Advances in Robot Manipulators Part 7 docx

232 Advances in Robot Manipulators Therefore, it is concluded that the designed neurocontroller provides a good tracking of desired trajectories Fig 3 Response of the Adaptive Controller with Gradient-Type tuning Actual and desired joint angles Fig 4 Response of the controller with gradient-type parameter tuning Representation of tracking errors Design of Adaptive Controllers based on Christoffel Symbols of First Kind 233 6 Appendix T Lemma 6: For K = diag (K ii )  R n´n and d = (d 1 ,d 2 , ,d n )  R n , if u = -Ksgn (x) and k ii ³ di then x T M (u - d) £ 0 (Ge et al., 1998)   Lemma 7: Let V (x, t) be a Lyapunov function so that V (x, t) > 0 , V (x, t) £ 0 If V (x, t) is uniformly continuous (Lewis et al., 2003), then  V (x, t)  0 as t  ¥ (66) The following theorem is very important in control of non-linear systems, and is due to Desoer and Vidyasagar, cf (Desoer & Vidyasagar, 2008) Theorem 2: Let the closed-loop transfer function H (s)   n´n (s) be exponentially stable and strictly proper, and h (t) the corresponding impulse response (obtained by evaluating n n n n  the inverse Laplace transform of H (s) ) If u  2 , then y = h * u  2 Ç ¥ , y  2 , y is continuous and y (t)  0 as t  ¥ , where h * u denotes the convolution product of h and u On the basis of this theorem, it is possible to state the following lemma, (Ge et al., 1998) Lemma 8: Let e ( t) = h (t) * r (t) , where h = -1 {H (s)} and H (s) is an n ´ n strictly n n n n  proper, exponentially stable transfer function Then r  2  e  2 Ç ¥ , e  2 , e is  continuous and e (t)  0 as t  ¥ If in addition r  0 as t  ¥ , then e  0 (Ge et al., 1998) Theorem 3 (UUB by Lyapunov Analysis): If for system  x = f (x, t) + g (t) (67) there exists a function V (x, t) with continuous partial derivatives such that for x compact set S Í  in a n V (x, t) is positive definite, V (x, t) > 0  V (x, t) < 0 for x > R (68) for some R > 0 , such that the ball of radius R is contained in S , then the system is UUB and the norm of the state is bounded to within a neighborhood of R The following theorem is a modified version of the uniformly ultimately boundedness theorem of Corless and Leitmann, cf (Corless & Leitmann, 1981) For more insights the reader may refer to theorems 1 and 2 in (Dawson et al., 1990) or the theorem 2.15 p 65 in (Qu, 1998) Theorem 4: If V is a Lyapunov candidate function for any given continuous-time system with the properties 2 λ 1 x (t) £ V (x (t)) £ λ 2 x (t) 2 (69) 234 Advances in Robot Manipulators  V (x (t)) < 0, if η 2 > x (t) > η1 (70) where η 2 > η1 λ2 λ1 (71) then x ( t) < η1 λ2 "t  [ t 0 + T, ¥) λ1 (72) where T is a finite positive constant The following lemma allows to connect the uniform complete observability (UCO) to the boundedness of the states, (Lewis et al., 1999) Lemma 9 (Technical Lemma): Consider the linear time-varying system (0,B (t) ,C (t)) defined by  x = B ( t) u (73) y = C ( t) x with x  n , u  m , y  p and the elements of B (t) and C (t) piecewise continuous functions of time Since the state transition matrix is the identity matrix, the observability grammian is t N (t, t 0 ) = ò C T (τ ) C (τ ) dτ t0 (74) Let the system be uniformly completely observable with B (t) bounded Then if u (t) and y (t) are bounded, the state x (t) is bounded 7 References Corless, M and Leitmann, G (1981) Continuous State Feedback Guaranteeing Uniform Ultimate Boundness for Uncertain Dynamics Systems IEEE Transactions on Automatic Control, Vol.26, No 5, (October 1981) (1139- 1144), ISSN 0018-9286 Dawson, D M., Qu, Z., Lewis, F L., and Dorsey, J F (1990) Robust Control for the Tracking of Robot Motion International Journal of Control, Vol.52, No 3, (1990) (581-595), ISSN 0020-7179 Desoer, C A., and Vidyasagar, M (2008) Feedback Systems: Input-Output Properties, Society for Industrial and Applied Mathematics, ISBN 978-0898716702 Ge, S S., Lee, T H and Harris, C J (1998) Adaptive Neural Network Control of Robotic Manipulators, World Scientific Publishing Company, ISBN 978-9810234522, London Horn, R A., and Johnson, C R (1999) Topics in Matrix Analysis, Cambridge University Press, ISBN 978-0521467131 Lewis, F L., Jagannathan, S and Yesildirek, A (1999) Neural Network Control of Robot Manipulators and Nonlinear Systems, Taylor and Francis Ltd., ISBN 978-0748405961 Design of Adaptive Controllers based on Christoffel Symbols of First Kind 235 Lewis, F L., Dawson, D M and Abdallah, C T (2003) Robot Manipulator Control: Theory and Practice, Marcel Dekker Inc., ISBN 978-0824740726 Mulero-Martínez, J.I (2007) Bandwidth of Mechanical Systems and Design of Emulators with RBF Neurocomputing, Vol.70, No.7-9, (2007) (1453-1465), ISSN 0925-2312 Mulero-Martínez, J.I (2007a) An Improved Dynamic Neurocontroller Based on Christoffel Symbols IEEE Transactions on Neural Networks, Vol.18, No.3, (May 2007) (865-879), ISSN 1045-9227 Mulero-Martínez, J.I (2007b) Uniform Bounds of the Coriolis/Centripetal Matrix of Serial Robot Manipulators IEEE Transactions on Robotics, Vol.23, No.5, (October 2007) (1083-1089), ISSN 1552-3098 Mulero-Martínez, J.I (2009) A New Factorization of the Coriolis/Centripetal Matrix Robotica, Vol.27, No.5, (September 2009) (689-700), ISSN 0263-5747 Qu, Z (1998) Robust Control of Nonlinear Uncertain Systems, John Wiley and Sons, ISBN 9780471115892 Slotine, J.J and Li, W (1991) Applied Nonlinear Control, Prentice-Hall, ISBN 978-0130408907 Spong, M W and Vidyasagar, M (1989) Robot Dynamics and Control, John Wiley and Sons Inc., ISBN 978-0471612438 Wen, J T (1990) A Unified Perspective on Robot Control: The Energy Lyapunov Function Approach International Journal of Adaptive Control and Signal Processing, Vol.4, No 6 (November, 1990) (487-500) 236 Advances in Robot Manipulators Development of a New 2 DOF Lightweight Wrist for the Humanoid Robot ARMAR 237 11 X Development of a New 2 DOF Lightweight Wrist for the Humanoid Robot ARMAR Albert Albers, Jens Ottnad and Christian Sander IPEK - Institute of Product Development, University of Karlsruhe (TH) Germany 1 Introduction The mechatronic design of a humanoid robot is fundamentally different from that of industrial robots Industrial robots generally have to meet requirements such as mechanical stiffness, accuracy and high velocities The key goal for this humanoid robot is not accuracy, but the ability to cooperate with humans In order to enable a robot to interact with humans, high standards are set for sensors and control of its movements The robot’s kinematic properties and range of movements must be adjusted to humans and their environment (Schäfer, 2000) 1.1 The Humanoid Robot ARMAR The collaborative research centre 588 “Humanoid Robots – learning and cooperating multimodal robots” was established by the “Deutsche Forschungsgemeinschaft” (DFG) in Karlsruhe in May 2001 In this project, scientists from different academic fields develop concepts, methods, and concrete mechatronic components for a humanoid robot called ARMAR (see figure 1) that can share its working space with humans Fig 1 Upper body of the humanoid robot ARMAR III 238 Advances in Robot Manipulators The long-term target is the interactive work of robots and humans to jointly accomplish specified tasks For instance, a simple task like putting dishes into a dishwasher requires sophisticated skills in cognition and the manipulation of objects Communication between robots and humans should be possible in different ways, including speech, touch, and gestures, thus allowing humans to interact with the robots easily and intuitively As this is the main focus of the collaborative research centre, a humanoid upper body on a holonomic platform for locomotion has been developed It is planned to increase the mobility of ARMAR by replacing the platform with legs within the next years, which will lead to modifications of the upper body 1.2 State of the Art and Motivation The focus of this paper is the design and the development process of a new wrist for the humanoid robot ARMAR The wrist serves as the connection between forearm and hand An implementation of the new modules is planned for the next generations of the humanoid robot, ARMAR IV and V The wrist of the current version, ARMAR III, has two degrees of freedom (Albers et al., 2006) and its rotational axes intersect in one point ARMAR III has the ability to move the wrist to the side (± 60°, adduction/abduction) as well as up and down (± 30°, flexion/extension) This is realized by a universal joint in a compact construction At the support structure of the forearm all motors for both degrees of freedom are fixed The gear ratio is obtained by a ball screw in conjunction with either a timing belt or a cable The load transmission is almost free from backlash The velocity control and the angular measurement in the wrist are realized by encoders at the motors and by quasi-absolute angular sensors directly at the joint To measure the load on the hand, a 6-axis force and torque sensor is fitted between the wrist and the hand One of the main points of criticism on the current version of the wrist is the offset between the rotational axes and the flange, as shown in figure 2 (left) Due to the joint design, this offset distance is necessary in order to provide the desired range of motion Also other wrists of humanoid robots show a similar design, see (Shadow), (Kaneko et al., 2004), (Park et al., 2005), (Kaneko et al., 2008) That offset is even greater due to the placement of the 6axis force and torque sensor The resulting movement, a circular path performed by the carpus, does not appear as a humanlike motion, as illustrated in figure 2 (right) offset offset Fig 2 Offset between the rotational axis and the hand flange at the wrist of the humanoid robot ARMAR III (left) and the resulting movement (right) Development of a New 2 DOF Lightweight Wrist for the Humanoid Robot ARMAR 239 The German Aerospace Centre DLR (Deutsches Zentrum für Luft- und Raumfahrt) has been working on seven degree of freedom robot arms for several years The result of this project is shown in figure 3 (left) Although their work is inspired by a human arm, their goal is not to design humanoid robots The wrists of the lightweight arms of the third generation imitate human wrist movements by a pitch-pitch combination with intersecting axes (kardanic) An alternative pitch-roll configuration is also utilized, mainly for applications using tools (Albu-Schäffer et al., 2007) Both versions have an offset comparable to the current wrist of ARMAR III Henry J Taylor and Philip N.P Ibbotson designed a so called “Powered Wrist Joint” (Rosheim, 1989) in order to load and unload space shuttles The concept of this wrist is illustrated in figure 3 (right) In a smaller version, the basic idea could be reused in humanoid robot’s wrist The second degree of freedom (pitch) of the wrist is guided by a spherical joint Such an assembly provides a slim design and relatively wide range of motion The actuators for the second degree of freedom (yaw) are located directly at the joint; therefore, the drive units are quite simple On the other hand, miniaturization seems to be very difficult due to the dimensions of common gears and motors Fig 3 The DLR/Kuka lightweight robot arm (Abu-Schäfer et al 2007) (left) and concept for a wrist actuator (Rosheim, 1989) (right) 2 New Concept 2.1 Requirements and Design Goals In this section the system of objectives is defined It describes all relevant objectives, their dependence and boundary conditions, which are necessary for the development of the correct object system, outgoing from the current condition to the future condition But the 240 Advances in Robot Manipulators solution itself is no part of the system of objectives It is permanently extended and concretized over the complete product lifecycle The correct, consistently and complete definition of this system is the basis of the successful product development and a core component of the development activity (Albers et al., 2008a) Since the robot is intended to get in contact with humans in order to achieve various functions, it is inevitable that the robot is accepted by the human The ability to move like a human is as important as a human-like appearance; therefore, specific demands (Asfour, 2003) on kinematics, dynamics and the design space must to be considered A human wrist consists of many different elements and has a relatively wide range of motions Figure 4 illustrates the different possible movements of the human wrist along with the corresponding reachable angular position of the joints (Whired, 2001) c 0° d b 0° a Fig 4 Human wrist and range of motion: a = palmar flexion 70°, b = dorsal flexion 90°, c = radial abduction 20°, d = ulnar abduction 40° (Whired, 2001) In order to implement a human-like wrist movement, two orthogonally arranged rotational degrees of freedom are necessary Both axes are orthogonal to the forearm’s axis and intersect in one point The two degrees of freedom need to be put in a kinematical series The requirements and design goals for a humanoid robot’s wrist can be deduced based on the range of motion of the human wrist The first degree of freedom should have a ±30° range of motion and the second about ±90° The wrist will be attached to the forearm’s structure on one side and provides the connection to the hand It should be possible to disconnect the mechanical joint between the hand and wrist in a simple way in order to enable a modular design To measure the load on the hand, a 6-axis force and torque sensor must be fitted between the wrist and the hand The electronic cables and pneumatic tubes supplying power to the hand actuators are the similar to those used in the previous models of ARMAR (Schulz, 2003; Beck et al., 2003) The design space for the robot’s wrist is based on human dimensions as far as possible; therefore, one aim is to keep a sphere of approximately 100 mm in diameter as a boundary At the same time, the control strategy aims to operate all degrees of freedom as individually as possible In keeping with the standardized drive concept of most modules of the robot, electronic motors are used as the source for actuation The drive units need to be dimensioned for a load of 3 kg All gears are designed to be free from backlash and not self-locking But friction, e.g in case of a loss of power, leads to a slow and damped sinking of the arm instead of abrupt movement That is of great importance for an interactive application of the 256 Advances in Robot Manipulators gripping objects with different griping force setting In addition to the mechanical design and sensor deployments, the motion trajectories for different griping behaviors (Parka et al., 2006) are also constructed These motion trajectories are desired to synchronously control the finger joints for achieving various griping behaviors Consequently, the tactile force sensing (Kawasaki et al., 2007; Kawasaki et al., 2002) may combine with the motion trajectories to perform force feedback based griping control systems Finally, the proposed dexterous robot hand prototype is developed to demonstrate its motion behaviors 2 System architecture Development of Tendon Based Dexterous Robot Hand In this section, the system architecture is described The proposed system architecture is composed of the mechanical design, behaviour based gripping motion planning with tactile force sensing, and system integrations, as shown in Fig 1 The mechanical design specifications include the size and skeleton of robot hand, degree-of-freedom, range of motions of each finger, and orientation of each finger These specifications are defined according to the hand profile and various gripping postures of a twenties male student in our laboratory Therefore, the proposed dexterous robot hand may demonstrate similar motions with the human beings In addition, a tendon wired control configuration is proposed in this study to reduce the weight and heat of the hand Especially, the ABS engineering plastic material is used to further reduce the weight of the robot hand Mechanical Design Design Specifications Tendon Wired Actuations Gripping Behavior Modeling Gripping Motion Planning Tactile Sensing Gripping Trajectory Planning System Integration/ Test Motion Control System Parameter Setting and Training System Fig 1 System development architecture The gripping motion planning module acts the supervisory controller of the proposed dexterous robot hand It is responsible of modelling gripping motions in terms of setting the initial and final postures of fingers, acquiring the tactile sensor data from the tips of all fingers, and planning the gripping trajectory based on the gripping models, maximum allowable tactile forces and maximum allowable joint angles Note that the gripping motion planning module may just model simple griping motions in the current stage Finally, the system integration and test module is desired to cooperate with the motor controller to manipulate the robot hand At the same time, the operation parameters such as the maximum tactile force and grip model selection can be also desired Development of Tendon Based Dexterous Robot Hand 257 3 Mechanical design In this study, a dexterous robot hand is proposed based on the design concepts of light weight, compact size, similar to human’s hand gripping motions, gripping force restriction, and low cost In order to meet these design concepts, the following design issues and directions are discussed before this research project 1 Light weight: Most of dexterous robot hands are designed based on directed gear train controls and tendon wired controls Because of the distance motor and gear train configurations of the tendon wired control robot hand, the weight of the robot hand can be reduced At the same time, an ABS engineering plastic material is also used to fabricate the hand to further reduce the weight of the robot hand In this manner, the light robot hand may reduce the loads of the robot arms for service robots as well as the loads of the upper extremity for hand amputees 2 Compact size: One of the study purposes of this dexterous robot hand is to produce a prosthesis hand for hand amputees preliminarily Therefore, in addition to the robot hand weight reductions, the hand size and profile must be similar to the human beings In this study, the proposed dexterous robot hand is designed referring to a twenties male student in our laboratory Consequently, a five-finger robot hand with 16 degreeof-freedom is presented 3 Emulating human’s hand gripping motions: In addition to similar hand structures, the range of motions of human’s hand is also evaluated The range of angles of the joint is defined via physically measuring the angle of finger joints In addition, several gripping motions such as gripping apples, eggs and pens are simulated using the computer aided design (CAD) software 4 Gripping force restriction: Gripping force restriction is important to the robot hand The maximum force restriction may provide a sufficient gripping force when the finger tip touches the objects, but the force will not damage the gripped objects At the same time, the maximum allowable tactile force may also protect the wire and motors of the robot hand 5 Low cost: In general, the cost of a dexterous robot hand is quite expensive because of using high performance DC/ AC servo motors In recent years, the advance RC (radio servo) techniques provide a simple and low cost position servo control solution Therefore, the RC servo motors are used in this work to reduce the cost of motors 6 Other concerns: In addition to the previous considerations, the tendon wired control robot hand may also eliminate the heats resulted from the motors and gear trains when compared to the directed gear train control robot hands At the same time, the distance actuated robot hand can be applied in more strict environments such as water Finally, to reduce the control complexity, the joint motions of distal interphalangeal joints of the index finger, middle finger, ring finder and little finger are designed to be dependent on the joint motions of the proximal interphalangeal joints of the corresponding fingers As a consequence, the motor number is reduced as 12 in this study Mechanical design of the proposed dexterous robot hand uses the Pro/E CAD software tool As described before, the robot hand profile and structure is referred to the hand of a twenties male student in our laboratory Fig 2 shows the hand photo of the volunteer Design parameters of this robot hand follow the hand structure of this hand profile In order to increase the producing efficiency of mechanical parts, geometries of these mechanical parts are modified and designed as several uniform specifications, as shown in the right- 258 Advances in Robot Manipulators hand-side of Fig 2 Note that the little finger just designed as a two-phalanx structure because of infrequent uses of this finger as well as reduction in the length of this finger when these uniform mechanical parts are used Unit: mm Thumb Index Middle Ring Little Finger Finger Finger Finger Finger 24.1 24.2 24.2 24.2 24.2 23.5 23.5 23.5 23.5 23.5 24.86 24.86 24.86 24.86 N/A Distal Phalanx Distal Phalanx Distal Phalanx Fig 2 Hand photo of volunteer and design parameter of robot hand mechanical structure Unit: degree Joint Symbol G I K L J Range of Angle Joint Symbol Range of Angle A Distal E G Distal 75 87 G Proximal 103 B H 89 A Proximal D 75 H 93 C B A I Distal 67 75 I Proximal 101 D Proximal C 45 D Distal 101 J 91 E 90 K 80 F F 32 L 93 Fig 3 Mechanical structure design and ranges of joint angles of the proposed robot hand In addition to design a similar structure with human being, range of joint motions are also discussed in this study The ranges of joint motions of fourteen volunteers are evaluated as shown in the right-hand-side of Fig 3 The joint symbols are referred to the left-hand-side CAD model These parameters are mean-values measured from fourteen volunteers Especially, to reduce the control complexity, the joint motions of distal interphalangeal joints and proximal interphalangeal joints of A, D, G and I (referred to Fig 3) are designed as dependently actuated The joint angles of distal and proximal joints are correlated in terms of the ranges of joint motions In practice, different diameters of pulleys and cable wires are used to produce synchronous actuations of distal and proximal joint within the defined angle ranges Fig 4 shows the design details The mechanical parts of this robot hand are produced in the machining shop of our university Bearings are used in all rotary parts to reduce the frictions, as shown in the lefthand-side of Fig 5 In addition, the tactile sensor socket is also desired at the distal phalanx part of each finger, as shown in the right-hand-side of Fig 5 Development of Tendon Based Dexterous Robot Hand 259 Fig 4 Design details of a finger CAD model In order to reduce the weights of mechanical parts, the ABS engineering plastic material is used, and all mechanical parts are shown in Fig 6 Fig 5 Parts with bearings and tactile sensor socket Fig 6 Photos of produced mechanical parts and assembly of the hand Because of referring the hand profile of a twenties volunteer, the size of the fingers are evaluated as shown in Fig 7 In this figure, the index finger of the volunteer are compared with the robot hand Apparently, they are in a similar finger profile Finally, because of using the ABS engineering plastic material, the weight of the hand can be reduced The weight for each finger is summarized in Table 1 To investigate the mechanism performance, several hand postures of human beings are simulated using the 3D CAD tool, as shown in Fig 8 As a consequence, these hand postures can be properly desired using the proposed mechanical structure of this robot hand 260 Advances in Robot Manipulators Fig 7 Finger profile comparisons for a twenties volunteer and the proposed robot hand Distal Phalanx Middle Phalanx Proximal Phalanx Metacarpal Phalanx Weight of a Finger Unit: gram Thumb Finger Index Finger Middle Finger Ring Finger Little Finger 4 3.5 3.5 3.5 3.5 4 4 4 4 4 3.5 4.5 4.5 4 3 N/A 3.5 3.5 3.5 N/A 11.5 15.5 15.5 15 10.5 Table 1 Weights of fingers of the robot hand Finally, the tendon wired control configuration is introduced In this study, a multi-cord steel wire with 0.8 mm diameter is used In addition, the tendon wire is surrounded with a spring cord as shown in Fig 9 I addition, the assembled tendon wired control robot hand is also presented in Fig 10 The photo of the wire actuated robot hand is shown in the lefthand-side of Fig 10; and the photo of the distance motor site is shown in the right-hand-side of Fig 10 All RC servos are mounted at the motor platform, and it can be installed off the hand and arm so that the load of the arm can be reduced I II III V Fig 8 3D CAD hand posture simulations IV Development of Tendon Based Dexterous Robot Hand 261 For example, the motor platform can be installed inside the body of a wheeled robot or a humanoid robot to increase the carry loads of the arm and hand Note that the motor platform is just installed under the robot hand for demonstrations in this chapter Finger Joints Spring Cord Tendon Wires RC Servo Motors Fig 9 Tendon wired control configuration Fig 10 Photos of wire actuated robot hand (robot hand site and distance motor site) 4 Behavior based gripping motion planning with tactile force sensing In this study, the developments of a dexterous robot hand do not focus on the mechanical structure design, but also on the gripping behavior modelling In order to simplify the gripping model as well as to perform more realistic approach, only simple and frequent gripping behaviors are discussed such as gripping an apple, cylinder, egg, etc It is noted that the precise position controls of all finger tips using inverse kinematics are not the focus of this study due to the difficulties of getting a precise spatial position and orientation of the gripped object in this study Instead, this study investigates the joint motions from an initial posture to a final posture of a hand for each interested gripping motion Fig 11 shows the initial and final postures of a robot hand for gripping an egg and an apple, respectively All joint angles of the initial hand and final postures are recorded The gripping motion can be synchronously desired according to the interpolations of the joint angles of the initial and final postures Therefore, the gripping model is formed based on the initial and final joint angles as the synchronous interpolations of these joint angles 262 Advances in Robot Manipulators Initial Posture Final Posture of Gripping an Egg Final Posture of Gripping an Apple Fig 11 Gripping postures simulations of an apple and an egg Most of initial postures are the same (complete extraction of all fingers, as shown in the top figure of Fig 11) However, the final postures are quite different for various gripping models Equation (1) shows the gripping model for a specific gripping motion n T T  k   k , f   k ,i n  k (t )   k ,i  t k (1) (2) (3) where T is time required for the gripping motion; ΔT is angular position command time interval for joint motors; n is theoretical count of position commands for a specific gripping motion; θk,i is the initial joint angle for joint motor k (k = 1 to 12); θk,f is the finial joint angle for joint motor k;Δθk is the angle increasements of joint motor k; t is the index (from zero) of position commands Especially, the gripping model just defines the synchronous joint angle increasements for all joint motors in each operation command with a pre-defined time interval The actual final (stop) joint angles will not be identical to the pre-defined final posture because it is difficult to get the actual positions and orientations of the gripped object online That means the real final postures will not refer to the pre-defined final postures; instead, they depend on the maximum allowable tactile sensor force as well as the maximum allowable joint angles to meet practical gripping situations Hence, the actual operation commands for a whole gripping motion may smaller or greater than the theoretical count of operation commands, as shown in Fig 12 Consequently, based on the tactile sensor data feedback and maximum allowable joint angle mechanisms, the final (stop) joint angles are determined finger-byfinger Note that the tactile sensor used in this study is a conventional force sensing resistor (FSR) On the other hand, the maximum allowable joint angle is desired for the finger being not damage the gripped object during gripping At the same time, the maximum allowable joint angle may also prevent the collisions and intersections of the hand mechanism for tactile sensor failures and gripping position uncertainties Development of Tendon Based Dexterous Robot Hand 263 Joint Motion Limits Maximum Allowable Angles Gripping Motion Models Gripping RC PWM Motion Servo Controller Joint Angles of Initial Postures Joint Angles of Final Postures Time Required for Gripping Motors A/D FSR Sensor Arrays Tactile Force Data -Finger Based Tactile Force Maximum Allowable Force Fig 12 Behavior-based gripping motions control architecture The algorithm of the proposed behavior-based gripping motion control system is described in Fig 13 At the beginning of gripping operations, a gripping model is selected The angle increasements of al joint angles are calculated according to the angular position (operation) command time interval and the time required for such a gripping motion The operation command index (t) is set as zero at the startup The joint angled are further updated to get closing to the object The maximum allowable tactile forces and joint angles are examined finger-by-finger Get Angle Increasements for All Joint Motors (k = 1 to 12) Select a Gripping Model Initialize Gripping (t = 0) Complete Gripping Update Operation Count (t) t = t+1 Update Angles for Active Fingers t = t+1 No No Yes If All Fingers Terminate Operations? Check Max Allowable Tactile Force/ Joint Angle (FbF) If a New Exceedance Event of a Finger occurs? Yes Terminate Operation for Corresponding Finger Note: FbF indicates Finger-by-Finger Fig 13 Algorithm of behavior-based gripping motion control system The active finger is defined as a finger with neither the tactile force being below the maximum allowable force nor the joint angles belong to this finger being within the 264 Advances in Robot Manipulators maximum allowable joint angles The system is running for all active fingers in terms of updating operation command index (t) as well as calculating new joint angle commands for active fingers Finally, the gripping motion is completed when no active fingers existed in this system 5 System integrations and experiments The system integration and test module is desired to cooperate with the motor controller to manipulate the robot hand via implementing the behavior based gripping motion control algorithm The control system of the proposed dexterous robot hand is constructed using the PSoC (Programmable System on a Chip) processor The PSoC is a mixed-signal array microcontroller, and it is a product of Cypress Semiconductor The core of PSoC is built based on a very-small Harvard architecture machine, named M8C In addition to the core of firmware, the most important feature is that PSoC provides reconfigurable integrated analog and digital peripherals Therefore, the PSoC is very suitable to integrate the sensing and actuation devices of the dexterous robot hand In addition, the analog multiplexer is also desired to extend the analog-to-digital channels of the FSR sensing At the same time, the gripping models are stored in an EEPROM and the data is accessed via the I2C communications In order to justify the tactile force variations among these five FSR sensors, the calibrations of FSR sensor are also desired in this study At the same time, the operation parameters such as the grip model selection, maximum allowable tactile force for each finger, maximum allowable joint angles, theoretical operation time required for each gripping motion, and operation command time interval are downloaded from a host computer via RS 232 communications Fig 14 shows the control circuit boards and the photo of gripping an egg Ideally, only the fingers of thumb and index and middle fingers are used for gripping Therefore, the terminations of the thumb, index and middle fingers should be done via checking the maximum allowable tactile forces Ideal Gripping Model One of Real Gripping Postures Side View Front View Fig 14 Egg gripping experiment with inconsistent egg posture (middle finger cannot touch the egg, and this finger is terminated via maximum allowable joint angle of the egg gripping model) Development of Tendon Based Dexterous Robot Hand 265 However, due to inconsistent spatial position and posture of the egg, only the thumb and index can touch the tactile sensors in this experiment, and middle finger are terminated via the maximum allowable joint angle for this egg gripping model Additionally, the terminations of the ring and little finger are also done in terms of the exceedances of their maximum allowable joint angles It is important that the maximum allowable gripping joint angles of different gripping models must be determined carefully according to practical considerations In addition to gripping an object, the proposed dexterous robot hand may perform several hand postures These hand postures are done via only using the maximum allowable joint angles Fig 15 shows several typical hand postures for presenting one-digit numbers, clenched hand, OK symbol, and YA symbol 6 Conclusions In this chapter, a dexterous robot hand is proposed based on the design concepts of light weight, compact size, similar to human’s hand gripping motions, gripping force restriction, and low cost The robot hand prototype is produced in this study Especially, complicated kinematics models and position control of joint angles are not constructed due to unpredictable object orientations and positions in this study Instead, the gripping motion behavior models for different gripping motions cooperating with maximum allowable tactile forces and joint angles are constructed to simplify the control architecture as well as to improve the practical gripping compatibility This chapter just represent a pilot study of a low cost dexterous robot hand; however, most of design and control parameters are not well justified to perform perfect performance On the other hand, the selection of tendon wire as well as the mechanical properties and dynamics of the tendon wire are still the major interests of the future works Digit-1 Digit-5 Digit-8 Digit-9 Digit-2 Digit-6 Digit-3 Digit-4 Digit-7 Clenched Hand OK Symbol Fig 15 Several hand posture demonstrations YA Symbol 266 Advances in Robot Manipulators 7 Acknowledgement This work was partially supported by the National Science Council, Taiwan, R.O.C., under Grants 95-2221-E-011-226-MY3 8 References Challoo, R.; Johnson, J.P.; McLauchlan, R.A.; & Omar, S.I (1994) Intelligent Control of a Stanford JPL Hand Attached to a 4 DOF Robot Arm, Proceedings of IEEE International Conference on Humans, Information and Technology, Vol 2, pp 1274 – 1278 Jacobsen, S.; Iversen, E.; Knutti, D.; Johnson, R.; & Biggers, K (1986) Design of the Utah/M.I.T Dextrous Hand, Proceedings of IEEE International Conference on Robotics and Automation, Vol 3, pp 1520 – 1532, San Francisco, U.S.A Kawasaki, H.; & Mouri, T (2007) Design and Control of Five-Fingered Haptic Interface Opposite to Human Hand IEEE Transactions on Robotics, Vol 23, No 5, pp 909 918 Kawasaki, H.; Komatsu, T.; & Uchiyama, K (2002) Dexterous Anthropomorphic Robot Hand with Distributed Tactile Sensor: Gifu Hand II IEEE/ASME Transactions on Mechatronics, Vol 7, No 3, pp 296 - 303 Kyriakopoulos, K.J.; Van Riper, J.; Zink, A.; & Stephanou, H.E (1997) Kinematic Analysis and Position/Force Control of the Anthrobot Dextrous Hand IEEE Transactions on Systems, Man, and Cybernetics, Part B, Vol 27, No 1, pp 95 - 104 Lin, L.R; & Huang, H.P (1996) Integrating Fuzzy Control of the Dexterous National Taiwan University (NTU) Hand IEEE/ASME Transactions on Mechatronics, Vol 1, No 3, pp 216 - 229 Namiki, A.; Imai, Y.; Ishikawa, M.; & Kaneko, M (2003) Development of a High-speed Multifingered Hand System and its Application to Catching, Proceedings of IEEE/RSJ International Conference on Intelligent Robots and Systems, Vol 3, pp 2666 2671 Parka, N.H.; Oh, Y.; & Oh, S.R (2006) Behavior-based Control of Robotic Hand by Tactile Servoing International Journal of Applied Electromagnetics and Mechanics, Vol 24, pp 311–321 Dimensional Synthesis and Analysis of the 2-UPS-PU Parallel Manipulator 267 13 x Dimensional Synthesis and Analysis of the 2-UPS-PU Parallel Manipulator Yunfeng Zhao, Yanhua Tang and Yongsheng Zhao1 School of Mechanical Engineering, Yanshan University Qinhuangdao 066004 Hebei China 1 Introduction ¶(6pt) Compare with conventional serial robots, parallel manipulators has the advantages of higher accuracy, higher stiffness, and higher ratio of force-to-weight, so it has been intensively researched and evaluated by industry and intuitions over the last two decades [1] It is well known that a main drawback of parallel manipulator is their reduced workspace Furthermore computing this workspace is not an easy task as, at the opposite of classical serial robot, the translational and orientation workspace are coupled [2] A number of authors have described the workspace of a parallel mechanism by discretizing the Cartesian workspace [3] In the case of three degree of freedom (3-DOF) manipulators, the workspace is limited to a region of the three-dimensional Cartesian space A more challenging problem is designing a parallel manipulator for a given workspace Merlet [4] propounded an algorithm to determine all the possible geometries of Gough-type 6-DOF parallel manipulators whose workspace must include a desired one Boudreau and Gosselin [5] proposed an algorithm that allows for the determination of some parameters of the parallel manipulators using a genetic algorithm method in order to obtain a workspace as close as possible to a prescribed one Kosinska et al [6] presented a method for the determination of the parameters of a Delta-4 manipulator, where the prescribed workspace has been given in the form of a set of points Snyman et al [7] proposed an algorithm for designing the planar 3-RPR manipulator parameters, for a prescribed two-dimensional physically reachable output workspace Laribi et al [8] presented an optimal dimensional synthesis method of the DELTA parallel manipulator for a prescribed workspace This problem was generally solved numerically, and none of the authors mentioned above took driving force into account In this paper, the 2-UPS-PU Parallel manipulator is designed to have a specified workspace The algorithm is proposed to solve the optimization problem，which not only takes into account the leg-length limits, the mechanical limits on the passive joints, and interference between links, but also the driving forces of the three legs 1 Corresponding author Tel./Fax: +86-335-807-4581 E-mail address: yszhao@ysu.edu.cn 268 Advances in Robot Manipulators This paper is organized as follows: Section 2 is devoted to the description of the 2-UPS-PU Parallel manipulator Section 3 deals with the position analysis of the Parallel manipulator Section 4 is devoted to the kinematic analysis of the Parallel manipulator Section 5 deals with the Statics analysis of the Parallel manipulator In Section 6, we carry out the formulation of the optimization problem Section 7 contains some conclusions 2 Displacement analysis The 2-UPS-PU parallel manipulator is shown in Fig 1 This manipulator consists of three kinematic chains, including two UPS legs with identical topology and one PU leg, connecting the fixed base to a moving platform In this parallel manipulator, the UPS legs, from base to platform, consist of a fixed Universal joint, an actuated prismatic joint and a spherical joint attached to the platform The PU leg connecting the base center to the platform consists of a prismatic joint attached to the base, a universal joint attached to the platform This branch is used to constrain the motion of the platform to the three degrees of freedom O Fig 1 The 2-UPS-PU parallel manipulator The reference frame O-XbYbZb is fixed on the base and mobile frame U0-XpYpZp is fixed on the moving platform (see Fig 1) At the initial position, the Xp-axis and Yp-axis of mobile frame are coincidence with the axes of the Universal joints U0 respectively The orientation of the first axis of U0 is fixed The orientation of the mobile frame can be represented by θ1 and θ2 shown in Fig 2, which are two Euler angles about two axes of U0, respectively Such Euler angles are defined by first rotating the mobile frame about the base xp-axis (first axis of U0) by an angle 1 , then about the mobile yp-axis by an angle For this choice of Euler angles, the rotation matrix is defined as ¶(9pt) Dimensional Synthesis and Analysis of the 2-UPS-PU Parallel Manipulator  cos 2 R  RX p 1   RYp  2    sin 1 sin  2    cos 1 sin  2  269 0 sin  2  cos 1  sin 1 cos 2   sin 1 cos1 cos  2   (1) where RX p   and RYp   are the basic rotation matrices The position of the mobile frame can be represented by l0, which is the distance between the Universal joint U0 and reference point O The homogeneous transform matrix T, which represents the orientation and position of the mobile frame, is ¶(9pt) 0 sin  2 0  cos 2  sin  sin  cos1  sin 1 cos 2 0  1 2  T  TransZ p (l0 ) RX p 1   RYp  2    (2)   cos 1 sin  2 sin 1 cos 1 cos  2 l0    0 0 0 1    ¶(9pt) ZP ZP Z'P U0 YP XP Initial orientation Fig 2 The 2-UPS-PU parallel manipulator  θ 2 XP U0 X'P θ YP 1 Y'P Current orientation The spherical joints (S1 and S2) of the UPS legs are arranged on the moving platform and their distances to the Universal joint U0 on the moving platform is r The Universal joints (U1 and U2) are fixed on the base platform and the distances to the reference point O on the base is R The coordinate of U0, S1 and S2 in mobile frame and the coordinate of U1 and U2 in reference frame are expressed as: ¶(9pt)  0  r cos    r cos    R cos    R cos             U 0   0  S1   r sin   S 2   r sin   U1   R sin   U 2   R sin   (3) 0  0   0   0   0            2.1 Inverse kinematics For a given position and orientation of the mobile platform, we can compute the related link lengths, denoted by li, using the following relation: 270 Advances in Robot Manipulators l0  l0 l1  T  S1  U1  a 2  b 2  c 2 l2  T  S 2  U 2  d  e  f 2 2 (4) 2 where a  r cos  cos 2  R cos  b  r cos  sin 1 sin  2  r sin  cos 1  R sin  c  r sin  sin 1  r cos  cos1 sin  2  l0 d  r cos  cos  2  R cos  e  r cos  sin 1 sin  2  r sin  cos 1  R sin  f  r sin  sin 1  r cos  cos 1 sin  2  l0 Eq (4) is the solution of the so-called inverse kinematics problem 2.2 Direct kinematics If set the second axis of Universal joint U0 pass through either S1 or S2 (   0 or   90 ), we can simply get analytical direct kinematics solution For example, let α=90°, then cosα=1 and sinα=0 As a result, Eq (4) for   90 is simplified as: ¶(9pt) l12  r 2  R 2  l0 2  2rl0 sin 1  2rR cos 1 l2 2  2rl0 sin  sin 1  2rR sin  sin  cos1  2rR cos  sin  sin 1 sin  2 (5)  2rl0 cos  cos 1 sin  2  2rR cos  cos  cos 2  r 2  R 2  l0 2 Then, we can calculate θ1 and θ2 by ¶(9pt)  l 2  r 2  R2  l 2  R 0   tan 1   1  sin 1  2 2 2    l0   2r l0  R   ab  1  d   2  sin    tan   2 2 c  c d  1 where r 2  R 2  l0 2  l１2 2r b  l0 sin  sin 1  R sin 2  cos 1 a c  l0 cos  cos1  R cos  sin  sin 1 d  R cos 2  It is easy to see that Eq (6) must satisfy: ¶(9pt) 1   90 90  2   90 90 Obviously, the same calculation can be drawn when α=0° ¶(14pt) (6) ... the joint angles belong to this finger being within the 264 Advances in Robot Manipulators maximum allowable joint angles The system is running for all active fingers in terms of updating operation... cos  sin 1 sin   r sin  cos 1  R sin  c  r sin  sin 1  r cos  cos1 sin   l0 d  r cos  cos   R cos  e  r cos  sin 1 sin   r sin  cos 1  R sin  f  r sin  sin 1 ... the gripping model is formed based on the initial and final joint angles as the synchronous interpolations of these joint angles 262 Advances in Robot Manipulators Initial Posture Final Posture