Kinematics-Based Simulation and Animation of Articulated Rovers Traversing Rough Terrain
|
|
- Jason Nigel Hunt
- 5 years ago
- Views:
Transcription
1 Int'l Conf. Modeling, Sim. and Vis. Methods MSV'16 3 Kinematics-Based Simulation and Animation of Articulated Rovers raversing Rough errain Mahmoud arokh Department of Computer Sence, San Diego State Universit San Diego, CA , U.S.A. Abstract he paper proposes a simple and computationall effient method for the modeling and animation of highl articulated rovers traversing rough terrain. he method is based on the propagation of position and orientation veloties through wheels and various joints and linkages of the rover. hese velot equations are combined to form the Jacobian matri of the rover that relates the position and orientation of the rover to various active (actuated) and passive rover joint variables. A rearrangement of the Jacobian equation allows determining the actuation of suspension joints for balance control to avoid tipover. his is done through a pseudoinverse method which optimies a balance performance criterion. o illustrate the kinematics modeling and balance control concepts, the method is applied to a rover similar to the NASA s Sample Return Rover and simulation and animation results are presented. 1. Introduction Articulated rovers are being used in variet of applications, espeall in planetar eplorations. Rovers with active suspension mechanisms are capable of modifing their configurations b adjusting their suspension linkages and joints so as to change their center of mass, thus avoiding tipover while traversing rough and slopp terrain. Rovers with adjustable suspension sstem have been researched in recent ears. Iagnemma and Dubowsk [1] presented stabilit-based suspension control for a spefic rover using an essentiall geometric approach and performing a rather comple optimiation procedure. Other contributions in the area of rover kinematics include [2] and [3]. We have developed a comprehensive method for rover kinematics modeling [4] and included motion control in [5] In a subsequent paper [6], we presented an alternative and more effient method for kinematics modeling and balance control. he purpose of the present paper is to demonstrate the modeling and control using simulations and animation of a rover over uneven terrain. 2. Overview In this section we provide an overall view of our proposed simulation and animation environment which has been developed in Matlab/Simulink. he simulations consist of a number of modules as shown in Fig. 1. he trajector generation module provides either a time trajector for the desired rover position (, ) and heading, or a desired path. hese quantities are assumed to be available from a path planner. hese desired quantities are compared with their respective sensed values in a trajector following module that produces the desired forward speed and turn (aw) rate of the rover. he actuation or control module then receives the these speed and turn rate commands as well as the current sensed rover roll, pitch and suspension sstems joint angles to determine the actuation commands for the rover steering, wheel motors and active suspension sstem joints. hese commands are applied to the rover model which interacts with the terrain and produces the actual (sensed) rover quantities. Since trajector generation and trajector following have been covered in the literature, we will not discuss these modules in this paper. Animation consists of drawing the terrain, rover bod, suspension sstem, wheels and their interaction with the terrain. he animation module receives various sensed quantities from the rover simulation and incrementall moves and displas the motion in a smooth manner. 3. Kinematic Based Actuation and Control In this section we develop a kinematics model for and articulated rover with active suspension sstem (ARAS), which will be used to determine the actuation commands. Such a rover is a wheeled mobile robot consisting of a main bod connected to wheels via a set of linkages and joints that can be adjusted, some activel and some passivel for keeping the rover balanced. he active linkages and joints have actuators through which their values can be controlled, whereas passive ones change their values to compl with the terrain topolog.
2 4 Int'l Conf. Modeling, Sim. and Vis. Methods MSV'16 Fig. 1 he main simulation modules For modeling, we must determine the contributions of each wheel and suspension mechanism to the overall motion of the rover. We attach a number of frames starting from the wheel-terrain contact frame then going through the steering and suspension frames and finall to the rover reference frame. Since we are interested in the motion, we relate the translational and rotational veloties of the net frame in terms of the previous frame. Let ua [ a a a ] and ub [ b b b ] denote the position of the current and net frames, respectivel. Similarl, let a [ a a a ] and b [ b b b ] be the orientation of the current and net frames, respectivel, where, and are the rotation around, and ais, or roll, pitch and aw, respectivel. he 31 translation velot vector of the net frame b is dependent on the translational and rotational veloties of the current frame a plus an translational velot added to the frame b itself. his can be written as [7] u a a pb u ob u b Rb,a (1) where R b, a and pb are, respectivel, the rotation matri and position vector of the frame b relative to the frame a, and u ob is the translational velot added to the frame b. he latter is ero if the joint assoated with the frame b is not prismatic. he rotational velot of the net frame b is dependent on the rotational velot of the frame a plus an rotational velot added to the frame b itself, i.e. [7] ob b Rb,a a ob (2) We start at wheel i ( i 1,2,, n ) contact frame which has the translational and rotational veloties u [ ] and [ ], and perform the frame to frame velot propagation until we reach to the rover reference frame to obtain rover veloties u r [ r r r ] and r [ r r r ]. Let the joint variable vector that includes each wheel-terrain contact angle, steering angle, and various prismatic and revolute joint variables be denoted b the i 1 vector i. hen we will obtain an equation of the general form u r J r i u ; i 1,2,, n (3) i where J i is the Jacobian matri of the wheel i. Note that the wheel translational and rotational velot vectors u and include various slips. Equation (3) describes the contribution of individual wheel motion and the connecting joints to the rover bod motion. he net bod motion is the composite effect of all wheels and can be obtained b combining (3) into a single matri equation as I6 u c u r J c r I6 where the composite identit matri on the left is 6n 6, u c u c1 u c2 u cn and c c1 c2 cn are 3n1 vectors of composite wheel veloties at the contact points, and is the 1 vector of the joint variables which has both active (actuated) and passive joints. Note that in general some wheels share common suspension links and joints so that i n 1 i. he composite Jacobian matri of the rover J has a dimension of 6n (6n ). he composite equation (4) reflects the contribution of various position and angular rates to the overall motion of the rover. In order to control, we must determine commands to the wheels, steering and joints actuators. For this, we rearrange (4) into an equation of the form (4)
3 Int'l Conf. Modeling, Sim. and Vis. Methods MSV'16 5 A B q (5) where is the n 1 vector of unknown quantities to be determined, and q is the n q 1 vector of known quantities. he unknown vector consists of actuation signals such as active suspension joints, wheel roll rates, and un-measurable quantities such as appropriate slips. he known vector consists of desired quantities such as the desired forward rover velot d and heading d. he matrices A and B are obtained from the elements of J and the identit matrices I1,I2,, I6 in (4). After partitioning (4) into the form (15), the dimensions of A and B are 6n n and 6n nq. In general n nq, in which case we have an underdetermined sstem of equations. he etra parameters can be used to achieve an optimiation goal. For a rove with an active suspension sstem, the optimiation goal would be balanng the rover b adjusting its suspension joints and linkages so as to avoid tip over when traversing rough terrain. A possible optimiation function is analed is shown in Fig. 3. he rover has four wheels with each independentl actuated and rotation angles subscripted with a clockwise direction so that 1, 4 are for the left side and 2, 3 are for the right side. At either side of the rover, two legs are connected via an adjustable hip joint. In Fig. 3 the hip angles on the left and right sides are denoted as 2 1 and 2 2, respectivel. hese joints are actuated and used for balanng the rover. he two hips are connected to the bod via a differential which has an angle on the left side and on the right side. On a flat surface is ero but becomes non-ero when one side moves up or down with respect to the other side. he differential joint is passive (unactuated) and provides for the compliance with the terrain. he wheels are steerable with steering angles denoted b i. he wheel terrain contact angle i is the angle between the -aes of the i-th wheel ale frame Ai and contact coordinate frame as shown in Fig. 4. f a1 a2 a ˆ a (6) he first term is a tip over measure which reflects the degree to which the rover configuration deviates from the perfectl balanced configurations. he latter occurs when the rover in the second moves over a flat surface. he quantit a term is the vector of actuated suspension joints and ˆ a its nominal or desired values under normal operating conditions (e.g., operating over flat surface). Note that without the second term, minimiing f would result in a rover configuration that is maimall flat or spread out even when the rover moves over a flat surface. he weighting factors a1 and a2 place relative emphasis between achieving rover balanng and the desire to operate near the nominal configuration. We solve (5) and minimie (6) b using the null space of A, to get [8] Fig. 2 he JPL s sample return rover steerin adjustable height differentia steerin # # f / A B q k ( E A A ) (7) # where A is the pseudo-inverse of A, k is a scalar, E is n n identit matri, and the partial derivative are gradients of the performance function with respect to the active suspension joints, roll and pitch, respectivel. In the net section we spef the above quantities for our ARAS. he gradient can be computed numericall or analticall or numericall. 4. Modeling of an Active Suspension Rover he articulated rover with active suspension (ARAS) to be considered here is similar to the JPL Sample Return Rover shown in Fig.2. he schematic diagram of ARAS to be wheel 1 wheel 4 Fig. 3 Schematic diagram of the left side of ARAS A i c i c i c i Ai c i Fig. 4 Definition of contact angle In order to derive the kinematics equations, we must assign coordinates frames. Fig. 5 illustrates our choice of
4 6 Int'l Conf. Modeling, Sim. and Vis. Methods MSV'16 coordinate frames for the left side of the rover. he right side is assigned similar frames. In Fig. 5, R is the rover reference frame whose origin is located on the center of gravit of the rover, its -ais along the rover straight line forward motion, its -ais across the rover bod and its -ais represents the up and down motion. he differential frame D has a vertical (along -ais) offset denoted b k1and a horiontal distance of k2 from D. he distance from the differential to the hip, denoted b k 3, is half the width of the rover. We now introduce three more frames, all of which have origin at the wheel ale. he length of the legs from the hip to the wheel ale is k 4. he hip frames H 1,, H 4 for the four wheels are obtained from the differential frame b rotation and translation as shown with the Denavit-Hartenberg (D-H) parameters dh,d dh, adh and dh in able 1 and in Fig 5. Similarl the steering frames S1,, S4 and ale frames A1,, A 4 are defined in able 1 and Fig 5. We now use the basic frame to frame equations (1)-(2) and go through the frames sequentiall from wheel i terrain contact c i, wheel ale A i, steering S i, hip H i, differential D, and finall to the rover reference R. Equation (1)-(2) for the contact to the ale becomes u Ai Ai R R Ai, Ai, u where the rotation matri is evident from Fig. 4. R Ai, r c s 1 (8) s, as c S1-9 Fig. 6 Side (left figure) and top views of wheel 1 ABLE 1- D-H PARAMEERS FOR HE ARAS Frame dh d dh adh dh D k1 k2-9 H1 9 1 k3 k4 H k3 k4 H k3 k4 H4 9 4 k3 k4 S S S S A1 1 A2 2 A3 3 A4 4 Net we form wheel i ale to steering velot propagation as H1 S1 u Si RSi, Ai u Ai Ai Si RSi, Ai Ai i H1 S1 A1 A1 S1 (9) D k 2 k1 R k3 k4 k 4 H 4 c i s i where RSi,Ai s i c i. he net in the chain is 1 the hip frame, and we can write u Hi RHi,Si u Si Si Hi RHi,Si Si hi i (1) H 1 Fig. 5 Reference R, differential D, and hip H coordinate frames s( hi i ) c( hi i ) with RHi,Si c( hi i ) s( hi i ), 4 1, 1 1 i 1,2 3 2, and h i. Similarl the differential 1 i 3,4 frame, and rover reference frame veloties are obtained using (1)-(2) and able 1.
5 Int'l Conf. Modeling, Sim. and Vis. Methods MSV'16 7 Substituting recursivel (5) through (8) into (9) we obtain an equation of the form (3) where i i i i. Due to space limitation, the Jacobian matrices Ji and their elements are not given here but can be found in our technical report [9]. he elements of Ji are trigonometric functions of the joint variables i, i, i and. 5. Simulation and Animation Results In this section we present the results of balance control for the ARAS introduced in Section II.A.. he full Jacobian equation is not given here due to space limitations but is provided in [9]. For the ARAS, the vector in (5) is r r r r u c c (11) where r, r and r, r are the unknown rover veloties and attitude angles rates and hip rate vector. Note that u c rates i and side slip rate 1 2 is the actuated contains onl the wheel rolling i, and wheels are assumed to be in contact with the terrain so that i. In addition, c consist of onl wheel turn slip rates and tilt rate, with other components are removed due to the particular geometr of the rover. Finall; c is set to ero as contact angle rates are ver nois and their estimation is prone to large errors. hus is a 231 vector and A is a 6n matri. Note that in general some rows of A are linearl dependent and thus rank(a) 24. he vector of the known quantities in (5) is q d d (12) where d and d are the desired (spefied) rover forward velot and heading (aw) rate, respectivel, and is the steering angle rates vector. Note that since the aes of steering and wheel turn slip are coindent in this rover, the steering angles are indistinguishable from turn slip. In this case, a geometric approach is used to determine the steering angle rates using the desired forward velot d and d, and thus is a known quantit. hus the dimension of the known vector q is 6 1, and B has the dimension We have developed a simulation and animation environment using Matlab/Simulink. he overall scheme is was described in Section 2. Fig 7 and Fig. 8 show the simulation environment where various quantities such as rover position and orientation, and various joint angle values are shown during the traversal. Various views of the rover can been observed. Fig. 7 he simulation environment Fig. 8 Side and front views
6 8 Int'l Conf. Modeling, Sim. and Vis. Methods MSV'16 We stud the behavior of the rover for three terrains. he rover speed is set at 1cm / s to ease the conversion between distance and time on the graphs. Case 1: Inclined errain he terrain and the trace of the rover wheels are shown in Fig. 9. he terrain is flat but has a 45 degree slope which could result in tipover without actuated suspension. he hip angles start at their nominal values, e.g degrees. he hip joint angles as given in Fig. 1 shows that the right joint has decreased to raise the right side but the left angle is increased to lower the left side. his has almost leveled the rover as is evident b the rover roll angle shown in Fig, 11 where the initial roll angle of about 38 degrees has been reduced to about 13 degrees. Case 2: Wav and Bump errain he terrain shown in Fig. 12 consists of a bump which is wav (sinusoidal) under the left wheels and smooth under the right wheels. he hip joint angles are depicted in Fig. 13. It is interesting to note that the right and left hip joint values also go through sinusoidal tpe changes but in the opposite directions to maintain a level and balanced rover bod. he rocker also shows sinusoidal behavior. he rover roll and pitch angles are seen in Fig. 14. he rover roll ehibits small changes due to the hip adjustments, whereas the rover pitch goes through relativel large variations due to the traversing up and then down the wav bump. Fig. 11 Rover bod roll and pitch angle profiles Fig. 12 Wav and bump terrain Fig. 9 Inclined terrain and traces of rover wheels Fig. 13 Hip joint angle trajectories Fig. 1 Hip joint angle trajectories Fig. 14 Rover roll and pitch trajectories
7 Int'l Conf. Modeling, Sim. and Vis. Methods MSV'16 9 Case 3: Inclined Ditch and Bump errain In this case, the terrain has a slope of 45 degrees with a bump under the left side wheels and a ditch under the right side wheels as shown in Fig. 15. he hip angles are adjusted accordingl to balance the rover as shown in Fig. 16. he rover ehibits a maimum roll angle of about 16 degrees as seen from Fig. 17; much smaller than the 45 degree terrain slope. Fig. 15 Inclined ditch and bump terrain Fig. 16 Hip joint angle trajectories Fig. 17 Rover roll and pitch trajectories 6. Conclusions A methodolog is presented for the kinematics modeling and control of articulated rovers for achieving rover balance when traversing rough and slopp terrain. he main feature of the work is the formulation of rover kinematics which uses simple velot propagation starting from wheel-terrain contact and going through various joints and linkages to finall reach the rover reference frame. his formulation makes the modeling and computer implementation ver effient through simple repeated function calls. Rover balance control is achieved through a pseudo-inverse method which optimies balance criterion. Simulation and animation package using Matlab have been developed that show the motion of the rover over rough terrain. References [1] Iagnemma, K. and S. Dubowski, raction Control of wheel mobile robots in rough terrain with applications to planetar rovers, Int. J. Robotics Res., vol. 23, No. 1-11, pp , 23. [2] H. D. Naar, I. A. D. Nesnas, Re-usable kinematics models and algorithms for manipulators and vehicles, Proc. IEEE/RSJ Int. Conf. Intelligent Robots and Sstems, San Diego, 27. [3] J. Balaram, Kinematic observers for articulated rovers,, Proc. IEEE Int. Conference on Robotics and Automation, pp , San Fransco, CA, 2 [4] M. arokh, M. and G. McDermott, Kinematics Modeling and Analsis of Articulated Rovers, IEEE rans. Robotics, vol. 21, No. 4, , 25. [5] G. McDermott, M. arokh, L. Mireles, Balance control of articulated rovers with active suspension sstems, Proc. 7th IFAC Int. Conf. on Robot Control, vol 8, Pt. 1, identifier: / I , Ital, Sept. 26. [6] M. arokh, H.D. Ho and A, Bouloubasis, Sstematic kinematics analsis and balance control of high mobilit rovers over roughterrain, J. Robotics and Autonomous Sstems, vol. 61, pp , 213. [7] Craig, J. Introduction to Robotics, Mechanics and Control, pp , Pearson Prentice-Hall, 25. [8] Nakamura, N., Advanced Robotics- Redundanc and Optimiation, Chapt. 4, Addison and Wesle, [9] Mireles, L., G. McDermott and M. arokh, wo approaches to kinematics modeling of articulated rovers, lab/publications.html.
MEM380 Applied Autonomous Robots Winter Robot Kinematics
MEM38 Applied Autonomous obots Winter obot Kinematics Coordinate Transformations Motivation Ultimatel, we are interested in the motion of the robot with respect to a global or inertial navigation frame
More informationA Full Analytical Solution to the Direct and Inverse Kinematics of the Pentaxis Robot Manipulator
A Full Analtical Solution to the Direct and Inverse Kinematics of the Pentais Robot Manipulator Moisés Estrada Castañeda, Luis Tupak Aguilar Bustos, Luis A. Gonále Hernánde Instituto Politécnico Nacional
More informationTHE ORTHOGLIDE: KINEMATICS AND WORKSPACE ANALYSIS
THE ORTHOGIDE: KINEMATICS AND WORKSPACE ANAYSIS A. Pashkevich Robotic aborator, Belarusian State Universit of Informatics and Radioelectronics 6 P. Brovka St., Minsk, 007, Belarus E-mail: pap@ bsuir.unibel.b
More informationA rigid body free to move in a reference frame will, in the general case, have complex motion, which is simultaneously a combination of rotation and
050389 - Analtical Elements of Mechanisms Introduction. Degrees of Freedom he number of degrees of freedom (DOF) of a sstem is equal to the number of independent parameters (measurements) that are needed
More informationMTRX4700 Experimental Robotics
MTRX 4700 : Experimental Robotics Lecture 2 Stefan B. Williams Slide 1 Course Outline Week Date Content Labs Due Dates 1 5 Mar Introduction, history & philosophy of robotics 2 12 Mar Robot kinematics &
More informationDynamic Stability of Off-Road Vehicles: Quasi-3D Analysis
28 IEEE International Conference on Robotics and Automation Pasadena, CA, USA, Ma 9-23, 28 Dnamic Stabilit of Off-Road Vehicles: Quasi-3D Analsis Moshe Mann and Zvi Shiller Abstract This paper presents
More informationNATIONAL UNIVERSITY OF SINGAPORE. (Semester I: 1999/2000) EE4304/ME ROBOTICS. October/November Time Allowed: 2 Hours
NATIONAL UNIVERSITY OF SINGAPORE EXAMINATION FOR THE DEGREE OF B.ENG. (Semester I: 1999/000) EE4304/ME445 - ROBOTICS October/November 1999 - Time Allowed: Hours INSTRUCTIONS TO CANDIDATES: 1. This paper
More informationKinematics, Kinematics Chains CS 685
Kinematics, Kinematics Chains CS 685 Previously Representation of rigid body motion Two different interpretations - as transformations between different coord. frames - as operators acting on a rigid body
More informationChapter 4 Dynamics. Part Constrained Kinematics and Dynamics. Mobile Robotics - Prof Alonzo Kelly, CMU RI
Chapter 4 Dynamics Part 2 4.3 Constrained Kinematics and Dynamics 1 Outline 4.3 Constrained Kinematics and Dynamics 4.3.1 Constraints of Disallowed Direction 4.3.2 Constraints of Rolling without Slipping
More informationCMSC 425: Lecture 10 Basics of Skeletal Animation and Kinematics
: Lecture Basics of Skeletal Animation and Kinematics Reading: Chapt of Gregor, Game Engine Architecture. The material on kinematics is a simplification of similar concepts developed in the field of robotics,
More informationChapter 3 : Computer Animation
Chapter 3 : Computer Animation Histor First animation films (Disne) 30 drawings / second animator in chief : ke frames others : secondar drawings Use the computer to interpolate? positions orientations
More information1. Introduction 1 2. Mathematical Representation of Robots
1. Introduction 1 1.1 Introduction 1 1.2 Brief History 1 1.3 Types of Robots 7 1.4 Technology of Robots 9 1.5 Basic Principles in Robotics 12 1.6 Notation 15 1.7 Symbolic Computation and Numerical Analysis
More information(x, y) (ρ, θ) ρ θ. Polar Coordinates. Cartesian Coordinates
Coordinate Sstems Point Representation in two dimensions Cartesian Coordinates: (; ) Polar Coordinates: (; ) (, ) ρ θ (ρ, θ) Cartesian Coordinates Polar Coordinates p = CPS1, 9: Computer Graphics D Geometric
More informationSTRUCTURAL ANALYSIS, GEOMETRY AND STATICS OF A COACH UNFOLDING MECHANISM
STRUTURL LYSIS, EOMETRY STTIS O O UOLI MEISM Ovidiu TOESU*, ătălina ROU ()**, Păun TOESU* *) ssociate Professor, Politehnica Universit of ucharest, e-mail: oval@hotmail.com **) iolog, igh School of iurgiu,
More informationDeveloping a Tracking Algorithm for Underwater ROV Using Fuzzy Logic Controller
5 th Iranian Conference on Fuzz Sstems Sept. 7-9, 2004, Tehran Developing a Tracking Algorithm for Underwater Using Fuzz Logic Controller M.H. Saghafi 1, H. Kashani 2, N. Mozaani 3, G. R. Vossoughi 4 mh_saghafi@ahoo.com
More informationForce control of redundant industrial robots with an approach for singularity avoidance using extended task space formulation (ETSF)
Force control of redundant industrial robots with an approach for singularity avoidance using extended task space formulation (ETSF) MSc Audun Rønning Sanderud*, MSc Fredrik Reme**, Prof. Trygve Thomessen***
More informationModeling of Wheeled Mobile Robots using Dextrous Manipulation Kinematics
Modeling of Wheeled Mobile Robots using Dextrous Manipulation Kinematics Joseph Auchter, Carl Moore, Ashitava Ghosal Abstract This document introduces a new kinematic simulation of a wheeled mobile robot
More informationMechanism Kinematics and Dynamics
Mechanism Kinematics and Dynamics Final Project Presentation 10:10-13:00, 12/21 and 12/28 1. The window shield wiper (2) For the window wiper in Fig.1.33 on p.26 of the PPT, (1). Select the length of all
More informationLecture «Robot Dynamics»: Kinematics 3
Lecture «Robot Dynamics»: Kinematics 3 151-0851-00 V lecture: CAB G11 Tuesday 10:15 12:00, every week exercise: HG E1.2 Wednesday 8:15 10:00, according to schedule (about every 2nd week) Marco Hutter,
More informationLecture «Robot Dynamics»: Multi-body Kinematics
Lecture «Robot Dynamics»: Multi-body Kinematics 151-0851-00 V lecture: CAB G11 Tuesday 10:15 12:00, every week exercise: HG E1.2 Wednesday 8:15 10:00, according to schedule (about every 2nd week) Marco
More informationInverse Kinematics Analysis for Manipulator Robot With Wrist Offset Based On the Closed-Form Algorithm
Inverse Kinematics Analysis for Manipulator Robot With Wrist Offset Based On the Closed-Form Algorithm Mohammed Z. Al-Faiz,MIEEE Computer Engineering Dept. Nahrain University Baghdad, Iraq Mohammed S.Saleh
More informationSlope Traversal Experiments with Slip Compensation Control for Lunar/Planetary Exploration Rover
Slope Traversal Eperiments with Slip Compensation Control for Lunar/Planetary Eploration Rover Genya Ishigami, Keiji Nagatani, and Kazuya Yoshida Abstract This paper presents slope traversal eperiments
More informationEfficient Closed-Form Solution of Inverse Kinematics for a Specific Six-DOF Arm
International Journal of Control, Automation, and Sstems (1) 1 Efficient Closed-Form Solution of Inverse Kinematics for a Specific Si-DOF Arm Thanhtam Ho, Chul-Goo Kang*, and Sangoon Lee Abstract: Inverse
More informationLecture «Robot Dynamics»: Kinematics 3
Lecture «Robot Dynamics»: Kinematics 3 151-0851-00 V lecture: CAB G11 Tuesday 10:15 12:00, every week exercise: HG E1.2 Wednesday 8:15 10:00, according to schedule (about every 2nd week) office hour: LEE
More information3-Dimensional Viewing
CHAPTER 6 3-Dimensional Vieing Vieing and projection Objects in orld coordinates are projected on to the vie plane, hich is defined perpendicular to the vieing direction along the v -ais. The to main tpes
More informationTable of Contents Introduction Historical Review of Robotic Orienting Devices Kinematic Position Analysis Instantaneous Kinematic Analysis
Table of Contents 1 Introduction 1 1.1 Background in Robotics 1 1.2 Robot Mechanics 1 1.2.1 Manipulator Kinematics and Dynamics 2 1.3 Robot Architecture 4 1.4 Robotic Wrists 4 1.5 Origins of the Carpal
More informationSYNTHESIS AND SIMULATION OF A MULTILINK SUSPENSION MECHANISM
Journal Mechanisms and Manipulators Vol. 5, Nr. 2, 26. pp. 55-6 ARoTMM - IFToMM SYNTHESIS AND SIMULATION OF A MULTILINK SUSPENSION MECHANISM Giorgio FIGLIOLINI*, Pierluigi REA* DiMSAT, Universit of Cassino
More informationExperimental study of Redundant Snake Robot Based on Kinematic Model
2007 IEEE International Conference on Robotics and Automation Roma, Italy, 10-14 April 2007 ThD7.5 Experimental study of Redundant Snake Robot Based on Kinematic Model Motoyasu Tanaka and Fumitoshi Matsuno
More informationRobot Geometry and Kinematics
CIS 68/MEAM 50 Robot Geometr and Kinematics CIS 68/MEAM 50 Outline Industrial (conventional) robot arms Basic definitions for understanding -D geometr, kinematics Eamples Classification b geometr Relationship
More informationMEAM 520. Mobile Robots
MEAM 520 Mobile Robots Katherine J. Kuchenbecker, Ph.D. General Robotics, Automation, Sensing, and Perception Lab (GRASP) MEAM Department, SEAS, Universit of Pennslvania Lecture 22: December 6, 2012 T
More informationMCE/EEC 647/747: Robot Dynamics and Control. Lecture 3: Forward and Inverse Kinematics
MCE/EEC 647/747: Robot Dynamics and Control Lecture 3: Forward and Inverse Kinematics Denavit-Hartenberg Convention Reading: SHV Chapter 3 Mechanical Engineering Hanz Richter, PhD MCE503 p.1/12 Aims of
More informationMobile Robots Locomotion
Mobile Robots Locomotion Institute for Software Technology 1 Course Outline 1. Introduction to Mobile Robots 2. Locomotion 3. Sensors 4. Localization 5. Environment Modelling 6. Reactive Navigation 2 Today
More informationThis week. CENG 732 Computer Animation. Warping an Object. Warping an Object. 2D Grid Deformation. Warping an Object.
CENG 732 Computer Animation Spring 2006-2007 Week 4 Shape Deformation Animating Articulated Structures: Forward Kinematics/Inverse Kinematics This week Shape Deformation FFD: Free Form Deformation Hierarchical
More information02/22/02. Assignment 1 on the web page: Announcements. Test login procedure NOW!
Announcements Assignment on the web page: www.cs.cmu.edu/~jkh/anim_class.html est login procedure NOW! 0//0 Forward and Inverse Kinematics Parent: Chapter 4. Girard and Maciejewski 985 Zhao and Badler
More informationMechanism Kinematics and Dynamics
Mechanism Kinematics and Dynamics Final Project 1. The window shield wiper For the window wiper, (1). Select the length of all links such that the wiper tip X p (t) can cover a 120 cm window width. (2).
More informationTwo Dimensional Viewing
Two Dimensional Viewing Dr. S.M. Malaek Assistant: M. Younesi Two Dimensional Viewing Basic Interactive Programming Basic Interactive Programming User controls contents, structure, and appearance of objects
More informationRobotics kinematics and Dynamics
Robotics kinematics and Dynamics C. Sivakumar Assistant Professor Department of Mechanical Engineering BSA Crescent Institute of Science and Technology 1 Robot kinematics KINEMATICS the analytical study
More informationResearch Subject. Dynamics Computation and Behavior Capture of Human Figures (Nakamura Group)
Research Subject Dynamics Computation and Behavior Capture of Human Figures (Nakamura Group) (1) Goal and summary Introduction Humanoid has less actuators than its movable degrees of freedom (DOF) which
More informationKinematics. Kinematics analyzes the geometry of a manipulator, robot or machine motion. The essential concept is a position.
Kinematics Kinematics analyzes the geometry of a manipulator, robot or machine motion. The essential concept is a position. 1/31 Statics deals with the forces and moments which are aplied on the mechanism
More informationINSTITUTE OF AERONAUTICAL ENGINEERING
Name Code Class Branch Page 1 INSTITUTE OF AERONAUTICAL ENGINEERING : ROBOTICS (Autonomous) Dundigal, Hyderabad - 500 0 MECHANICAL ENGINEERING TUTORIAL QUESTION BANK : A7055 : IV B. Tech I Semester : MECHANICAL
More informationIntroduction to Robotics
Université de Strasbourg Introduction to Robotics Bernard BAYLE, 2013 http://eavr.u-strasbg.fr/ bernard Modelling of a SCARA-type robotic manipulator SCARA-type robotic manipulators: introduction SCARA-type
More informationWhat and Why Transformations?
2D transformations What and Wh Transformations? What? : The geometrical changes of an object from a current state to modified state. Changing an object s position (translation), orientation (rotation)
More informationDefinitions. Kinematics the study of constrained motion without regard to forces that cause that motion
Notes_0_0 of efinitions Kinematics the stud of constrained motion without regard to forces that cause that motion namics the stud of how forces cause motion ausalit the relationship between cause and effect
More informationKinematics of Wheeled Robots
CSE 390/MEAM 40 Kinematics of Wheeled Robots Professor Vijay Kumar Department of Mechanical Engineering and Applied Mechanics University of Pennsylvania September 16, 006 1 Introduction In this chapter,
More informationImage Metamorphosis By Affine Transformations
Image Metamorphosis B Affine Transformations Tim Mers and Peter Spiegel December 16, 2005 Abstract Among the man was to manipulate an image is a technique known as morphing. Image morphing is a special
More informationMatlab Simulator of a 6 DOF Stanford Manipulator and its Validation Using Analytical Method and Roboanalyzer
Matlab Simulator of a 6 DOF Stanford Manipulator and its Validation Using Analytical Method and Roboanalyzer Maitreyi More 1, Rahul Abande 2, Ankita Dadas 3, Santosh Joshi 4 1, 2, 3 Department of Mechanical
More information3. Manipulator Kinematics. Division of Electronic Engineering Prof. Jaebyung Park
3. Manipulator Kinematics Division of Electronic Engineering Prof. Jaebyung Park Introduction Kinematics Kinematics is the science of motion which treats motion without regard to the forces that cause
More information[ ] [ ] Orthogonal Transformation of Cartesian Coordinates in 2D & 3D. φ = cos 1 1/ φ = tan 1 [ 2 /1]
Orthogonal Transformation of Cartesian Coordinates in 2D & 3D A vector is specified b its coordinates, so it is defined relative to a reference frame. The same vector will have different coordinates in
More informationAUTONOMOUS PLANETARY ROVER CONTROL USING INVERSE SIMULATION
AUTONOMOUS PLANETARY ROVER CONTROL USING INVERSE SIMULATION Kevin Worrall (1), Douglas Thomson (1), Euan McGookin (1), Thaleia Flessa (1) (1)University of Glasgow, Glasgow, G12 8QQ, UK, Email: kevin.worrall@glasgow.ac.uk
More informationResearch Article Dynamic Rocker-Bogie: Kinematical Analysis in a High-Speed Traversal Stability Enhancement
Aerospace Engineering Volume 216, Article ID 518197, 8 pages http://dx.doi.org/1.1155/216/518197 Research Article Dynamic Rocker-Bogie: Kinematical Analysis in a High-Speed Traversal Stability Enhancement
More informationEXPANDING THE CALCULUS HORIZON. Robotics
EXPANDING THE CALCULUS HORIZON Robotics Robin designs and sells room dividers to defra college epenses. She is soon overwhelmed with orders and decides to build a robot to spra paint her dividers. As in
More informationKinematic Modeling of Quadruped Robot
Kinematic Modeling of Quadruped Robot Smita A. Ganjare, V S Narwane & Ujwal Deole 1&2 K. J Somaiya College of Engineering, Mumbai University, Product Development, Larsen & Toubro LTD, Powai E-mail : smita.ganjare15@gmail.com,
More informationSingularity Handling on Puma in Operational Space Formulation
Singularity Handling on Puma in Operational Space Formulation Denny Oetomo, Marcelo Ang Jr. National University of Singapore Singapore d oetomo@yahoo.com mpeangh@nus.edu.sg Ser Yong Lim Gintic Institute
More informationON THE RE-CONFIGURABILITY DESIGN OF PARALLEL MACHINE TOOLS
33 ON THE RE-CONFIGURABILITY DESIGN OF PARALLEL MACHINE TOOLS Dan Zhang Faculty of Engineering and Applied Science, University of Ontario Institute of Technology Oshawa, Ontario, L1H 7K, Canada Dan.Zhang@uoit.ca
More informationRobots are built to accomplish complex and difficult tasks that require highly non-linear motions.
Path and Trajectory specification Robots are built to accomplish complex and difficult tasks that require highly non-linear motions. Specifying the desired motion to achieve a specified goal is often a
More informationOptimization of Watt s Six-bar Linkage to Generate Straight and Parallel Leg Motion
intehweb.com Optimization of Watt s Six-bar Linkage to Generate Straight and Parallel Leg Motion Hamid Mehdigholi and Saeed Akbarnejad Sharif University of Technology mehdi@sharif.ir Abstract: This paper
More informationSimulation and Modeling of 6-DOF Robot Manipulator Using Matlab Software
Simulation and Modeling of 6-DOF Robot Manipulator Using Matlab Software 1 Thavamani.P, 2 Ramesh.K, 3 Sundari.B 1 M.E Scholar, Applied Electronics, JCET, Dharmapuri, Tamilnadu, India 2 Associate Professor,
More informationKinematic calibration of Orthoglide-type mechanisms from observation of parallel leg motions
Pashkevich A, Chablat D. et Wenger P., Kinematic calibration of Orthoglide-tpe mechanisms from observation of parallel leg motions, Mechatronics, Vol. 19(4), June 29, pp. 478-488 Kinematic calibration
More informationA New Concept on Automatic Parking of an Electric Vehicle
A New Concept on Automatic Parking of an Electric Vehicle C. CAMUS P. COELHO J.C. QUADRADO Instituto Superior de Engenharia de Lisboa Rua Conselheiro Emídio Navarro PORTUGAL Abstract: - A solution to perform
More informationCalibration and measurement reconstruction
Scuola universitaria professionale della Svizzera italiana Dipartimento Tecnologie Innovative Metrolog laborator Calibration and measurement reconstruction Scope Tasks - Calibration of a two-degree-of-freedom
More informationDESIGN AND MODELLING OF A 4DOF PAINTING ROBOT
DESIGN AND MODELLING OF A 4DOF PAINTING ROBOT MSc. Nilton Anchaygua A. Victor David Lavy B. Jose Luis Jara M. Abstract The following project has as goal the study of the kinematics, dynamics and control
More information3D Geometry and Camera Calibration
3D Geometr and Camera Calibration 3D Coordinate Sstems Right-handed vs. left-handed 2D Coordinate Sstems ais up vs. ais down Origin at center vs. corner Will often write (u, v) for image coordinates v
More informationLecture 3. Planar Kinematics
Matthew T. Mason Mechanics of Manipulation Outline Where are we? s 1. Foundations and general concepts. 2.. 3. Spherical and spatial kinematics. Readings etc. The text: By now you should have read Chapter
More informationOpen Access The Kinematics Analysis and Configuration Optimize of Quadruped Robot. Jinrong Zhang *, Chenxi Wang and Jianhua Zhang
Send Orders for Reprints to reprints@benthamscience.ae The Open Automation and Control Systems Journal, 014, 6, 1685-1690 1685 Open Access The Kinematics Analysis and Configuration Optimize of Quadruped
More informationComputer Animation. Rick Parent
Algorithms and Techniques Kinematic Linkages Hierarchical Modeling Relative motion Parent-child relationship Simplifies motion specification Constrains motion Reduces dimensionality Modeling & animating
More informationFreely Available for Academic Use!!! March 2012
RoboAnalyzer User Manual Freely Available for Academic Use!!! March 2012 Developed by Prof S. K. Saha & Team Mechatronics Lab, Mechanical Engineering Department, IIT Delhi Courtesy: CD Cell, QIP, IIT Delhi
More informationThink About. Unit 5 Lesson 3. Investigation. This Situation. Name: a Where do you think the origin of a coordinate system was placed in creating this
Think About This Situation Unit 5 Lesson 3 Investigation 1 Name: Eamine how the sequence of images changes from frame to frame. a Where do ou think the origin of a coordinate sstem was placed in creating
More informationMarch 30, Abstract. 1 Introduction
Estimation Model for Kinematic Calibration of Manipulators with a Parallel Structure Dimitris Kugiumtzis Dept. of Informatics University of Oslo Pb. 1080 Blindern, N-0314 Oslo, Norway Bj rn Lillekjendlie
More informationRobotics I. March 27, 2018
Robotics I March 27, 28 Exercise Consider the 5-dof spatial robot in Fig., having the third and fifth joints of the prismatic type while the others are revolute. z O x Figure : A 5-dof robot, with a RRPRP
More informationApplications. Human and animal motion Robotics control Hair Plants Molecular motion
Multibody dynamics Applications Human and animal motion Robotics control Hair Plants Molecular motion Generalized coordinates Virtual work and generalized forces Lagrangian dynamics for mass points
More informationPrototyping a Three-link Robot Manipulator
Prototyping a Three-link Robot Manipulator Tarek M Sobh, Mohamed Dekhil, Thomas C Henderson, and Anil Sabbavarapu Department of Computer Science and Engineering University of Bridgeport Bridgeport, CT
More informationAn Iterative Algorithm for Inverse Kinematics of 5-DOF Manipulator with Offset Wrist
World Academy of Science, Engineering and echnology An Iterative Algorithm for Inverse Kinematics of 5-DOF Manipulator with Offset Wrist Juyi Park, Jung-Min Kim, Hee-Hwan Park, Jin-Wook Kim, Gye-Hyung
More informationDesign of Spider Mechanism for Extraterrestrial Rover
Design of Spider Mechanism for Extraterrestrial Rover Abin Simon 1, Kailash Dutt 1, Praveen Basil 1, Sreekuttan TK 1, Adithye Suresh 1, Arun M 1, Dr.Ganesh Udupa 2, Pramod Sreedharan 3 U.G. Student, Dept.
More informationKinematic and Gait Analysis Implementation of an Experimental Radially Symmetric Six-Legged Walking Robot
Journal of Computer & Robotics 5 (2, 202 33-38 33 Abstract Kinematic and Gait Analsis Implementation of an Eperimental Radiall Smmetric Si-Legged Walking Robot Mohammadali Shahriari *, Kambi Ghaemi Osguie
More information10/11/07 1. Motion Control (wheeled robots) Representing Robot Position ( ) ( ) [ ] T
3 3 Motion Control (wheeled robots) Introduction: Mobile Robot Kinematics Requirements for Motion Control Kinematic / dynamic model of the robot Model of the interaction between the wheel and the ground
More informationChapter 2 Intelligent Behaviour Modelling and Control for Mobile Manipulators
Chapter Intelligent Behaviour Modelling and Control for Mobile Manipulators Ayssam Elkady, Mohammed Mohammed, Eslam Gebriel, and Tarek Sobh Abstract In the last several years, mobile manipulators have
More information4 Kinematic Linkages. Chapter 4. Kinematic Linkages. Department of Computer Science and Engineering 4-1
Kinematic Linkages 4-1 Introduction In describing an object s motion, it is often useful to relate it to another object. Consider, for eample a coordinate system centered at our sun in which the moon s
More informationUse of multilayer perceptrons as Inverse Kinematics solvers
Use of multilayer perceptrons as Inverse Kinematics solvers Nathan Mitchell University of Wisconsin, Madison December 14, 2010 1 of 12 Introduction 1. Scope 2. Background 3. Methodology 4. Expected Results
More informationGRAPHS AND GRAPHICAL SOLUTION OF EQUATIONS
GRAPHS AND GRAPHICAL SOLUTION OF EQUATIONS 1.1 DIFFERENT TYPES AND SHAPES OF GRAPHS: A graph can be drawn to represent are equation connecting two variables. There are different tpes of equations which
More informationSCREW-BASED RELATIVE JACOBIAN FOR MANIPULATORS COOPERATING IN A TASK
ABCM Symposium Series in Mechatronics - Vol. 3 - pp.276-285 Copyright c 2008 by ABCM SCREW-BASED RELATIVE JACOBIAN FOR MANIPULATORS COOPERATING IN A TASK Luiz Ribeiro, ribeiro@ime.eb.br Raul Guenther,
More information1498. End-effector vibrations reduction in trajectory tracking for mobile manipulator
1498. End-effector vibrations reduction in trajectory tracking for mobile manipulator G. Pajak University of Zielona Gora, Faculty of Mechanical Engineering, Zielona Góra, Poland E-mail: g.pajak@iizp.uz.zgora.pl
More informationChapter 3: Kinematics Locomotion. Ross Hatton and Howie Choset
Chapter 3: Kinematics Locomotion Ross Hatton and Howie Choset 1 (Fully/Under)Actuated Fully Actuated Control all of the DOFs of the system Controlling the joint angles completely specifies the configuration
More information7-Degree-Of-Freedom (DOF) Cable-Driven Humanoid Robot Arm. A thesis presented to. the faculty of. In partial fulfillment
Mechanism Design, Kinematics and Dynamics Analysis of a 7-Degree-Of-Freedom (DOF) Cable-Driven Humanoid Robot Arm A thesis presented to the faculty of the Russ College of Engineering and Technology of
More informationFORCE CONTROL OF LINK SYSTEMS USING THE PARALLEL SOLUTION SCHEME
FORCE CONTROL OF LIN SYSTEMS USING THE PARALLEL SOLUTION SCHEME Daigoro Isobe Graduate School of Systems and Information Engineering, University of Tsukuba 1-1-1 Tennodai Tsukuba-shi, Ibaraki 35-8573,
More informationWritten exams of Robotics 1
Written exams of Robotics 1 http://www.diag.uniroma1.it/~deluca/rob1_en.php All materials are in English, unless indicated (oldies are in Year Date (mm.dd) Number of exercises Topics 2018 06.11 2 Planar
More informationSerially-Linked Parallel Leg Design for Biped Robots
December 13-15, 24 Palmerston North, New ealand Serially-Linked Parallel Leg Design for Biped Robots hung Kwon, Jung H. oon, Je S. eon, and Jong H. Park Dept. of Precision Mechanical Engineering, School
More informationComputer Graphics. P04 Transformations. Aleksandra Pizurica Ghent University
Computer Graphics P4 Transformations Aleksandra Pizurica Ghent Universit Telecommunications and Information Processing Image Processing and Interpretation Group Transformations in computer graphics Goal:
More informationNMT EE 589 & UNM ME 482/582 ROBOT ENGINEERING. Dr. Stephen Bruder NMT EE 589 & UNM ME 482/582
ROBOT ENGINEERING Dr. Stephen Bruder Course Information Robot Engineering Classroom UNM: Woodward Hall room 147 NMT: Cramer 123 Schedule Tue/Thur 8:00 9:15am Office Hours UNM: After class 10am Email bruder@aptec.com
More informationRedundancy Resolution by Minimization of Joint Disturbance Torque for Independent Joint Controlled Kinematically Redundant Manipulators
56 ICASE :The Institute ofcontrol,automation and Systems Engineering,KOREA Vol.,No.1,March,000 Redundancy Resolution by Minimization of Joint Disturbance Torque for Independent Joint Controlled Kinematically
More informationAnalysis of Six-legged Walking Robots
Analysis of Six-legged Walking Robots Shibendu Shekhar Roy 1*, Ajay Kumar Singh 1, and Dilip Kumar Pratihar 1 Department of Mechanical Engineering, National Institute of echnology, Durgapur, India Department
More informationEstimation of Tikhonov Regularization Parameter for Image Reconstruction in Electromagnetic Geotomography
Rafał Zdunek Andrze Prałat Estimation of ikhonov Regularization Parameter for Image Reconstruction in Electromagnetic Geotomograph Abstract: he aim of this research was to devise an efficient wa of finding
More informationModeling the manipulator and flipper pose effects on tip over stability of a tracked mobile manipulator
Modeling the manipulator and flipper pose effects on tip over stability of a tracked mobile manipulator Chioniso Dube Mobile Intelligent Autonomous Systems Council for Scientific and Industrial Research,
More informationPerformance evaluation of locomotion modes of an hybrid wheel-legged robot for self-adaptation to ground conditions
In Proceedings of the 8th ESA Workshop on Advanced Space Technologies for Robotics and Automation 'ASTRA 2004' ESTEC, Noordwijk, The Netherlands, November 2-4, 2004 Performance evaluation of locomotion
More informationSYNTHESIS AND RAPID PROTOTYPING OF MOTION FOR A FOUR-LEGGED MAMMAL-STRUCTURED ROBOT
SYNTHESIS AND RAPID PROTOTYPING OF MOTION FOR A FOUR-LEGGED MAMMAL-STRUCTURED ROBOT Macie Tronacki* Industrial Research Institute for Automation and Measurements, Warsaw, Poland Corresponding author (mtronacki@piap.pl)
More informationStackable 4-BAR Mechanisms and Their Robotic Applications
The 010 IEEE/RSJ International Conference on Intelligent Robots and Systems October 18-, 010, Taipei, Taiwan Stackable 4-BAR Mechanisms and Their Robotic Applications Hoyul Lee and Youngjin Choi Abstract
More informationMotion Control (wheeled robots)
Motion Control (wheeled robots) Requirements for Motion Control Kinematic / dynamic model of the robot Model of the interaction between the wheel and the ground Definition of required motion -> speed control,
More informationDETC THREE-DIMENSIONAL KINEMATIC ANALYSIS OF THE ACTUATED SPOKE WHEEL ROBOT. September 10-13, 2006, Philadelphia, Pennsylvania, USA
Proceedings Proceedings of IDETC/CIE of IDETC 06 2006 ASME 2006 ASME International International Design Design Engineering Engineering Technical Technical Conferences Conferences & September Computers
More informationSingularity Management Of 2DOF Planar Manipulator Using Coupled Kinematics
Singularity Management Of DOF lanar Manipulator Using oupled Kinematics Theingi, huan Li, I-Ming hen, Jorge ngeles* School of Mechanical & roduction Engineering Nanyang Technological University, Singapore
More informationA new 6-DOF parallel robot with simple kinematic model
A new -DOF parallel robot with simple kinematic model Nicholas Seward, Ilian A. Bonev, Senior Member, IEEE Abstract his paper presents a novel si-legged parallel robot, the kinematic model of which is
More informationθ x Week Date Lecture (M: 2:05p-3:50, 50-N202) 1 23-Jul Introduction + Representing Position & Orientation & State 2 30-Jul
θ x 2018 School of Information Technology and Electrical Engineering at the University of Queensland Lecture Schedule Week Date Lecture (M: 2:05p-3:50, 50-N202) 1 23-Jul Introduction + Representing Position
More information