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Meshbased inverse kinematics
 ACM Trans. Graph
, 2005
"... The ability to position a small subset of mesh vertices and produce a meaningful overall deformation of the entire mesh is a fundamental task in mesh editing and animation. However, the class of meaningful deformations varies from mesh to mesh and depends on mesh kinematics, which prescribes valid m ..."
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Cited by 71 (7 self)
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The ability to position a small subset of mesh vertices and produce a meaningful overall deformation of the entire mesh is a fundamental task in mesh editing and animation. However, the class of meaningful deformations varies from mesh to mesh and depends on mesh kinematics, which prescribes valid mesh configurations, and a selection mechanism for choosing among them. Drawing an analogy to the traditional use of skeletonbased inverse kinematics for posing skeletons, we define meshbased inverse kinematics as the problem of finding meaningful mesh deformations that meet specified vertex constraints. Our solution relies on example meshes to indicate the class of meaningful deformations. Each example is represented with a feature vector of deformation gradients that capture the affine transformations which individual triangles undergo relative to a reference pose. To pose a mesh, our algorithm efficiently searches among all meshes with specified vertex positions to find the one that is closest to some pose in a nonlinear span of the example feature vectors. Since the search is not restricted to the span of example shapes, this produces compelling deformations even when the constraints require poses that are different from those observed in the examples. Furthermore, because the span is formed by a nonlinear blend of the example feature vectors, the blending component of our system may also be used independently to pose meshes by specifying blending weights or to compute multiway morph sequences.
Geometric Phases And Robotic Locomotion
, 1994
"... . Robotic locomotion is based in a variety of instances upon cyclic changes in the shape of a robot mechanism. Certain variations in shape exploit the constrained nature of a robot's interaction with its environment to generate net motion. This is true for legged robots, snakelike robots, and w ..."
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Cited by 70 (3 self)
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. Robotic locomotion is based in a variety of instances upon cyclic changes in the shape of a robot mechanism. Certain variations in shape exploit the constrained nature of a robot's interaction with its environment to generate net motion. This is true for legged robots, snakelike robots, and wheeled mobile robots undertaking maneuvers such as parallel parking. In this paper we explore the use of tools from differential geometry to model and analyze this class of locomotion mechanisms in a unified way. In particular, we describe locomotion in terms of the geometric phase associated with a connection on a principal bundle, and address issues such as controllability and choice of gait. We also provide an introduction to the basic mathematical concepts which we require and apply the theory to numerous example systems. 1. Introduction The term "locomotion" refers to autonomous movement from place to place. Robotic locomotion employs a variety of mechanisms. Though most of today's mobile r...
Means and Averaging in the Group of Rotations
, 2002
"... In this paper we give precise definitions of different, properly invariant notions of mean or average rotation. Each mean is associated with a metric in SO(3). The metric induced from the Frobenius inner product gives rise to a mean rotation that is given by the closest special orthogonal matrix to ..."
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Cited by 65 (1 self)
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In this paper we give precise definitions of different, properly invariant notions of mean or average rotation. Each mean is associated with a metric in SO(3). The metric induced from the Frobenius inner product gives rise to a mean rotation that is given by the closest special orthogonal matrix to the usual arithmetic mean of the given rotation matrices. The mean rotation associated with the intrinsic metric on SO(3) is the Riemannian center of mass of the given rotation matrices. We show that the Riemannian mean rotation shares many common features with the geometric mean of positive numbers and the geometric mean of positive Hermitian operators. We give some examples with closedform solutions of both notions of mean.
Hybrid Zero Dynamics of Planar Biped Walkers
 IEEE Transactions on Automatic Control
, 2001
"... Planar, underactuated, biped walkers form an important domain of applications for hybrid dynamical systems. This paper presents the design of exponentially stable walking controllers for general planar bipedal systems that have one degree of freedom greater than the number of available actuators. Th ..."
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Cited by 64 (22 self)
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Planar, underactuated, biped walkers form an important domain of applications for hybrid dynamical systems. This paper presents the design of exponentially stable walking controllers for general planar bipedal systems that have one degree of freedom greater than the number of available actuators. The withinstep control action creates an attracting invariant seta two dimensional zero dynamics submanifold of the full hybrid modelwhose restriction dynamics admits a scalar LTI return map. Exponentially stable periodic orbits of the zero dynamics correspond to exponentially stabilizable orbits of the full model. A convenient parameterization of the hybrid zero dynamics is imposed through the choice of a class of output functions. Parameter optimization is used to tune the hybrid zero dynamics in order to achieve closedloop, exponentially stable walking with low energy consumption, while meeting natural kinematic and dynamic constraints. The general theory developed in the paper is illustrated on a five link walker, consisting of a torso and two legs with knees.
Mechanical Integrators Derived from a Discrete Variational Principle
"... Many numerical integrators for mechanical system simulation are created by using discrete algorithms to approximate the continuous equations of motion. In this paper, we present a procedure to construct timestepping algorithms that approximate the flow of continuous ODE's for mechanical system ..."
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Cited by 61 (11 self)
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Many numerical integrators for mechanical system simulation are created by using discrete algorithms to approximate the continuous equations of motion. In this paper, we present a procedure to construct timestepping algorithms that approximate the flow of continuous ODE's for mechanical systems by discretizing Hamilton's principle rather than the equations of motion. The discrete equations share similarities to the continuous equations by preserving invariants, including the symplectic form and the momentum map. We girst present a formulation of discrete mechanics along with a discrete variational principle. We then show that the resulting equations of motion preserve the symplectic form and that this formulation of mechanics leads to conservation laws from a discrete version of Noether's theorem. We then use the discrete mechanics formulation to develop a procedure for constructing mechanical integrators for continuous Lagrangian systems. We apply the construction procedure to the rigid body and the double spherical pendulum to demonstrate numerical properties of the integrators.
The Geometric Mechanics of Undulatory Robotic Locomotion
 INTERNATIONAL JOURNAL OF ROBOTICS RESEARCH
, 1996
"... This paper uses geometric methods to study basic problems in the mechanics and control of locomotion. We consider in detail the case of "undulatory locomotion," in which net motion is generated by coupling internal shape changes with external nonholonomic constraints. Such locomotion pro ..."
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Cited by 57 (15 self)
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This paper uses geometric methods to study basic problems in the mechanics and control of locomotion. We consider in detail the case of "undulatory locomotion," in which net motion is generated by coupling internal shape changes with external nonholonomic constraints. Such locomotion problems have a natural geometric interpretation as a connection on a principal fiber bundle. The properties of connections lead to simplified results for studying both dynamics and issues of controllability for locomotion systems. We demonstrate the utility of this approach using a novel "Snakeboard" and a multisegmented serpentine robot which is modeled after Hirose's Active Cord Mechanism.
Vision Guided Navigation for A Nonholonomic Mobile Robot
 IEEE TRANSACTIONS ON ROBOTICS AND AUTOMATION
, 1997
"... Visual servoing, i.e. the use of the vision sensor in feedback control, has been of increasing interest. A fair amount of work has been done in applications in autonomous driving, manipulation, mobile robot navigation and surveillance. However, the theoretical and analytical aspects of the problem h ..."
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Cited by 53 (5 self)
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Visual servoing, i.e. the use of the vision sensor in feedback control, has been of increasing interest. A fair amount of work has been done in applications in autonomous driving, manipulation, mobile robot navigation and surveillance. However, the theoretical and analytical aspects of the problem have not received much attention. Furthermore, the problem of estimation from the vision measurements has been considered separately from the design of the control strategies. Instead of addressing the pose estimation and control problems separately, we attempt to characterize the types of control tasks which can be achieved using only quantities directly measurable in the image, bypassing the pose estimation phase. We consider the navigation task for a nonholonomic ground mobile base tracking an arbitrarily shaped continuous ground curve. This tracking problem is formulated as one of controlling the shape of the curve in the image plane. We study the controllability of the system characteriz...
Exponential Stabilization of Driftless Nonlinear Control Systems
, 1995
"... This dissertation lays the foundation for practical exponential stabilization of driftless control systems. Driftless systems have the form, x = X 1 (x)u 1 + \Delta \Delta \Delta + Xm (x)um ; x 2 R n : Such systems arise when modeling mechanical systems with nonholonomic constraints. In engineer ..."
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Cited by 53 (3 self)
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This dissertation lays the foundation for practical exponential stabilization of driftless control systems. Driftless systems have the form, x = X 1 (x)u 1 + \Delta \Delta \Delta + Xm (x)um ; x 2 R n : Such systems arise when modeling mechanical systems with nonholonomic constraints. In engineering applications it is often required to maintain the mechanical system around a desired configuration. This task is treated as a stabilization problem where the desired configuration is made an asymptotically stable equilibrium point. The control design is carried out on an approximate system. The approximation process yields a nilpotent set of input vector fields which, in a special coordinate system, are homogeneous with respect to a nonstandard dilation. Even though the approximation can be given a coordinatefree interpretation, the homogeneous structure is useful to exploit: the feedbacks are required to be homogeneous functions and thus preserve the homogeneous structure in the close...
Developing Haptic and Visual Perceptual Categories for Reaching and Grasping with a Humanoid Robot
, 2000
"... Properties of the human embodiment  sensorimotor apparatus and neurological structure  participate directly in the growth and development of cognitive processes against enormous worst case complexity. It is our position that relationships between morphology and perception over time lead to incre ..."
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Cited by 50 (12 self)
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Properties of the human embodiment  sensorimotor apparatus and neurological structure  participate directly in the growth and development of cognitive processes against enormous worst case complexity. It is our position that relationships between morphology and perception over time lead to increasingly comprehensive models that describe the agent's relationship to the world. We are applying insight derived from neuroscience, neurology, and developmental psychology to the design of advanced robot architectures. To investigate developmental processes, we have begun to approximate the human sensorimotor configuration and to engage sensory and motor subsystems in developmental sequences. Many such sequences have been documented in studies of infant development, so we intend to bootstrap cognitive structures in robots by emulating some of these growth processes that bear an essential resemblance to the human morphology. In this paper, we will show two related examples in which a humanoid robot determines the models and representations that govern its behavior. The first is a model that captures the dynamics of a haptic exploration of an object with a dextrous robot hand that supports skillful grasping. The second example constructs constellations of visual features to predict relative hand/object postures that lead reliably to haptic utility. The result is a rst step in a trajectory toward associative visualhaptic categories that bounds the incremental complexity of each stage of development.
A Practical Model for Hair Mutual Interactions
, 2002
"... Hair exhibits strong anisotropic dynamic properties which demand distinct dynamic models for single strands and hairhair interactions. While a single strand can be modeled as a multibody open chain expressed in generalized coordinates, modeling hairhair interactions is a more difficult problem. A ..."
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Cited by 47 (0 self)
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Hair exhibits strong anisotropic dynamic properties which demand distinct dynamic models for single strands and hairhair interactions. While a single strand can be modeled as a multibody open chain expressed in generalized coordinates, modeling hairhair interactions is a more difficult problem. A dynamic model for this purpose is proposed based on a sparse set of guide strands. Long range connections among the strands are modeled as breakable static links formulated as nonreversible positional springs. Dynamic hairtohair collision is solved with the help of auxiliary triangle strips among nearby strands. Adaptive guide strands can be generated and removed on the fly to dynamically control the accuracy of a simulation. A highquality dense hair model can be obtained at the end by transforming and interpolating the sparse guide strands. Fine imagery of the final dense model is rendered by considering both primary scattering and selfshadowing inside the hair volume which is modeled as being partially translucent.