Multi-objective search (MOS) has emerged as a unifying framework for planning and decision-making problems where multiple, often conflicting, criteria must be balanced. While the problem has been studied for decades, recent years have seen renewed interest in the topic across AI applications such as robotics, transportation, and operations research, reflecting the reality that real-world systems rarely optimize a single measure. This paper surveys developments in MOS while highlighting cross-disciplinary opportunities, and outlines open challenges that define the emerging frontier of MOS research.

In this work we introduce the problem of task assistance planning where we are given two robots Rtask and Rassist. The first robot, Rtask, is in charge of performing a given task by executing a precomputed path. The second robot, Rassist, is in charge of assisting the task performed by Rtask using on-board sensors. The ability of Rassist to provide assistance to Rtask depends on the locations of both robots. Since Rtask is moving along its path, Rassist may also need to move to provide as much assistance as possible. The problem we study is how to compute a path for Rassist so as to maximize the portion of Rtask's path for which assistance is provided. We limit the problem to the setting where Rassist moves on a roadmap which is a graph embedded in its configuration space and show that this problem is NP-hard. Fortunately, we show that when Rassist moves on a given path, and all we have to do is compute the times at which Rassist should move from one configuration to the following one, we can solve the problem optimally in polynomial time. Together with carefully-crafted upper bounds, this polynomial-time algorithm is integrated into a Branch and Bound-based algorithm that can compute optimal solutions to the problem outperforming baselines by several orders of magnitude. We demonstrate our work empirically in simulated scenarios containing both planar manipulators and UR robots as well as in the lab on real robots.

We consider the motion-planning problem of planning a collision-free path of a robot in the presence of risk zones. The robot is allowed to travel in these zones but is penalized in a super-linear fashion for consecutive accumulative time spent there. We suggest a natural cost function that balances path length and risk-exposure time. Specifically, we consider the discrete setting where we are given a graph, or a roadmap, and we wish to compute the minimal-cost path under this cost function. Interestingly, paths defined using our cost function do not have an optimal substructure.