3,732 research outputs found
Aerial navigation in obstructed environments with embedded nonlinear model predictive control
We propose a methodology for autonomous aerial navigation and obstacle
avoidance of micro aerial vehicles (MAV) using nonlinear model predictive
control (NMPC) and we demonstrate its effectiveness with laboratory
experiments. The proposed methodology can accommodate obstacles of arbitrary,
potentially non-convex, geometry. The NMPC problem is solved using PANOC: a
fast numerical optimization method which is completely matrix-free, is not
sensitive to ill conditioning, involves only simple algebraic operations and is
suitable for embedded NMPC. A C89 implementation of PANOC solves the NMPC
problem at a rate of 20Hz on board a lab-scale MAV. The MAV performs smooth
maneuvers moving around an obstacle. For increased autonomy, we propose a
simple method to compensate for the reduction of thrust over time, which comes
from the depletion of the MAV's battery, by estimating the thrust constant
An Inexact Successive Quadratic Approximation Method for Convex L-1 Regularized Optimization
We study a Newton-like method for the minimization of an objective function
that is the sum of a smooth convex function and an l-1 regularization term.
This method, which is sometimes referred to in the literature as a proximal
Newton method, computes a step by minimizing a piecewise quadratic model of the
objective function. In order to make this approach efficient in practice, it is
imperative to perform this inner minimization inexactly. In this paper, we give
inexactness conditions that guarantee global convergence and that can be used
to control the local rate of convergence of the iteration. Our inexactness
conditions are based on a semi-smooth function that represents a (continuous)
measure of the optimality conditions of the problem, and that embodies the
soft-thresholding iteration. We give careful consideration to the algorithm
employed for the inner minimization, and report numerical results on two test
sets originating in machine learning
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