@prefix vivo: . @prefix edm: . @prefix ns0: . @prefix dcterms: . @prefix dc: . @prefix skos: . vivo:departmentOrSchool "Applied Science, Faculty of"@en, "Mechanical Engineering, Department of"@en ; edm:dataProvider "DSpace"@en ; ns0:degreeCampus "UBCV"@en ; dcterms:creator "Gupta, Arun"@en ; dcterms:issued "2009-03-09T16:12:49Z"@en, "2008"@en ; vivo:relatedDegree "Master of Applied Science - MASc"@en ; ns0:degreeGrantor "University of British Columbia"@en ; dcterms:description """This thesis focuses on the study of failure detection and identification of an innovative multi-modular robot that has been designed and developed in our laboratory. The interest in this class of manipulators developed after Canada's participation in the development of the international space station. All the existing space based manipulators have exclusively revolute joints, providing rotational motions. However, our laboratory manipulator has combined revolute (rotational) and prismatic (translational) joints in each module. Several such modules are connected in series to form the multi-modular deployable manipulator system (MDMS), as desired. This innovative design has several advantages when compared with its counterparts; for example, reduced singular configurations, reduced dynamic interactions, and improved obstacle avoidance capability for a specified number of degrees of freedom. Structural failures of a robotic system are critical in remote and dangerous surroundings such as space, radioactive sites or areas of explosion or battle. During the course of a robotic undertaking if there is a malfunction or failure in the manipulator, still one would wish to have the task completed autonomously, without human intervention. A manipulator that accomplishes such tasks has to be highly reliable, safe, and cost effective, and must possess good maintainability and survival rate. In the present thesis, methodology is developed for identification of structural failures in the multi-modular manipulator system MDMS, which through the use of a decision-making strategy, effective control and kinematic redundancy is capable of satisfactorily executing the intended task in the presence of joint malfunction or failure. The Bayes hypothesis testing method is used to identify the failure. First, a possible set of failure modes is defined, and a hypothesis is associated with each considered failure mode. The most likely hypothesis is selected depending on the observations of the response of the manipulator and a suitable test. This test minimizes the maximum risk of accepting a false hypothesis and thus the identification methodology is considered as most optimal. This failure identification methodology is general and can be used for any failure detection strategy. In the present thesis, the physical MDMS is subjected to several critical failure scenarios in our laboratory. In particular we consider failure due to locked joint, freewheeling of the joint and the sensor failure. The results are studied to evaluate the effectiveness of the methodology for fault-tolerant operation of a class of robotic manipulators."""@en ; edm:aggregatedCHO "https://circle.library.ubc.ca/rest/handle/2429/5742?expand=metadata"@en ; dcterms:extent "5095116 bytes"@en ; dc:format "application/pdf"@en ; skos:note "FAILURE DETECTION AND DIAGNOSIS IN A MULTI-MODULE DEPLOYABLE MANIPULATOR SYSTEM (MDMS) by ARUN GUPTA B.Eng., The Maharaja Sayaji Rao University, Baroda, 1985 M.S., Southern Illinois University, Edwardsville, Illinois, 1999 A THESIS SUBMITTED IN THE PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF APPLIED SCIENCE in THE FACULTY OF GRADUATE STUDIES (Mechanical Engineering) THE UNIVERSITY OF BRITISH COLUMBIA (Vancouver) June 2008 © Arun Gupta, 2008 ABSTRACT This thesis focuses on the study of failure detection and identification of an innovative multi-modular robot that has been designed and developed in our laboratory. The interest in this class of manipulators developed after Canada's participation in the development of the international space station. All the existing space based manipulators have exclusively revolute joints, providing rotational motions. However, our laboratory manipulator has combined revolute (rotational) and prismatic (translational) joints in each module. Several such modules are connected in series to form the multi-modular deployable manipulator system (MDMS), as desired. This innovative design has several advantages when compared with its counterparts; for example, reduced singular configurations, reduced dynamic interactions, and improved obstacle avoidance capability for a specified number of degrees of freedom. Structural failures of a robotic system are critical in remote and dangerous surroundings such as space, radioactive sites or areas of explosion or battle. During the course of a robotic undertaking if there is a malfunction or failure in the manipulator, still one would wish to have the task completed autonomously, without human intervention. A manipulator that accomplishes such tasks has to be highly reliable, safe, and cost effective, and must possess good maintainability and survival rate. In the present thesis, methodology is developed for identification of structural failures in the multi-modular manipulator system MDMS, which through the use of a decision-making strategy, effective control and kinematic redundancy is capable of satisfactorily executing the intended task in the presence of joint malfunction or failure. The Bayes hypothesis testing method is used to identify the failure. First, a possible set of failure modes is defined, and a hypothesis is associated with each considered failure mode. The most likely hypothesis is selected depending on the observations of the response of the manipulator and a suitable test. This test minimizes the maximum risk of accepting a false hypothesis and thus the identification methodology is considered as most optimal. This failure identification methodology is general and can be used for any failure detection strategy. In the present thesis, the physical MDMS is subjected to several critical failure scenarios in our laboratory. In particular we consider failure due to locked joint, freewheeling of the joint and the sensor failure. The results are studied to evaluate the effectiveness of the methodology for fault-tolerant operation of a class of robotic manipulators. ii TABLE OF CONTENTS ABSTRACT ii TABLE O F CONTENTS iii LIST O F FIGURES v LIST O F SYMBOLS \". vi ACKNOWLEDGEMENT ix CHAPTER 1 INTRODUCTION... . 1 1.1 Preliminary Remarks 1 1.2 Objectives 3 1.3 Review of Literature 6 1.4 Scope of the Investigation 9 CHAPTER 2 EXPERIMENTAL ROBOTIC SYSTEM 11 2.1 Introduction 11 2.2 Physical Robotic System 12 2.3 Design Requirements and Criteria 17 2.4 Computer Control System 19 2.4.1 Optical Encoders 19 2.4.2 Motion Control Interface Board 21 2.4.3 Servo Amplifiers and Power Supplies 22 2.4.4 Control System 22 2.5 Advantages 24 2.6 Manipulator Model 26 CHAPTER 3 STRUCTURAL FAILURE DETECTION 30 3.1 Introduction 30 3.2 Bayesian Hypothesis Testing 31 3.2.1 Gaussian Problem 34 3.3 Joint Failure Modes 38 3.3.1 Sensor Failure 38 3.3.2 Locked Joint Failure 38 3.3.3 Freewheeling Joint Failure 39 iii CHAPTER 4 FAULT DIAGNOSIS A N D CONTROL 40 4.1 Introduction 40 4.2 Joint Failure Identification 40 4.2.1 No Failure 40 4.2.2 Sensor Failure 42 4.2.3 Locked Joint Failure 43 4.2.4 Free Wheeling Joint Failure 48 4.2.5 Prismatic Joint Locking Failure 52 4.3 Discussion of the Results 56 CHAPTER 5 CONCLUDING REMARKS 57 5.1 Significance of the Work 57 5.2 Main Contributions 58 5.3 Summary and Conclusions 59 5.4 Recommendations for Future Work 60 BIBLIOGRAPHY 62 APPENDIX 1 65 iv LIST OF FIGURES Figure 1-1: Canadarm 2 Figure 1-2: Shell Pump in California 2 Figure 1-3: ASIMO by Honda 2 Figure 2-1: MDMS Mobile Base 13 Figure 2-2: Schematic Layout of MDMS 14 Figure 2-3: AUTOCAD Layout of MDMS 15 Figure 2-4 : The MDMS System Developed in Our Laboratory 16 Figure 2-5: Servo Control System Schematic 20 Figure 2-6: Schematic Diagram of the Robot Control System 23 Figure 2-7: Underground Arm by Numet Engineering 25 Figure 2-8: Hydraulic Excavators 25 Figure 2-9: Forestry Equipment 26 Figure 2-10: Schematic diagram of the two-module manipulator 28 Figure 3-1: Fault Diagnosis and Control System Block Diagram 37 Figure 4-1: Joint Responses Under Normal Operation 41 Figure 4-2: Tip Trajectory of the Manipulator Under Normal Operating conditions 42 Figure 4-3: Manipulator Response Under Sensor Failure 43 Figure 4-4: Manipulator Response Under Locked Joint 45 Figure 4-5: Trajectory of the Manipulator Tip 46 Figure 4-6: Manipulator Response Under Locked Joint 1 47 Figure 4-7: Manipulator Response Under Freewheeling of Base Link 49 Figure 4-8: Tip Trajectory of the Manipulator 50 Figure 4-9: Manipulator Response Under Freewheeling of Joint 1 51 Figure 4-10: Tip Trajectory of the Manipulator 52 Figure 4-11: Manipulator Response Under Failure of the Base Link Prismatic Joint 53 Figure 4-12: Tip Trajectory of the Manipulator 54 Figure 4-13: Manipulator Response Under Failure of the Prismatic Joint of Link 1 55 Figure 4-14: Tip Trajectory of the Manipulator 56 v LIST OF SYMBOLS B risk function C discrete system output matrix C cost function Cy cost of accepting //,. when H j is true /Y/H (y IHj) conditional probability density function of the observation vector given that Hj is true F vector containing the terms associated with the centrifugal, Coriolis, gravitational, elastic and internal dissipative forces g gravitational acceleration Hi i'h hypothesis K^ derivative gain matrix of the PID controller K, integral gain matrix of the PID controller K^ proportional gain matrix of the PID or FLT controller /,. length of i* link ld ,ls length of deployable and slewing links, respectively M number of hypotheses M coupled system mass matrix M decoupled system mass matrix P(Hi, Hj) joint probability that Hj is accepted when Hj is true PyHjl H t) conditionalprobability of accepting Hi when Hj is true PH apriori probability of occurrence of / / . q set of generalized coordinates leading to the coupled mass matrix M q set of generalized coordinates leading to the decoupled mass matrix M Q vector containing the external non-conservative generalized forces i*j position vector of the elemental mass dmj with respect to the frame Ft Rd Rayleigh dissipation function for the whole system R, R c first velocity transformation matrices VI R second velocity transformation matrix t time u control input vector V. covariance matrix of the hypothesis conditioned measurement error y-y,- measurement error (x;, y.) Cartesian components of r, xd, y d desired target point x(k) discrete system state vector y observation vector y(k) discrete system observation vector j>,.. expected value of the measurement vector conditioned on hypothesis y observation estimation error Z observation space Z, i'h observation subspace Greek Symbols aj rigid body angular motion of the revolute joint i Pi flexibility contribution to angular motion of the revolute joint i <5N+1 generalized coordinate for the elastic deformation of the payload desired pointing direction {k + 1 , k) discrete system state transition matrix T(k +1, k) discrete system input distribution matrix A dot above a character refers to differentiation with respect to time. A boldface lower case character denotes a vector. A boldface uppercase character denotes a matrix. Subscript ' being the desired target and the pointing direction, respectively, and /, fixed at an arbitrary value, we can express the joint locus with respect to the manipulator tip as: 28 (xd - l2 cos^f + (yd -1\\ sin^)2 = if (2. 5) This is a quadratic equation in l2, which may be solved to give l2 = {xd cos^ + yd sm0)±^(xdcos0 + yd sin^)2 - [xd + y] -If) 6X =arctan f 7 • J.\\ yd-i2sm0 (2.6) (2.7) v x r f - / 2 c o s ^ and e2=(j)-dx (2.8) The obvious choice for the possible solution for l2 is the smaller value, for the reasons of less movement and lower inertia of module # 2, thus less effort for the slew manoeuvre of this module. Now the inverse kinematics is carried out with the shoulder joint of the two-module manipulator failed. In this case the revolute joint is locked at some position. The manipulator is left with three other degrees of freedom to complete the desired manoeuvre. When 6X is fixed, then in order to achieve the desired orientation, 62 has to be equal to (2.9) y coordinate: /, sin^ = yd -12 sin^ (2. 10) Solving these equations simultaneously yields the expressions for /, and l2 as: yd-xd*z+ ( 2 U ) sin 6X - cos 9X tan h=_yA-xito*&i_ ( 2 1 2 ) sin - tan 0X cos (/> 29 CHAPTER 3 STRUCTURAL FAILURE DETECTION 3.1 Introduction This chapter deals with the development and formulation of the methodology for the detection and identification of structural failure for the multi-modular deployable manipulator system (MDMS). There are several possibilities of structural failure in the MDMS. The failure could be a partial or total. The various scenarios for total failure are: • Free swinging of a revolute joint or alternatively free sliding of a prismatic joint. This could be due to disengagement of transmission, loss of power, and so on • Locked joint (rotary or translatory) because of jamming of bearings or transmission or failure of motor in the braked condition • Failure of data acquisition for a joint • Sensor failure at j oint The partial failure may occur due to: • Slippage in a joint. This can be due to increased backlash, partial disengagement of transmission, and wear or malfunction of some part • Increased resistance in joint movement. This may happen due to the misalignment in transmission or bearing, loss of lubrication, and so on • Increase in vibration. This can be due to wear, damage, or misalignment of gearing, bearings, and other moving parts. It is of utmost importance to study these failure modes in order to detect them accurately and quickly during operation of the robotic manipulator. The manipulators under study are useful in remote locations or hazardous environments where it may not be feasible to use humans. Hence the reliability and dependability of these manipulators is of prime importance. The various types of failures listed previously represent some of the common and important failure modes. A robot may get stuck or buried under a heavy load while performing a task. A link may bend or crack due to the impact of a falling or colliding object and may fail to function normally. Containment seals may break and allow dust and contaminants to penetrate into the system thereby causing abrasion of the sliding surfaces, increased friction, and corrosion. In view of all such known and unknown hazards that a manipulator may have to face it is very important that a practical manipulator is thoroughly evaluated using experimentation as well as computer simulation before it is commissioned for a task. In particular, fault tolerance with respect to real failure scenarios has to be investigated to gain confidence in the system. Through such investigations it is possible to understand the behaviour of the manipulator system under practical conditions and to determine in advance the failure modes under which the manipulator will be able to function adequately and complete the task. Also, one will be able to develop alternative approaches to overcome other failure situations. The identification of a malfunction or failure involves two tasks; namely, decision and estimation. In the present work the decision of the type of failure that exists is done in an optimal manner on the basis of the cost associated with various decisions that include both correct and incorrect decisions. The development of the failure identification process is based on Bayesian hypothesis testing. The assumption of a Gaussian problem is done in this context. The Gaussian assumption is justified in view of the familiar central limit theorem [2] and it is commonly used in various engineering systems, as in the present work. The formulated decision logic requires the measurement errors and the corresponding covariance matrices, conditioned on each failure hypothesis at each sampling instant. Information on this is obtained by sensing and estimation, through a bank of Kalman filters. 3.2 Bayesian Hypothesis Testing The main objective of a manipulator system whether fully operational or experiencing some type of malfunction is to detect the operating state and bring the job to a satisfactory conclusion using the detected information and proper control. In the present work, Bayes hypothesis testing is applied to identify the operating conditions of the manipulator, before taking corrective control if a malfunction exists. In the development of Bayes hypothesis testing, first the system is assumed to take one of several, say M, disjoint states each of which is associated with a considered failure mode. Based upon a suitable test and observations, the most likely hypothesis is selected. The various common tests used for this purpose are: • Bayes test • Likelihood ratio test • Minimax test The Bayes test is the most general method and the other two are special cases derived from it. In the likelihood ratio test, different hypotheses are given the same apriori probabilities of occurrence. In the minimax test, the maximum risk is minimized. The objective is to find the Bayes risk function corresponding to the least favourable apriori probability distribution. The test is derived using the general Bayesian procedure. 31 The present method of failure identification is based on Bayes hypothesis testing. First, a possible set of failure modes is defined, and a hypothesis is associated with each considered failure mode. The most likely hypothesis is selected depending on the observations of the response of the manipulator and a suitable test. This test minimizes the maximum risk of accepting a false hypothesis, and accordingly the identification methodology is considered optimal. The general Bayesian hypothesis testing algorithm is derived by first defining M disjoint states or hypotheses, denoted by Hl,H2,H3,...,HM . The observation spaceZ is partitioned into M subspaces Z,, Z2, Z3,..., ZM . The system is assumed to take one of the several, say M, disjoint states each of which is associated with a considered failure mode. Then the observation space is given as M Z = (JZ: (3.1) If the observation vector falls into a particular observation subspace Z,, then H, is chosen as the most likely hypothesis. Mathematically, we can state that as yeZ ,=> accept H, (3. 2) The subspaces Z;. are determined by minimizing the risk function B , which is defined as the expected value of the cost function denoted by C(H,H). This cost function specifies the penalty or loss or cost of making an incorrect decision. Here H denotes the hypothesis set {//, ,H2,H3,..., HM }. Particularly, C,y is the cost of accepting the hypothesis Hi when the hypothesis H. is actually true. The risk function can be expressed as MM . . B = E[C{U, H)] = £ £ CijP(Hi, Hj) (3. 3) where P\\Hi, H'.) is the joint probability that Hj is accepted when Hj is true: p{H„Hj)=P(Hi/Hj)PHj (3.4) and P(H,IHJ)= If^iy/HjW (3.5) z, where P\\HJHj) is the conditional probability of accepting//,, given that H j is true, 32 PH is the apriori probability of occurrence of H j and fY/H xy/Hj) is the conditional probability density function of the observation random vector given that B is true. The substitution of equation (3.5) in equation (3.3) yields, MM e l \\ B = TLCijpHj\\fm\\ylHj)dy (3.6) i=l 7=1 Since we get J/v/H(y/^)* = i M M °=I V*, - 1 1 % jfwb/Hjte 7=1 1=1 Thus the risk function may be expressed as M M J M 7=1 ^ (3.7) where ^ = ( Q - ^ K / Y / H ( y / ^ ) (3-8) The first term on the right hand side of equation (3.7) is a constant and therefore can be disregarded in the minimization. Also from equation (3.8) we see that /?,.,. = 0 for all i and fiv > 0 for / * j because, for a realistic problem with non-zero probability density functions, there is Cy>Cij for any / and all j*i (3.9) and PH/Y»iy^j)>o (3. 10) Thus, the risk function (3.7) can be simplified further as M f U \\ *-=Xj U, '=1 z, dy (3. 11) \\j=hj*i / 33 Hence, for a particular observation vector say y, if the minimum of ^Py corresponds to i = / then we accept H, as the most likely hypothesis because then and only then each integral in the summation over /will be at its minimum, hence B* will be minimum. Suppose that the apriori probabilities of occurrence of different hypotheses are the same; in particular, PHj =PH forall j and the cost of selecting a correct hypothesis is zero: C,. = 0 for i = j = C > 0 for i* j Then M M . . As the minimum of this expression is resulted if and only if the largest term in the summation is eliminated, the decision logic becomes: Accept: H, if fYia {ylH,)> fYfH (y/H,) for all i*l (3.12) 3.2.1 Gaussian Problem The various inputs to the manipulator system and the measurements through the sensors generally contain the disturbances usually in the form of noise. The common assumption is that the disturbances and noise are independent zero mean Gaussian white noise vectors. This common assumption is justified in view of the central limit theorem [2]. If the system initial states are Gaussian, then the state vector is also Gaussian because it is a linear combination of the initial state and the input disturbances. Accordingly, the measurement vector is also Gaussian. Therefore, one has fymb'Hj^ wa. , e 2 (3-13) Here j>(. is the expected value of the measurement vector conditioned on hypothesis Hj and V,. is the covariance matrix of the hypothesis conditioned measurement error y - y,. Since logarithm is a monotonic function, the test (3.12) is similar to the following: Accept H, if In /y/H {ylH,)> fY/H (y/H,) for all / * I 34 Applying equation (3.13) results in: Accept H, if a, < aj for all / * / (3. 14) where a ^ l n l v J + I C y - y J V ^ y - y , . ) (3.15) The decision logic developed here requires the information of the measurement errors y - y. and the corresponding covariance matrices V,. conditioned on each hypothesis Ht at every instant when the system is checked for any failure and the decision is made. We can obtain this at either each sampling instant or after we have some accumulated observations. It is desirable to opt for the later as that will produce more accurate decisions, because more information will be available at each hypothesis testing stage. In the present work, a decision is made at every sampling instant. The hypothesis conditioned errors and the covariance matrices are obtained from a bank of M Kalman filters. Consider a robotic manipulator whose dynamics given by the following discrete state-space equations, which are linearized by expanding the system equation using the Taylor series and neglecting the higher order terms: x(ifc + l) - j , the optimal estimate of (3.24) is obtained as i{k/jj=<*(k/j)kU/j)+ X^(^0r(/,/-l)u(z-l) (3.25) 1=7+1 The conditional distribution of a Gaussian random vector x given another one y, is Gaussian with mean and the covariance matrix given by the following [20]: E[xly] = x + YxyV^{y-y) (3.26) P w v = P « - P x , P ; X (3-27) where, E[x]=x 4x-xXy-y)1=P„ For Gaussian random vectors x, y, and z one has 36 E[x/y, z] = E[x/y, z] = E[x/y] = E[x/z] - x (3. 28) where z = z- E\\zl y] Since x(0) and w(j) are Gaussian, x(k) ismerely a sum of Gaussian random vectors, and thus is Gaussian. Similarly, y(k) is Gaussian as v(z') and x(z') are Gaussian. The operation of this fault diagnosis and control system is shown in the block diagram of Figure 3-1. The desired motion is the reference motion that is fed to the system. The actual robotic motion is compared to the desired motion and is fed to the controller along with the estimated output. The corrected output is then linearized and passed through various Kalman filters. The results are then processed using the failure mode detection logic. Thereafter the output is estimated and compared to the desired output. The PID controller used here controls the manipulator motion so that the estimated output matches the desired output. Identification of the Linearized Robot Model Linearized System Output Kalman Filter Conditioned forH, Kalman Filter Conditioned forH,, Desired Joint Motion Conditioned upon Current States Desired Motion tes ^>. \" \" K y - * - Controller Robot System System Output Failure Mode Detection Logic Joint Motion Computer Estimated Output Identified System States Figure 3-1: Fault Diagnosis and Control System Block Diagram 37 3.3 Joint Failure Modes As seen in Section 3.1 there are several failure modes classified as total or partial failure. In the current study, the three main failure modes considered are locked joint, free joint and sensor failure. These are some of the major failure modes. For a manipulator, a revolute joint and a prismatic joint provide the key movements of rotation and translation. The sensor provides the target location. Hence in the present work, the focus is made on the study of failure modes on account of freewheeling, locking of shoulder joint, locking of prismatic joint and sensor failure. The failures can be caused due to various reasons such as those listed in Section 3.1. In the current work we have used situations when a power failure takes place, which is quite convenient to realize in the laboratory set up. Another advantage is that this does not damage the manipulator system. It is to be noted that any other failure mode must be carried out with due care as it may damage the robotic system. The errors and the error covariance matrices conditioned on different hypotheses, which are associated with the considered failure modes, require system models that represent the corresponding failure modes. 3.3.1 Sensor Failure In this mode, the optical encoder (motion sensor) of a revolute joint or a deployable link fails. In the normal state the optical encoder provides a reading in number of pulses, which correspond to the angular or linear position of the joint. However in the faulty state it is assumed that the sensor gives a zero output though the joint motion continues according to the actuator input signal. In the present study, this was achieved by replacing the row of the measurement (output) matrix corresponding to the sensor that has failed by a null row. The time history graph plotted shows that the magnitude of the count increases with time as the manipulator moves with the constant torque and force applied to the joints. 3.3.2 Locked Joint Failure Here the relative motion of the joint is stopped due to some form of jamming, power failure, an obstacle, or seizure in a joint component such as the gear transmission or the bearings. Once locked, the position of the locked joint stays the same as that at the instant just prior to the locking, and its relative velocity drops to zero and maintains at this value throughout the locked state. The study was also performed where the translatory motion of the unit was locked. In the present study, this was achieved by reducing the total degrees of freedom of the manipulator system by one, by fixing the generalized coordinate corresponding to the locked joint. In this 38 manner, the equation corresponding to the coordinate for the locked joint is left out from the original system of nonlinear equations of motion. 3.3.3 Freewheeling Joint Failure In this failure mode the study is done where there is a free swinging of a revolute joint. This is the result of a loss of connection between the harmonic-drive motor and the slew link. This could be due to a broken link, slipping or disengagement in the transmission or loss of torque in the actuator as a result of malfunction in the drive system or the actuator. When this occurs, the corresponding actuator torque drops to zero, having no effect on the manipulator motion. 39 CHAPTER 4 FAULT DIAGNOSIS AND CONTROL 4.1 Introduction In this chapter, experimental investigations are carried out using the physical robotic system multi-module deployable manipulator system (MDMS) to establish the effectiveness of the developed procedure in detecting a set of important failure modes. Also investigated is the effectiveness of the experimental robot in completing a robotic task, under joint failure, by using kinematic redundancy. The results presented in this chapter verify through experimentation the conclusions arrived at, from earlier work by computer simulation [27]. 4.2 Joint Failure Identification The failure mode identification algorithm that uses Bayesian hypothesis testing, as developed, is implemented in the experimental manipulator, MDMS for detecting joint failures. To gain confidence in the operation of the experimental robot developed in our laboratory, in the presence of sensor failure and a locked joint, the algorithm has been tested on a single module of the manipulator, and thereafter on the two-module manipulator. The sampling period for the linearized and discretized models is chosen to be equal to the control time step. The outputs that are measured in the present study are the position for the revolute and prismatic joints. They are measured with the optical encoders mounted on the joint motor shafts. The inputs to the manipulator are the forces and torques provided to the motors. In the current study, the following four hypotheses are investigated through experimentation: 1. HI: No failure 2. H2: Sensor failure 3. H3: Locked joint 4. H4: Free joint The matrix R in equation (3.21) is selected such that there is a higher noise covariance associated with a failed sensor. The actual value of Q in equation (3.20) and R depend on the sensors used and the engineering units that vary from one system to another. 4.2.1 No Failure Necessarily, the case where there is no failure is also one of the hypotheses that is tested. This is in fact the normal state when the manipulator is functioning properly. The revolute joint for the base link, after initial fluctuations, reaches the steady state. A similar pattern is observed for joint one of the manipulator. The prismatic joints in both cases extend to the desired level to reach the 40 target point. The experimental results are plotted in Figure 4-1 for each link. It is seen that each joint motion attains the steady state, as required. The velocity curves for the revolute joints, after initial disturbance, attains the equilibrium state and reaches the steady state when reaching the target. The revolute joints attain the normal state and the prismatic joint extends to reach the target point, under PID control. Velocity of Revolute Joint 0 Velocity of Revolute Joint 1 100 ~l o i o 0> I -50 -100 f\\ | U - C ( V 40 B0 100 Time s e c 0.481- s 0.46 - 1 0 4 S . 1- 0 43 • 042 • 041 0 4 . i ' 1 10 20 30 40 50 Time s e c 80 90 100 80 90 100 Figure 4-1: Joint Responses Under Normal Operation 41 The trip trajectory of the robot, under normal operation corresponding to Figure 4-1, is shown in Figure 4-2. It is seen that a desired target is reached while initial motions of the tip fluctuation are suppressed by PID controller. Compensation for the inertial forces and the torque has been required to correctly achieve the target. This gives us the confidence in the proper function of the physical manipulator and its control hardware and software, under conditions of normal operation. o.e 0.6 0.4 > ol- -0.2 •0.4 •0.6 Tip path Starting Point Figure 4-2: Tip Trajectory of the Manipulator Under Normal Operating conditions 4.2.2 Sensor Failure In the mode of sensor failure, the optical encoder of a revolute or deployable joint is considered to fail. In normal operation, these encoders provide a reading in terms of pulses that correspond to the angular or linear position of the joint. In the case of a sensor failure the corresponding sensor provides a zero output reading although the joint motion continues according to the actuator input signal. In simulation studies [27] the row of the measurement matrix C corresponding to the failed sensor was replaced by a null row. This was done with the realistic as stated before. In the physical experimentation the connection to the sensor is removed to give a zero reading, the manipulator is allowed to function, and the corresponding joint response is plotted. As the sensor power was disconnected for the first joint, the revolute joint of the base link was unaffected and reached the steady state. However, the first joint could not reach the steady state. The prismatic joint of the base link failed to extend, and the magnitude of prismatic joint of the first link increased (i.e. the link extended) as the manipulator moved with the constant torque and force applied to the joints. The manipulator was able to reach the target, under control. The corresponding results are presented in Figure 4-3. 42 10.44 I \" 0.42 0 10 20 30 40 50 r- Figure 4-3: Manipulator Response Under Sensor Failure It is observed that since the sensor failed for link 1, the rotational motion of link 1 could not achieve the target position. While the base link was operating in a normal manner, the prismatic joint extended with time as the manipulator operated. The joint adjusted and extended under control, to compensate for incorrect sensor reading, and reached the desired target point. The failure in sensor did not affect the speed of the controller and hence due to the availability of the redundant degree of freedom the manipulator was able to reach the target in the same time as in the normal operation scenario. 4.2.3 Locked Joint Failure To implement the case of joint failure, the relative motion of a joint is stopped by some mechanism. This reduces the total number of degrees of freedom of the manipulator system by one. Once locked, the position of the locked joint stays the same as that at the instant just prior to the locking, while its relative velocity drops to zero and maintains the same value throughout the locked state. 43 In the present experiment, this case of failure is achieved by disconnecting the power to a particular joint motor while the braking is engaged. This represents a real state scenario where the power leads to a joint motor gets snapped due to some reason. The time response for this case is presented in Figure 4-4. There is an abrupt change in the velocity of the deployable base link at the instant the shoulder joint is locked; specifically, between the 15 to 30 sec period. The time delay corresponds to the disconnection of the power. However, the revolute joint of the first link is unaffected and functions in the normal fashion achieving the desired state. Though the velocity response attains the steady state, the base revolute joint gets locked at the instant the power is disconnected and stays in the same position for the rest of the cycle. During this stage the base prismatic joint tries to extend in the positive direction and then decreases as the moment of inertia of module 2 increases due to the extension of its deployable link. Through dynamic coupling, the shoulder joint rotates in the opposite direction to the elbow joint. Also the module moves at a slower pace because of the higher load and inertia, which it is driving. The locked shoulder joint fails to provide the torque to move the link and the manipulator fails to achieve the target. 44 Velocity of Revolute Joint D Velocity of Revolute Joint 1 0 10 20 30 40 50 Time sec 80 90 100 0 10 20 30 40 50 \"Time s e c 80 90 100 5 0 4B 046 0.44 0.42 ' I - f 1 ' • - u 13 0 10 20 30 40 50 80 90 100 Time seC ' 0 10 20 30 40 50 Time sec Figure 4-4: Manipulator Response Under Locked Joint It is observed that when the failure occurs in the base revolute joint, then joint 1 tries to provide some compensation. However the prismatic joints fail to extend and achieve the target due to the increase of inertial force due to extension of the adjoining link. This is verified from the plot of the end effector trajectory of the manipulator, as shown in Figure 4-5. It is noticed that the tip failed to reach the target. 45 Locked Joint 0 0.6 0.4 0.2 3 -0.2 -0.4 - j 1— —i r- End Point Starting Point 3.35 0.4 0.45 0.5 0.55 \"•\" \" B5 0.7 075 0.8 x mt Figure 4-5: Trajectory of the Manipulator Tip The same test was repeated while locking the shoulder joint. Similar results were obtained when joint 1 was locked, as seen in Figure 4-6. The prismatic joint extended to achieve the target as seen. However, the velocity response of base joint and joint 1 maintained equilibrium, and joint 1 extended to reach the goal position. The manipulator was unable to reach the target. 46 . Velocity of revolute joint 0 * 60 3 3 0 20 •40 . i ' «f~—~~ I Velocity of Revolute Joint 1 • - • 0 10 20 30 40 50 Time Sec 80 90 100 0 10 20 30 40 50 ~ ~ 80 90 100 Time sec | 0 44 • I 0-43 [ 1 p— - 10 20 30 40 50 Time Sec 80 90 100 80 90 100 Figure 4-6: Manipulator Response Under Locked Joint 1 47 4.2.4 Free Wheeling Joint Failure In the case of free-wheeling failure, we consider free swinging of a revolute joint. This could result from disconnection of gear engagement, breakage of a link or gear, slippage of transmission, or loss of connection between the motor and the link. All these failures result in the loss of torque in the actuator. As the actuator torque drops to zero, it fails to control the manipulator motion. In the experimental system this state is achieved by disconnecting the power to the actuator motor when the braking is not engaged. We observe that when the shoulder joint is set free, the movement of the shoulder becomes faster and it swings further in the negative direction. This is because a positive torque is not available to counteract the negative torque generated through dynamic coupling. The uncontrolled movement induces increased deployment and higher velocity in the base prismatic joint. As for joint # 1 in spite of the constant slew joint torque, the magnitudes of the position and velocity responses are larger. The results are presented in Figure 4-7. 48 Free wheeling in Joint 0 Velocity of Revolute Joint 1 -20 • -30 • -40 • 0 10 20 30 40 50 3 80 90 100 Time S e c 50 3D 1 I \"SO -100 [} K I •\"- J 0 10 20 30 40 50 I 80 90 100 Time S e c 30 40 50 Time 0 10 20 3D 40 50 0 80 90 100 Time sec Figure 4-7: Manipulator Response Under Freewheeling of Base Link As the revolute joint of the manipulator base loses its torque, joint 1 tries to achieve the equilibrium state and prismatic joint extends to reach the target. Prismatic joints function in the normal manner. In the absence of a positive torque the revolute joint fails to achieve the direction and there exists a free swinging of the base arm that swings further and faster in an uncontrolled manner in the negative direction. This faster motion induces an increased deployment and higher velocity in link 1. As expected in the absence of a positive torque, the manipulator fails to stay in control and fails to reach the target point. The final trajectory of the tip point is shown in Figure 4-8. Free wheeling of Joint 0 0.7 0.6 0.5 s 0.3 0.2 0.1 -B.1 0 ST 02 03 0~- \"^ 06 07 0 8 » mt Figure 4-8: Tip Trajectory of the Manipulator Similar results are obtained when the free swinging occurs in joint 1. The base revolute joint achieves the steady state; however, the negative torque in joint 1 causes free swinging of the arm. This response is shown in Figure 4-9. 50 Prismatic Joint 0 m t a a o T j £ i-l a ' - & • ^D s p 3 T3 C P o !-t ^ o Wl T3 O 3 c« 0) c s CL ct> I-I a> re 3 tr- ee n> 13 CfQ O !-b «—i O P r-K i — ' B a ^ i s en s s s ^ 'S a s | ' 8 m s s 8 Prismatic Joint 1 Revolute Joint 0 0 & o a £ Revolute Joint 0 R a d / s e C Revolute Joint 1 & b i$ o o ^ Revolute Joint 1 R a d / s e C The traced path of the tip is shown in Figure 4-10. It is seen that due to the absence of a positive torque, the tip swings and the target is never achieved. Free wheeling in Joint 1 0.8 06 \" 4 E U.2 0 -0.2 -0.4 \" -0.4 '-0.2 0 0.2\" \" ; 0.6 0.8 \" ~ 1 x mt Figure 4-10: Tip Trajectory of the Manipulator 4.2.5 Prismatic Joint Locking Failure The study is extended to carry out an experimental investigation when jamming of a prismatic link takes place so that it cannot extend or retrieve further. In a real life scenario this may result from jamming of the links due to additional friction generated on site due to bending of a link, dust collection, failure of the retracting motor or snapping of the power line to the motor. In the present experiments, this is achieved by disconnecting the power to the prismatic link motor. In particular, when the power supply to the base link prismatic joint is disconnected, it is observed that the revolute joint of the base and link 1 achieve steady state. The revolute joints move as a result of the applied constant torque and force. There is an abrupt change in the velocity of the base link approximately at 50 sec instant and reduces to zero. Link 1 extends to its deployable length and moves due to the inertial force, and due to the redundant degree of freedom the target is achieved, as shown in Figure 4-11. 52 Velocity of Revolute Joint 0 Velocity of Revolute Joint 1 w - D 10 20 30 40 50 80 90 100 Time sec Measured revolute Joint 1 • H i u r^_ ' - b • 0 10 20 30 40 50 B 101 o I 0-4101 I 04101 041 0 10 20 30 40 50 Time sec BO 90 100 Figure 4-11: Manipulator Response Under Failure of the Base Link Prismatic Joint 53 The corresponding trip trajectory is shown in Figure 4-12. It is observed that the failure in one of the prismatic joints is accounted for and is compensated by the movements in the other link, and the tip achieves the target position. 0.6 0.E 0.4 J.2 0 -0.2 -0.4 *& • 1 0.2 0.3 Tip Path 0.4 ^ ^ . End Point ^ \\ 1 ' \\ \\\\1 \" l_fl-4g • / // ' ^J/^ - Starting Point D.B 0.7 0. mt Figure 4-12: Tip Trajectory of the Manipulator Similar experimental results were obtained when the prismatic joint of the second link was jammed. The corresponding responses of the manipulator are presented in Figure 4-13. 54 Velocity of Revolute Joint 0 80 y •a « 0 a -20 -40 -60 n Velocity of Revolule Joint 1 \\ - __ . - - \\ 0 10 20 30 40 50 Time Sec 40 60 ~ Time gee 80 90 100 80 90 100 Figure 4-13: Manipulator Response Under Failure of the Prismatic Joint of Link 1 55 In this case link 1 has the fixed inertia. It is observed that all the slew movements achieve the steady state. The deployable length of base link compensates with its inertial force and the target is achieved. The tip trajectory plot shown in Figure 4-14 is similar to the results obtained in the previously. Tip Path End Point /^ ^ \\ Starting Point \"0.6 0.7 0.B Figure 4-14: Tip Trajectory of the Manipulator 4.3 Discussion of the Results The experimental results presented here are as obtained from the laboratory MDMS. It is observed that by and large, the failure detection scheme has performed satisfactorily. Furthermore, in view of the availability of redundant kinematics in the MDMS, the manipulator has been able to complete a given task satisfactorily, under control, even in the presence of a joint failure or a sensor failure. These results verify the computer simulations as carried out previously [27]. In the simulation study, the manipulator achieved the target position with a joint locked. In the experimental investigation it was found to be true in the case of failure in a prismatic joint and sensor failure. The same was not found to hold, however, when a revolute joint (slew motion) failed. An inference can be made that if the direction is consistent, that is as long as the manipulator links have the right direction of motion, the target position can be reached under a joint failure. For this reason greater emphasis must be placed on the slew drives of the manipulator. 56 CHAPTER 5 CONCLUDING REMARKS 5.1 Significance of the Work The present thesis focused on the study of failure detection and identification, and fault tolerant operation of an innovative multi-modular robot, the Multi-modular Deployable Manipulator System (MDMS), which has been designed and developed in our laboratory. In particular, Bayesian hypothesis testing was used to identify the failures in the MDMS. The work has a significant experimental component where the physical MDMS is subjected to several critical failure scenarios in our laboratory. As the technology related to automatic control of robotic manipulators advance and as the required robotic tasks become increasingly critical and autonomous, the issue of reliability becomes more and more important. The ability to detect and identify a fault or a failure mode in a system and to continue the execution of the specified tasks in a satisfactory manner without the need for immediate human intervention is desirable. This calls for higher system reliability, better maintainability, improved survivability, increased efficiency, and greater cost effectiveness. Fault tolerant operation of robotic manipulators takes a centre stage in this context. In the present work various structural failure modes in a multi-module deployable manipulator system were studied through experimentation with a manipulator system developed in our laboratory. A methodology based on Bayesian hypothesis testing was implemented in the experimental robot, for on-line detection of a set of structural failures and sensor failure in the robot. The methodology was integrated into the control system of the manipulator so that, through the use of redundant kinematics, a faulty manipulator could operate satisfactorily in completing the assigned task, under certain situations. The experimental manipulator used in the present investigation has two modules, each having a revolute degree of freedom and a prismatic degree of freedom, to give a total of four degrees of freedom. In planar tasks of positioning and orientation, which require three degrees of freedom, the experimental robot has one degree of kinematic redundancy. It is this extra degree of freedom that is utilized in the fault tolerant operation of the manipulator under joint failure or sensor failure. Past work on the subject has relied exclusively on computer simulation. The present work is particularly significant since it has involved implementation of an analytically sound strategy of failure identification into the control system of a sufficiently complex and practical manipulator system and using this manipulator for experimental investigation of the techniques of fault identification and fault tolerant operation. 57 5.2 Main Contributions In the present work, Bayesian hypothesis testing that uses minimization of a cost function to identify a faulty condition, and a bank of Kalman filters for the estimation of fault-conditioned response were implemented in the control system of an innovative practical robotic manipulator. The experimental manipulator has been designed and developed in our laboratory (Industrial Automation Laboratory—IAL) of the University of British Columbia. The manipulator, MDMS, was intended for research in space-based applications of robotics, in view of the involvement of Canada in the development of the International Space Station (ISS) in cooperation with other countries. All the existing space based manipulators have exclusively revolute joints, providing rotational motions. However, our laboratory manipulator has combined revolute (rotational) and prismatic (translational) joints in each module. Several such modules are connected in series to form the MDMS, as desired. This innovative design has several advantages when compared with its counterparts with purely revolute joints and the same number of links. The main advantages are: • Simpler decision making requirements; • Reduced inertia coupling or dynamic interaction; • Better capability to avoid obstacles; and • Reduced number of singular positions. Fault tolerant operation is critical in autonomous applications in remote locations and under hazardous conditions, as in space-based applications. In the current work the experimental robotic manipulator was tested under a set of realistic scenarios, as encountered in the field, under the conditions of failure in manipulator joints and joint sensors. The failure could result from snapping of the power leads, motor failure, gear failure, slippage of gear, jamming of joints or gears, collisions resulting in bending or breakage of links and joints, and so on. The experimental robot consisted of two modules, each having a revolute joint and a prismatic joint, providing a total of four degrees of freedom. Only three degrees of freedom are needed, however, for positioning and orientation tasks on a plane; consequently the experimental robot has one redundant degree of freedom. This redundant kinematics is key to fault tolerant operation of the manipulator. It was observed that when there is a failure in the motor of the telescopic (deployable or prismatic) link, the manipulator managed to reach the target point with the remaining three degrees of freedom. The manipulator compensated for the loss of a degree of 58 freedom and reached the target in a normal manner, under the command of its control system. Similar results were obtained for operation under sensor failure. In the case of a slew (revolute) joint failure, it was observed that though there was a redundant degree of freedom available to assist the manipulator, the manipulator failed to reach the target location. This was due to the counter-productive torque produced in the system. The manipulator swung in an uncontrolled manner, in the absence of the necessary torque to counter it and bring the manipulator under control. Similar results were obtained when the revolute joint was locked. In this case manipulator did not swing; however, the manipulator failed to reach the target. The reason is the same as before; there was no adequate torque to provide the necessary movement to the joint. Contrary to the findings through computer simulation, the manipulator system is not to be relied upon in all situations. In the case of failure in a revolute, the manipulator link would swing in uncontrolled manner, and the manipulator would fail to achieve the target position. In the case of failure in a translatory (telescopic, deployable, prismatic) link, the manipulator was able to compensate for the failure and reach the target position. In summary, when the manipulator is able to position in the desired direction it achieves the goal. Specifically, if the revolute drive mechanism works satisfactorily, the manipulator will overcome a fault in another drive and reach the goal. 5.3 Summary and Conclusions MDMS, which has been designed and developed in our laboratory, consists of a set of serially connected modules, each having a revolute joint and a prismatic link. A general methodology for failure detection and identification based on Bayesian hypothesis testing was developed and implemented in the control system of this unique deployable manipulator system. Based on Bayesian hypothesis testing and using a bank of Kalman filters, the methodology was able to accurately identify the structural failures and joint sensor failure in MDMS. The MDMS has redundant kinematics. In particular, this planar manipulator system needs only three degrees of freedom for a positioning and orientation task. However, the two-module experimental manipulator has four degrees of freedom. The present study is used in experimental investigation to study the fault tolerant behaviour of the experimental manipulator, which uses on-line fault identification and compensation through redundant kinematics. The response of the physical manipulator system was obtained experimentally and analysed on- line to determine possible presence of joint failure or sensor failure. If failure is present, by 59 correctly identifying it and using the Kalman filter output corresponding to the particular failure mode, the manipulator is commanded to complete the task, with compensation from the redundant degree of freedom and under proper feedback control. Four failure scenarios were studied in the present experimental investigation, namely: sensor failure; free wheeling of a revolute joint; locking of a revolute joint; and locking in a telescopic joint. It was observed that in the case of failure in a revolute joint, possibly due to gear failure, gear slippage, dust accumulation, power failure, and so on, the manipulator system failed to reach the target and thus became unreliable. However, in the case of failure in a telescopic joint or sensor failure, the manipulator was able to properly compensate for it and accurately track a specified trajectory and reach the target position, with the functional degrees of freedom and under command of the manipulator control system. Significant dynamic coupling was observed in the presence of joint flexibility, faster manoeuvre, and larger point payloads. It can be concluded that even though the methodology of fault identification and control is quite effective, the manipulator system needs improvement in its revolute joints. For example, a back-up drive may be provided for each revolute joint, to work in synchronism so that the failure of one drive can be accommodated by the stand-by drive. 5.4 Recommendations for Future Work The present work has been an experimental investigation, where an analytically sound method of fault identification was implemented in the control system of a laboratory manipulator system, and tested for several important fault scenarios. This was an extension to computer simulations that have been carried out in our laboratory. This main objective has been accomplished in the present thesis. The simulation results were verified for the most part; however, it was found that only in some scenarios the manipulator succeeded in correctly reaching the target position. The experimental investigation utilized the MDMS, which has been designed and developed in our laboratory, which consists of a set of serially connected modules, each having a revolute joint and a prismatic link. The present study was done using only two modules of manipulators, with a total of four degrees of freedom. Apart from the failure conditions studied in the present work, there are various other causes such as gear failure, increased backlash, motor failure, jamming of gears or links due to increased friction, bending of links, dust accumulation, and so on. It is important to further investigate the outcomes for various other types of failure and the behaviour of the manipulator under those conditions. While conducting the tests, utmost care must be taken as it can result in damage to the manipulator. It must also be noticed that the tests were carried 60 out in the horizontal plane with support provided by rollers. This mimics the zero gravity situation and is similar to application in space. However, further investigation may be done without the supports, as the links even though rigid, must be able to overcome the bending moment at each joint due to further links and dynamic coupling. In summary, there are several issues that remain to be studied and demands further investigation, as listed below: I. As a future investigation, one may perform experiments with more than two manipulator modules. This should lead to the exploration of other dynamic issues and stability considerations. II. Extension of the inverse kinematics algorithm to account for a larger number of modules or N modules in general. III. Implementation of other, probably more advanced control methodology to perform control studies and evaluate the performance of the manipulator. IV. The studies can be expanded to various other failure modes scenarios such as slip in joint coupling due to backlash, wear or actuator loading, high resistance to joint motion, increased vibration due to gear malfunction, actuators or bearings, data acquisition failure, and so on. However, before such study is undertaken it is necessary to weigh the possible damage to the prototype manipulator, as the necessary repairs could be quite costly and time consuming. V. Further studies can be conducted by studying the manipulator without roller supports. The rollers in the present experimental set up provide support and counter-bending moment at each joint. However, if there are more units connected together, then the weights of the links will add to the bending moment and will load each consecutive drive mechanism, thus generating coupling dynamic forces, which need to be overcome. VI. Multiple failure modes can be applied simultaneously to the manipulator and the results studied. The present method of fault identification will have to be modified, or the number of hypotheses has to be correspondingly increased, in this case. For example, the failure of two degrees of freedom simultaneously may be studied in this manner. 61 BIBLIOGRAPHY 1. Alekseev, Y.K., Kostenko, V.V., and Shumsky, A.Y., \"Use of Identification and Fault Diagnostic Methods for Underwater Robotics,\" Proceedings of OCEANS '94 Oceans Engineering for Today's Technology and Tomorrow's Preservation, San Diego, California, U.S.A., Vol. 2, pp 489-494, September 13-16, 1994. 2. Anderson, T.W., An Introduction to Multivariate Statistical Analysis, John Wiley & Sons, New York, NY, 1984. 3. Cao. Y., Dynamics and Control of Orbiting Deployable Multimodule Manipulators, M.A.Sc. Thesis, Department of Mechanical Engineering, University of British Columbia, Vancouver, Canada, pp. 8-13, 1999. 4. Cao. 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Department of Mechanical Engineering, Thesis, University of British Columbia, Vancouver, Canada, pp. 46-71, 1997. 27. Wong, H. K. K., \"Structural Failure Identification and Control of the Multi-Module Deployable Manipulator System\", Ph.D. Thesis, Department of Mechanical Engineering, University of British Columbia, Vancouver, Canada, April 2006. 28. Zhang, J., Modi, V.J., de Silva, C.W., and Misra, A.K., \"An Assessment of Flexibility Effects for a Novel Manipulator,\" Proceedings of the Eighth International Conference of Pacific-Basin Societies, Xi'an, China, Editor: K.T. Uesugi et al., Chinese Society of Astronautics Publisher, pp. 22-26, June 1999. 64 APPENDIX I Numerical data for the parameter values of the experimental manipulator (MDMS) used in the present investigation are listed below: • Slewing link length, ls = 0.29 m • Deploying link length, ld =0.18 m • Slewing link linear mass density, ps =3.21 kg/m • Deploying link linear mass density, pd = 1.122 kg/m • Revolute j oint actuator mass: • Module #1: mal =3.6 kg • Module #2: ma2 = 0.78 kg • Module #3: ma3 =0.51 kg • Module #4: ma4 = 0.31 kg • Revolute joint actuator inertia: • Module #1: Jal =1.2 kg.m2 • Module #2: Ja2 = 0.0816 kg.m2 • Module #3: Ja3 =0.043 kg.m2 • Module #4: Ja4 =0.015 kg.m2 • Revolute j oint stiffness: • Module # 1: Kx = 10000 Nm/rad • Module #2: K2 = 8830 Nm/rad • Module #3: K, = 1823 Nm/rad • Module #4: K4 =712.3 Nm/rad 65"@en ; edm:hasType "Thesis/Dissertation"@en ; vivo:dateIssued "2008-11"@en ; edm:isShownAt "10.14288/1.0067056"@en ; dcterms:language "eng"@en ; ns0:degreeDiscipline "Mechanical Engineering"@en ; edm:provider "Vancouver : University of British Columbia Library"@en ; dcterms:publisher "University of British Columbia"@en ; dcterms:rights "Attribution-NonCommercial-NoDerivatives 4.0 International"@en ; ns0:rightsURI "http://creativecommons.org/licenses/by-nc-nd/4.0/"@en ; ns0:scholarLevel "Graduate"@en ; dcterms:title "Failure detection and diagnosis in a multi-module deployable manipulator system (MDMS)"@en ; dcterms:type "Text"@en ; ns0:identifierURI "http://hdl.handle.net/2429/5742"@en .