  We propose a novel holistic approach for safe autonomous exploration and map
building based on constrained Bayesian optimisation. This method finds optimal
continuous paths instead of discrete sensing locations that inherently satisfy
motion and safety constraints. Evaluating both the objective and constraints
functions requires forward simulation of expected observations. As such
evaluations are costly, the Bayesian optimiser proposes only paths which are
likely to yield optimal results and satisfy the constraints with high
confidence. By balancing the reward and risk associated with each path, the
optimiser minimises the number of expensive function evaluations. We
demonstrate the effectiveness of our approach in a series of experiments both
in simulation and with a real ground robot and provide comparisons to other
exploration techniques. Evidently, each method has its specific favourable
conditions, where it outperforms all other techniques. Yet, by reasoning on the
usefulness of the entire path instead of its end point, our method provides a
robust and consistent performance through all tests and performs better than or
as good as the other leading methods.
