4,182 research outputs found
Ball on a beam: stabilization under saturated input control with large basin of attraction
This article is devoted to the stabilization of two underactuated planar
systems, the well-known straight beam-and-ball system and an original circular
beam-and-ball system. The feedback control for each system is designed, using
the Jordan form of its model, linearized near the unstable equilibrium. The
limits on the voltage, fed to the motor, are taken into account explicitly. The
straight beam-and-ball system has one unstable mode in the motion near the
equilibrium point. The proposed control law ensures that the basin of
attraction coincides with the controllability domain. The circular
beam-and-ball system has two unstable modes near the equilibrium point.
Therefore, this device, never considered in the past, is much more difficult to
control than the straight beam-and-ball system. The main contribution is to
propose a simple new control law, which ensures by adjusting its gain
parameters that the basin of attraction arbitrarily can approach the
controllability domain for the linear case. For both nonlinear systems,
simulation results are presented to illustrate the efficiency of the designed
nonlinear control laws and to determine the basin of attraction
Motion Planning of Uncertain Ordinary Differential Equation Systems
This work presents a novel motion planning framework, rooted in nonlinear programming theory, that treats uncertain fully and under-actuated dynamical systems described by ordinary differential equations. Uncertainty in multibody dynamical systems comes from various sources, such as: system parameters, initial conditions, sensor and actuator noise, and external forcing. Treatment of uncertainty in design is of paramount practical importance because all real-life systems are affected by it, and poor robustness and suboptimal performance result if it’s not accounted for in a given design. In this work uncertainties are modeled using Generalized Polynomial Chaos and are solved quantitatively using a least-square collocation method. The computational efficiency of this approach enables the inclusion of uncertainty statistics in the nonlinear programming optimization process. As such, the proposed framework allows the user to pose, and answer, new design questions related to uncertain dynamical systems.
Specifically, the new framework is explained in the context of forward, inverse, and hybrid dynamics formulations. The forward dynamics formulation, applicable to both fully and under-actuated systems, prescribes deterministic actuator inputs which yield uncertain state trajectories. The inverse dynamics formulation is the dual to the forward dynamic, and is only applicable to fully-actuated systems; deterministic state trajectories are prescribed and yield uncertain actuator inputs. The inverse dynamics formulation is more computationally efficient as it requires only algebraic evaluations and completely avoids numerical integration. Finally, the hybrid dynamics formulation is applicable to under-actuated systems where it leverages the benefits of inverse dynamics for actuated joints and forward dynamics for unactuated joints; it prescribes actuated state and unactuated input trajectories which yield uncertain unactuated states and actuated inputs.
The benefits of the ability to quantify uncertainty when planning the motion of multibody dynamic systems are illustrated through several case-studies. The resulting designs determine optimal motion plans—subject to deterministic and statistical constraints—for all possible systems within the probability space
Whole-Body MPC for a Dynamically Stable Mobile Manipulator
Autonomous mobile manipulation offers a dual advantage of mobility provided
by a mobile platform and dexterity afforded by the manipulator. In this paper,
we present a whole-body optimal control framework to jointly solve the problems
of manipulation, balancing and interaction as one optimization problem for an
inherently unstable robot. The optimization is performed using a Model
Predictive Control (MPC) approach; the optimal control problem is transcribed
at the end-effector space, treating the position and orientation tasks in the
MPC planner, and skillfully planning for end-effector contact forces. The
proposed formulation evaluates how the control decisions aimed at end-effector
tracking and environment interaction will affect the balance of the system in
the future. We showcase the advantages of the proposed MPC approach on the
example of a ball-balancing robot with a robotic manipulator and validate our
controller in hardware experiments for tasks such as end-effector pose tracking
and door opening
On Neuromechanical Approaches for the Study of Biological Grasp and Manipulation
Biological and robotic grasp and manipulation are undeniably similar at the
level of mechanical task performance. However, their underlying fundamental
biological vs. engineering mechanisms are, by definition, dramatically
different and can even be antithetical. Even our approach to each is
diametrically opposite: inductive science for the study of biological systems
vs. engineering synthesis for the design and construction of robotic systems.
The past 20 years have seen several conceptual advances in both fields and the
quest to unify them. Chief among them is the reluctant recognition that their
underlying fundamental mechanisms may actually share limited common ground,
while exhibiting many fundamental differences. This recognition is particularly
liberating because it allows us to resolve and move beyond multiple paradoxes
and contradictions that arose from the initial reasonable assumption of a large
common ground. Here, we begin by introducing the perspective of neuromechanics,
which emphasizes that real-world behavior emerges from the intimate
interactions among the physical structure of the system, the mechanical
requirements of a task, the feasible neural control actions to produce it, and
the ability of the neuromuscular system to adapt through interactions with the
environment. This allows us to articulate a succinct overview of a few salient
conceptual paradoxes and contradictions regarding under-determined vs.
over-determined mechanics, under- vs. over-actuated control, prescribed vs.
emergent function, learning vs. implementation vs. adaptation, prescriptive vs.
descriptive synergies, and optimal vs. habitual performance. We conclude by
presenting open questions and suggesting directions for future research. We
hope this frank assessment of the state-of-the-art will encourage and guide
these communities to continue to interact and make progress in these important
areas
Finite element reduced order models for nonlinear vibrations of piezoelectric layered beams with applications to NEMS
This article presents a finite element reduced order model for the nonlinear vibrations of piezoelectric layered beams with application to NEMS. In this model, the geometrical nonlinearities are taken into account through a von Kármán nonlinear strain–displacement relationship. The originality of the finite element electromechanical formulation is that the system electrical state is fully described by only a couple of variables per piezoelectric patches, namely the electric charge contained in the electrodes and the voltage between the electrodes. Due to the geometrical nonlinearity, the piezoelectric actuation introduces an original parametric excitation term in the equilibrium equation. The reduced-order formulation of the discretized problem is obtained by expanding the mechanical displacement unknown vector onto the short-circuit eigenmode basis. A particular attention is paid to the computation of the unknown nonlinear stiffness coefficients of the reduced-order model. Due to the particular form of the von Kármán nonlinearities, these coefficients are computed exactly, once for a given geometry, by prescribing relevant nodal displacements in nonlinear static solutions settings. Finally, the low-order model is computed with an original purely harmonic-based continuation method. Our numerical tool is then validated by computing the nonlinear vibrations of a mechanically excited homogeneous beam supported at both ends referenced in the literature. The more difficult case of the nonlinear oscillations of a layered nanobridge piezoelectrically actuated is also studied. Interesting vibratory phenomena such as parametric amplification or patch length dependence of the frequency output response are highlighted in order to help in the design of these nanodevices.This research is part of the NEMSPIEZO project, under funds from the French National Research Agency (Project ANR-08-NAN O-015-04), for which the authors are grateful
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