9,552 research outputs found
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
A flow-based approach to rough differential equations
These are lecture notes for a Master 2 course on rough differential equations
driven by weak geometric Holder p-rough paths, for any p>2. They provide a
short, self-contained and pedagogical account of the theory, with an emphasis
on flows. The theory is illustrated by some now classical applications to
stochastic analysis, such as the basics of Freidlin-Wentzel theory of large
deviations for diffusions, or Stroock and Varadhan support theorem.Comment: 63 page
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