Various robotic problems (e.g., map exploration, environmental monitoring and spatial search) can be formulated as submodular maximization problems with routing constraints. These problems involve two NP-hard problems, maximal coverage and traveling salesman problems. The generalized cost-benefit algorithm (GCB) is able to solve this problem with a 1 2 (1-1 e)\widetilde OPT guarantee, where OPT is the approximation of optimal performance. There is a gap between the OPT and the optimal solution (OPT). In this research, the proposed algorithms, Tree-Structured Fourier Supports Set (TS-FSS), utilize the submodularity and sparsity of routing trees to boost GCB performance. The theorems show that the proposed algorithms have a higher optimum bound than GCB. The experiments demonstrate that the proposed approach outperforms benchmark approaches.
- motion and path planning
- search and rescue robots