Abstract
This paper is concerned with on-line coverage of unknown planar environments by a mobile robot of size \(D\) operating with a limited energy capacity battery. The battery capacity is represented by the path length \(L\) that the robot can travel under a full battery charge. Starting at \(S\), the robot has to cover a planar environment containing unknown obstacles, and return to \(S\) upon task completion. During task execution the robot may return to \(S\) at any time to recharge its battery. The paper first describes a battery powered off-line coverage methodology, then introduces the BPC (Battery Powered Coverage) algorithm that performs on-line battery powered coverage using position and local obstacle detection sensors. The performance of the BPC algorithm is measured by its competitiveness, determined by measuring its total on-line path length, \(l\), relative to the optimal off-line solution \(l_{\textit{opt}}\). The paper establishes that the BPC algorithm has a competitive performance of \(l \le \tfrac{L}{D} l_{\textit{opt}}\). The paper additionally establishes a universal lower bound of \(l \ge \log (\tfrac{L}{4 D}) l_{\textit{opt}}\) over all on-line battery powered coverage algorithms. Execution example illustrates the usefulness of the BPC algorithm.
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Notes
- 1.
An internal obstacle is any obstacle surrounded by a loop of obstacle free cells.
- 2.
Two continuous paths \(\alpha ,\beta : [a,b] \rightarrow \mathbb {R}^2\) connecting S to \(p\) in the free environment belong to the same homotopy class if there is a continuous mapping , \(F(t,s): [a,b] \times [0,1] \rightarrow \mathbb {R}^2\), such that \(F(t,0) = \alpha (t),F(t,1) = \beta (t)\) for \(t\in [a,b]\), and \(F(a,s) = S,F(b,s) = p\) for \(s \in [0,1]\).
- 3.
If the selected algorithm is non-deterministic, in worst case one outcome of the algorithm will be as bad as a deterministic algorithm.
- 4.
Assume for convenience that \(L\) is an integer multiple of \(D\).
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Shnaps, I., Rimon, E. (2015). On-line Coverage of Planar Environments by a Battery Powered Autonomous Mobile Robot. In: Akin, H., Amato, N., Isler, V., van der Stappen, A. (eds) Algorithmic Foundations of Robotics XI. Springer Tracts in Advanced Robotics, vol 107. Springer, Cham. https://doi.org/10.1007/978-3-319-16595-0_33
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