Towards Planning in Generalized Belief Space
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Abstract
We investigate the problem of planning under uncertainty, which is of interest in several robotic applications, ranging from autonomous navigation to manipulation. Recent effort from the research community has been devoted to design
planning approaches working in a continuous domain, relaxing the assumption that
the controls belong to a finite set. In this case robot policy is computed from the current robot belief (planning in belief space), while the environment in which the
robot moves is usually assumed to be known or partially known. We contribute to
this branch of the literature by relaxing the assumption of known environment; for
this purpose we introduce the concept of
generalized belief space
(GBS), in which
the robot maintains a joint belief over its state and the state of the environment. We
use GBS within a Model Predictive Control (MPC) scheme; our formulation is valid for general cost functions and incorporates a dual-layer optimization: the outer layer
computes the best control action, while the inner layer computes the generalized belief given the action. The resulting approach does not require prior knowledge of
the environment and does not assume maximum likelihood observations. We also present an application to a specific family of cost functions and we elucidate on the theoretical derivation with numerical examples.
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2013-12
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