30,340 research outputs found
A Structured Systems Approach for Optimal Actuator-Sensor Placement in Linear Time-Invariant Systems
In this paper we address the actuator/sensor allocation problem for linear
time invariant (LTI) systems. Given the structure of an autonomous linear
dynamical system, the goal is to design the structure of the input matrix
(commonly denoted by ) such that the system is structurally controllable
with the restriction that each input be dedicated, i.e., it can only control
directly a single state variable. We provide a methodology that addresses this
design question: specifically, we determine the minimum number of dedicated
inputs required to ensure such structural controllability, and characterize,
and characterizes all (when not unique) possible configurations of the
\emph{minimal} input matrix . Furthermore, we show that the proposed
solution methodology incurs \emph{polynomial complexity} in the number of state
variables. By duality, the solution methodology may be readily extended to the
structural design of the corresponding minimal output matrix (commonly denoted
by ) that ensures structural observability.Comment: 8 pages, submitted for publicatio
Incremental Sampling-based Algorithms for Optimal Motion Planning
During the last decade, incremental sampling-based motion planning
algorithms, such as the Rapidly-exploring Random Trees (RRTs) have been shown
to work well in practice and to possess theoretical guarantees such as
probabilistic completeness. However, no theoretical bounds on the quality of
the solution obtained by these algorithms have been established so far. The
first contribution of this paper is a negative result: it is proven that, under
mild technical conditions, the cost of the best path in the RRT converges
almost surely to a non-optimal value. Second, a new algorithm is considered,
called the Rapidly-exploring Random Graph (RRG), and it is shown that the cost
of the best path in the RRG converges to the optimum almost surely. Third, a
tree version of RRG is introduced, called the RRT algorithm, which
preserves the asymptotic optimality of RRG while maintaining a tree structure
like RRT. The analysis of the new algorithms hinges on novel connections
between sampling-based motion planning algorithms and the theory of random
geometric graphs. In terms of computational complexity, it is shown that the
number of simple operations required by both the RRG and RRT algorithms is
asymptotically within a constant factor of that required by RRT.Comment: 20 pages, 10 figures, this manuscript is submitted to the
International Journal of Robotics Research, a short version is to appear at
the 2010 Robotics: Science and Systems Conference
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