An integrated multi-population genetic algorithm for multi-vehicle task assignment in a drift field

This paper investigates the task assignment problem for a team of autonomous aerial/marine vehicles driven by constant thrust and maneuvering in a planar lateral drift field. The aim is to minimize the total traveling time in order to guide the vehicles to deliver a number of customized sensors to a set of target points with different sensor demands in the drift field. To solve the problem, we consider together navigation strategies and target assignment algorithms; the former minimizes the traveling time between two given locations in the drift field and the latter allocates a sequence of target locations to each vehicle. We first consider the effect of the weight of the carried sensors on the speed of each vehicle, and construct a sufficient condition to guarantee that the whole operation environment is reachable for the vehicles. Then from optimal control principles, time-optimal path planning is carried out to navigate each vehicle from an initial position to its given target location. Most importantly, to assign the targets to the vehicles, we combine the virtual coding strategy, multiple offspring method, intermarriage crossover strategy, and the tabu search mechanism to obtain a co-evolutionary multi-population genetic algorithm, short-named CMGA. Simulations on sensor delivery scenarios in both fixed and time-varying drift fields are shown to highlight the satisfying performances of the proposed approach against popular greedy algorithms

Efficient Routing for Precedence-Constrained Package Delivery for Heterogeneous Vehicles

This paper studies the precedence-constrained task assignment problem for a team of heterogeneous vehicles to deliver packages to a set of dispersed customers subject to precedence constraints that specify which customers need to be visited before which other customers. A truck and a micro drone with complementary capabilities are employed where the truck is restricted to travel in a street network and the micro drone, restricted by its loading capacity and operation range, can fly from the truck to perform the last-mile package deliveries. The objective is to minimize the time to serve all the customers respecting every precedence constraint. The problem is shown to be NP-hard, and a lower bound on the optimal time to serve all the customers is constructed by using tools from graph theory. Then, integrating with a topological sorting technique, several heuristic task assignment algorithms are proposed to solve the task assignment problem. Numerical simulations show the superior performances of the proposed algorithms compared with popular genetic algorithms. Note to Practitioners - This paper presents several task assignment algorithms for the precedence-constrained package delivery for the team of a truck and a micro drone. The truck can carry the drone moving in a street network, while the drone completes the last-mile package deliveries. The practical contributions of this paper are fourfold. First, the precedence constraints on the ordering of the customers to be served are considered, which enables complex logistic scheduling for customers prioritized according to their urgency or importance. Second, the package delivery optimization problem is shown to be NP-hard, which clearly shows the need for creative approximation algorithms to solve the problem. Third, the constructed lower bound on the optimal time to serve all the customers helps to clarify for practitioners the limiting performance of a feasible solution. Fourth, the proposed task assignment algorithms are efficient and can be adapted for real scenarios

A Path Planning Algorithm for a Dynamic Environment Based on Proper Generalized Decomposition

[EN] A necessity in the design of a path planning algorithm is to account for the environment. If the movement of the mobile robot is through a dynamic environment, the algorithm needs to include the main constraint: real-time collision avoidance. This kind of problem has been studied by different researchers suggesting different techniques to solve the problem of how to design a trajectory of a mobile robot avoiding collisions with dynamic obstacles. One of these algorithms is the artificial potential field (APF), proposed by O. Khatib in 1986, where a set of an artificial potential field is generated to attract the mobile robot to the goal and to repel the obstacles. This is one of the best options to obtain the trajectory of a mobile robot in real-time (RT). However, the main disadvantage is the presence of deadlocks. The mobile robot can be trapped in one of the local minima. In 1988, J.F. Canny suggested an alternative solution using harmonic functions satisfying the Laplace partial differential equation. When this article appeared, it was nearly impossible to apply this algorithm to RT applications. Years later a novel technique called proper generalized decomposition (PGD) appeared to solve partial differential equations, including parameters, the main appeal being that the solution is obtained once in life, including all the possible parameters. Our previous work, published in 2018, was the first approach to study the possibility of applying the PGD to designing a path planning alternative to the algorithms that nowadays exist. The target of this work is to improve our first approach while including dynamic obstacles as extra parameters.This research was funded by the GVA/2019/124 grant from Generalitat Valenciana and by the RTI2018-093521-B-C32 grant from the Ministerio de Ciencia, Innovacion y Universidades.Falcó, A.; Hilario, L.; Montés, N.; Mora, MC.; Nadal, E. (2020). A Path Planning Algorithm for a Dynamic Environment Based on Proper Generalized Decomposition. Mathematics. 8(12):1-11. https://doi.org/10.3390/math8122245S111812Gonzalez, D., Perez, J., Milanes, V., & Nashashibi, F. (2016). A Review of Motion Planning Techniques for Automated Vehicles. IEEE Transactions on Intelligent Transportation Systems, 17(4), 1135-1145. doi:10.1109/tits.2015.2498841Rimon, E., & Koditschek, D. E. (1992). Exact robot navigation using artificial potential functions. IEEE Transactions on Robotics and Automation, 8(5), 501-518. doi:10.1109/70.163777Khatib, O. (1986). Real-Time Obstacle Avoidance for Manipulators and Mobile Robots. The International Journal of Robotics Research, 5(1), 90-98. doi:10.1177/027836498600500106Kim, J.-O., & Khosla, P. K. (1992). Real-time obstacle avoidance using harmonic potential functions. IEEE Transactions on Robotics and Automation, 8(3), 338-349. doi:10.1109/70.143352Connolly, C. I., & Grupen, R. A. (1993). The applications of harmonic functions to robotics. Journal of Robotic Systems, 10(7), 931-946. doi:10.1002/rob.4620100704Garrido, S., Moreno, L., Blanco, D., & Martín Monar, F. (2009). Robotic Motion Using Harmonic Functions and Finite Elements. Journal of Intelligent and Robotic Systems, 59(1), 57-73. doi:10.1007/s10846-009-9381-3Bai, X., Yan, W., Cao, M., & Xue, D. (2019). Distributed multi‐vehicle task assignment in a time‐invariant drift field with obstacles. IET Control Theory & Applications, 13(17), 2886-2893. doi:10.1049/iet-cta.2018.6125Bai, X., Yan, W., Ge, S. S., & Cao, M. (2018). An integrated multi-population genetic algorithm for multi-vehicle task assignment in a drift field. Information Sciences, 453, 227-238. doi:10.1016/j.ins.2018.04.044Falcó, A., & Nouy, A. (2011). Proper generalized decomposition for nonlinear convex problems in tensor Banach spaces. Numerische Mathematik, 121(3), 503-530. doi:10.1007/s00211-011-0437-5Chinesta, F., Leygue, A., Bordeu, F., Aguado, J. V., Cueto, E., Gonzalez, D., … Huerta, A. (2013). PGD-Based Computational Vademecum for Efficient Design, Optimization and Control. Archives of Computational Methods in Engineering, 20(1), 31-59. doi:10.1007/s11831-013-9080-xFalcó, A., Montés, N., Chinesta, F., Hilario, L., & Mora, M. C. (2018). On the Existence of a Progressive Variational Vademecum based on the Proper Generalized Decomposition for a Class of Elliptic Parameterized Problems. Journal of Computational and Applied Mathematics, 330, 1093-1107. doi:10.1016/j.cam.2017.08.007Domenech, L., Falcó, A., García, V., & Sánchez, F. (2016). Towards a 2.5D geometric model in mold filling simulation. Journal of Computational and Applied Mathematics, 291, 183-196. doi:10.1016/j.cam.2015.02.043Falcó, A., & Nouy, A. (2011). A Proper Generalized Decomposition for the solution of elliptic problems in abstract form by using a functional Eckart–Young approach. Journal of Mathematical Analysis and Applications, 376(2), 469-480. doi:10.1016/j.jmaa.2010.12.003Falcó, A., & Hackbusch, W. (2012). On Minimal Subspaces in Tensor Representations. Foundations of Computational Mathematics, 12(6), 765-803. doi:10.1007/s10208-012-9136-6Canuto, C., & Urban, K. (2005). Adaptive Optimization of Convex Functionals in Banach Spaces. SIAM Journal on Numerical Analysis, 42(5), 2043-2075. doi:10.1137/s0036142903429730Ammar, A., Chinesta, F., & Falcó, A. (2010). On the Convergence of a Greedy Rank-One Update Algorithm for a Class of Linear Systems. Archives of Computational Methods in Engineering, 17(4), 473-486. doi:10.1007/s11831-010-9048-

Combining motion planning with social reward sources for collaborative human-robot navigation task design

Across the human history, teamwork is one of the main pillars sustaining civilizations and technology development. In consequence, as the world embraces omatization, human-robot collaboration arises naturally as a cornerstone. This applies to a huge spectrum of tasks, most of them involving navigation. As a result, tackling pure collaborative navigation tasks can be a good first foothold for roboticists in this enterprise. In this thesis, we define a useful framework for knowledge representation in human-robot collaborative navigation tasks and propose a first solution to the human-robot collaborative search task. After validating the model, two derived projects tackling its main weakness are introduced: the compilation of a human search dataset and the implementation of a multi-agent planner for human-robot navigatio