Efficient planning of scarce resources in hospitals is a challenging task for which a large variety of Operations Research and Management Science approaches have been developed since the 1950s. While efficient planning of single resources such as operating rooms, beds, or specific types of staff can already lead to enormous efficiency gains, integrated planning of several resources has been shown to hold even greater potential, and a large number of integrated planning approaches have been presented in the literature over the past decades. This paper provides the first literature review that focuses specifically on the Operations Research and Management Science literature related to integrated planning of different resources in hospitals. We collect the relevant literature and analyze it regarding different aspects such as uncertainty modeling and the use of real-life data. Several cross comparisons reveal interesting insights concerning, e.g., relations between the modeling and solution methods used and the practical implementation of the approaches developed. Moreover, we provide a high-level taxonomy for classifying different resource-focused integration approaches and point out gaps in the literature as well as promising directions for future research.

Methods for inverse kinematics computation and path planning of a three degree-of-freedom (DOF) manipulator using the algorithm for quantifier elimination based on Comprehensive Gr\"obner Systems (CGS), called CGS-QE method, are proposed. The first method for solving the inverse kinematics problem employs counting the real roots of a system of polynomial equations to verify the solution's existence. In the second method for trajectory planning of the manipulator, the use of CGS guarantees the existence of an inverse kinematics solution. Moreover, it makes the algorithm more efficient by preventing repeated computation of Gr\"obner basis. In the third method for path planning of the manipulator, for a path of the motion given as a function of a parameter, the CGS-QE method verifies the whole path's feasibility. Computational examples and an experiment are provided to illustrate the effectiveness of the proposed methods.

R2 is a novel online any-angle path planner that uses heuristic bug-based or ray casting approaches to find optimal paths in 2D maps with non-convex, polygonal obstacles. R2 is competitive to traditional free-space planners, finding paths quickly if queries have direct line-of-sight. On large sparse maps with few obstacle contours, which are likely to occur in practice, R2 outperforms free-space planners, and can be much faster than state-of-the-art free-space expansion planner Anya. On maps with many contours, Anya performs faster than R2. R2 is built on RayScan, introducing lazy-searches and a source-pledge counter to find successors optimistically on contiguous contours. The novel approach bypasses most successors on jagged contours to reduce expensive line-of-sight checks, therefore requiring no pre-processing to be a competitive online any-angle planner.

Abstract--Whereas dedicated scene representations are required for each different task in conventional robotic systems, this paper demonstrates that a unified representation can be used directly for multiple key tasks. We propose the Log-Gaussian Process Implicit Surface for Mapping, Odometry and Planning (Log-GPIS-MOP): a probabilistic framework for surface reconstruction, localisation and navigation based on a unified representation. Our framework applies a logarithmic transformation to a Gaussian Process Implicit Surface (GPIS) formulation to recover a global representation that accurately captures the Euclidean distance field with gradients and, at the same time, the implicit surface. By directly estimating the distance field and its gradient through Log-GPIS inference, the proposed incremental odometry technique computes the optimal alignment of an incoming frame and fuses it globally to produce a map. Concurrently, an optimisation-based planner computes a safe collision-free path using the same Log-GPIS surface representation. We validate the proposed framework on simulated and real datasets in 2D and 3D and benchmark against the state-of-the-art approaches. Our experiments show that Log-GPIS-MOP produces competitive results in sequential odometry, surface mapping and obstacle avoidance. Using the built map and the key objective of the mapping task is to reconstruct an accurate, estimated location, a path planner may produce collision-free dense and high-resolution map of the scene for, e.g., inspection paths for the robot to navigate safely. Path planning similarly requires dense information raises varying requirements leading to dedicated environment such as obstacle occupancy or closest distance to collision representations. The choice of scene representation strongly in order to avoid obstacles. As a unified representation for affects the performance of the localisation, mapping, and path multiple purposes, a feature-based representation such as a set planning tasks. Personal use of this material is permitted.

Planning is a pivotal ability of any intelligent system being developed for real-world applications. AI planning is concerned with researching and developing planning systems that automatically compute plans that satisfy some user objective. Identifying and understanding the relevant and realistic aspects that characterise real-world application domains are crucial to the development of AI planning systems. This provides guidance to knowledge engineers and software engineers in the process of designing, identifying, and categorising resources required for the development process. To the best of our knowledge, such support does not exist. We address this research gap by developing a conceptual framework that identifies and categorises the aspects of real-world planning domains in varying levels of granularity. Our framework provides not only a common terminology but also a comprehensive overview of a broad range of planning aspects exemplified using the domain of sustainable buildings as a prominent application domain of AI planning. The framework has the potential to impact the design, development, and applicability of AI planning systems in real-world application domains.

This paper presents a solution for the problem of optimal planning for a robot in a collaborative human-robot team, where the human supervisor is intermittently available to assist the robot in completing tasks more quickly. Specifically, we address the challenge of computing the fastest path between two configurations in an environment with time constraints on how long the robot can wait for assistance. To solve this problem, we propose a novel approach that utilizes the concepts of budget and critical departure times, which enables us to obtain optimal solutions while scaling to larger problem instances than existing methods. We demonstrate the effectiveness of our approach by comparing it with several baseline algorithms on a city road network and analyzing the quality of the solutions obtained. Our work contributes to the field of robot planning by addressing the critical issue of incorporating human assistance and environmental restrictions, which has significant implications for real-world applications.

The automatic inspection of surface defects is an important task for quality control in the computers, communications, and consumer electronics (3C) industry. Conventional devices for defect inspection (viz. line-scan sensors) have a limited field of view, thus, a robot-aided defect inspection system needs to scan the object from multiple viewpoints. Optimally selecting the robot's viewpoints and planning a path is regarded as coverage path planning (CPP), a problem that enables inspecting the object's complete surface while reducing the scanning time and avoiding misdetection of defects. However, the development of CPP strategies for robotic line scanners has not been sufficiently studied by researchers. To fill this gap in the literature, in this paper, we present a new approach for robotic line scanners to detect surface defects of 3C free-form objects automatically. Our proposed solution consists of generating a local path by a new hybrid region segmentation method and an adaptive planning algorithm to ensure the coverage of the complete object surface. An optimization method for the global path sequence is developed to maximize the scanning efficiency. To verify our proposed methodology, we conduct detailed simulation-based and experimental studies on various free-form workpieces, and compare its performance with a state-of-the-art solution. The reported results demonstrate the feasibility and effectiveness of our approach.

Many robotics applications benefit from being able to compute multiple locally optimal paths in a given configuration space. Examples include path planning for of tethered robots with cable-length constraints, systems involving cables, multi-robot topological exploration & coverage, and, congestion reduction for mobile robots navigation without inter-robot coordination. Existing paradigm is to use topological path planning methods that can provide optimal paths from distinct topological classes available in the underlying configuration space. However, these methods usually require non-trivial and non-universal geometrical constructions, which are prohibitively complex or expensive in 3 or higher dimensional configuration spaces with complex topology. Furthermore, topological methods are unable to distinguish between locally optimal paths that belong to the same topological class but are distinct because of genus-zero obstacles in 3D or due to high-cost or high-curvature regions. In this paper we propose an universal and generalized approach to multiple, locally-optimal path planning using the concept of a novel neighborhood-augmented graph, search-based planning in which can compute paths that are topo-geometrically distinct. This approach can find desired number of locally optimal paths in a wider variety of configuration spaces without requiring any complex pre-processing or geometric constructions. Unlike the existing topological methods, resulting optimal paths are not restricted to distinct topological classes, thus making the algorithm applicable to many other problems where locally optimal and geometrically distinct paths are of interest. We demonstrate the use of our algorithm to planning for shortest traversible paths for a tethered robot in 3D with cable-length constraint, and validate the results in simulations and real robot experimentation.

Motivated by a plethora of practical examples where bias is induced by automated-decision making algorithms, there has been strong recent interest in the design of fair algorithms. However, there is often a dichotomy between fairness and efficacy: fair algorithms may proffer low social welfare solutions whereas welfare optimizing algorithms may be very unfair. This issue is exemplified in the machine scheduling problem where, for $n$ jobs, the social welfare of any fair solution may be a factor $\Omega(n)$ worse than the optimal welfare. In this paper, we prove that this dichotomy between fairness and efficacy can be overcome if we allow for a negligible amount of bias: there exist algorithms that are both "almost perfectly fair" and have a constant factor efficacy ratio, that is, are guaranteed to output solutions that have social welfare within a constant factor of optimal welfare. Specifically, for any $\epsilon>0$, there exist mechanisms with efficacy ratio $\Theta(\frac{1}{\epsilon})$ and where no agent is more than an $\epsilon$ fraction worse off than they are in the fairest possible solution (given by an algorithm that does not use personal or type data). Moreover, these bicriteria guarantees are tight and apply to both the single machine case and the multiple machine case. The key to our results are the use of Pareto scheduling mechanisms. These mechanisms, by the judicious use of personal or type data, are able to exploit Pareto improvements that benefit every individual; such Pareto improvements would typically be forbidden by fair scheduling algorithms designed to satisfy standard statistical measures of group fairness. We anticipate this paradigm, the judicious use of personal data by a fair algorithm to greatly improve performance at the cost of negligible bias, has wider application.

We consider the problem of routing a team of energy-constrained Unmanned Aerial Vehicles (UAVs) to drop unmovable sensors for monitoring a task area in the presence of stochastic wind disturbances. In prior work on mobile sensor routing problems, sensors and their carrier are one integrated platform, and sensors are assumed to be able to take measurements at exactly desired locations. By contrast, airdropping the sensors onto the ground can introduce stochasticity in the landing locations of the sensors. We focus on addressing this stochasticity in sensor locations from the path-planning perspective. Specifically, we formulate the problem (Multi-UAV Sensor Drop) as a variant of the Submodular Team Orienteering Problem with one additional constraint on the number of sensors on each UAV. The objective is to maximize the Mutual Information between the phenomenon at Points of Interest (PoIs) and the measurements that sensors will take at stochastic locations. We show that such an objective is computationally expensive to evaluate. To tackle this challenge, we propose a surrogate objective with a closed-form expression based on the expected mean and expected covariance of the Gaussian Process. We propose a heuristic algorithm to solve the optimization problem with the surrogate objective. The formulation and the algorithms are validated through extensive simulations.