5,380 research outputs found
Posing 3D Models from Drawing
Inferring the 3D pose of a character from a drawing is a complex and under-constrained problem. Solving it may help automate various parts of an animation production pipeline such as pre-visualisation. In this paper, a novel way of inferring the 3D pose from a monocular 2D sketch is proposed. The proposed method does not make any external assumptions about the model, allowing it to be used on different types of characters. The inference of the 3D pose is formulated as an optimisation problem and a parallel variation of the Particle Swarm Optimisation algorithm called PARAC-LOAPSO is utilised for searching the minimum. Testing in isolation as well as part of a larger scene, the presented method is evaluated by posing a lamp, a horse and a human character. The results show that this method is robust, highly scalable and is able to be extended to various types of models
Discrete Routh Reduction
This paper develops the theory of abelian Routh reduction for discrete
mechanical systems and applies it to the variational integration of mechanical
systems with abelian symmetry. The reduction of variational Runge-Kutta
discretizations is considered, as well as the extent to which symmetry
reduction and discretization commute. These reduced methods allow the direct
simulation of dynamical features such as relative equilibria and relative
periodic orbits that can be obscured or difficult to identify in the unreduced
dynamics. The methods are demonstrated for the dynamics of an Earth orbiting
satellite with a non-spherical correction, as well as the double
spherical pendulum. The problem is interesting because in the unreduced
picture, geometric phases inherent in the model and those due to numerical
discretization can be hard to distinguish, but this issue does not appear in
the reduced algorithm, where one can directly observe interesting dynamical
structures in the reduced phase space (the cotangent bundle of shape space), in
which the geometric phases have been removed. The main feature of the double
spherical pendulum example is that it has a nontrivial magnetic term in its
reduced symplectic form. Our method is still efficient as it can directly
handle the essential non-canonical nature of the symplectic structure. In
contrast, a traditional symplectic method for canonical systems could require
repeated coordinate changes if one is evoking Darboux' theorem to transform the
symplectic structure into canonical form, thereby incurring additional
computational cost. Our method allows one to design reduced symplectic
integrators in a natural way, despite the noncanonical nature of the symplectic
structure.Comment: 24 pages, 7 figures, numerous minor improvements, references added,
fixed typo
Physical Dissipation and the Method of Controlled Lagrangians
We describe the effect of physical dissipation on stability of
equilibria which have been stabilized, in the absence of damping,
using the method of controlled Lagrangians. This method
applies to a class of underactuated mechanical systems including
“balance” systems such as the pendulum on a cart. Since
the method involves modifying a system’s kinetic energy metric
through feedback, the effect of dissipation is obscured.
In particular, it is not generally true that damping makes a
feedback-stabilized equilibrium asymptotically stable. Damping
in the unactuated directions does tend to enhance stability,
however damping in the controlled directions must be “reversed”
through feedback. In this paper, we suggest a choice
of feedback dissipation to locally exponentially stabilize a class
of controlled Lagrangian systems
The Hamiltonian structure of a two-dimensional rigid circular cylinder interacting dynamically with N point vortices
This paper studies the dynamical fluid plus rigid-body system consisting of a two-dimensional rigid cylinder of general cross-sectional shape interacting with N point vortices. We derive the equations of motion for this system and show that, in particular, if the vortex strengths sum to zero and the rigid-body has a circular shape, the equations are Hamiltonian with respect to a Poisson bracket structure that is the sum of the rigid body Lie–Poisson bracket on Se(2)*, the dual of the Lie algebra of the Euclidean group on the plane, and the canonical Poisson bracket for the dynamics of N point vortices in an unbounded plane. We then use this Hamiltonian structure to study the linear and nonlinear stability of the moving Föppl equilibrium solutions using the energy-Casimir method
Dissipation and Controlled Euler-Poincaré Systems
The method of controlled Lagrangians is a technique for stabilizing underactuated mechanical systems which involves modifying a system’s energy and dynamic structure through feedback. These modifications can obscure the effect of physical dissipation in the closed-loop. For example,
generic damping can destabilize an equilibrium which is closed-loop stable for a conservative system model. In this paper, we consider the effect of damping on Euler-Poincaré (special reduced Lagrangian) systems which have been stabilized about an equilibrium using the method of controlled Lagrangians. We describe a choice of feed-back dissipation which asymptotically stabilizes a sub-class of controlled Euler-Poincaré systems subject to physical damping. As an example, we consider intermediate axis rotation of a damped rigid body with a single internal rotor
Friction force microscopy : a simple technique for identifying graphene on rough substrates and mapping the orientation of graphene grains on copper
At a single atom thick, it is challenging to distinguish graphene from its substrate using conventional techniques. In this paper we show that friction force microscopy (FFM) is a simple and quick technique for identifying graphene on a range of samples, from growth substrates to rough insulators. We show that FFM is particularly effective for characterizing graphene grown on copper where it can correlate the graphene growth to the three-dimensional surface topography. Atomic lattice stick–slip friction is readily resolved and enables the crystallographic orientation of the graphene to be mapped nondestructively, reproducibly and at high resolution. We expect FFM to be similarly effective for studying graphene growth on other metal/locally crystalline substrates, including SiC, and for studying growth of other two-dimensional materials such as molybdenum disulfide and hexagonal boron nitride
Discrete Variational Optimal Control
This paper develops numerical methods for optimal control of mechanical
systems in the Lagrangian setting. It extends the theory of discrete mechanics
to enable the solutions of optimal control problems through the discretization
of variational principles. The key point is to solve the optimal control
problem as a variational integrator of a specially constructed
higher-dimensional system. The developed framework applies to systems on
tangent bundles, Lie groups, underactuated and nonholonomic systems with
symmetries, and can approximate either smooth or discontinuous control inputs.
The resulting methods inherit the preservation properties of variational
integrators and result in numerically robust and easily implementable
algorithms. Several theoretical and a practical examples, e.g. the control of
an underwater vehicle, will illustrate the application of the proposed
approach.Comment: 30 pages, 6 figure
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