Planning in the Continuous Domain: a Generalized Belief Space Approach for Autonomous Navigation in Unknown Environments
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Abstract
We investigate the problem of planning under uncertainty, with application
to mobile robotics. We propose a probabilistic framework in
which the robot bases its decisions on the generalized belief, which is a probabilistic description of its own state and of external variables of interest.
The approach naturally leads to a dual-layer architecture: an
inner estimation layer, which performs inference to predict the outcome
of possible decisions, and an outer decisional layer which is in charge of
deciding the best action to undertake. Decision making is entrusted to
a Model Predictive Control (MPC) scheme. The formulation is valid for
general cost functions and does not discretize the state or control space,
enabling planning in continuous domain. Moreover, it allows to relax the
assumption of maximum likelihood observations: predicted measurements
are treated as random variables, and binary random variables are used to model the event that a measurement is actually taken by the robot. We
successfully apply our approach to the problem of uncertainty-constrained
exploration, in which the robot has to perform tasks in an unknown environment, while maintaining localization uncertainty within given bounds.
We present an extensive numerical analysis of the proposed approach and
compare it against related work. In practice, our planning approach produces
smooth and natural trajectories and is able to impose soft upper
bounds on the uncertainty. Finally, we exploit the results of this analysis to identify current limitations and show that the proposed framework can accommodate several desirable extensions.
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Date
2015
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