Autonomous exploration is an essential capability for mobile robots, as the majority of their applications require the ability to efficiently collect information about their surroundings. In the literature, there are several approaches, ranging from frontier-based methods to hybrid solutions involving the ability to plan both local and global exploring paths, but only few of them focus on improving local exploration by properly tuning the planned trajectory, often leading to "stop-and-go" like behaviors. In this work we propose a novel RRT-inspired B\'ezier-based next-best-view trajectory planner able to deal with the problem of fast local exploration. Gaussian process inference is used to guarantee fast exploration gain retrieval while still being consistent with the exploration task. The proposed approach is compared with other available state-of-the-art algorithms and tested in a real-world scenario. The implemented code is publicly released as open-source code to encourage further developments and benchmarking.
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