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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, eflecting 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 multi-objective search, we consider a graph whose edges are annotated with multiple cost components. A typical task is to compute the Pareto frontier, i.e., the set of all undominated paths from a given start state to a given goal state of the graph. However, the size of the Pareto frontier can be exponential in the size of the graph, and computing the entire Pareto frontier can be very time-consuming. Therefore, in this paper, we study how to find an approximate frontier for a user-provided approximation factor. Such a frontier can be significantly smaller than the Pareto frontier, enabling the design of efficient approximate multi-objective search algorithms. We present such an algorithm called A*pex, which uses an efficient, albeit approximate, representation of paths with similar costs to compute an approximate frontier. During the search, it avoids storing all paths explicitly, thereby reducing the search effort. We show that A*pex can be used as an algorithmic building block to solve additional problems by presenting (1) an anytime variant of A*pex, which computes an initial approximate frontier quickly and then works to find better approximate frontiers until eventually finding the entire Pareto frontier and (2) a variant of A*pex for approximately solving the Weight-Constrained Shortest Path (WCSP) problem, a problem that is closely related to multi-objective search. For evaluation, we use road networks from the 9th DIMACS Implementation Challenge: Shortest Path for evaluation. Our experimental results show that A*pex and its WCSP variant can outperform respective state-of-the-art algorithms by orders of magnitude in terms of runtime. We also show that the anytime variant of A*pex often computes better approximate frontiers than state-of-the-art algorithms, given a limited runtime. 

In Bi-Objective Search (BOS), the task is to compute the Pareto-optimal frontier of paths in a graph with two cost values per edge. Recent work introduced a general BOS framework that classifies search nodes and studies how ordering functions affect expansion order. In this paper, we continue this line of research. We further refine the classes of nodes and show that many nodes that were added to the open list and are classified as never-expand nodes still need to be extracted and further examined. Additionally, we introduce a method that enables constant-time dominance checks for the MIN and MAX ordering functions. This allows a practical usage of these ordering functions, as we demonstrate in our experimental section. 

Medical steerable needles can follow 3D curvilinear trajectories to avoid anatomical obstacles and reach clinically significant targets inside the human body. Automating steerable needle procedures can enable physicians and patients to harness the full potential of steerable needles by maximally leveraging their steerability to safely and accurately reach targets for medical procedures such as biopsies. For the automation of medical procedures to be clinically accepted, it is critical from a patient care, safety, and regulatory perspective to certify the correctness and effectiveness of the planning algorithms involved in procedure automation. In this paper, we take an important step toward creating a certifiable optimal planner for steerable needles. We present an efficient, resolution-complete motion planner for steerable needles based on a novel adaptation of multi-resolution planning. This is the first motion planner for steerable needles that guarantees to compute in finite time an obstacle-avoiding plan (or notify the user that no such plan exists), under clinically appropriate assumptions. Based on this planner, we then develop the first resolution-optimal motion planner for steerable needles that further provides theoretical guarantees on the quality of the computed motion plan, that is, global optimality, in finite time. Compared to state-of-the-art steerable needle motion planners, we demonstrate with clinically realistic simulations that our planners not only provide theoretical guarantees but also have higher success rates, have lower computation times, and result in higher quality plans. 

Steerable needles are capable of accurately targeting difficult-to-reach clinical sites in the body. By bending around sensitive anatomical structures, steerable needles have the potential to reduce the invasiveness of many medical procedures. However, inserting these needles with curved trajectories increases the risk of tissue damage due to perpendicular forces exerted on the surrounding tissue by the needle’s shaft, potentially resulting in lateral shearing through tissue. Such forces can cause significant tissue damage, negatively affecting patient outcomes. In this work, we derive a tissue and needle force model based on a Cosserat string formulation, which describes the normal forces and frictional forces along the shaft as a function of the planned needle path, friction model and parameters, and tip piercing force. We propose this new force model and associated cost function as a safer and more clinically relevant metric than those currently used in motion planning for steerable needles. We fit and validate our model through physical needle robot experiments in a gel phantom. We use this force model to define a bottleneck cost function for motion planning and evaluate it against the commonly used path-length cost function in hundreds of randomly generated three-dimensional (3D) environments. Plans generated with our force-based cost show a 62% reduction in the peak modeled tissue force with only a 0.07% increase in length on average compared to using the path-length cost in planning. Additionally, we demonstrate planning with our force-based cost function in a lung tumor biopsy scenario from a segmented computed tomography (CT) scan. By directly minimizing the modeled needle-to-tissue force, our method may reduce patient risk and improve medical outcomes from steerable needle interventions. 

Inspection planning, the task of planning motions for a robot that enable it to inspect a set of points of interest, has applications in domains such as industrial, field, and medical robotics. Inspection planning can be computationally challenging, as the search space over motion plans grows exponentially with the number of points of interest to inspect. We propose a novel method, Incremental Random Inspection-roadmap Search (IRIS), that computes inspection plans whose length and set of successfully inspected points asymptotically converge to those of an optimal inspection plan. IRIS incrementally densifies a motion-planning roadmap using a sampling-based algorithm and performs efficient near-optimal graph search over the resulting roadmap as it is generated. We prove the resulting algorithm is asymptotically optimal under very general assumptions about the robot and the environment. We demonstrate IRIS’s efficacy on a simulated inspection task with a planar five DOF manipulator, on a simulated bridge inspection task with an Unmanned Aerial Vehicle (UAV), and on a medical endoscopic inspection task for a continuum parallel surgical robot in cluttered human anatomy. In all these systems IRIS computes higher-quality inspection plans orders of magnitudes faster than a prior state-of-the-art method. 

The inspection-planning problem calls for computing motions for a robot that allow it to inspect a set of points of interest (POIs) while considering plan quality (e.g., plan length). This problem has applications across many domains where robots can help with inspection, including infrastructure maintenance, construction, and surgery. Incremental Random Inspection-roadmap Search (IRIS) is an asymptotically-optimal inspection planner that was shown to compute higher-quality inspection plans orders of magnitudes faster than the prior state-of-the-art method. In this paper, we significantly accelerate the performance of IRIS to broaden its applicability to more challenging real-world applications. A key computational challenge that IRIS faces is effectively searching roadmaps for inspection plans—a procedure that dominates its running time. In this work, we show how to incorporate lazy edge-evaluation techniques into IRIS’s search algorithm and how to reuse search efforts when a roadmap undergoes local changes. These enhancements, which do not compromise IRIS’s asymptotic optimality, enable us to compute inspection plans much faster than the original IRIS. We apply IRIS with the enhancements to simulated bridge inspection and surgical inspection tasks and show that our new algorithm for some scenarios can compute similar-quality inspection plans 570× faster than prior work.