64,215 research outputs found
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
Inverse polynomial optimization
We consider the inverse optimization problem associated with the polynomial
program f^*=\min \{f(x): x\in K\}y\in
K\tilde{f}fy\tilde{f}Kd\tilde{f}\Vert f-\tilde{f}\Vert\ell_1\ell_2\ell_\infty\tilde{f}_df(\y)f^*\ell_1\tilde{f}$ takes a
simple and explicit canonical form. Some variations are also discussed.Comment: 25 pages; to appear in Math. Oper. Res; Rapport LAAS no. 1114
Conic Optimization Theory: Convexification Techniques and Numerical Algorithms
Optimization is at the core of control theory and appears in several areas of
this field, such as optimal control, distributed control, system
identification, robust control, state estimation, model predictive control and
dynamic programming. The recent advances in various topics of modern
optimization have also been revamping the area of machine learning. Motivated
by the crucial role of optimization theory in the design, analysis, control and
operation of real-world systems, this tutorial paper offers a detailed overview
of some major advances in this area, namely conic optimization and its emerging
applications. First, we discuss the importance of conic optimization in
different areas. Then, we explain seminal results on the design of hierarchies
of convex relaxations for a wide range of nonconvex problems. Finally, we study
different numerical algorithms for large-scale conic optimization problems.Comment: 18 page
Computationally Efficient Trajectory Optimization for Linear Control Systems with Input and State Constraints
This paper presents a trajectory generation method that optimizes a quadratic
cost functional with respect to linear system dynamics and to linear input and
state constraints. The method is based on continuous-time flatness-based
trajectory generation, and the outputs are parameterized using a polynomial
basis. A method to parameterize the constraints is introduced using a result on
polynomial nonpositivity. The resulting parameterized problem remains
linear-quadratic and can be solved using quadratic programming. The problem can
be further simplified to a linear programming problem by linearization around
the unconstrained optimum. The method promises to be computationally efficient
for constrained systems with a high optimization horizon. As application, a
predictive torque controller for a permanent magnet synchronous motor which is
based on real-time optimization is presented.Comment: Proceedings of the American Control Conference (ACC), pp. 1904-1909,
San Francisco, USA, June 29 - July 1, 201
Setting Parameters by Example
We introduce a class of "inverse parametric optimization" problems, in which
one is given both a parametric optimization problem and a desired optimal
solution; the task is to determine parameter values that lead to the given
solution. We describe algorithms for solving such problems for minimum spanning
trees, shortest paths, and other "optimal subgraph" problems, and discuss
applications in multicast routing, vehicle path planning, resource allocation,
and board game programming.Comment: 13 pages, 3 figures. To be presented at 40th IEEE Symp. Foundations
of Computer Science (FOCS '99
Synthesis and Optimization of Reversible Circuits - A Survey
Reversible logic circuits have been historically motivated by theoretical
research in low-power electronics as well as practical improvement of
bit-manipulation transforms in cryptography and computer graphics. Recently,
reversible circuits have attracted interest as components of quantum
algorithms, as well as in photonic and nano-computing technologies where some
switching devices offer no signal gain. Research in generating reversible logic
distinguishes between circuit synthesis, post-synthesis optimization, and
technology mapping. In this survey, we review algorithmic paradigms ---
search-based, cycle-based, transformation-based, and BDD-based --- as well as
specific algorithms for reversible synthesis, both exact and heuristic. We
conclude the survey by outlining key open challenges in synthesis of reversible
and quantum logic, as well as most common misconceptions.Comment: 34 pages, 15 figures, 2 table
Trajectory generation for multi-contact momentum-control
Simplified models of the dynamics such as the linear inverted pendulum model
(LIPM) have proven to perform well for biped walking on flat ground. However,
for more complex tasks the assumptions of these models can become limiting. For
example, the LIPM does not allow for the control of contact forces
independently, is limited to co-planar contacts and assumes that the angular
momentum is zero. In this paper, we propose to use the full momentum equations
of a humanoid robot in a trajectory optimization framework to plan its center
of mass, linear and angular momentum trajectories. The model also allows for
planning desired contact forces for each end-effector in arbitrary contact
locations. We extend our previous results on LQR design for momentum control by
computing the (linearized) optimal momentum feedback law in a receding horizon
fashion. The resulting desired momentum and the associated feedback law are
then used in a hierarchical whole body control approach. Simulation experiments
show that the approach is computationally fast and is able to generate plans
for locomotion on complex terrains while demonstrating good tracking
performance for the full humanoid control
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