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This paper investigates a collaborative rover-copter path planning andexploration with temporal logic specifications under uncertain environments.The objective of the rover is to complete a mission expressed by asyntactically co-safe linear temporal logic (scLTL) formula, while theobjective of the copter is to actively explore the environment and reduce itsuncertainties, aiming at assisting the rover and enhancing the efficiency ofthe mission completion. To formalize our approach, we first capture theenvironmental uncertainties by environmental beliefs of the atomicpropositions, under an assumption that it is unknown which properties (or,atomic propositions) are satisfied in each area of the environment. Theenvironmental beliefs of the atomic propositions are updated according to theBayes rule based on the Bernoulli-type sensor measurements provided by both therover and the copter. Then, the optimal policy for the rover is synthesized bymaximizing a belief of the satisfaction of the scLTL formula through animplementation of an automata-based model checking. An exploration policy forthe copter is then synthesized by employing the notion of an entropy that isevaluated based on the environmental beliefs of the atomic propositions, and apath that the rover intends to follow according to the optimal policy. As such,the copter can actively explore regions whose uncertainties are high and thatare relevant to the mission completion. Finally, some numerical examplesillustrate the effectiveness of the proposed approach.

Collaborative rover-copter path planning and exploration with temporal logic specifications based on Bayesian update under uncertain environments