The multi-objective coverage control problem requires a robot swarm to collaboratively provide sensor coverage to multiple heterogeneous importance density fields (IDFs) simultaneously. We pose this as an optimization problem with constraints and study two different formulations: (1) Fair coverage, where we minimize the maximum coverage cost for any field, promoting equitable resource distribution among all fields; and (2) Constrained coverage, where each field must be covered below a certain cost threshold, ensuring that critical areas receive adequate coverage according to predefined importance levels. We study the decentralized setting where robots have limited communication and local sensing capabilities, making the system more realistic, scalable, and robust. Given the complexity, we propose a novel decentralized constrained learning approach that combines primal-dual optimization with a Learnable Perception-Action-Communication (LPAC) neural network architecture. We show that the Lagrangian of the dual problem can be reformulated as a linear combination of the IDFs, enabling the LPAC policy to serve as a primal solver. We empirically demonstrate that the proposed method (i) significantly outperforms state-of-the-art decentralized controllers by 30% on average in terms of coverage cost, (ii) transfers well to larger environments with more robots, and (iii) is scalable in the number of IDFs and robots in the swarm.

Coverage control is the problem of navigating a robot swarm to collaboratively monitor features or a phenomenon of interest not knowna priori. The problem is challenging in decentralized settings with robots that have limited communication and sensing capabilities. We propose a learnable Perception-Action-Communication (LPAC) architecture for the problem, wherein a convolutional neural network (CNN) processes localized perception; a graph neural network (GNN) facilitates robot communications; finally, a shallow multi-layer perceptron (MLP) computes robot actions. The GNN enables collaboration in the robot swarm by computingwhatinformation to communicate with nearby robots andhowto incorporate received information. Evaluations show that the LPAC models—trained using imitation learning—outperform standard decentralized and centralized coverage control algorithms. The learned policy generalizes to environments different from the training dataset, transfers to larger environments with more robots, and is robust to noisy position estimates. The results indicate the suitability of LPAC architectures for decentralized navigation in robot swarms to achieve collaborative behavior.

The line coverage problem involves finding efficient routes for the coverage of linear features by one or more resource-constrained robots. Linear features model environments such as road networks, power lines, and oil and gas pipelines. Two modes of travel are defined for robots: servicing and deadheading. A robot services a feature if it performs task-specific actions, such as taking images, as it traverses the feature; otherwise, it is deadheading. Traversing the environment incurs costs (e.g., travel time) and resource demands (e.g., battery life). Servicing and deadheading can have different cost and demand functions, which can be direction dependent. The environment is modeled as a graph, and an integer linear program is provided. As the problem is NP-hard, we design a fast and efficient heuristic algorithm, Merge-Embed-Merge (MEM). Exploiting the constructive property of the MEM algorithm, algorithms for line coverage of large graphs with multiple depots are developed. Furthermore, turning costs and nonholonomic constraints are efficiently incorporated into the algorithm. The algorithms are benchmarked on 100 road networks and demonstrated in experiments with aerial robots.

We propose a new formulation for the multi-robot task planning and allocation problem that incorporates (a) precedence relationships between tasks; (b) coordination for tasks allowing multiple robots to achieve increased efficiency; and (c) cooperation through the formation of robot coalitions for tasks that cannot be performed by individual robots alone. In our formulation, the tasks and the relationships between the tasks are specified by a task graph. We define a set of reward functions over the task graph's nodes and edges. These functions model the effect of robot coalition size on task performance while incorporating the influence of one task's performance on a dependent task. Solving this problem optimally is NP-hard. However, using the task graph formulation allows us to leverage min-cost network flow approaches to obtain approximate solutions efficiently. Additionally, we explore a mixed integer programming approach, which gives optimal solutions for small instances of the problem but is computationally expensive. We also develop a greedy heuristic algorithm as a baseline. Our modeling and solution approaches result in task plans that leverage task precedence relationships and robot coordination and cooperation to achieve high mission performance, even in large missions with many agents.

Abstract Line coverage is the task of servicing a given set of one‐dimensional features in an environment. It is important for the inspection of linear infrastructure such as road networks, power lines, and oil and gas pipelines. This paper addresses the single robot line coverage problem for aerial and ground robots by modeling it as an optimization problem on a graph. The problem belongs to the broad class of arc routing problems and is closely related to the rural postman problem (RPP) on asymmetric graphs. The paper presents an integer linear programming formulation with proofs of correctness. Using the minimum cost flow problem, we develop approximation algorithms with guarantees on the solution quality. These guarantees also improve the existing results for the asymmetric RPP. The main algorithm partitions the problem into three cases based on the structure of therequired graph, that is, the graph induced by the features that require servicing. We evaluate our algorithms on road networks from the 50 most populous cities in the world, consisting of up to 730 road segments. The algorithms, augmented with improvement heuristics, run within 3 s and generate solutions that are within 10% of the optimum. We experimentally demonstrate our algorithms with commercial UAVs on the UNC Charlotte campus road network.

The line coverage problem is the coverage of linear environment features (e.g., road networks, power lines), modeled as 1D segments, by one or more robots while respecting resource constraints (e.g., battery capacity, flight time) for each of the robots. The robots incur direction dependent costs and resource demands as they traverse the edges. We treat the line coverage problem as an optimization problem, with the total cost of the tours as the objective, by formulating it as a mixed integer linear program (MILP). The line coverage problem is NP-hard and hence we develop a heuristic algorithm, Merge-Embed-Merge (MEM). We compare it against the optimal MILP approach and a baseline heuristic algorithm, Extended Path Scanning. We show the MEM algorithm is fast and suitable for real-time applications. To tackle large-scale problems, our approach performs graph simplification and graph partitioning, followed by robot tour generation for each of the partitioned subgraphs. We demonstrate our approach on a large graph with 4,658 edges and 4,504 vertices that represents an urban region of about 16 sq. km. We compare the performance of the algorithms on several small road networks and experimentally demonstrate the approach using UAVs on the UNC Charlotte campus road network.

This paper presents algorithms to simultaneously compute the optimal assignments and formation parameters for a team of robots from a given initial formation to a variable goal formation (where the shape of the goal formation is given, and its scale and location parameters must be optimized). We assume the$n$robots are identical spheres. We use the sum of squared travel distances as the objective function to be minimized, which also ensures that the trajectories are collision free. We show that this assignment with variable goal formation problem can be transformed to a linear sum assignment problem (LSAP) with pseudo costs that we establish are independent of the formation parameters. The transformed problem can then be solved using the Hungarian algorithm in O (n3) time. Thus the assignment problem with variable goal formations using this new approach has the same O (n3) time complexity as the standard assignment problem with fixed goal formations. Results from simulations on 200 and 600 robots are presented to show the algorithm is sufficiently fast for practical applications.

Simultaneous localization and planning (SLAP) is a crucial ability for an autonomous robot operating under uncertainty. In its most general form, SLAP induces a continuous partially observable Markov decision process (POMDP), which needs to be repeatedly solved online. This paper addresses this problem and proposes a dynamic replanning scheme in belief space. The underlying POMDP, which is continuous in state, action, and observation space, is approximated offline via sampling-based methods, but operates in a replanning loop online to admit local improvements to the coarse offline policy. This construct enables the proposed method to combat changing environments and large localization errors, even when the change alters the homotopy class of the optimal trajectory. It further outperforms the state-of-the-art Feedback-based Information RoadMap (FIRM) method by eliminating unnecessary stabilization steps. Applying belief space planning to physical systems brings with it a plethora of challenges. A key focus of this paper is to implement the proposed planner on a physical robot and show the SLAP solution performance under uncertainty, in changing environments and in the presence of large disturbances, such as a kidnapped robot situation.

The SLAM problem is known to have a special property that when robot orientation is known, estimating the history of robot poses and feature locations can be posed as a standard linear least squares problem. In this work, we develop a SLAM framework that uses relative feature-to-feature measurements to exploit this structural property of SLAM. Relative feature measurements are used to pose a linear estimation problem for pose-to-pose orientation constraints. This is followed by solving an iterative non-linear on-manifold optimization problem to compute the maximum likelihood estimate for robot orientation given relative rotation constraints. Once the robot orientation is computed, we solve a linear problem for robot position and map estimation. Our approach reduces the computational complexity of non-linear optimization by posing a smaller optimization problem as compared to standard graph-based methods for feature-based SLAM. Further, empirical results show our method avoids catastrophic failures that arise in existing methods due to using odometery as an initial guess for non-linear optimization, while its accuracy degrades gracefully as sensor noise is increased. We demonstrate our method through extensive simulations and comparisons with an existing state-of-the-art solver.

Motion planning in belief space (under motion and sensing uncertainty) is a challenging problem due to the computational intractability of its exact solution. The Feedback-based Information RoadMap (FIRM) framework made an important theoretical step toward enabling roadmap-based planning in belief space and provided a computationally tractable version of belief space planning. However, there are still challenges in applying belief space planners to physical systems, such as the discrepancy between computational models and real physical models. In this paper, we propose a dynamic replanning scheme in belief space to address such challenges. Moreover, we present techniques to cope with changes in the environment (e.g., changes in the obstacle map), as well as unforeseen large deviations in the robot's location (e.g., the kidnapped robot problem). We then utilize these techniques to implement the first online replanning scheme in belief space on a physical mobile robot that is robust to changes in the environment and large disturbances. This method demonstrates that belief space planning is a practical tool for robot motion planning.