the gas flow controller. The units are controlled by a computer via an optical or an RS485 interface. The accelerating voltage and discharge power supply units are made by the classical circuit design of a bridge inverter with the phase-shift control circuit. In the inverter, the resonance method of switching MOSFET transistors is realized that provides a low level of electromagnetic noise and reduced dynamic losses in switching power transistors. The high conversion frequency (30 kHz) makes it possible to reduce the output capacitance of the power supplies to 10 nF and to increase the rate of processing of control signals. Figure 4 The accelerating voltage unit can operate in one of the two modes: stabilization of the accelerating voltage and limitation of the output current. In the first mode, a given accelerating voltage is stabilized as the load current increases from 0 to 150 mA. This is the normal operation of the unit. As the load current increases to more than 150 mA, the accelerating voltage unit goes over to the current limitation mode within 50 s. This makes it possible to protect the load and to prevent the development of an arc discharge in case of breakdown in the electron gun. As the load current decreases, the accelerating voltage unit is back to normal operation. If the load current does not decrease, the unit is switched off for 20-100 m and then returns to normal operation. This algorithm provides fault-free operation in extreme transient and arcing environments. The discharge power supply unit is a current source with the output voltage ranging between 50 and 1500 V. It operates in the current stabilization mode throughout the output voltage range.Structurally, the accelerating voltage and discharge power supply units are made as two sections: a low-voltage section containing inverters and an oil-filled high-voltage tank in which the output stages are housed (Fig. 4). The control and stabilization of the beam current are performed by varying the discharge current with a control time constant no more than 0.1 s. 5. Arrangement and operation of the installation Fig. 5. Deposition of coatings is carried out in the vacuum chamber of the installation. Two e-guns mounted on the two-rectilinear manipulator are placed in the chamber. The manipulator, providing independent horizontal movement of the guns, is intended for deposition of coatings on large-area plane surfaces. The use of two simultaneously operating guns increases the productivity of the installation. For deposition of coatings on ring surfaces an additional manipulator is used which provides rotation of the workpieces. The appearance of the installation is shown in Fig. 5. The operation of the vacuum system, the power supply, the movement of the guns, and the technological process are controlled with an automated computer system. The choice of the mode of operation and the monitoring of technological parameters are performed with the help of commercial displays. To change the mode or a parameter, it suffices to press the graphical label of controls on the display with a finger. The control system can operate in one of the three modes: Vacuum System, E-Gun, and Manipulator. In the Vacuum System mode, it is possible to switch the pumps on and off and to open and close the valves of the vacuum system. The display shows the readings of the vacuum meters at different points of the vacuum system and the state of the pump cooling system. In this mode, it is possible to program all sequences of switchings of the valves and pumps for automated pumpdown of the vacuum chamber. Fig.6 Fig.7a Fig.7b The power supply of the electron-beam guns is controlled in the E-Gun mode (Fig.6).In this mode, it is possible to control the accelerating voltage,to change the magnitude of the beam current, and to control the gas flow rate and the parameters of the beam scanning over the surface of the workpiece. The Manipulator mode (Fig. 7, a, b) is intended to control the movement of the workpiece and eguns. Depending on the properties of the workpieces, two modes of operation of the manipulator are possible. For deposition of coatings on large plane surfaces the Manipulator-Plane Body mode(Fig. 7, a) is intended. In this mode, the workpiece is immobile, and two eabove its surface along a prescribed trajectory. The Manipulator-Body of Revolution mode(Fig. 7, b) is intended for deposition of coatings on axisymmetric surfaces. In this mode, the gun is immobile, and the workpiece is rotated at a certain angle with a given velocity. Table. Principal characteristics of the installation Voltage of the supply line, V 3805±5% Power input, kW 30 Limiting pressure in the vacuum chamber, Pa 10-2 Number of simultaneously operating e-guns 2 Rate of powder supply by the dispenser, g/min. 10-50 Accelerating voltage, kV up to 30 Beam current, mA up to 150 Dimensions of the vacuum chamber: diameter, mm length, mm 2020 3500 Conclusion The installation created by us is used on one of the world's largest metallurgical works-the West Siberian Iron and Steel Plant-for deposition of wear-resistant coatings on aerial and oxygen lances,on crystallizers of continuous casting of steel, and on rolls. References [1]V.E. Panin, S.I. Belyuk, V.G. Durakov, G.A. Pribytkov, and N.G.Rempe, Svarochnoe Proizvodstvo, 2, 34 (2000). [2]V.E. Panin, V.G. Durakov, G.A. Pribytkov,I.V.Polev, and S.I.Belyuk, Fizika i Khimia Obra botki Materialov, 6, 53 (1998). [3]V.L. Galansky, V.A. Gruzdev, I.V. Osipov, and N.G. Rempe, J. Phys. D: Appl. Phys., 27, 953(1994). [4]I. Osipov and N. Rempe, RSI, 1, 1638 (2000). 用電子束車削改善冶金設備零部件表面特性的自動裝置 S.I. Belyuk, A.G. Rau, I.V. Osipov*, N.G. Rempe* 能量物理和材料科學學院，2/1 Akademicheskii Ave.,Tomsk, Russia 湯姆斯卡雅斯州立大學的控制系統(tǒng)和無線電子學， 40 Lenin Ave., Tomsk, Russia, 摘要：電子束車削裝置是為金屬物件表面涂料的生產(chǎn)而設計的。涂料具有磨損保護和熱保護的性能。該裝置具有在大面積表面高效率制造涂料的能力。這個工藝流程是自動的。 在該車削裝置中有兩個陰極等離子體電子槍。這有可能增加車削效率和生產(chǎn)率。這使提高車削效率和生產(chǎn)率成為可能。這兩個電子槍被安裝在一個正交垂直機械手上的真空腔內，并且可以同時運行。 該裝置用于生產(chǎn)冶金中用在空氣噴槍、鋼連鑄晶體、輥碎機等上的耐磨涂料。 1 簡介 在真空狀態(tài)下的電子束車削，允許生產(chǎn)具有獨特性質的涂料。用該方法的涂料沉積無粘連問題。用這種方法生產(chǎn)的材料和在這些材料表面生產(chǎn)的涂料具有廣泛的多元化。與工藝流程適應能力控制結合的結果的高重復性，使生產(chǎn)滿足規(guī)定結構和預期性能成為可能。 為了增加熱空氣鼓風爐噴槍操作耐久性，我們?yōu)槠涑练e作用和各種機械零件和冶金設備的恢復開發(fā)了一套裝置。同樣該裝置可以被用于各種金屬和合金的焊接，包括高熔點金屬。 單層和多層涂料用于各種根據(jù)由各種金屬、鋼和鑄鐵組成的制品表面的切屑的組成的用途（硬化、耐磨、耐熱、耐高溫等），該裝置是生產(chǎn)此類型涂料成為可能。 用該裝置可以在最長為2100mm、最寬為900mm、最厚為200mm的飛機工件和直徑最大為1200mm，最長為21mm的回轉體工件表面上沉淀上涂料。 涂料沉淀的工藝流程是全自動的。 2 電子束車削 電子束切削的原理見圖1。電子束在工件表面建立一個熔融金屬池。在該表面上，來自具有需求特性的涂料的粉末顆粒由分配器提供給熔融金屬。工件在真空室內相對于電子槍（固定的）和分配器是移動的，或電子槍和分配器相對于工件（固定的）在移動。 多工序電子束切削技術是以凍結一個粉末進熔融金屬池的現(xiàn)象為基礎的。在每一個后續(xù)的工序，粉末的一個新部分是“凍結”的，以前的部分是融化的。供應給融池的粉末加速了金屬的結晶作用，從而促進了細粒結構的形成和緩解涂料中的殘余應力。所需沉積層的厚度通過改變粉末供應的速率或通過增加工序的數(shù)量來獲得。 這個切削的過程以下列參數(shù)為特征：加速電壓、電子束電流、調焦系統(tǒng)到工件表面的距離、電子束掃描直徑和長度、工件運動速度和粉末供應速率。 圖1 電子束切削原理 3 電子槍 切削過程伴隨著從切削層噴出的強烈的蒸汽和氣體。因此，真空腔內的電子槍被用來產(chǎn)生電子束。這些電子槍不含有在運行中被加熱的熱電極或組件，并且這使得它們反應遲鈍和在處理下的材料的高熔點蒸汽。它們可以在對發(fā)射器不使用特殊保護措施的切削條件下運行。 電子槍中的電子發(fā)射產(chǎn)生于空心腔低電壓反射放電的等離子體。從等離子體中發(fā)出的電子在高壓電場加速、匯聚成束和在調焦系統(tǒng)磁場中聚焦。來自等離子體的電子發(fā)射電流由不同的放電電流控制。 在電子槍的設計中，利用其密封性和機械強度的金屬均采用電子束焊接。電子槍的外殼均為內腔結構。這種外殼設計為陰極的定期維護提供了方便。圖2呈現(xiàn)了一個裝在該裝置機械臂上的電子槍的外觀。 圖2 該裝置機械臂上的電子槍 4 電源模塊 圖3 該設備的供電系統(tǒng) 該設備的供電系統(tǒng)（圖3），包括一個加速電壓單元（AVU），發(fā)射電源供電單元（DPU）、一個電子束聚焦和偏移控制單元（BFDU）和一個氣流控制器的控制單元。這個單元是由計算機經(jīng)由一個光學或一個RS485接口控制的。 加速電壓和發(fā)射電源供電單元是由帶相位控制回路的橋變換器這一經(jīng)典電路構成的。在變換器中，開關MOSFET晶體管這一共振法實現(xiàn)了提供一個低電平電噪聲和降低在開關電源晶體管的動態(tài)損失。高變換頻率能夠將供電電源輸出電容降低到10nF和增加控制信號的處理速度。 加速電壓單元可以在兩個模式下運行：加速電壓的穩(wěn)定性和輸出電流的有限性。在第一個模式下，當負載電流從0增加到150mA的過程中，給定的加速電壓是穩(wěn)定的。這是該單元的正常運行。當負載電流增加到超過150mA時，加速電壓單元在50s內穿越電流極限模式。這使得它能夠保護負載和防止電子槍故障時產(chǎn)生電弧放電。當負載電流減小時，加速電壓單元恢復正常運行。如果負載電流不減少，該單元關斷20-100ms，然后恢復正常運行。該算法在極端瞬態(tài)提供無故障運行和弧電環(huán)境。 放電供電電源單元是一個輸出電壓范圍為50V-1500V的電流源。它運行在貫穿整個輸出電壓范圍內的電流穩(wěn)定模式。從結構上來講,加速電壓和放電供電單元被做成兩個部分：一個低壓區(qū)包含了變換器和一個充滿油狀物的高壓蓄電池，其輸出級是被封裝的(圖4)。電子束電流的控制和穩(wěn)定由控制時間常數(shù)不超過0.1s的不同放電電流執(zhí)行的。 5 裝置的布置和操作 涂料的沉淀是在該裝置的真空腔內進行的。安裝在正交垂直機械手上的兩個電子槍被放置在真空腔內。為電子槍提供獨立橫向運動的機械手是專門用于大面積飛機表面涂料的沉淀。兩個同時運行的電子槍的使用提高了該裝置的生產(chǎn)率。為了在環(huán)形面上沉淀涂料，使用一個額外的機械手為工件提供旋轉。該裝置的外觀見圖5. 圖5 真空系統(tǒng)的運行、供電、電子槍的運動,工藝流程是由自動化的計算機系統(tǒng)控制的。運行 圖6 圖7a 圖7b 模式的選擇和工藝參數(shù)的監(jiān)測是通過工業(yè)顯示器的幫助執(zhí)行的。用手指點擊顯示器上的圖形控件可以去改變模式和參數(shù)。 該控制系統(tǒng)可以運行于三種模式：真空系統(tǒng)、電子槍、機械臂。 在真空系統(tǒng)的模式,可以起動和關停泵,開啟和關閉真空系統(tǒng)的閥。顯示器顯示在該真空系統(tǒng)的不同點的真空表的讀數(shù)和泵冷卻系統(tǒng)的狀態(tài)。在這種模式下，為真空腔的自動降壓可以預先確定閥門和泵的開關順序。 電子束槍的電力供應是在電子槍模式控制的(圖7)。在這種模式下，可以控制加速電壓、改變電子束電流的大小、和控制氣流速率和掃描工件表面的電子束的參數(shù)。 機械手模式（圖7a,b）是用來控制工件和電子槍的運動的。根據(jù)工件的性質,機械手的兩種操作模式都是可能的。機械手-飛機體模式用在大型飛機表面涂料的沉淀（圖7a）。在這種模式下，工件不動，兩個電子槍在其表面同時沿著規(guī)定的軌跡移動。 機械手旋轉模式用在軸對稱表面涂料的沉淀。在這種模式下,電子槍是不動的,工件以某一角度和給定的速度旋轉。 表1 該裝置的主要特點 供應管的電壓，V 3805±5% 輸入功率，KW 30 真空腔壓力極限，Pa 10-2 同時運行的電子槍的數(shù)目 2 分配器供應粉末的速率，g/min 10-50 加速電壓，KV up to 30 電子束電流，mA up to 150 真空腔的規(guī)格： 半徑，mm 長度，mm 2020 3500 結論 我們制造的該裝置用在世界上最大的冶金工程-西方的西伯利亞鋼鐵工廠，為了空氣噴槍、鋼連鑄晶體和輥碎機上耐磨涂料的沉淀。 參考文獻 [1] V.E. Panin, S.I. Belyuk, V.G. Durakov, G.A. Pribytkov, and N.G.Rempe, Svarochnoe Proizvodstvo, 2, 34 (2000). [2] V.E. Panin, V.G. Durakov, G.A. Pribytkov,I.V.Polev, and S.I.Belyuk, Fizika i Khimia Obra botki Materialov, 6, 53 (1998). [3] V.L. Galansky, V.A. Gruzdev, I.V. Osipov, and N.G. Rempe, J. Phys. D: Appl. Phys., 27, 953(1994). [4] I. Osipov and N. Rempe, RSI, 1, 1638 (2000).  １３ Designing Fault Tolerant Manipulators: How Many Degrees-of-Freedom? Christiaan J. J. Paredis and Pradeep K. Khosla Department of Electrical and Computer Engineering and The Robotics Institute,Carnegie Mellon University,Pittsburgh, Pennsylvania 15213. Abstract One of the most important parameters to consider when designing a manipulator is the number of degrees-of-freedom (DOFs). This article focuses on the question: How many DOFs are necessary and sufficient for fault tolerance and how should these DOFs be distributed along the length of the manipulator? A manipulator is fault tolerant if it can complete its task even when one of its joints fail sand is immobilized. The number of degrees-of-freedom needed for fault tolerance strongly depends on the knowledge available about the task. In this article, two approaches are explored. First, for the design of a General Purpose Fault Tolerant manipulator, it is assumed that neither the exact task trajectory, nor the redundancy resolution algorithm are known a priori and that the manipulator has no joint limits. In this case, two redundant DOFs are necessary and sufficient to sustain one joint failure as is demonstrate din two design templates for spatial fault tolerant manipulators. In a second approach, both the Cartesian task path and the redundancy resolution algorithm are assumed to be known. The design of such a Task Specific Fault Tolerant Manipulator requires only one degree-of-redundancy. 1 Introduction As robots are being used in a growing range of applications, the issue of reliability becomes more and more important. Recently, with the Hubble telescope and the Mars Observer, NASA has experienced firsthand how devastating the consequences can be when a critical component fails during a multi-billion dollar mission. Space applications are particularly vulnerable to failure, because of the adverse environment (cosmic rays, solar particles etc.) and the demand for long term operation. In this context, NASA has started to incorporate fault tolerance in their robot designs (Wu et al. 1993). Reliability is also important in medical robotics, because of the risk of the loss of human life. Although medical staff will probably always be on standby to take over in the case of a manipulator failure, the robot should at least be fail-safe, meaning it should fail into a safe configuration. A third domain of robot applications in which reliability is a major issue is the Environmental Restoration and Waste Management (ER&WM) program of the Department of Energy. Consider, for instance, the use of a manipulator in a nuclear environment where equipment has to be repaired or space has to be searched for radioactive contamination. The manipulator system deployed in these kinds of critical tasks must be reliable, so that the successful completion of the task or the safe removal of the robot system is assured. In this article, we focus on fault tolerance as a technique to achieve reliability in manipulator systems. The traditional approach to reliability has been that of fault intolerance, where the reliability of the system is assured by the use of high quality components. However, increasing system complexity and the necessity for long term operation have proven this approach inadequate. The system reliability can be further improved through redundancy. This design approach was already advocated in the early fifties by von Neumann in connection with the design of reliable computers: “The complete system must be organized in such a manner, that a malfunction of the whole automaton cannot be caused by the malfunctioning of a single component, ... , but only by the malfunctioning of a large number of them”(von Neumann 1956, p. 70). This is the basic principle of fault tolerance: add redundancy to compensate for possible failures of components. However, this does not mean that any kind of redundancy added to a system results in fault tolerance. The main goal of this article is therefore to shed some light on the redundancy requirements for fault tolerant manipulators. That is, how much redundancy is needed and how should this redundancy be distributed over the manipulator structure? The redundancy provisions needed for fault tolerance can be incorporated only at a price of increased complexity. This drawback can be overcome by a modular and structured design philosophy, as is advocated in (Schmitz, Khosla, and Kanade 1988; Fukuda et al. 1992; Sreevijayan 1992; Hui et al. 1993;Chen and Burdick 1995). Modularity in hardware and software has the advantage of facilitating testing during the design phase and therefore reducing the chances for unanticipated faults. Modules also constitute natural boundaries to which faults can be confined. By including fault detection and recovery mechanisms in critical modules, the effect of local faults remains internal to the modules, totally transparent to the higher levels of the manipulator system. Such a modular design philosophy is embodied in the Reconfigurable Modular Manipulator System (RMMS) developed in the Advanced Manipulators Laboratory at Carnegie Mellon University (Schmitz, Khosla, and Kanade 1988). The RMMS utilizes a stock of interchangeable link modules of different lengths and shapes, and joint modules of various sizes and performance specifications. By combining these general purpose modules, a wide range of manipulator configurations can be assembled. When one needs a different configurations for a specific task (Paredis, and Khosla 1993), a robot created with the RMMS can be easily taken apart and reconfigured suitably. This reconfigurability can be further exploited to reduce the complexity of fault tolerant manipulators, as is shown in Section 4. Over the past decade, a lot of research has been done in fault tolerance for computer systems (refer to Johnson (1989) for and overview), but only recently has the concept been applied in robotics. Most of the work in fault tolerant robotics is directly based on the results from computer science, and can be classified in three categories: 1. Design of fault tolerant robots, 2. Fault detection and identification (FDI), 3. Fault recovery and intelligent control. When designing a fault tolerant manipulator, one should decide where to include redundancy so that the overall reliability is maximum. One should distinguish between hardware, software, analytical, information, and time redundancy (Johnson 1989). Our focus will be on hardware redundancy, which consists of actuation, sensor, communication and computing redundancy. Each of these types of redundancies can still be implemented at different levels. In Sreevijayan (1992), for instance, a four-level subsumptive architecture for actuation redundancy is proposed: Level 1: Dual actuators—extra actuators per joint, Level 2: Parallel structures—extra joints per DOF, Level 3: Redundant manipulators—extra DOFs per manipulator arm, Level 4: Multiple arms—extra arms per manipulator system. A system can possibly be designed with redundancies at all four levels, resulting in the ability to sustain multiple simultaneous faults. An example of a fault tolerant design for the space shuttle manipulator is described in Wu et al. (1993). Fault tolerance is here guaranteed by using a differential gear train with dual input actuators for every DOF—an implementation of the first level of the four-level subsumptive architecture. In this article, we are more interested in achieving fault tolerance using redundant DOFs (Level 3). We envision the following scenario. A fault detection and identification algorithm monitors the proper functioning of each DOF of a redundant manipulator. As soon as a failure of a subcomponent is detected, one immobilizes the corresponding DOF by activating its fail-safe brake. Automatically, the joint trajectory is adapted to the new manipulator structure and the task is continued without interruption. The strength of this scenario resides in the fact that it can handle a large variety of possible faults, ranging from sensor failures to transmission and actuation failures. All these failures can be treated in the same manner, namely, by eliminating the whole DOF through immobilization. Although fault detection and identification (FDI) is an important part of our scenario for fault tolerance, we will not cover this subject in this article. Instead we refer to the following references (Chow and Willsky 1984; Stengel 1988; Ting, Tosunoglu, and Tesar 1993; Visinsky, Walker, and Cavallaro 1993;Visinsky, Walker, and Cavallaro 1994). In Visinsky, Walker, and Cavallaro (1993), using the concept of analytical redundancy, an FDI algorithm is presented along the lines of Chow and Willsky (1984). The result is a set of four simple equations which test for consistency between the measured position and velocity and the expected acceleration and jerk. This FDI algorithm fits into a three-layer intelligent control framework, consisting of a servo layer, and interface layer and a supervisory layer. The main problem presented to the intelligent controller is to distinguish between failures, disturbances and modeling errors, and to respond to each in the proper way. An overview of intelligent fault tolerant control is given in Stengel (1988). A range of approaches is reported, beginning with robust control, progressing through parallel and analytical redundancy, and ending with rule-based systems and artificial neural networks. The task of the robotics researcher is to apply and modify these approaches to the highly non-linear dynamics of robot manipulators. After a fault has been detected, the failing DOF is immobilized by activating its brake. In Pradeepetal. (1988), the authors analyze the effect of the immobilization of one of the DOFs of three commercial manipulators. They conclude that the robots with decoupled DOFs are more severely “crippled” by the loss of a joint than the ones with strongly coupled DOFs. This can be translated into the guideline that, for the design of fault tolerant manipulators, strong coupling between the DOFs is highly desirable. The results presented in Lewis and Maciejewski (1994a) can be interpreted similarly. A kinematic fault tolerance measure is defined as the minimum kinematic dexterity after joint failure. The maximum kinematic fault tolerance is achieved in a manipulator posture in which each joint contributes equally to the null-space motion—a posture with strong coupling between the DOFs. For a manipulator with at least one decoupled DOF, the kinematic fault tolerance measure is always minimal, that is, zero. The same measure can be used as a criterion for the redundancy resolution of the fault-free manipulator. It is shown that the chances for task completion, after immobilization of one joint due to failure, are much better than when traditional pseudo-inverse control is used. However, due to the local nature of the fault tolerance measure, completion of the task cannot be guaranteed on a global scale (Lewis and Maciejewski 1994b). An important conclusion is that the ability to recover from a fault depends strongly on the joint trajectory followed by the fault-free manipulator system. This conclusion led us to explore two approaches to the problem of manipulator fault tolerance. The two approaches differ in the assumptions that are made with regard to the task and with regard to the choice of redundancy resolution algorithm. In a first approach, the goal is to design a general purpose fault tolerant manipulator. We assume that the task is only characterized by the size and position of the task space which is the portion of the Cartesian output space in which the task will take place. No assumptions are made about the path that needs to be followed within the task space or about the redundancy resolution algorithm used to execute the task. Such a general purpose fault tolerant manipulator can fault tolerantly execute any task of which the task space lies inside the fault tolerant workspace of the manipulator. This approach to fault tolerance is further explored in Section 3. In a second approach, the goal is to design a task specific fault tolerant manipulator. In this approach, we assume that the Cartesian path to be followed is known a priori and that the corresponding set of possible joint trajectories can be limited by an appropriate choice of a redundancy resolution algorithm. We show in Section 4 how these additional assumptions allow us to design a fault tolerant manipulator with fewer DOFs than a general purpose fault tolerant manipulator. For both approaches, we will in this article answer the question: How many degrees-of-redundancy (DORs) are necessary and sufficient for fault tolerance? 2 Fault Tolerance and Reliability The basic idea presented in this article is to use a manipulator’s redundant DOFs to compensate for a possible failure of one of the joints. The underlying assumption is that a manipulator that can sustain a joint failure is more reliable than one that cannot. The question is: “Does fault tolerance always result in an increase in reliability?” The answer is given by reliability theory (Johnson 1989). The reliability, R(t), of a component or a system is the conditional probability that the component operates correctly throughout the interval [t0, t] , given that it was operating correctly at the time t0 . For non-fault-tolerant serial link manipulators, the system fails when any single subsystem—a DOF or joint module for modular manipulators—fails. The system reliability can then be computed as the product of the module reliabilities, Ri(t)： Or, in the case that every module is equally reliable with reliability Rmod(t)： If there are n modules and only of those are required for the system to function properly—the system can tolerate (n – m) module failures—then the system reliability is the sum of the reliabilities of all systems with (n – m) or fewer faults. Since there are different systems with faults, the system reliability of a fault tolerant system with equal module reliabilities can be written concisely as We can apply this formula to the example of an 8-DOF fault tolerant manipulator, which needs only seven DOFs to function properly. The system reliability of the fault tolerant system is: Compared to for an equivalent 6-DOF non-fault-tolerant system. Both reliabilities are plotted as a function of the module reliability in Figure 1a, while Figure 1b shows the relative system reliability which equals 1 for and . These graphs should be interpreted as follows: ? when then The system reliability is zero in both cases, i.e.,both systems are guaranteed to fail. ? when , then That is, both systems are 100% reliable. ? when then meaning that the fault tolerant system is more reliable than the non-fault-tolerant one. ? when then The modules are so unreliable that the added complexity of the fault tolerant system reduces the overall performance. Preferably, one would like to operate a system at a reliability close to one, for which the fault tolerant system is the more reliable. To compare both alternatives for modules with a high reliability, it is more instructive to rewrite Equation (4) as an expression for the system’s unreliability, When The unreliability for the non-fault-tolerant system is In general, the unreliability of a k-fault tolerant system—one that can sustain k faults—is of the order This means that the reliability of a fault tolerant system increases more significantly when the reliability of the individual modules is high. Best results are thus obtained when fault tolerance is combined with high component reliability, or fault intolerance. 3 General Purpose Fault Tolerant Manipulators In this section, we discuss the kinematic design of a general purpose fault tolerant manipulator without joint limits. As for non-fault-tolerant manipulators, the kinematic capabilities are mainly characterized by the shape and size of the workspace or rather the fault tolerant workspace (FTWS) in this case. We identify several properties of general purpose fault tolerant manipulators and their workspaces, and propose an 8-DOF design template.To set the stage for our development, we define the following concepts relating to general purpose fault tolerant manipulators: ? General Purpose Fault Tolerant Manipulator: A manipulator that will still be able to meet the task specifications, even if any one or more of its joints fail and are frozen at any arbitrary joint angles. ? k-Reduced Order Derivative (k-ROD): When k joints of an n-DOF manipulator fail, the effective number of joints is (n – k). The resulting faulty manipulator is called a k-reduced order derivative. ? Order of Fault Tolerance: A manipulator is fault tolerant of the k-th order, if and only if all possible k-reduced order derivatives can still perform the specified task. We call the manipulator k-fault tolerant. ? Fault Tolerant Workspace (FTWS): The fault tolerant workspace of a -fault tolerant manipulator is the set of points reachable by all possible -reduced order derivatives. Notice that our definition of a general purpose fault tolerant manipulator reflects the assumption that the redundancy resolution algorithm is not known a priori: a joint failure can occur at an arbitrary angle. n the remainder of this section, if no specific task is mentioned, it is assumed that the task is to reach a onzero volume of points. That is, the task space is an m-dimensional manifold in the m-dimensional utput space of the manipulator. A manipulator with a FTWS of dimension less than m is considered ot to be fault tolerant. 3.1 Properties of General Purpose Fault Tolerant Manipulators 3.1.1 Existence A general purpose manipulator has six DOFs which allow it to position its end effector in an arbitrary sition and orientation anywhere in its workspace. An obvious way to make this manipulator fault tolerant is to esign every joint with a redundant actuator. If one of the actuators of the resulting 2n-DOF fault tolerant manipulator were to fail, the redundant actuator could take over and the manipulator ould still be functional. imilarly, a k-fault tolerant manipulator can be constructed by duplicating very DOF k times, resulting in a (k+1)n-DOF pulator. This argument illustrates that (k+1)nDOFs are sufficient for -th order fault tolerance. In the remainder of this section, we determine the number of DOFs necessary to achieve general purpose fault tolerance. 3.1.2 Boundary of the Fault Tolerant Workspace In this section, we show that a boundary point of the FTWS is a critical value. Consider a k–fault tolerant planar manipulator, M . A boundary point, , of the FTWS has to be an element of the boundary of the workspace of at least one ROD, M*, obtained by freezing k joints of M. Indeed, if were an interior point of the workspaces of all RODs, then it would by definition be an interior point of the FTWS and not a boundary point. The Jacobian of M* , , can be obtained from the Jacobian of M,, by deleting the columns corresponding to the frozen DOFs. Because is a boundary point of the workspace of M*, the Jacobian of M*at Pb is singular. We prove now that JM is singular too.Suppose that JM were non-singular, then at least one of the columns corresponding to a frozen DOF would be outside the column space of the singular matrix, . Physically this means that a small change in the angle of that frozen DOF would cause the end effector of to move in a direction with a component perpendicular to the boundary of the workspace of the ROD, M*, as illustrated in Figure 2.The ROD with this new frozen angle would be unable to reach the point,. As a result, would be outside the FTWS, contradicting the fact that is a boundary point of the FTWS. Thus, is singular and is a critical va