2 research outputs found
General Purpose Incremental Covariance Update and Efficient Belief Space Planning via Factor-Graph Propagation Action Tree
Fast covariance calculation is required both for SLAM (e.g.~in order to solve
data association) and for evaluating the information-theoretic term for
different candidate actions in belief space planning (BSP). In this paper we
make two primary contributions. First, we develop a novel general-purpose
incremental covariance update technique, which efficiently recovers specific
covariance entries after any change in the inference problem, such as
introduction of new observations/variables or re-linearization of the state
vector. Our approach is shown to recover them faster than other
state-of-the-art methods. Second, we present a computationally efficient
approach for BSP in high-dimensional state spaces, leveraging our incremental
covariance update method. State of the art BSP approaches perform belief
propagation for each candidate action and then evaluate an objective function
that typically includes an information-theoretic term, such as entropy or
information gain. Yet, candidate actions often have similar parts (e.g. common
trajectory parts), which are however evaluated separately for each candidate.
Moreover, calculating the information-theoretic term involves a costly
determinant computation of the entire information (covariance) matrix which is
O(n^3) with n being dimension of the state or costly Schur complement
operations if only marginal posterior covariance of certain variables is of
interest. Our approach, rAMDL-Tree, extends our previous BSP method rAMDL, by
exploiting incremental covariance calculation and performing calculation re-use
between common parts of non-myopic candidate actions, such that these parts are
evaluated only once, in contrast to existing approaches
iX-BSP: Incremental Belief Space Planning
Deciding what's next? is a fundamental problem in robotics and Artificial
Intelligence. Under belief space planning (BSP), in a partially observable
setting, it involves calculating the expected accumulated belief-dependent
reward, where the expectation is with respect to all future measurements. Since
solving this general un-approximated problem quickly becomes intractable, state
of the art approaches turn to approximations while still calculating planning
sessions from scratch. In this work we propose a novel paradigm, Incremental
BSP (iX-BSP), based on the key insight that calculations across planning
sessions are similar in nature and can be appropriately re-used. We calculate
the expectation incrementally by utilizing Multiple Importance Sampling
techniques for selective re-sampling and re-use of measurement from previous
planning sessions. The formulation of our approach considers general
distributions and accounts for data association aspects. We demonstrate how
iX-BSP could benefit existing approximations of the general problem,
introducing iML-BSP, which re-uses calculations across planning sessions under
the common Maximum Likelihood assumption. We evaluate both methods and
demonstrate a substantial reduction in computation time while statistically
preserving accuracy. The evaluation includes both simulation and real-world
experiments considering autonomous vision-based navigation and SLAM. As a
further contribution, we introduce to iX-BSP the non-integral wildfire
approximation, allowing one to trade accuracy for computational performance by
averting from updating re-used beliefs when they are "close enough". We
evaluate iX-BSP under wildfire demonstrating a substantial reduction in
computation time while controlling the accuracy sacrifice. We also provide
analytical and empirical bounds of the effect wildfire holds over the objective
value.Comment: 60 pages, 22 figure