Extended Performance Guarantees for Receding Horizon Search with Terminal Cost

Experiments in Underwater Feature Tracking with Performance Guarantees Using a Small AUV

“…As in [13], we consider that the state of a mobile search agent may be represented by the tuple s = {p, x} where x gives all states of the mobile search agent excluding the position states p. We say that a state s i is feasible from the state s i−1 if there exists an action a available to the search agent such that applying a to the state s i−1 results in the new state s i . An n-length path may then be represented as a sequence of states γ n (s 0 ) = {s 0 , s 1 , .…”

“…In prior works [12] and [13], it was shown that the appropriate use of a terminal reward when constructing receding horizon paths can guarantee a lower bound on the value of receding horizon paths produced. The primary tool in producing this lower bound is a lower bound on the value-togo or a lower bound on the optimal value of the remainder of the path normally ignored during receding horizon planning.…”

“…Significantly, it is shown in Corollary 4.3 of [13] that the lower bound on the value-to-go may be defined using the value of the highest-reward path from a set of naive paths. This allows the receding horizon planner to leverage the strengths of distinct naive paths to produce a receding horizon path that will perform at least as well as the best naive solution and possibly much better.…”

“…However, the sequence of path segments in a receding horizon implementation do not inherit the near-optimality of each individual segment. In prior work [12], [13] the authors showed how to append a specific terminal reward to the short horizon optimization problem used for each path segment such that the reward of the overall receding horizon path is guaranteed to exceed a desirable lower bound. This result was demonstrated for the explicit reward function associated with a robotic search problem in a discrete environment through numerical experiments.…”

“…The specific reward function used for evaluating paths is presented in Section III. The path planning methods proposed in [13] and used in this work are presented and discussed in Section IV. The usage and relevant capabilities of the 690 vehicle are discussed in Section V. The experimental procedure and selection of parameters is presented in Section VI.…”