Showing papers on "Kinematics published in 2004"

Neuromusculoskeletal Modeling: Estimation of Muscle Forces and Joint Moments and Movements From Measurements of Neural Command

Abstract: This paper provides an overview of forward dynamic neuromusculoskeletal modeling The aim of such models is to estimate or predict muscle forces, joint moments, and/or joint kinematics from neural signals This is a four-step process In the first step, muscle activation dynamics govern the transformation from the neural signal to a measure of muscle activation—a time varying parameter between 0 and 1 In the second step, muscle contraction dynamics characterize how muscle activations are transformed into muscle forces The third step requires a model of the musculoskeletal geometry to transform muscle forces to joint moments Finally, the equations of motion allow joint moments to be transformed into joint movements Each step involves complex nonlinear relationships The focus of this paper is on the details involved in the first two steps, since these are the most challenging to the biomechanician The global process is then explained through applications to the study of predicting isometric elbow moments and dynamic knee kinetics

Sliding-mode tracking control of nonholonomic wheeled mobile robots in polar coordinates

Abstract: This brief proposes a sliding-mode control method for wheeled-mobile robots in polar coordinates. A new sliding-mode control method is proposed for mobile robots with kinematics in two-dimensional polar coordinates. In the proposed method, two controllers are designed to asymptotically stabilize the tracking errors in position and heading direction, respectively. By combining these controllers together, both asymptotic posture (position and heading direction) stabilization and trajectory tracking are achieved for reference trajectories at global regions except the arbitrary small region around the origin. In particular, constraints on the desired linear and angular velocities as well as the posture of the mobile robot are eliminated unlike the previous studies based on kinematics expressed in polar coordinates. Accordingly, arbitrary trajectories including a circle and a straight line in various forms can be followed even with large initial tracking errors and bounded disturbances. The stability and performance analyzes are performed and also simulations are included to confirm the effectiveness of the proposed scheme.

Fundamentals of Mechanics of Robotic Manipulation

Abstract: Preface 1: Introduction to Automation and Robotics 1.1 Automatic systems and robots 1.2 Evolution and applications of robots 1.3 Examples and technical characteristics of industrial robots 1.4 Evaluation of a robotization 1.4.1 An economic estimation 1.5 Forum for discussions on Robotics 2: Analysis of Manipulations 2.1 Decomposition of manipulative actions 2.2 A procedure for analyzing manipulation tasks 2.3 Programming for robots 2.3.1 A programming language for robots: VAL II 2.3.2 A programming language for robots: ACL 2.4 Illustrative examples 2.4.1 Education practices 2.4.1.1 Simulation of an industrial process 2.4.1.2 Writing with a robot 2.4.1.3 An intelligent packing 2.4.2 Industrial applications 2.4.2.1 Designing a robotized manipulation 2.4.2.2 Optimizing a robotized manipulation 3: Fundamentals of Mechanics of Manipulators 3.1 Kinematic model and position analysis 3.1.1 Transformation Matrix 3.1.2 Joint variables and actuator space 3.1.3 Workspace analysis 3.1.3.1 A binary matrix formulation 3.1.3.2 An algebraic formulation 3.1.3.3 A Workspace evaluation 3.1.4 Manipulator design with prescribed workspace 3.2 Inverse kinematics and path planning 3.2.1 A formulation for inverse kinematics 3.2.1.1 An example 3.2.2 Trajectory generation in Joint Space 3.2.3 A formulation for path planning in Cartesian coordinates 3.2.3.1 Illustrative examples 3.3 Velocity and acceleration analysis 3.3.1 An example 3.4 Jacobian and singularity configurations 3.4.1 An example 3.5 Statics of manipulators 3.5.1A mechanical model 3.5.2 Equations of equilibrium 3.5.3 Jacobian mapping of forces 3.5.4 An example 3.6 Dynamics of manipulators 3.6.1 Mechanical model and inertia characteristics 3.6.2 Newton-Euler equations 3.6.2.1 An example 3.6.3 Lagrange formulation 3.6.3.1An example 3.7 Stiffness of manipulators 3.7.1 A mechanical model 3.7.2 A formulation for stiffness analysis 3.7.3 A numerical example 3.8 Performance criteria for manipulators 3.8.1 Accuracy and repeatability 3.8.2 Dynamic characteristics 3.8.3 Compliance response 3.9 Fundamentals of Mechanics of parallel manipulators 3.9.1 A numerical example for CaPaMan (Cassino Parallel Manipulator) 4: Fundamentals of Mechanics of Grasp 4.1 Gripping devices and their characteristics 4.2 A mechatronic analysis for two-finger grippers 4.3 Design parameters and operation requirements for grippers 4.4 Configurations and phases of two-finger grasp 4.5 Model and analysis of two-finger grasp 4.6 Mechanisms for grippers 4.6.1 Modeling gripper mechanisms 4.6.2 An evaluation of gripping mechanisms 4.6.2.1 A numerical example of index evaluation 4.7 Designing two-finger grippers 4.7.1 An optimum design procedure for gripping mechanisms 4.7.1.1 A numerical example of optimum design 4.8 Electropneumatic actuation and grasping force control 4.8.1 An illustrative example for laboratory practice 4.8.1.1 An acceleration sensored gripper 4.9 Fundamentals on multifinger grasp and articulated fingers Bibliography Index Biographical Notes

Capturing human motion using body-fixed sensors: Outdoor measurement and clinical applications

Abstract: Motion capture is mainly based on standard systems using optic, magnetic or sonic technologies. In this paper, the possibility to detect useful human motion based on new techniques using different types of body-fixed sensors is shown. In particular, a combination of accelerometers and angular rate sensors (gyroscopes) showed a promising design for a hybrid kinematic sensor measuring the 2D kinematics of a body segment. These sensors together with a portable datalogger, and using simple biomechanical models, allow capture of outdoor and long-term movements and overcome some limitations of the standard motion capture systems. Significant parameters of body motion, such as nature of motion (postural transitions, trunk rotation, sitting, standing, lying, walking, jumping) and its spatio-temporal features (velocity, displacement, angular rotation, cadence and duration) have been evaluated and compared to the camera-based system. Based on these parameters, the paper outlines the possibility to monitor physical activity and to perform gait analysis in the daily environment, and reviews several clinical investigations related to fall risk in the elderly, quality of life, orthopaedic outcome and sport performance. Taking advantage of all the potential of these body-fixed sensors should be promising for motion capture and particularly in environments not suitable for standard technology such as in any field activity. Copyright © 2004 John Wiley & Sons, Ltd.

Modeling and control of a 4-wheel skid-steering mobile robot

Abstract: A mathematical model of a 4-wheel skid-steering mobile robot is presented in a systematic way. The robot is considered as a subsystem consisting of kinematic, dynamic and drive levels. Next, a designing process of a kinematic controller based on the algorithm introduced by (Dixon et al., 2001) is shown. An extension of the kinematic control law at the dynamic and motor levels using the Lyapunov analysis and the backstepping technique is developed. To validate the designed algorithm, extensive simulation results for trajectory tracking and set-point cases are discussed. Some deliberations concerning the tuning of the controller are presented, too.

Twist Based Acquisition and Tracking of Animal and Human Kinematics

Abstract: This paper demonstrates a new visual motion estimation technique that is able to recover high degree-of-freedom articulated human body configurations in complex video sequences. We introduce the use and integration of a mathematical technique, the product of exponential maps and twist motions, into a differential motion estimation. This results in solving simple linear systems, and enables us to recover robustly the kinematic degrees-of-freedom in noise and complex self occluded configurations. A new factorization technique lets us also recover the kinematic chain model itself. We are able to track several human walk cycles, several wallaby hop cycles, and two walk cycels of the famous movements of Eadweard Muybridge's motion studies from the last century. To the best of our knowledge, this is the first computer vision based system that is able to process such challenging footage.

Synthesizing animations of human manipulation tasks

Abstract: Even such simple tasks as placing a box on a shelf are difficult to animate, because the animator must carefully position the character to satisfy geometric and balance constraints while creating motion to perform the task with a natural-looking style. In this paper, we explore an approach for animating characters manipulating objects that combines the power of path planning with the domain knowledge inherent in data-driven, constraint-based inverse kinematics. A path planner is used to find a motion for the object such that the corresponding poses of the character satisfy geometric, kinematic, and posture constraints. The inverse kinematics computation of the character's pose resolves redundancy by biasing the solution toward natural-looking poses extracted from a database of captured motions. Having this database greatly helps to increase the quality of the output motion. The computed path is converted to a motion trajectory using a model of the velocity profile. We demonstrate the effectiveness of the algorithm by generating animations across a wide range of scenarios that cover variations in the geometric, kinematic, and dynamic models of the character, the manipulated object, and obstacles in the scene.

Robots and screw theory : applications of kinematics and statics to robotics

Abstract: 1.1 INTRODUCTION 1.2 FREEDOM OF THE END-EFFECTOR 1.3 THE INSTANTANEOUS CENTRES IN A PLANAR ROBOT-ARM 1.3.1 THE 'INVERSE VELOCITY-PROBLEM' SOLVED BY INSTANTANEOUS CENTRES 1.3.2 INSTANTANEOUS KINEMATICS AND STATIC EQUILIBRIUM 1.3.3 THE 'FORWARD VELOCITY-PROBLEM' SOLVED BY INSTANTANEOUS CENTRES EXERCISES 1A 7 1.4 VELOCITIES BY SUPERPOSITION 1.5 THE LINEAR SLIDING JOINT 1.6 TORQUES AT THE ACTUATED JOINTS 1.7 THE ASSEMBLY-CONFIGURATIONS OF A PLANAR ROBOT-ARM EXERCISES 1B 2. DESCRIBING THE SCREW 2.1 THE SCREW IN MECHANICS 2.1.1 THE SCREW IN STATICS 2.1.2 THE SCREW IN INSTANTANEOUS KINEMATICS 2.1.3 OTHER APPLICATIONS IN MECHANICS 2.2 THE FINITE TWIST 30 2.3 FREEDOM AND CONSTRAINT OF A RIGID BODY 2.4 TWISTS, WRENCHES, AND SCREWS SUMMARIZED EXERCISES 2A 3.1 BACKGROUND 3.2 SCREW COORDINATES 3.2.1 THE COORDINATES 3.2.2 PHYSICAL INTERPRETATION OF THE COORDINATES 3.2.3 THE AXIS AND PITCH OF A SCREW NORMALIZATION OF ITS COORDINATES 3.2.4 HOMOGENEITY OF SCREW COORDINATES 3.3 A LINE AS THE JOIN OF TWO FINITE POINTS EXERCISES 3A 3.4 HOMOGENEOUS COORDINATES OF A POINT 3.4.1 A POINT IN PROJECTIVE SPACE 3.4.2 A LINE AS THE JOIN OF TWO POINTS "FM" - 2004/1/22 - PAGE VIII - #8 VIII CONTENTS 3.5 HOMOGENEOUS COORDINATES OF A PLANE 3.5.1 A LINE AS THE MEET OF TWO PLANES 3.6 HOMOGENEITY, DIMENSIONS, AND UNITS 3.7 RAY- AND AXIS-COORDINATE ORDERS FOR SCREW COORDINATES 3.8 DUALITY AND LINES EXERCISES 3B A RIGID BODY 4.1 INTRODUCTION 4.1.1 COORDINATES 4.2 COORDINATE TRANSFORMATIONS FOR TWO DIMENSIONS 4.2.1 ROTATIONAL TRANSFORMATIONS WITH POINTS 4.2.2 GENERAL TRANSFORMATIONS WITH POINTS ON COPLANAR LAMINAE 4.2.3 DETERMINING FROM [AIJ ] THE AXIS AND ANGLE OF ROTATION 4.2.4 DETERMINING [AIJ ] FROM THE AXIS AND ANGLE OF ROTATION 4.2.5 TRANSFORMATIONS WITH FREE VECTORS AND PLANES 4.3 GENERAL ROTATIONAL TRANSFORMATIONS 4.3.1 SUCCESSIVE ROTATIONS 4.3.2 ROTATIONAL TRANSFORMATIONS WITH SCREWS, LINES, WRENCHES, AND TWISTS 4.4 INTERPRETATIONS OF A TRANSFORMATION 4.4.1 THE ACTIVE INTERPRETATION AND THE ACTIVE TRANSFORMATION EXERCISES 4A 4.5 COORDINATE TRANSFORMATIONS FOR THREE DIMENSIONS 4.5.1 THE GENERAL TRANSFORMATIONS WITH POINTS 4.5.2 TRANSFORMATIONS WITH VECTORS AND PLANES 4.5.3 GENERAL TRANSFORMATIONS WITH SCREWS, LINES, WRENCHES, AND TWISTS 4.6 THE FINITE TWIST 4.6.1 THE FINITE TWIST AND THE FINITE SCREW 4.6.2 THE PITCH H AND Q-PITCH Q OF A FINITE TWIST OR A FINITE SCREW 4.6.3 DETERMINING [AIJ ] FROM A FINITE TWIST $IJ (Q) 4.6.4 DETERMINING THE FINITE TWIST $IJ (Q) FROM [AIJ ] AND [$$IJ ] EXERCISES 4B LINEAR AND NON-LINEAR SCREW SYSTEMS 5.1 LINEAR DEPENDENCE OF POINTS AND PLANES 5.2 THE LINEAR TWO-SYSTEM OF SCREWS EXERCISES 5A 5.3 LINEAR SCREW SYSTEMS 5.3.1 THE ONE-SYSTEM 5.3.2 THE TWO-SYSTEM 5.3.3 THE THREE-SYSTEM 5.3.4 THE FOUR-SYSTEM "FM" - 2004/1/22 - PAGE IX - #9 CONTENTS IX 5.3.5 THE FIVE-SYSTEM 5.3.6 THE SIX-SYSTEM 5.3.7 SYSTEMS THAT ARE INVARIANT WITH FINITE JOINT-DISPLACEMENTS EXERCISES 5B 5.4 RECIPROCITY OF SCREWS 5.4.1 A ROTATING BODY ACTED ON BY A FORCE 5.4.2 A TWISTING BODY ACTED ON BY A WRENCH 5.5 RECIPROCITY AND LINEAR SCREW SYSTEMS EXERCISES 5C 5.6 LINEAR AND NON-LINEAR SCREW SYSTEMS 5.7 SOME FINITE DISPLACEMENTS AND THEIR SCREW SYSTEMS 5.7.1 THE SYSTEM OF FINITE SCREWS FOR THE TWISTS THAT DISPLACE A POINT 5.7.2 THE SYSTEM OF FINITE SCREWS FOR THE TWISTS THAT DISPLACE A DIRECTED LINE A 5.7.3 THE SYSTEM OF FINITE SCREWS FOR THE TWISTS THAT DISPLACE A POINT ON A DIRECTED LINE 5.7.4 COMMUTATIVITY AND SEQUENTIAL FINITE TWISTS EXERCISES 5D 6.1 INTRODUCTION 6.2 SOME TYPICAL SIX-ACTUATOR ARMS 6.3 A GANTRY ARM 6.3.1 AXES OF THE ACTUATED JOINTS AND THE JACOBIAN 6.3.2 DET [J] AND SPECIAL CONFIGURATIONS 6.3.3 THE RECIPROCAL SCREW AT A SPECIAL CONFIGURATION 6.3.4 THE UBIQUITY OF SPECIAL CONFIGURATIONS 6.3.5 THE INVERSE OF THE JACOBIAN 6.3.6 [J]-1 AND SPECIAL CONFIGURATIONS 6.3.7 THE GANTRY ARM WITH AN 'OFFSET ROLL-PITCH-ROLL' WRIST 6.3.8 THE 'PITCH-YAW-ROLL' WRIST 6.3.9 THE SPHERICAL '3-ROLL WRIST' 6.3.10 OTHER WRIST DESIGNS EXERCISES 6A 6.4 THE CM T3-566 ARM (ELBOW MANIPULATOR) 6.4.1 THE FORWARD AND INVERSE RATE-PROBLEMS 6.4.2 SPECIAL CONFIGURATIONS: INDIVIDUAL CONDITIONS 6.4.3 TRANSVERSALS AND RECIPROCAL SCREWS 6.4.4 SPECIAL CONFIGURATIONS: COMBINATIONS OF CONDITIONS 6.5 A UNIMATE PUMA ARM 6.6 A MANIPULATOR WITH ROTARY JOINTS IN JUST THREE DIRECTIONS 6.7 GENERAL FEATURES OF SPECIAL CONFIGURATIONS 6.8 WORKSPACE 6.8.1 GEOMETRICAL CONSTRUCTIONS 6.8.2 CONFIGURATIONS OF A ROBOT-ARM WHEN B IS AT THE BOUNDARY "FM" - 2004/1/22 - PAGE X - #10 X CONTENTS 6.8.3 TRANSVERSALS AND RECIPROCAL SCREWS INWORKSPACE IDENTIFICATION 6.8.4 INFLUENCE OF EXCURSION-LIMITS AT THE JOINTS 6.8.5 SUBSPACES WITHIN THE REACHABLE POINT-WORKSPACE 6.8.6 WORKSPACES OF REFERENCE PLANES AND LINES ON THE END-EFFECTOR 6.9 FIVE-ACTUATOR ARMS EXERCISES 6B 6.10 CONTROL 6.10.1 JOINT CONTROL AND CARTESIAN CONTROL 6.10.2 CLOSING THE FEEDBACK LOOP ON THE TASK 6.10.3 WRENCH CONTROL AND HYBRID CONTROL 6.11 TORQUES (FORCES) AT THE JOINTS OF A SIX-ACTUATOR ARM EXERCISES 6C ROBOT-ARMS 7.1 INTRODUCTION 7.1.1 PLACEMENT OF CARTESIAN COORDINATE FRAMES ON LINKS 7.1.2 FORWARD AND INVERSE KINEMATICS FOR POSITION 7.1.3 THE SCALAR EQUATION A COS F + B SIN F = C 7.2 THE ASSEMBLY-CONFIGURATIONS OF SIX-ACTUATOR ROBOT-ARMS 7.2.1 A GANTRY ARM 7.2.2 THE CM T3-566 ARM (ELBOW MANIPULATOR) 7.2.3 A UNIMATE PUMA ARM 7.2.4 THE INVERTED CM T3-566 ARM WITH AN EQUIVALENT SPHERICAL JOINT 7.3 A FIVE-ACTUATOR ARM EXERCISES 7A 7.4 SIX-ACTUATOR ROBOT-ARMS WITH GENERALLY PLACED AXES 7.4.1 A STANDARD PLACEMENT OF CARTESIAN COORDINATE FRAMES ON LINKS 7.4.2 THE FUNDAMENTAL EQUATIONS 7.4.3 TWO ALTERNATIVE METHODS 7.4.4 THE MOTOMAN-V6 ROBOT-ARM 7.4.5 CONTINUATION METHODS 7.5 ROBOT-ARMS WITH CLOSED-FORM SOLUTIONS EXERCISES 7B 8.1 INTRODUCTION 8.2 THE 6-6 FULLY IN-PRALLEL MANIPULATOR 8.2.1 THE BRICARD-BOREL PHENOMENA 8.2.2 ASSEMBLY CONFIGURATIONS 8.2.3 SPECIAL CONFIGURATIONS AND OTHER LIMITATIONS: GENERALITIES 8.3 THE OCTAHEDRAL MANIPULATOR: GEOMETRY 8.3.1 POLYHEDRA AND CAUCHY'S THEOREM 8.3.2 ASSEMBLY-CONFIGURATIONS AND CONCAVITY EXERCISES 8A "FM" - 2004/1/22 - PAGE XI - #11 CONTENTS XI 8.4 TRANSITORY KINEMATIC EQUIVALENCE: SERIAL VERSUS IN-PARALLEL 8.4.1 THE GENERAL 'CANONICAL' WRENCH-APPLICATOR AND THE UNACTUATED SCREW-SUPPORT 8.4.2 SERIES-PARALLEL COMPARISONS 8.4.3 THE WRENCH-APPLICATOR FOR A PURE COUPLE 8.4.4 THE WRENCH-APPLICATOR FOR A PURE FORCE 8.4.5 SOME VARIANTS OF WRENCH-APPLICATORS EXERCISES 8B 8.5 STATICS AND KINEMATICS OF FULLY IN-PARALLEL ROBOTS 8.5.1 CHARTS OF ANALOGUES 8.6 THE OCTAHEDRAL MANIPULATOR: PROPORTIONS AND CONFIGURATIONS 8.6.1 THE DATUM CONFIGURATION 8.6.2 DEPARTURES FROM THE DATUM CONFIGURATION 8.6.3 A SUBSTITUTION FOR THE DOUBLE-SPHERICAL JOINTS 8.6.4 SEPARATION OF THE DOUBLE-SPHERICAL JOINTS 8.6.5 ACTUATION OF FORCE-APPLICATORS 8.6.6 OTHER POSSIBLE SEPARATION ARRANGEMENTS FOR DOUBLE-SPHERICAL JOINTS 8.6.7 AN ACTUATED RECIPROCAL CONNECTION 8.6.8 COGNATE OCTAHEDRAL MANIPULATORS EXERCISES 8C 8.7 SPECIAL CONFIGURATIONS: FURTHER OBSERVATIONS 8.7.1 A CASE STUDY 8.7.2 SERIES-PARALLEL COMPARISONS EXERCISES 8D SERIAL DEVICES 9.1 INTRODUCTION 9.2 TWO COMPOSITE ROBOTS 9.3 THE FORCE-APPLICATOR: SOME VARIANTS IN SIX-ACTUATOR ROBOTS 9.4 MOBILITY, CONNECTIVITY, AND OVER-CONSTRAINT 9.4.1 THE GENERAL MOBILITY CRITERION 9.4.2 CONNECTIVITY CIJ 9.4.3 ONE CLASS OF OVER-CONSTRAINED DEVICES EXERCISES 9A 9.5 THE ADJUSTABLE TRIPOD AS A MANIPULATOR 9.5.1 STRUCTURE, MOBILITY, AND KINEMATIC SUBSTITUTIONS 9.5.2 PERFORMANCE AND PROPORTIONS OF THE TRIPOD EXERCISES 9B 9.6 GENERALIZED RECIPROCAL CONNECTIONS: SOME DERIVED ROBOTS 9.6.1 THREE-FREEDOM PLANAR-MOTION ROBOTS 9.6.2 HOMOKINETIC SHAFT COUPLINGS FOR PARALLEL SHAFTS 9.7 TWO PLANAR IN-PARALLEL ROBOTS 9.7.1 THE PLANAR IN-PARALLEL ROBOT WITH THREE LINEAR ACTUATORS 9.7.2 A PLANAR IN-PARALLEL ROBOT WITH THREE ROTARY ACTUATORS "FM" - 2004/1/22 - PAGE XII - #12 XII CONTENTS EXERCISES 9C 9.8 HOMOKINETIC COUPLING ROBOTS AND DERIVATIVE 9.8.1 A TRANSLATORY ROBOT BASED ON A HOMOKINETIC COUPLING 9.8.2 THE THREE TRANSLATORY FREEDOMS OF THE DELTA ROBOT 9.9 THE INVERSE KINEMATICS FOR POSITION OF COMPOSITE AND PLANAR IN-PARALLEL ROBOTS 9.9.1 THE PLANAR IN-PARALLEL ROBOT WITH THREE LINEAR ACTUATORS 9.9.2 A PLANAR IN-PARALLEL ROBOT WITH THREE ROTARY ACTUATORS 9.9.3 A COUPLING ROBOT AND THE TRANSLATORY FREEDOMS OF THE DELTA ROBOT 9.10 TWO OVER-CONSTRAINED TRANSLATORY MANIPULATORS EXERCISES 9D 10.1 INTRODUCTION 10.1.1 KINEMATIC REDUNDANCY 10.2 PSEUDOINVERSE CONTROL 10.2.1 THE COORDINATES OF A SCREW AND THE JACOBIAN [J] 10.2.2 THE PSEUDOINVERSE OF [J] AND OTHER SOLUTIONS TO EQNS (10.3) 10.2.3 SOLUTIONS TO EQNS (10.3) BY AUGMENTING [J] 10.2.4 COMPARISON OF [J]# TO [J]-1 10.3 THE CONTROL OF A FOUR-AXIS SPHERICAL WRIST 10.3.1 OVERSPEEDING IN THE THREE-AXIS ORTHOGONAL SPHERICAL WRIST 10.3.2 PSEUDOINVERSE CONTROL OF THE FOUR-AXIS ORTHOGONAL SPHERICAL WRIST 10.3.3 REDUNDANT SERIAL ARMS WITH ROTARY JOINTS IN JUST FOUR DIRECTIONS 10.4 ACTUATOR-TORQUES (FORCES) AT THE JOINTS OF REDUNDANT SERIAL ARMS EXERCISES 10A 10.5 STATICALLY REDUNDANT ROBOTS AND MANIPULATORS 10.5.1 SCREW SYSTEMS AT LOCALIZED CONTACTS 10.5.2 THE EQUILIBRATING AND INTERACTING FORCE FIELDS 10.5.3 FRICTIONAL CONTACTS 10.5.4 THE JACOBIAN OF FORCE-COMPONENTS FOR FRICTIONAL CONTACTS 10.5.5 THE PSEUDOINVERSE SOLUTION AND THE EQUILIBRATING SYSTEM 10.5.6 THE FRICTIONAL GRASP OF A DISC 10.5.7 OPTIMIZATION OF A GRASP USING INTERACTING SYSTEMS OF FORCES EXERCISES 10B 11.1 INTRODUCTION 11.2 WHEELED AND LEGGED VEHICLES 11.3 MARGIN OF STATIC STABILITY 11.3.1 THE PRINCIPLE OF NORMALIZED VIRTUAL POWER 11.3.2 OTHER MEASURES FOR MARGIN OF STABILITY 11.4 APPLICATION TO GENERAL LOCATIONS OF THE CONTACTS 11.4.1 FOUR CONTACTS WITH THE GROUND 11.4.2 THREE CONTACTS WITH THE GROUND 11.4.3 COMPARISON WITH A HORIZONTAL PROJECTION CONTENTS XIII 11.5 VIRTUAL POWER USED IN CONTROL 11.6 A DISPLAY FOR MARGIN OF STATIC STABILITY 11.6.1 THE RECTANGULAR DISPLAY 11.6.2 THREE CONTACTS WITH THE GROUND 11.7 CONCLUSION EXERCISES 11A ANSWERS TO EXERCISES REFERENCES INDEX

Type synthesis of 3T1R 4-DOF parallel manipulators based on screw theory

Abstract: 3T1R four-degrees-of-freedom (DOF) parallel manipulators (3T1R-PMs) are the parallel counterparts of the 4-DOF SCARA serial robots. In a 3T1R-PM, the moving platform can generate 3T1R motion (also called Schonflies motion), which refers to a rotation about any axis with a given direction in conjunction with 3-DOF translations. A method is proposed for the type synthesis of 3T1R-PMs based on screw theory. The wrench systems of a 3T1R parallel kinematic chain (3T1R-PKC) and its legs are first analyzed. A general procedure is then proposed for the type synthesis of 3T1R-PMs. The type synthesis of legs for 3T1R-PKCs, the type synthesis of 3T1R-PKCs, as well as the selection of actuated joints of 3T1R-PMs, are dealt with in sequence. 3T1R-PKCs with and without inactive joints are synthesized. The phenomenon of dependent joint groups in a 3T1R-PKC is revealed for the first time. Several 3T1R-PMs with identical type of legs are obtained.

Real time markerless motion tracking using linked kinematic chains

Abstract: A markerless method is described for tracking the motion of subjects in a three dimensional environment using a model based on linked kinematic chains. The invention is suitable for tracking robotic, animal or human subjects in real-time using a single computer with inexpensive video equipment, and does not require the use of markers or specialized clothing. A simple model of rigid linked segments is constructed of the subject and tracked using three dimensional volumetric data collected by a multiple camera video imaging system. A physics based method is then used to compute forces to align the model with subsequent volumetric data sets in real-time. The method is able to handle occlusion of segments and accommodates joint limits, velocity constraints, and collision constraints and provides for error recovery. The method further provides for elimination of singularities in Jacobian based calculations, which has been problematic in alternative methods.

Internal models of target motion: expected dynamics overrides measured kinematics in timing manual interceptions.

Abstract: Prevailing views on how we time the interception of a moving object assume that the visual inputs are informationally sufficient to estimate the time-to-contact from the object's kinematics. Here we present evidence in favor of a different view: the brain makes the best estimate about target motion based on measured kinematics and an a priori guess about the causes of motion. According to this theory, a predictive model is used to extrapolate time-to-contact from expected dynamics (kinetics). We projected a virtual target moving vertically downward on a wide screen with different randomized laws of motion. In the first series of experiments, subjects were asked to intercept this target by punching a real ball that fell hidden behind the screen and arrived in synchrony with the visual target. Subjects systematically timed their motor responses consistent with the assumption of gravity effects on an object's mass, even when the visual target did not accelerate. With training, the gravity model was not switched off but adapted to nonaccelerating targets by shifting the time of motor activation. In the second series of experiments, there was no real ball falling behind the screen. Instead the subjects were required to intercept the visual target by clicking a mousebutton. In this case, subjects timed their responses consistent with the assumption of uniform motion in the absence of forces, even when the target actually accelerated. Overall, the results are in accord with the theory that motor responses evoked by visual kinematics are modulated by a prior of the target dynamics. The prior appears surprisingly resistant to modifications based on performance errors.

Obstacle avoidance for kinematically redundant manipulators using a dual neural network

Abstract: One important issue in the motion planning and control of kinematically redundant manipulators is the obstacle avoidance. In this paper, a recurrent neural network is developed and applied for kinematic control of redundant manipulators with obstacle avoidance capability. An improved problem formulation is proposed in the sense that the collision-avoidance requirement is represented by dynamically-updated inequality constraints. In addition, physical constraints such as joint physical limits are also incorporated directly into the formulation. Based on the improved problem formulation, a dual neural network is developed for the online solution to collision-free inverse kinematics problem. The neural network is simulated for motion control of the PA10 robot arm in the presence of point and window-shaped obstacle.

System and method for designing a physiometric implant system

Abstract: A system improves the design of artificial implant components for use in joint replacement surgeries. The system includes an anthropometric static image data analyzer, an implant model data generator, a kinematic model simulator, and a dynamic response data analyzer. The implant model data generator may also use image data of a joint in motion for modification of the implant model data used in the kinematic simulation. Dynamic response data generated by the kinematic model simulation is analyzed by the dynamic response data analyzer to generate differential data that may be used to further refine the implant model data.

Passive dynamic walking model with upper body

Abstract: This paper presents the simplest walking model with an upper body. The model is a passive dynamic walker, i.e. it walks down a slope without motor input or control. The upper body is confined to the midway angle of the two legs. With this kinematic constraint, the model has only two degrees of freedom. The model achieves surprisingly successful walking results: it can handle disturbances of 8% of the initial conditions and it has a specific resistance of only 0.0725(−).

Fundamentals of a Vector Form Intrinsic Finite Element: Part I. Basic Procedure and A Plane Frame Element

Abstract: In a series of three articles, fundamentals of a vector form intrinsic finite element procedure (VFIFE) are summarized. The procedure is designed to calculate motions of a system of rigid and deformable bodies. The motion may include large rigid body motions and large geometrical changes. Newton's law, or a work principle, for particle is assumed to derive the governing equations of motion. They are obtained by using a set of deformation coordinates for the description of kinematics. A convected material frame approach is proposed to handle very large deformations. Numerical results are calculated by using an explicit algorithm. In the first article, using the plane frame element as an example, basic procedures are described. In the accompanied articles, plane solid elements, convected material frame procedures and numerical results of patch tests are given.

Path following using visual odometry for a Mars rover in high-slip environments

Abstract: A system for autonomous operation of Mars rovers in high slip environments has been designed, implemented, and tested. This system is composed of several key technologies that enable the rover to accurately follow a designated path, compensate for slippage, and reach intended goals independent of the terrain over which it is traversing (within the mechanical constraints of the mobility system). These technologies include: visual odometry, full vehicle kinematics, a Kalman filter pose estimator, and a slip compensation/path follower. Visual odometry tracks distinctive scene features in stereo imagery to estimate rover motion between successively acquired stereo image pairs using a maximum likelihood motion estimation algorithm. The full vehicle kinematics for a rocker-bogie suspension system estimates motion, with a no-slip assumption, by measuring wheel rates, and rocker, bogie, and steering angles. The Kalman filter merges data from an inertial measurement unit (IMU) and visual odometry. This merged estimate is then compared to the kinematic estimate to determine (taking into account estimate uncertainties) if and how much slippage has occurred. If no statistically significant slippage has occurred then the kinematic estimate is used to complement the Kalman filter estimate. If slippage has occurred then a slip vector is calculated by differencing the current Kalman filter estimate from the kinematic estimate. This slip vector is then used, in conjunction with the inverse kinematics, to determine the necessary wheel velocities and steering angles to compensate for slip and follow the desired path.

A 3D Generic Inverse Dynamic Method using Wrench Notation and Quaternion Algebra

Abstract: In the literature, conventional 3D inverse dynamic models are limited in three aspects related to inverse dynamic notation, body segment parameters and kinematic formalism. First, conventional notation yields separate computations of the forces and moments with successive coordinate system transformations. Secondly, the way conventional body segment parameters are defined is based on the assumption that the inertia tensor is principal and the centre of mass is located between the proximal and distal ends. Thirdly, the conventional kinematic formalism uses Euler or Cardanic angles that are sequence-dependent and suffer from singularities. In order to overcome these limitations, this paper presents a new generic method for inverse dynamics. This generic method is based on wrench notation for inverse dynamics, a general definition of body segment parameters and quaternion algebra for the kinematic formalism.

Optimal kinematic design of 2-DOF parallel manipulators with well-shaped workspace bounded by a specified conditioning index

Abstract: This paper presents a hybrid method for the optimum kinematic design of two-degree-of-freedom (2-DOF) parallel manipulators with mirror symmetrical geometry. By taking advantage of both local and global approaches, the proposed method can be implemented in two steps. In the first step, the optimal architecture, in terms of isotropy and the behavior of the direct Jacobian matrix, is achieved, resulting in a set of closed-form parametric relationships that enable the number of design variables to be reduced. In the second step, the workspace bounded by the specified conditioning index is generated, which allows only one design parameter to be determined by optimizing a comprehensive index in a rectangular workspace. The kinematic optimization of a revolute-jointed 2-DOF parallel robot has been taken as an example to illustrate the effectiveness of this approach.

Sampling-Based Motion Planning under Kinematic Loop-Closure Constraints.

Abstract: Kinematic loop-closure constraints significantly increase the difficulty of motion planning for articulated mechanisms. Configurations of closed-chain mechanisms do not form a single manifold, easy to parameterize, as the configurations of open kinematic chains. In general, they are grouped into several subsets with complex and a priori unknown topology. Sampling-based motion planning algorithms cannot be directly applied to such closed-chain systems. This paper describes our recent work [7] on the extension of sampling-based planners to treat this kind of mechanisms.

Optimal kinematic design of 2-DOF parallel manipulators with well-shaped workspace bounded by a specified conditioning index.

Abstract: This paper presents a hybrid method for the optimum kinematic design of two-degree-of-freedom (2-DOF) parallel manipulators with mirror symmetrical geometry. By taking advantage of both local and global approaches, the proposed method can be implemented in two steps. In the first step, the optimal architecture, in terms of isotropy and the behavior of the direct Jacobian matrix, is achieved, resulting in a set of closed-form parametric relationships that enable the number of design variables to be reduced. In the second step, the workspace bounded by the specified conditioning index is generated, which allows only one design parameter to be determined by optimizing a comprehensive index in a rectangular workspace. The kinematic optimization of a revolute-jointed 2-DOF parallel robot has been taken as an example to illustrate the effectiveness of this approach.

Adaptive regulation of amplitude limited robot manipulators with uncertain kinematics and dynamics

Abstract: Common assumptions in most of the previous robot controllers are that the robot kinematics and manipulator Jacobian are perfectly known and that the robot actuators are able to generate the necessary level of torque inputs. In this paper, an amplitude-limited torque input controller is developed for revolute robot manipulators with uncertainty in the kinematic and dynamic models. The adaptive controller yields semi-global asymptotic regulation of the task-space set-point error. The advantages of the proposed controller include the ability to actively compensate for unknown parametric effects in the dynamic and kinematic model and the ability to ensure that actuator constraints are not breached by calculating the maximum required torque a priori.

An Interval Analysis Based Study for the Design and the Comparison of 3-DOF Parallel Kinematic Machines

Abstract: This paper addresses an interval analysis based study that is applied to the design and the comparison of 3-DOF parallel kinematic machines. Two design criteria are used, (i) a regular workspace shape and, (ii) a kinetostatic performance index that needs to be as homogeneous as possible throughout the workspace. The interval analysis based method takes these two criteria into account: on the basis of prescribed kinetostatic performances, the workspace is analysed to find out the largest regular dextrous workspace enclosed in the Cartesian workspace. An algorithm describing this method is introduced. Two 3-DOF translational parallel mechanisms designed for machining applications are compared using this method. The first machine features three fixed linear joints which are mounted orthogonally and the second one features three linear joints which are mounted in parallel. In both cases, the mobile platform moves in the Cartesian x y z space with fixed orientation.

Dynamical modelling of stars and gas in NGC2974: determination of mass-to-light ratio, inclination and orbital structure by Schwarzschild's method

Abstract: We study the large-scale stellar and gaseous kinematics of the E4 galaxy NGC2974, based on panoramic integral-field data obtained with SAURON. We quantify the velocity fields with Fourier methods (kinemetry), and show that the large-scale kinematics is largely consistent with axisymmetry. We construct general axisymmetric dynamical models for the stellar motions using Schwarzschild's orbit-superposition method, and compare the inferred inclination and mass-to-light ratio with the values obtained by modelling the gas kinematics. Both approaches give consistent results. However we find that the stellar models provide fairly weak constraints on the inclination. The intrinsic orbital distribution of NGC2974, which we infer from our model, is characterised by a large-scale stellar component of high angular momentum. We create semi-analytic test models, resembling NGC2974, to study the ability of Schwarzschild's modelling technique to recover the given input parameters (mass-to-light ratio and inclination) and the distribution function. We also test the influence of a limited spatial coverage on the recovery of the distribution function (i.e. the orbital structure). We find that the models can accurately recover the input mass-to-light ratio, but we confirm that even with perfect input kinematics the inclination is only marginally constrained. This suggests a possible degeneracy in the determination of the inclination, but further investigations are needed to clarify this issue. For a given potential, we find that the analytic distribution function of our test model is well recovered by the three-integral model within the spatial region constrained by integral-field kinematics.

A study on lateral speed estimation methods

Abstract: The estimation of vehicle lateral speed, a critical variable for vehicle stability control, four-wheel-steering and other advanced dynamic control systems, is studied in this paper. We presented three different approaches, one each from three categories: transfer function approach, state-space approach, and kinematics approach. The first two methods rely on a vehicle dynamic (bicycle) model, and the last approach is based on the kinematics relationship of measured signals. The basic formulation of all three methods assumed that the road bank angle is negligible, and thus needs to be enhanced by a road bank angle estimation algorithm to work satisfactorily when the road bank is significant. The performance of these three (enhanced) methods are investigated using simulation and experimental data. For the experimental verification, we present four cases: nominal (high friction, flat road), banked road, low-friction, and low-friction-near-spin. Weakness of the three estimation algorithms is discussed.