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Technical Report: A Receding Horizon Algorithm for Informative Path Planning with Temporal Logic Constraints
This technical report is an extended version of the paper 'A Receding Horizon
Algorithm for Informative Path Planning with Temporal Logic Constraints'
accepted to the 2013 IEEE International Conference on Robotics and Automation
(ICRA). This paper considers the problem of finding the most informative path
for a sensing robot under temporal logic constraints, a richer set of
constraints than have previously been considered in information gathering. An
algorithm for informative path planning is presented that leverages tools from
information theory and formal control synthesis, and is proven to give a path
that satisfies the given temporal logic constraints. The algorithm uses a
receding horizon approach in order to provide a reactive, on-line solution
while mitigating computational complexity. Statistics compiled from multiple
simulation studies indicate that this algorithm performs better than a baseline
exhaustive search approach.Comment: Extended version of paper accepted to 2013 IEEE International
Conference on Robotics and Automation (ICRA
An efficient method for multiobjective optimal control and optimal control subject to integral constraints
We introduce a new and efficient numerical method for multicriterion optimal
control and single criterion optimal control under integral constraints. The
approach is based on extending the state space to include information on a
"budget" remaining to satisfy each constraint; the augmented
Hamilton-Jacobi-Bellman PDE is then solved numerically. The efficiency of our
approach hinges on the causality in that PDE, i.e., the monotonicity of
characteristic curves in one of the newly added dimensions. A semi-Lagrangian
"marching" method is used to approximate the discontinuous viscosity solution
efficiently. We compare this to a recently introduced "weighted sum" based
algorithm for the same problem. We illustrate our method using examples from
flight path planning and robotic navigation in the presence of friendly and
adversarial observers.Comment: The final version accepted by J. Comp. Math. : 41 pages, 14 figures.
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