1,688 research outputs found
A Discrete Geometric Optimal Control Framework for Systems with Symmetries
This paper studies the optimal motion control of
mechanical systems through a discrete geometric approach. At
the core of our formulation is a discrete Lagrange-d’Alembert-
Pontryagin variational principle, from which are derived discrete
equations of motion that serve as constraints in our optimization
framework. We apply this discrete mechanical approach to
holonomic systems with symmetries and, as a result, geometric
structure and motion invariants are preserved. We illustrate our
method by computing optimal trajectories for a simple model of
an air vehicle flying through a digital terrain elevation map, and
point out some of the numerical benefits that ensue
Structured Linearization of Discrete Mechanical Systems for Analysis and Optimal Control
Variational integrators are well-suited for simulation of mechanical systems
because they preserve mechanical quantities about a system such as momentum, or
its change if external forcing is involved, and holonomic constraints. While
they are not energy-preserving they do exhibit long-time stable energy
behavior. However, variational integrators often simulate mechanical system
dynamics by solving an implicit difference equation at each time step, one that
is moreover expressed purely in terms of configurations at different time
steps. This paper formulates the first- and second-order linearizations of a
variational integrator in a manner that is amenable to control analysis and
synthesis, creating a bridge between existing analysis and optimal control
tools for discrete dynamic systems and variational integrators for mechanical
systems in generalized coordinates with forcing and holonomic constraints. The
forced pendulum is used to illustrate the technique. A second example solves
the discrete LQR problem to find a locally stabilizing controller for a 40 DOF
system with 6 constraints.Comment: 13 page
Structured Linearization of Discrete Mechanical Systems for Analysis and Optimal Control
Variational integrators are well-suited for simulation of mechanical systems
because they preserve mechanical quantities about a system such as momentum, or
its change if external forcing is involved, and holonomic constraints. While
they are not energy-preserving they do exhibit long-time stable energy
behavior. However, variational integrators often simulate mechanical system
dynamics by solving an implicit difference equation at each time step, one that
is moreover expressed purely in terms of configurations at different time
steps. This paper formulates the first- and second-order linearizations of a
variational integrator in a manner that is amenable to control analysis and
synthesis, creating a bridge between existing analysis and optimal control
tools for discrete dynamic systems and variational integrators for mechanical
systems in generalized coordinates with forcing and holonomic constraints. The
forced pendulum is used to illustrate the technique. A second example solves
the discrete LQR problem to find a locally stabilizing controller for a 40 DOF
system with 6 constraints.Comment: 13 page
Predictive Coding for Dynamic Visual Processing: Development of Functional Hierarchy in a Multiple Spatio-Temporal Scales RNN Model
The current paper proposes a novel predictive coding type neural network
model, the predictive multiple spatio-temporal scales recurrent neural network
(P-MSTRNN). The P-MSTRNN learns to predict visually perceived human whole-body
cyclic movement patterns by exploiting multiscale spatio-temporal constraints
imposed on network dynamics by using differently sized receptive fields as well
as different time constant values for each layer. After learning, the network
becomes able to proactively imitate target movement patterns by inferring or
recognizing corresponding intentions by means of the regression of prediction
error. Results show that the network can develop a functional hierarchy by
developing a different type of dynamic structure at each layer. The paper
examines how model performance during pattern generation as well as predictive
imitation varies depending on the stage of learning. The number of limit cycle
attractors corresponding to target movement patterns increases as learning
proceeds. And, transient dynamics developing early in the learning process
successfully perform pattern generation and predictive imitation tasks. The
paper concludes that exploitation of transient dynamics facilitates successful
task performance during early learning periods.Comment: Accepted in Neural Computation (MIT press
Geometric, Variational Integrators for Computer Animation
We present a general-purpose numerical scheme for time integration of Lagrangian dynamical systems—an important
computational tool at the core of most physics-based animation techniques. Several features make this
particular time integrator highly desirable for computer animation: it numerically preserves important invariants,
such as linear and angular momenta; the symplectic nature of the integrator also guarantees a correct energy
behavior, even when dissipation and external forces are added; holonomic constraints can also be enforced quite
simply; finally, our simple methodology allows for the design of high-order accurate schemes if needed. Two key
properties set the method apart from earlier approaches. First, the nonlinear equations that must be solved during
an update step are replaced by a minimization of a novel functional, speeding up time stepping by more than a
factor of two in practice. Second, the formulation introduces additional variables that provide key flexibility in the
implementation of the method. These properties are achieved using a discrete form of a general variational principle
called the Pontryagin-Hamilton principle, expressing time integration in a geometric manner. We demonstrate
the applicability of our integrators to the simulation of non-linear elasticity with implementation details
FLSH -- Friendly Library for the Simulation of Humans
Computer models of humans are ubiquitous throughout computer animation and
computer vision. However, these models rarely represent the dynamics of human
motion, as this requires adding a complex layer that solves body motion in
response to external interactions and according to the laws of physics. FLSH is
a library that facilitates this task for researchers and developers who are not
interested in the nuisances of physics simulation, but want to easily integrate
dynamic humans in their applications. FLSH provides easy access to three
flavors of body physics, with different features and computational complexity:
skeletal dynamics, full soft-tissue dynamics, and reduced-order modeling of
soft-tissue dynamics. In all three cases, the simulation models are built on
top of the pseudo-standard SMPL parametric body model.Comment: Project website: https://gitlab.com/PabloRamonPrieto/fls
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