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Ships from and sold by Amazon.com. Register a free business account Key Features A step-by-step computational approach helps you derive and compute the forward kinematics, inverse kinematics, and Jacobians for the most common robot designs. Detailed coverage of vision and visual servo control enables you to program robots to manipulate objects sensed by cameras. An entire chapter on dynamics prepares you to compute the dynamics of the most common manipulator designs. The most common motion planning and trajectory generation algorithms are presented in an elementary style. The comprehensive treatment of motion and force control includes both basic and advanced methods. The text’s treatment of geometric nonlinear control is more readable than in more advanced texts. Many worked examples and an extensive list of problems illustrate all aspects of the theory. About the authors Mark W. Spong is Donald Biggar Willett Professor of Engineering at the University of Illinois at Urbana-Champaign. Dr. Spong is the 2005 President of the IEEE Control Systems Society and past Editor-in-Chief of the IEEE Transactions on Control Systems Technology. Seth Hutchinson is currently a Professor at the University of Illinois in Urbana-Champaign, and a senior editor of the IEEE Transactions on Robotics and Automation. He has published extensively on the topics of robotics and computer vision. Mathukumalli Vidyasagar is currently Executive Vice President in charge of Advanced Technology at Tata Consultancy Services (TCS), India 's largest IT firm. Dr. Vidyasagar was formerly the director of the Centre for Artificial Intelligence and Robotics (CAIR), under Government of India’s Ministry of Defense.Key Features A step-by-step computational approach helps you derive and compute the forward kinematics, inverse kinematics, and Jacobians for the most common robot designs. Dr.http://loppisidjupdalen.se/images/uploaded/commvault-sysadmin-manual.xml Vidyasagar was formerly the director of the Centre for Artificial Intelligence and Robotics (CAIR), under Government of India’s Ministry of Defense.Dr. Spong is the 2005 President of the IEEE Control Systems Society and past Editor-in-Chief of the IEEE Transactions on Control Systems Technology. Dr. Vidyasagar was formerly the director of the Centre for Artificial Intelligence and Robotics (CAIR), under Government of India’s Ministry of Defense.Full content visible, double tap to read brief content. Videos Help others learn more about this product by uploading a video. Upload video To calculate the overall star rating and percentage breakdown by star, we don’t use a simple average. Instead, our system considers things like how recent a review is and if the reviewer bought the item on Amazon. It also analyzes reviews to verify trustworthiness. Please try again later. Minxing Pan 5.0 out of 5 stars This book covers robot kinematics amazingly well because it not only has vision representations of the joints and links, but also shows detailed mathematical equations for each computation. The well-formatted equations are easy to use for code implementation on physical robots. The graphical illustrations really help me understand the important concepts in robot kinematics. It has been 30 years, and I can't believe the computer vision section of this book is still relevant and useful to this date. The comprehensive mathematical background on camera calibration and linear algebra are most fundamental to modern vision processing. This book is tremendously helpful for learning the basics of robots.The explanation is clear and a lot of examples are shown. However, other chapters on control or vision has almost no content. Those later chapters are NOT for teaching, but just brief overview of technology. If you are trying to learn robot kinematics, this is an excellent book. However, don't expect to learn beyond that.http://fscl.ru/content/bose-lifestyle-50-manual-pdf (You can't learn control or vision from this book)Very satisfied. I recommend itI've found the book primarily useful as a roadmap of concepts to learn for robot modelling, but otherwise terrible as an educational resource. Getting through the book required frequent consultation of other materials. For many of the concepts in the book, reading the relevant wikipedia page provided a much clearer explanation of the subject. The problem with the book is that it is highly math intensive, and there's little or no attempt to relate the mathematics to specific examples. The book is filled with rapid fire derivations of equations with often minimal explanation. Should you fail to follow any particular step, you're left with little recourse but to consult other (clearer) descriptions of the theory at hand. The book is also lacking in problems for the student to work to assist with understanding the material. My background is a dual degree in mathematics and computer science from the University of California at the end of the 80's. I've spent the subsequent years working as an engineer. I'm sure that readers who are very current on differential equations and linear algebra will find the equations in the text easier to follow. But I'm also sure that such students would still find that the explanations are thin and relating the material back to the real world is lacking. Any professor choosing to use this text as the basis for a course is likely to find that they need to create so much supplementary material as to render the book of questionable value. All in all, I feel that publishing this book damages Wiley's reputation.One thing you might find interesting when unboxing is that the book is very thin comparing to any other engineering books. Yes, it is very thin, but it is also very informative.http://8forwine.com/images/canon-bge2n-manual.pdf A lot of people might underestimate this book because it was published in 2005, but you might want to think of it again because all the modern robot was built on the same practical modeling and control theory. So, this book is teaching you how to walk first before you are ready to run.Explain the kinematics, dynamics and control (KDC) in an intuitive and thorough way. These authors are all top experts in this field, specializing in robotics and controls. Spong and Hutchinson were EIC's in top control and robotics journals, while Vidyasagar won the 2000 Bode Lecture Prize. If you want to lay solid foundation in KDC, this is the book to begin with. PS: I am a postdoc at CMU Robotics Institute.Explains the dynamics of manipulators with trigonometry and linear algebra. I complemented the excesises by using MathCAD, MathLAB, and Soliworks.Los temas son explicados de manera sencilla y clara. Besides, the achieved gain in accuracy of capturing the reactive load related to vibrations is not necessarily high. Recall that the primary objective here is to determine the reactive torque fed back from the oscillating elastic link and thus to improve the prediction of ?. An accurate computation of the link end-position due to link elasticities is surely also an important task in robotics. However, this falls beyond the scope of the current work whose aim is to describe the robot joint transmission with nonlinearities.The lightweight metals an d composite materials deployed n ot only in the links but also in the joint assemblies affect the overall stiffness of robotic system. The elastic joints provide t he loaded robot motion with additional compliance and can lead to signi?cant control errors and vibrations in the joint as well as operational space. A better understanding of the compliant joint behavi or can help not only to analyze and simulate robotic systems but also to improve their control perfor mance. Elastic robot joints are often denoted as ?ex ible joints or compliant joints as we ll. The former modeling approaches aimed to describe the dynamic b ehavior of elastic robot joints lead back to Spong (1987). Spong extended the ge neral motion equation o f a rigid robotic manipulator to the case of joint elasticity captured by a linear connecti ng spring. R n is the vecto r of generalized input forces. The con?guration dependent matrixes M. R n ? n, C ? R n ? n, and G ? R n constitute the inertia, Cor iolis-centrifug al, and gravity terms correspondingly. The model introduced by Spong (1987 ) has been widely used in the later works which deal with a compliance co ntrol (Zollo et al. (2005)) and passivi ty-based impedance control (Ott et al. (2008)) of robots with joint elasticiti es. Des pite a g ood acceptance for the control applications this m odeling strategy miss es the damping factor rel ated to the connecting spring. In this regard, the approach prop osed by Ferretti e t al. (2004) which provides two masses connected by a linear spring and damper arran ged in parallel is more consisten t with the physical jo int structure. Also the inverse d ynamic model used for vibr ation control of elastic joint robo ts (Thummel et al. (2005)) incorpor ates a torsional spring with both stiffness and damping chara cteristics. From a slightly diversing point of view th e modeling of elastic robot join ts was signi?cantly in?uenced by the studies of harmon ic drive gear transmi ssion perform ed in the end -nineties and last decade. The har monic drives are widely spread in the robotic sys tems due to their compact size, hig h reduction ratios, high torque capacity, and low (nearly zero) backlash. Ho wever, a speci?c mechanical assembly 15 The model comp oses multiple component-related frictio nal elements and an additional structural damp ing attributed to the ?exspline. Another notable mod eling issue provided by Dhaouadi et al. (2003) presents the torsional torque in harmo nic drives as an integro-di fferential hysteresis function of both angular displacement and angul ar velocity across the ?exspline. Later, Tjahjowidodo et al. (2006) descri be the dynamics i n harmonic dri ves using nonlinear stiffness characteristics combined with distribute d Maxwell-slip elements that capture the hyste resis behavior. A complex phenomenological model of elastic robot joints with coupled hysteresis, friction and backlash nonlineariti es was proposed by Ruderman et al. (2009). However, realizing the complexity of decomposing and identifying the single nonlinearities a simpli?ed nonlinear dynamic model was l ater introduced in Rud erman et al. (2010). The leitmotif provi ded in this Chapter is to i ncorporate a combined phy sical as well as phenomenological view when modelin g the joint transmission with elasticities. Unlike the classical approache s which rather operate with l inear stiffness and dampi ng elements arranged either in series or in parallel the struct ure-oriented effects are emph asized here. The inherently nonlinear compliance an d damping of elastic robot joints are tackled from the cause-and-effect point of view. It is important to note that such approaches can rapidly increase the number of free para meters to be identi?ed, so that the model complexity ha s to be guarded carefully. T he Chapter is organi zed as follows. Section 2 introduce s the robot joint topology which ca ptures equally the dyna mic behavior of both rigid and elastic revolute joints. Three closed subsystems are described in terms of their eigenbehavior and feedforward and feedback interactions within the o verall joint structure. Section 3 provides the reader with description of the developed joint model capable to capture two main non linearities acting in the joint transmission. Fi rst, the dynamic joint friction is addressed. Secondly, the nonlinear stiffness combined with hysteresis map is described in detail. An experimental case study provided in Section 4 shows s ome characteristical obser vations obtained on a labor atory setup of the joint with el asticities and gives s ome identi?cation resul ts in this relation. Here it is impo rtant at which level of detail the robot join t transmission could be described. Mostly it is conditioned by the available knowledge about the mecha nical joint structure and the accessib ility of system measurements required for the identi?cation. In majority of applicatio ns, the actuator measurements such as the ang ular position and vel ocity as well as active motor current are available only prior to the gear transmi ssion.Although those hard ware solutions are often not technically o r (and) economically pro?table, a prototypic lab oratory measurement performed on t he load side of robotic joints can yiel d adequate data suf?cient for analysis and i denti?cation. Here, one can think about highly accur ate static as well as dynamic measurements o f the joint output position perfo rmed by means of the laser inter ferometry or laser triang ulation. The load torques can also be determined exter nally either by applying an appropr iate accelerometer or by using locked-load mechanisms equippe d by the torque (load) cells. Howev er, the latter solution is re stricted to the quas i-static exper iments with a constr ained output motio n. Now let us consider the topology of an elastic robot joint as shown in Fig. 1. In terms of the input-output behavior the proposed structure does not substantially differ from a simple fourth-order linear dynamic model of two connected masses. An external exciting torque u constitutes the input value and the relati ve position of the second moving mass.Goi ng into the input-output representati on, joint load gear transmission joint actuator u q W T Fig. 1. Topology of elastic robot joint let us subdivid e the robotic joint into three cl ose subsystems connected by the fe edforward and feedback actio ns realized by appropri ate physical states. The joint actuator loaded by the feedback torque.This value is an inherent determinant of the relative motio n entering the gear transmission and mostly measurable prior to that one. Since the gear transmission captures the intrinsic joint elasticity, the angular out put displacement of the j oint load constitutes t he second feedback state. Assuming that the gear with e lasticities behaves like a torsion sp ring with a certain stiffness capacity its output val ue represents the transmitted torque whi ch drives the joint load. When cutting f ree the forward and feedback paths the joint model decompos es into three stand-alone submodels, each one des cribing the speci?ed physical subsystem. Note that from energy conversion point of view we obt ain three dissipative mappings with two dif ferent sets of the input values. The ?rst input s et constitutes the f orward propagation of the energ y fed to the system. The second input set represe nts the system reaction with a negative or positive energy feedback d epending on the instantaneo us operatio n state. The actual joint topology r epresents a general c ase which covers both elastic and rigid transmission. The actuator submo del can be equally used for a rigid joint modeling, where.At this, each in?nitesimal chan ge in q will lead to an immediate exci tation of the load part, so that the eigendynamics o f the joint transmi ssion disapp ears. The following analytical example of two equivalent linear joint models explains the upper mentioned ideas in more detail. For instant, consider a simple motion problem of two connected masses m and M with two damping facto rs d and D, once with a rigid and once with an elastic joint. Assu me that the last one is represented by the spr ing with the stiffness K. The case described by H 3 ( s ) should approxima te a rigid system at which the sti ffness increases towards unlimi ted. Note that the residual parameter s of Eqs. (2) and (3) remain constant. It is easy to recognize that the step respo nse of H 3 ( s ) coincides well with those one of the a bsolute rigid joint H 1 ( s ). When analyzing the frequency response function it can be seen that the resonance p eak of H 3 ( s ) is shifted far to the r ight comparing to H 2 ( s ). Up to the resonance range the freque ncy response function H 3 ( s ) coincides exactly with H 1 ( s ). Note that the shifted resona nce of H 3 ( s ) provides t he same peak value as H 2 ( s ). Hence, during an exceptional excitation exactly at the resonance frequency the oscillatory output will arise again. However, from the practical point of view such a h igh-frequently excitation appears as hard ly realizable in a mechanical sys tem.Being condition al upon the gear and bearing structure an optimal level of d etail for modeling can be deter mined using a top-down approach. Starting from the s implest rigid case with a sing le actuator damping, add itional compliant and frictional element s can be included hierarch ically in order to pa rticularize the case-speci?c system behavior. In the following, we co nsider the single modeling steps re quired to achieve an adequate description of each subsystem included in the topology of a nonlinear elastic joint. 2.1 Joint actuator Considering the joint actuator which is dr iven by an electrical servo motor the angular velocity and angular pos ition of the output shaft are deter mined by two input values. The ?r st one is the input torque u which induces the angular accele ration of the rotor. The second one is a feedback load torque.The conjoint moment of inertia m includes the rotor with shaft as well as the additio nal rotating elements such as encoders, breaks, and coupl ings. Mostly, it can be supposed that all rotating bodies are homog enous and axially symme trical. This straightforward simpl i?cation allows us to deal with the concentrate d model parameters and to consider the relati ve motion at this stage as the si ngle body dynamics. T he joint actuator can be d escribed as follo ws m. Hence, the transi ent behavior of the current control loop can be easily neglecte d taking into account the time cons tants of the mechanical syste m part. The latter amount to several tens up to some hundr ed milliseconds. Howeve r, since a particular joint actuator can be mo unted on the robotic manipulator with multip le degrees of freedom (DOF) its frictional characte ristics can vary depende nt on the actual robot con?guration. Particularl y, the orientation of the supported motor shaft to the gravity ?eld can in?uence the brea kaway and sliding friction properties to a c ertain degree. Aside of the dependency from the robotic con?guration the most signi?cant fri ctional variations, as well known, are due to the therm al effects. Both the e xternal environment tem perature and the internal temper ature of contacting ele ments play a decis ive role, whereas the last o ne increases usually with the ope rating time and intensity. Howeve r, the thermal frictional effects can be rather attributed to a slow time-variant process and a correspond ing adaptivity of the mod el parameters. For reason of clarity an explicit temper ature dependency is omitted here just as in most known approach es of modeling the robot dyn amics. In the following, we also assume that no signi?cant eccentriciti es are present in the system, so that almost no periodic torque ripples occur o n a shaft revo lution. The complexity of the obtained actuator mod el can differ in number of the free parameters to be identi?ed, mostly dependent on the selected mapping of the friction beh avior. The lumped 297 Modeling of Elastic Robot Joints with Nonlinear Damping and Hysteresis However, in doing so a linear damping has to be assumed. Since the motion is essentially damped by a nonlin ear friction it appears as more r easonable to identify the actuator inertia tog ether with the corresponding friction paramete rs. Often, it is ad vantageous to identify the actuator friction toge ther with the friction acting in the gear transmis sion. The friction effects in the actuato r and gear assembl y are strongly coupled with each othe r since no signi?cant elas ticities appear between bo th. When id entifying the dynam ic friction one has to keep in mind that the captured torque val ue, mostly compu ted from the measured moto r current, represents a p ersistent interp lay between the s ystem inertia and f rictional damping. 2.2 Gear transmissi on The mechanical gear tra nsmission can be consider ed as a passive transducer of the actu ator motion to the output torque which drives the joint load. At this, the angular po sition of the joint load constitutes the feedback value which contains the s ignature of elasticities and backlash acting in the tr ansmission syste m. Often, the g ear transmissio n provides the main source of nonlin earities when analyzing t he joint behavior, the reason for whic h several applications arrange the direct drives without gear reduction (see e.g. by Ruderman et al. (2010)). However, most nowadays robotic syste ms operate using the gear units which offer the transmis sion ratios from 30: 1 up to 300:1. Apart from the classical s pur gears the more technologically elaborated planet ary and harmonic drive gears have been established in robotics for several years.In f act, it is rather expecte d that the teeth interactio n exhibits a hardening stiffness property. Due to internal frictional me chanisms within the teeth e ngagement area the overall tors ional joint compliance can behave piece wise as elasto-plas tic and thus give rise to substantial hyste resis effects. T he backlash, eve n when marginal, is couple d with an internal teeth friction and thus provides a damped bedstop moti on. Due to a mutual interaction between the mentioned nonlinear phenomena the resulting hysteresis is hardly decomposable in prope r frictional, structural and backl ash elements. In this re gard, it could be necessary ?rst to saturate the trans mission load in order to determine a prope r hysteresis state which offe rs a well known me mory effect. Here, the hysteresis memory m anifests itself in the transmitted torque value which d epends not only on the recent relative dis placement between the gear input and output but equall y on the history of the previous values. T hus, the dynamic hys teresis map has to repl ace the static stiffness characte ristic curve of the gear transmissio n. Howe ver, the last one remains a still suitable approx imation suf?cient for numerous practical appli cations. Well understood, the hy steretic torque transmissi on includes an inherent d amping which is characterize d by the energy dissi pation on a closed load-release cycle. The enclosed hysteresis loop a rea provides a measure of the corresponding structural losses, where the damping r atio is both ampli tude- an frequency-dep endent. T hus, the structural hysteresis damping differs from the linear viscous one and can lead to the limit cycles and multiple equilibrium states. The following numer ical example demonstr ates the damping character istics of the joint transmission in a more illustrative way. For instance, the single mass with one DOF is connected to the ground, once using a linear spring with linea r viscous damping, and once using a nonlinear hysteretic spring. At this, the linear stiffness is selected so as to coincide with the average value of the nonlinear stiffness map included in the hysteresis model. In case (b), the nonline ar hysteretic spring is higher dam ped at the beginning, though does not provide a ?nal equilibrium state. Instead of that, the motion enters a stable limit cycle up from a certain amplitude. The last one indicates the hysteresis cancelation close to zero displacement th at is however case-speci?c and can vary dependent 299 Modeling of Elastic Robot Joints with Nonlinear Damping and Hysteresis F rom a physical point of view an autonomous m echanical system will surely conve rge to a static idle state due to additio nal damping mechanisms not necessarily captured by the hyste resis. However, theoretically s een the hysteresi s damping does not guarantee the full de cay of all eigenmoti ons. An interesti ng and more realistic case (c) represents a combination of the li near and nonlinear hysteretic damping. Due to an additional velocity-dependent dampin g term the eigenmotion does not stay in side of a limit cycle and converges towards a non-zero idle state, thus providing the sy stem response with memory. The characteristical nonzero equilibrium states denote the forces remaining in the gear transmissio n after the input and output l oads drop out. 2.3 Joint load The robot links which connect the single joints within the k inematic chain of manipulator constitute the moving bodie s with additional inertia and elasticiti es. They may gener ate lightly damped vibrational mode s, which red uce the robot accuracy in tracking tasks according to Zoll o et al. (2005). The overall multi-body manip ulator dynamics (1) provide s the interaction between the actuated joints and passive links. Re call that Eq. (1) captures a r igid robot structure with no elasticitie s at all. However in general case, the contribution of the g ravity and Coriolis-centri fugal forces has to be taken into account independent of the consid ered rigid or elastic manipulator. For reason of traceability, we cut free the kinematic chain and consider the single robot j oint with the following link as depicted in Fig. 5. At this, the joint link can be represented either as the concentrated L or distributed L 1,., L n mass. Here, no additional inertia and Cori olis-centrifugal terms fed back from the followi ng joints and links contr ibute to the overall load balance. Note that the recent approach constitutes a strong simpli?cati on of the link dynamics so that the add itional degree of freedom. The transmitted torque.Recall that the pri mary objective here is to determine t he reactive torque fed back fr om the oscillating elastic link a nd thus to im prove the predicti on of ?. A n accurate computation of the link end-posi tion due to link elasticities is surely also a n important task in robotics. However, this falls beyond the scope of the current w ork whose aim is to describe the robot joint transmission with nonlinearities.For all physically reasonable parameter values the system proves to be controll able whereas the input torque.F urther, two relative stiffness values 1 k and 10 k are considered. Since the gravi ty term is not directly involved into vibrational characteristics it can be omi tted at this stage. In the same manner the Coulomb frictio n nonlinearity whi ch constitutes a constant torq ue disturbance dur ing an unidirectional m otion is also excluded from the computation. The response of the simulated, insofar linear, joint load is shown in Fig. 6. Two stiffn ess values differing in order of magnit ude lead to the oscillating link de?ection depicted in Fig. 6 (b) and (c). Besides the differing eigenfrequencies the principal shape of the enveloping function a ppears as quite similar for both stif fness values.