Decentralized multi-robot exploration under low-bandwidth communications

In this work, we propose a route planning strategy for heterogeneous mobile robots in Precision Agriculture (PA) settings. Given a set of agricultural tasks to be performed at specific locations, we formulate a multi-Steiner Traveling Salesman Problem (TSP) to define the optimal assignment of these tasks to the robots as well as the respective optimal paths to be followed. The optimality criterion aims to minimize the total time required to execute all the tasks, as well as the cumulative execution times of the robots. Costs for travelling from one location to another, for maneuvering and for executing the task as well as limited energy capacity of the robots are considered. In addition, we propose a sub-optimal formulation to mitigate the computational complexity by leveraging the fact that generally in PA settings only a few locations require agricultural tasks in a certain period of interest compared to all possible locations in the field. A formal analysis of the optimality gap between the optimal and the sub-optimal formulations is provided. The effectiveness of the approach is validated in a simulated orchard where three heterogeneous aerial vehicles perform inspection tasks. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —This paper aims at providing an efficient solution to PA needs by deploying a team of robots able to perform agricultural tasks at given locations in large-scale orchards. In particular, a novel general optimization problem is proposed that, given a set of mobile and possibly heterogeneous robots and a set of agricultural tasks to carry out, defines the assignment of these tasks to the robots as well as the routes to follow, while minimizing the total and the cumulative execution times of the robots. Existing approaches for route optimization in PA generally involves complete coverage of the field by one or multiple robots and do not account for maneuvering costs with general layouts of the field. We consider costs for travelling from one location to another, for executing the task and for maneuvering without any restriction on the layout of the plants as well as we take into account the limited energy capacity of the robots. We also provide a sub-optimal formulation which reduces the computational burden by relaxing the optimization of the maneuvering costs at the locations where agricultural tasks are carried out and formally derive the optimality gap. The proposed approach is flexible and can be easily adapted to any PA setting involving multiple mobile robots that are required to accomplish given tasks in an area of interest. We validate its effectiveness in a realistic simulated setup composed of three heterogeneous aerial vehicles performing inspection tasks. In future research, we aim to design algorithms to solve the proposed optimization problems in an efficient manner as well as to validate the formulations on real-world robotic platforms.

The Traveling Salesman Problem (TSP) is a well-known combinatorial optimization problem that has various implications in a variety of industries. Even the purest formulation of TSP has applications on from logistics routes to microchip manufacturing, unexpectedly, it can be used on DNA sequencing with slight modification as a sub-problem. In this paper, two versions of TSP were studied, a classical TSP and the TSP containing traffic congestion data. Two state-of-the-art solution methods were used, Ant Colony Optimization (ACO) and Beam-ACO. These algorithms were hybridized with 2-Opt local search and their performances compared on the same benchmark instances. The experimental results show the efficiency of Beam-ACO compared to ACO.

The traveling salesman problem (TSP) can be mapped to the problem of optimal component placement for printed circuit boards (PCBs). An innovation that consists of adapting a neural network formulation of TSP to multiobjective component placement on the basis of wire-length criteria, as well as thermal reliability, is described. The author shows that the mathematical formulation of the Hopfield energy function for TSP is identical to the energy for the placement problem except for the cost (distance) function. The Hopfield cost function can be modified by introducing terms to model the wire-length and thermal reliability for alternative component placements. This approach was tested by coding a neural network simulator and comparing the quality of the resulting placement with standard methods. The positive results of that testing, the potential for a dramatic improvement in the time needed to calculate such optimal placements, and the natural way of extending the formulation to include more design criteria lead to a confidence that similar approaches will have a significant impact on multiobjective design.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Summary form only given, as follows. A stochastic neural model is proposed for the solution of hard combinatorial optimization problems, inspired by the Hopfield-Tank model and the stochastic search ability of simulated annealing. The authors start with a discrete-time algorithm for the simulation of a Hopfield-Tank network and modify it through the incorporation of probabilistic decisions which allow energy increases at each time step. The algorithm has been tested on the traveling salesman problem (TSP), and the results are encouraging. For these tests the authors used a formulation of TSP which ensures that every stable state of the network corresponds to a feasible TSP tour. From the simulation algorithm they then extract some possible foundations for the formalization of their model. >

It is well-known that if a customer follows a longer path while shopping then the expected value of his/her purchased amount is increased; therefore the sale amount of the supermarket can be increased. This study deals with a new problem: how to re-layout a supermarket the impulsive purchases of the average customer are maximized. Supermarket is a shop of limited size and is definitely smaller than the hypermarket. It is assumed that it is located in a living area and customers know its layout well. In many countries, there are plenty of shops like that. In a case study 27 clusters of customers are defined based on 13,300 real buying. To assume that actors behave in a rational way, is traditional in analysis of economic problems. Rationality means in that case that customers choose the shortest possible path according to their a priori purchase plan. Thus, traveling salesman problem (TSP) can be used to simulate the customer’s shopping path. Dantzig–Fulkerson–Johnson formulation of TSP is used to maximize the shortest traveled path of each customer type by rearranging the items of the supermarket as a max–min problem. The computational experiences on the case study show that the total distance is increased in the new layout proposed by the model.

Traveling salesman problem (TSP) is a typical NP-hard problem. How to design an effective and efficient algorithm to solve TSP within a limited time is of great theoretical significance and practical significance. This paper studies how the greedy search improves simulated annealing algorithm for solving large-scale TSP. First, the TSP formulation is presented. The aim of the TSP is to structure a shortest route for one traveling salesman starting from a certain location, through all the given cities and finally returning to the original city. Second, a simple simulated annealing (SA) algorithm is developed for the TSP. The orthogonal test is employed to optimize the key parameters. Third, a group of benchmark instances are tested to verify the performance of the SA. The experimental results show that for the small-scale and medium-scale instances the simply SA can search the optimal solution easily. Finally, to solve the large-scale instance, we integrate a greedy search to improve SA. A greedy coefficient is proposed to control the balance of the exploration and the exploitation. Different levels of the greedy coefficient are tested and discussed. The results show that the greedy search can improve SA greatly with a suitable greedy coefficient.

The travelling salesman problem (TSP) is one of combinatorial optimization problems of huge importance to practical applications. However, the TSP in its “pure” form may lack some essential issues for a decision maker—e.g., time-dependent travelling conditions. Among those shortcomings, there is also a lack of possibility of not visiting some nodes in the network—e.g., thanks to the existence of some more cost-efficient means of transportation. In this article, an extension of the TSP in which some nodes can be skipped at the cost of penalties for skipping those nodes is presented under a new name and in a new mathematical formulation. Such an extension can be applied as a model for transportation cost reduction due to the possibility of outsourcing deliveries to some nodes in a TSP route. An integer linear programming formulation of such a problem based on the Gavish–Graves-flow-based TSP formulation is introduced. This formulation makes it possible to solve the considered problem by using any integer linear programming optimization software. Numerical examples and opportunities for further research are presented.

The Time Dependent Traveling Salesman Problem (TDTSP) is a generalization of the classical Traveling Salesman Problem (TSP), where arc costs depend on their position in the tour with respect to the source node. While TSP instances with thousands of vertices can be solved routinely, there are very challenging TDTSP instances with less than 60 vertices. In this work, we study the polytope associated to the TDTSP formulation by Picard and Queyranne, which can be viewed as an extended formulation of the TSP. We determine the dimension of the TDTSP polytope and identify several families of facet defining cuts. In particular, we also show that some facet defining cuts for the usual Asymmetric TSP formulation define low dimensional faces of the TDTSP formulation and give a way to lift them. We obtain good computational results with a branch-cut-and-price algorithm using the new cuts, solving several instances of reasonable size at the root node.

In practice, solving realistically sized combinatorial optimization problems to optimality is often too time-consuming to be affordable; therefore, heuristics are typically implemented within most applications software. A specific category of heuristics has attracted considerable attention, namely local search methods. Most local search methods are primal in nature; that is, they start the search with a feasible solution and explore the feasible space for better feasible solutions. In this research, we propose a dual local search method and customize it to solve the traveling salesman problem (TSP); that is, a search method that starts with an infeasible solution, explores the dual space—each time reducing infeasibility, and lands in the primal space to deliver a feasible solution. The proposed design aims to replicate the designs of optimal solution methodologies in a heuristic way. To be more specific, we solve a combinatorial relaxation of a TSP formulation, design a neighborhood structure to repair such an infeasible starting solution, and improve components of intermediate dual solutions locally. Sample-based evidence along with statistically significant t-tests support the superiority of this dual design compared to its primal design counterpart.

Given an instance of the Traveling Salesman Problem (TSP), a reasonable way to get a lower bound on the optimal answer is to solve a linear programming relaxation of an integer programming formulation of the problem. These linear programs typically have an exponential number of constraints, but in theory they can be solved efficiently with the ellipsoid method as long as we have an algorithm that can take a solution and either declare it feasible or find a violated constraint. In practice, it is often the case that many constraints are violated, which raises the question of how to choose among them so as to improve performance. For the simplest TSP formulation it is possible to efficiently find all the violated constraints, which gives us a good chance to try to answer this question empirically. Looking at random two dimensional Euclidean instances and the large instances from TSPLIB, we ran experiments to evaluate several strategies for picking among the violated constraints. We found some information about which constraints to prefer, which resulted in modest gains, but were unable to get large improvements in performance.

Given an instance of the Traveling Salesman Problem (TSP), a reasonable way to get a lower bound on the optimal answer is to solve a linear programming relaxation of an integer programming formulation of the problem. These linear programs typically have an exponential number of constraints, but in theory they can be solved efficiently with the ellipsoid method as long as we have an algorithm that can take a solution and either declare it feasible or find a violated constraint. In practice, it is often the case that many constraints are violated, which raises the question of how to choose among them so as to improve performance. For the simplest TSP formulation it is possible to efficiently find all the violated constraints, which gives us a good chance to try to answer this question empirically. Looking at random two dimensional Euclidean instances and the large instances from TSPLIB, we ran experiments to evaluate several strategies for picking among the violated constraints. We found some information about which constraints to prefer, which resulted in modest gains, but were unable to get large improvements in performance.

This study introduces a hierarchical reinforcement learning (RL) framework tailored to object manipulation tasks by quadrupedal robots, emphasizing their real-world deployment. The proposed approach adopts a sensor-driven control structure capable of addressing challenges in dense and cluttered environments filled with walls and obstacles. A novel reward function is central to the method, incorporating sensor-based obstacle observations to optimize the decision-making. This design minimizes the computational demands while maintaining adaptability and robust functionality. Simulated trials conducted in NVIDIA Isaac Sim, utilizing ANYbotics quadrupedal robots, demonstrated a high manipulation accuracy, with a mean positioning error of 11 cm across object-target distances of up to 10 m. Furthermore, the RL framework effectively integrates path planning in complex environments, achieving energy-efficient and stable operations. These findings establish the framework as a promising approach for advanced robotics requiring versatility, efficiency, and practical deployability.

To solve the problem that the walking jitter of quadruped robots leads to the degradation of clarity of visual imaging, a quadruped robot visual imaging jitter compensation algorithm based on the theory of walking jitter is proposed. The D-H coordinate transformation method is used to establish the coordinate system of each joint of the leg. The kinetic equations of the leg are derived from the relationship between the rotational velocity and the moment of the leg joint, and the kinetic equilibrium equations of the quadruped robot body are established based on the spatial moment equilibrium theorem; the spring-mass model of the leg of the quadruped robot is used to construct the kinetic equations of the leg jittering, and the kinetic equations of the body jittering are derived using the moment equilibrium condition of the body center of gravity position and under the effect of the leg and body jitter to obtain the visual imaging device jitter quantity; finally, the tremor quantity is combined with the jitter quantity and rotation matrix to derive the walking jitter mathematical model of the quadruped robot visual imager, and the jitter compensation algorithm of quadruped robot visual imager is verified. The experimental results show that compared with the traditional Wiener filter algorithm for jitter compensation and the BP neural network jitter compensation algorithm, this algorithm improves the visual imaging by 10.8% and 3.3% in the two evaluation indexes of peak signal-to-noise ratio and structural similarity, respectively, and the de-jittering effect is better.

A unique integer linear programming formulation is proposed to define a Hamiltonian tour in which the cost between a node pair is determined by the number of nodes between each pair on the tour. In addition, a node separation requirement may be conditional on other node separations. Properties of this new traveling salesman problem formulation are discussed, along with an a priori solution to the probabilistic traveling salesman problem with equal node coverage probability as a linear programming alternative to the probabilistic programming method in the literature. A linear programming-based heuristic is proposed and numerically tested.

The use of Unmanned Aerial Vehicles (UAVs) in different inspection tasks is increasing. This technology reduces inspection costs and collects high quality data of distinct structures, including areas that are not easily accessible by human operators. However, the reduced energy available on the UAVs limits their flight endurance. To increase the autonomy of a single flight, it is important to optimize the path to be performed by the UAV, in terms of energy loss. Therefore, this work presents a novel formulation of the Travelling Salesman Problem (TSP) and a path planning algorithm that uses a UAV energy model to solve this optimization problem. The novel TSP formulation is defined as Asymmetric Travelling Salesman Problem with Precedence Loss (ATSP-PL), where the cost of moving the UAV depends on the previous position. The energy model relates each UAV movement with its energy consumption, while the path planning algorithm is focused on minimizing the energy loss of the UAV, ensuring that the structure is fully covered. The developed algorithm was tested in both simulated and real scenarios. The simulated experiments were performed with realistic models of wind turbines and a UAV, whereas the real experiments were performed with a real UAV and an illumination tower. The inspection paths generated presented improvements over 24% and 8%, when compared with other methods, for the simulated and real experiments, respectively, optimizing the energy consumption of the UAV.