17,202 research outputs found
Information-Theoretic Stochastic Optimal Control via Incremental Sampling-based Algorithms
This paper considers optimal control of dynamical systems which are
represented by nonlinear stochastic differential equations. It is well-known
that the optimal control policy for this problem can be obtained as a function
of a value function that satisfies a nonlinear partial differential equation,
namely, the Hamilton-Jacobi-Bellman equation. This nonlinear PDE must be solved
backwards in time, and this computation is intractable for large scale systems.
Under certain assumptions, and after applying a logarithmic transformation, an
alternative characterization of the optimal policy can be given in terms of a
path integral. Path Integral (PI) based control methods have recently been
shown to provide elegant solutions to a broad class of stochastic optimal
control problems. One of the implementation challenges with this formalism is
the computation of the expectation of a cost functional over the trajectories
of the unforced dynamics. Computing such expectation over trajectories that are
sampled uniformly may induce numerical instabilities due to the exponentiation
of the cost. Therefore, sampling of low-cost trajectories is essential for the
practical implementation of PI-based methods. In this paper, we use incremental
sampling-based algorithms to sample useful trajectories from the unforced
system dynamics, and make a novel connection between Rapidly-exploring Random
Trees (RRTs) and information-theoretic stochastic optimal control. We show the
results from the numerical implementation of the proposed approach to several
examples.Comment: 18 page
Parallel ADMM for robust quadratic optimal resource allocation problems
An alternating direction method of multipliers (ADMM) solver is described for
optimal resource allocation problems with separable convex quadratic costs and
constraints and linear coupling constraints. We describe a parallel
implementation of the solver on a graphics processing unit (GPU) using a
bespoke quartic function minimizer. An application to robust optimal energy
management in hybrid electric vehicles is described, and the results of
numerical simulations comparing the computation times of the parallel GPU
implementation with those of an equivalent serial implementation are presented
Topology-Guided Path Integral Approach for Stochastic Optimal Control in Cluttered Environment
This paper addresses planning and control of robot motion under uncertainty
that is formulated as a continuous-time, continuous-space stochastic optimal
control problem, by developing a topology-guided path integral control method.
The path integral control framework, which forms the backbone of the proposed
method, re-writes the Hamilton-Jacobi-Bellman equation as a statistical
inference problem; the resulting inference problem is solved by a sampling
procedure that computes the distribution of controlled trajectories around the
trajectory by the passive dynamics. For motion control of robots in a highly
cluttered environment, however, this sampling can easily be trapped in a local
minimum unless the sample size is very large, since the global optimality of
local minima depends on the degree of uncertainty. Thus, a homology-embedded
sampling-based planner that identifies many (potentially) local-minimum
trajectories in different homology classes is developed to aid the sampling
process. In combination with a receding-horizon fashion of the optimal control
the proposed method produces a dynamically feasible and collision-free motion
plans without being trapped in a local minimum. Numerical examples on a
synthetic toy problem and on quadrotor control in a complex obstacle field
demonstrate the validity of the proposed method.Comment: arXiv admin note: text overlap with arXiv:1510.0534
Constrained optimal control theory for differential linear repetitive processes
Differential repetitive processes are a distinct class of continuous-discrete two-dimensional linear systems of both systems theoretic and applications interest. These processes complete a series of sweeps termed passes through a set of dynamics defined over a finite duration known as the pass length, and once the end is reached the process is reset to its starting position before the next pass begins. Moreover the output or pass profile produced on each pass explicitly contributes to the dynamics of the next one. Applications areas include iterative learning control and iterative solution algorithms, for classes of dynamic nonlinear optimal control problems based on the maximum principle, and the modeling of numerous industrial processes such as metal rolling, long-wall cutting, etc. In this paper we develop substantial new results on optimal control of these processes in the presence of constraints where the cost function and constraints are motivated by practical application of iterative learning control to robotic manipulators and other electromechanical systems. The analysis is based on generalizing the well-known maximum and -maximum principles to the
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