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We present a possible method for integrating high level and low levelplanning. To do so, we introduce the global plan random \emph{trajectory}$\boldsymbol{\eta}_0 \colon [1,T] \to \mathbb R^2$, measured by goals $G_i$ andgoverned by the distribution $p(\boldsymbol{\eta}_0 \mid \{ G_i\}_{i=1}^m)$.This distribution is combined with the low level robot-crowd planner$p(\mathbf{f}^{R},\mathbf{f}^{1},\ldots,\mathbf{f}^{n}\mid\mathbf{z}_{1:t})$(from~\cite{trautmanicra2013, trautmaniros}) in the distribution$p(\boldsymbol{\eta}_0,\mathbf{f}^{(R)},\mathbf{f}\mid\mathbf{z}_{1:t})$. Weexplore this \emph{integrated planning} formulation in three case studies, andin the process find that this formulation 1) generalizes the ROS navigationstack in a practically useful way 2) arbitrates between high and low leveldecision making in a statistically sound manner when unanticipated localdisturbances arise and 3) enables the integration of an onboard operatorproviding real time input at either the global (e.g., waypoint designation) orlocal (e.g., joystick) level. Importantly, the integrated planning formulation$p(\boldsymbol{\eta}_0,\mathbf{f}^{(R)},\mathbf{f}\mid\mathbf{z}_{1:t})$highlights failure modes of the ROS navigation stack (and thus for standardhierarchical planning architectures); these failure modes are resolved by using$p(\boldsymbol{\eta}_0,\mathbf{f}^{(R)},\mathbf{f}\mid\mathbf{z}_{1:t})$.Finally, we conclude with a discussion of how results from formal methods canguide our factorization of$p(\boldsymbol{\eta}_0,\mathbf{f}^{(R)},\mathbf{f}\mid\mathbf{z}_{1:t})$.

Integrating High Level and Low Level Planning