Smooth 3D Path Planning by Means of Multiobjective Optimization for Fixed-Wing UAVs

[EN] Demand for 3D planning and guidance algorithms is increasing due, in part, to the increase in unmanned vehicle-based applications. Traditionally, two-dimensional (2D) trajectory planning algorithms address the problem by using the approach of maintaining a constant altitude. Addressing the problem of path planning in a three-dimensional (3D) space implies more complex scenarios where maintaining altitude is not a valid approach. The work presented here implements an architecture for the generation of 3D flight paths for fixed-wing unmanned aerial vehicles (UAVs). The aim is to determine the feasible flight path by minimizing the turning effort, starting from a set of control points in 3D space, including the initial and final point. The trajectory generated takes into account the rotation and elevation constraints of the UAV. From the defined control points and the movement constraints of the UAV, a path is generated that combines the union of the control points by means of a set of rectilinear segments and spherical curves. However, this design methodology means that the problem does not have a single solution; in other words, there are infinite solutions for the generation of the final path. For this reason, a multiobjective optimization problem (MOP) is proposed with the aim of independently maximizing each of the turning radii of the path. Finally, to produce a complete results visualization of the MOP and the final 3D trajectory, the architecture was implemented in a simulation with Matlab/Simulink/flightGear.The authors would like to acknowledge the Spanish Ministerio de Ciencia, Innovacion y Universidades for providing funding through the project RTI2018-096904-B-I00 and the local administration Generalitat Valenciana through projects GV/2017/029 and AICO/2019/055. Franklin Samaniego thanks IFTH (Instituto de Fomento al Talento Humano) Ecuador (2015-AR2Q9209), for its sponsorship of this work.Samaniego, F.; Sanchís Saez, J.; Garcia-Nieto, S.; Simarro Fernández, R. (2020). Smooth 3D Path Planning by Means of Multiobjective Optimization for Fixed-Wing UAVs. Electronics. 9(1):1-23. https://doi.org/10.3390/electronics9010051S12391Kyriakidis, M., Happee, R., & de Winter, J. C. F. (2015). Public opinion on automated driving: Results of an international questionnaire among 5000 respondents. Transportation Research Part F: Traffic Psychology and Behaviour, 32, 127-140. doi:10.1016/j.trf.2015.04.014Münzer, S., Zimmer, H. D., Schwalm, M., Baus, J., & Aslan, I. (2006). Computer-assisted navigation and the acquisition of route and survey knowledge. Journal of Environmental Psychology, 26(4), 300-308. doi:10.1016/j.jenvp.2006.08.001Morales, Y., Kallakuri, N., Shinozawa, K., Miyashita, T., & Hagita, N. (2013). Human-comfortable navigation for an autonomous robotic wheelchair. 2013 IEEE/RSJ International Conference on Intelligent Robots and Systems. doi:10.1109/iros.2013.6696743Krotkov, E., & Hebert, M. (s. f.). Mapping and positioning for a prototype lunar rover. Proceedings of 1995 IEEE International Conference on Robotics and Automation. doi:10.1109/robot.1995.525697Rodriguez-Seda, E. J. (2014). Decentralized trajectory tracking with collision avoidance control for teams of unmanned vehicles with constant speed. 2014 American Control Conference. doi:10.1109/acc.2014.6859184Xiaoping Ren, & Zixing Cai. (2010). Kinematics model of unmanned driving vehicle. 2010 8th World Congress on Intelligent Control and Automation. doi:10.1109/wcica.2010.5554512Jun, J.-Y., Saut, J.-P., & Benamar, F. (2016). Pose estimation-based path planning for a tracked mobile robot traversing uneven terrains. Robotics and Autonomous Systems, 75, 325-339. doi:10.1016/j.robot.2015.09.014Li, Y., Ding, L., & Liu, G. (2016). Attitude-based dynamic and kinematic models for wheels of mobile robot on deformable slope. Robotics and Autonomous Systems, 75, 161-175. doi:10.1016/j.robot.2015.10.006Mekonnen, G., Kumar, S., & Pathak, P. M. (2016). Wireless hybrid visual servoing of omnidirectional wheeled mobile robots. Robotics and Autonomous Systems, 75, 450-462. doi:10.1016/j.robot.2015.08.008Xu, J., Wang, M., & Qiao, L. (2015). Dynamical sliding mode control for the trajectory tracking of underactuated unmanned underwater vehicles. Ocean Engineering, 105, 54-63. doi:10.1016/j.oceaneng.2015.06.022Gafurov, S. A., & Klochkov, E. V. (2015). Autonomous Unmanned Underwater Vehicles Development Tendencies. Procedia Engineering, 106, 141-148. doi:10.1016/j.proeng.2015.06.017Qi, X., & Cai, Z. (2018). Three-dimensional formation control based on nonlinear small gain method for multiple underactuated underwater vehicles. Ocean Engineering, 151, 105-114. doi:10.1016/j.oceaneng.2018.01.032Ramasamy, S., Sabatini, R., Gardi, A., & Liu, J. (2016). LIDAR obstacle warning and avoidance system for unmanned aerial vehicle sense-and-avoid. Aerospace Science and Technology, 55, 344-358. doi:10.1016/j.ast.2016.05.020Zhu, L., Cheng, X., & Yuan, F.-G. (2016). A 3D collision avoidance strategy for UAV with physical constraints. Measurement, 77, 40-49. doi:10.1016/j.measurement.2015.09.006Chee, K. Y., & Zhong, Z. W. (2013). Control, navigation and collision avoidance for an unmanned aerial vehicle. Sensors and Actuators A: Physical, 190, 66-76. doi:10.1016/j.sna.2012.11.017Courbon, J., Mezouar, Y., Guénard, N., & Martinet, P. (2010). Vision-based navigation of unmanned aerial vehicles. Control Engineering Practice, 18(7), 789-799. doi:10.1016/j.conengprac.2010.03.004Aguilar, W., & Morales, S. (2016). 3D Environment Mapping Using the Kinect V2 and Path Planning Based on RRT Algorithms. Electronics, 5(4), 70. doi:10.3390/electronics5040070Yan, F., Liu, Y.-S., & Xiao, J.-Z. (2013). Path Planning in Complex 3D Environments Using a Probabilistic Roadmap Method. International Journal of Automation and Computing, 10(6), 525-533. doi:10.1007/s11633-013-0750-9Yeh, H.-Y., Thomas, S., Eppstein, D., & Amato, N. M. (2012). UOBPRM: A uniformly distributed obstacle-based PRM. 2012 IEEE/RSJ International Conference on Intelligent Robots and Systems. doi:10.1109/iros.2012.6385875Liang, Y., & Xu, L. (2009). Global path planning for mobile robot based genetic algorithm and modified simulated annealing algorithm. Proceedings of the first ACM/SIGEVO Summit on Genetic and Evolutionary Computation - GEC ’09. doi:10.1145/1543834.1543875Liu, J., Yang, J., Liu, H., Tian, X., & Gao, M. (2016). An improved ant colony algorithm for robot path planning. Soft Computing, 21(19), 5829-5839. doi:10.1007/s00500-016-2161-7Cao, H., Sun, S., Zhang, K., & Tang, Z. (2016). Visualized trajectory planning of flexible redundant robotic arm using a novel hybrid algorithm. Optik, 127(20), 9974-9983. doi:10.1016/j.ijleo.2016.07.078Duan, H., & Qiao, P. (2014). Pigeon-inspired optimization: a new swarm intelligence optimizer for air robot path planning. International Journal of Intelligent Computing and Cybernetics, 7(1), 24-37. doi:10.1108/ijicc-02-2014-0005Pandey, A., & Parhi, D. R. (2017). Optimum path planning of mobile robot in unknown static and dynamic environments using Fuzzy-Wind Driven Optimization algorithm. Defence Technology, 13(1), 47-58. doi:10.1016/j.dt.2017.01.001Samaniego, F., Sanchis, J., García-Nieto, S., & Simarro, R. (2019). Recursive Rewarding Modified Adaptive Cell Decomposition (RR-MACD): A Dynamic Path Planning Algorithm for UAVs. Electronics, 8(3), 306. doi:10.3390/electronics8030306Dubins, L. E. (1957). On Curves of Minimal Length with a Constraint on Average Curvature, and with Prescribed Initial and Terminal Positions and Tangents. American Journal of Mathematics, 79(3), 497. doi:10.2307/2372560Fleury, S., Soueres, P., Laumond, J.-P., & Chatila, R. (1995). Primitives for smoothing mobile robot trajectories. IEEE Transactions on Robotics and Automation, 11(3), 441-448. doi:10.1109/70.388788Vanegas, G., Samaniego, F., Girbes, V., Armesto, L., & Garcia-Nieto, S. (2018). Smooth 3D path planning for non-holonomic UAVs. 2018 7th International Conference on Systems and Control (ICSC). doi:10.1109/icosc.2018.8587835Brezak, M., & Petrovic, I. (2014). Real-time Approximation of Clothoids With Bounded Error for Path Planning Applications. IEEE Transactions on Robotics, 30(2), 507-515. doi:10.1109/tro.2013.2283928Barsky, B. A., & DeRose, T. D. (1989). Geometric continuity of parametric curves: three equivalent characterizations. IEEE Computer Graphics and Applications, 9(6), 60-69. doi:10.1109/38.41470Kim, H., Kim, D., Shin, J.-U., Kim, H., & Myung, H. (2014). Angular rate-constrained path planning algorithm for unmanned surface vehicles. Ocean Engineering, 84, 37-44. doi:10.1016/j.oceaneng.2014.03.034Isaacs, J., & Hespanha, J. (2013). Dubins Traveling Salesman Problem with Neighborhoods: A Graph-Based Approach. Algorithms, 6(1), 84-99. doi:10.3390/a6010084Masehian, E., & Kakahaji, H. (2014). NRR: a nonholonomic random replanner for navigation of car-like robots in unknown environments. Robotica, 32(7), 1101-1123. doi:10.1017/s0263574713001276Fraichard, T., & Scheuer, A. (2004). From Reeds and Shepp’s to Continuous-Curvature Paths. IEEE Transactions on Robotics, 20(6), 1025-1035. doi:10.1109/tro.2004.833789Pepy, R., Lambert, A., & Mounier, H. (s. f.). Path Planning using a Dynamic Vehicle Model. 2006 2nd International Conference on Information & Communication Technologies. doi:10.1109/ictta.2006.1684472Girbés, V., Vanegas, G., & Armesto, L. (2019). Clothoid-Based Three-Dimensional Curve for Attitude Planning. Journal of Guidance, Control, and Dynamics, 42(8), 1886-1898. doi:10.2514/1.g003551De Lorenzis, L., Wriggers, P., & Hughes, T. J. R. (2014). Isogeometric contact: a review. GAMM-Mitteilungen, 37(1), 85-123. doi:10.1002/gamm.201410005Pigounakis, K. G., Sapidis, N. S., & Kaklis, P. D. (1996). Fairing Spatial B-Spline Curves. Journal of Ship Research, 40(04), 351-367. doi:10.5957/jsr.1996.40.4.351Pérez, L. H., Aguilar, M. C. M., Sánchez, N. M., & Montesinos, A. F. (2018). Path Planning Based on Parametric Curves. Advanced Path Planning for Mobile Entities. doi:10.5772/intechopen.72574Huh, U.-Y., & Chang, S.-R. (2014). A G2 Continuous Path-smoothing Algorithm Using Modified Quadratic Polynomial Interpolation. International Journal of Advanced Robotic Systems, 11(2), 25. doi:10.5772/57340Chang, S.-R., & Huh, U.-Y. (2014). A Collision-Free G2 Continuous Path-Smoothing Algorithm Using Quadratic Polynomial Interpolation. International Journal of Advanced Robotic Systems, 11(12), 194. doi:10.5772/59463Yaochu Jin, & Sendhoff, B. (2008). Pareto-Based Multiobjective Machine Learning: An Overview and Case Studies. IEEE Transactions on Systems, Man, and Cybernetics, Part C (Applications and Reviews), 38(3), 397-415. doi:10.1109/tsmcc.2008.919172Velasco-Carrau, J., García-Nieto, S., Salcedo, J. V., & Bishop, R. H. (2016). Multi-Objective Optimization for Wind Estimation and Aircraft Model Identification. Journal of Guidance, Control, and Dynamics, 39(2), 372-389. doi:10.2514/1.g001294Honig, E., Schucking, E. L., & Vishveshwara, C. V. (1974). Motion of charged particles in homogeneous electromagnetic fields. Journal of Mathematical Physics, 15(6), 774-781. doi:10.1063/1.1666728Iyer, B. R., & Vishveshwara, C. V. (1988). The Frenet-Serret formalism and black holes in higher dimensions. Classical and Quantum Gravity, 5(7), 961-970. doi:10.1088/0264-9381/5/7/005Laumanns, M., Thiele, L., Deb, K., & Zitzler, E. (2002). Combining Convergence and Diversity in Evolutionary Multiobjective Optimization. Evolutionary Computation, 10(3), 263-282. doi:10.1162/106365602760234108Blasco, X., Herrero, J. M., Sanchis, J., & Martínez, M. (2008). A new graphical visualization of n-dimensional Pareto front for decision-making in multiobjective optimization. Information Sciences, 178(20), 3908-3924. doi:10.1016/j.ins.2008.06.01

4D waypoints based optimal trajectory generation for unmanned aerial vehicles

The constant technological developments recently observed on unmanned aerial vehicles allow its use on diverse activities. With the arrival of new opportunities new challenges arrive as well. Nowadays the navigation methods used is limited to following pre-defined points in space, waypoints, by using the flight parameters values in its control. This work proposes an alternative method, consisting in creating trajectories from 4D waypoints, i.e. three spatial coordinates plus a temporal one. So, it is possible to foresee the path e guarantee that it will be on the desired place at the right time. Because passing through the exact position of a waypoint is rather difficult and not always required, a tolerance is used around it, allowing the passage on the vicinity defined by a sphere whose radius is equal to that tolerance. In this work an algorithm is proposed to find the tridimensional point in the interior of that said sphere which minimizes the path length between the previous and next waypoint. The trajectory is defined interpolating the waypoint coordinates, using a fifth order polynomial function. This way, it is possible to constrain said function in order to create a trajectory whose flight parameters comply with navigation limits associated with the vehicle. By using the limits associated with a small unmanned aerial vehicle, it was possible to create a trajectory defined by 4D waypoints with a consistent behavior and quite smooth. The path chosen is a Racetrack Pattern loiter defined by six waypoints whose time was defined in order to attempt to maintain a constant velocity through the path. The simulation was a successfully performed, being the limits imposed respected through the entire domain of time. Therefore, the possibility of creating 4D waypoint based trajectories is proven, generating a new area of opportunities for time based missions where time plays a critical role, or the shape of the path is crucial.Os constantes desenvolvimentos tecnológicos observados recentemente em veículos aéreos não tripulados permitem o seu uso nas mais diversas actividades. Com o aparecimento de novas oportunidades surgem também novos desafios. Atualmente a navegação utilizada limita-se apenas ao seguimento de pontos pré-definidos no espaço, waypoints, utilizando parâmetros de voo no seu controlo. Este trabalho propõe um método alternativo, que consiste em criar trajectórias a partir de waypoints em 4D, ou seja, com três coordenadas espaciais e uma quarta temporal. Assim, é possível antever o percurso e garantir que se encontra no local pretendido no tempo certo. Como passar pela posição exata de um waypoint é muitas vezes difícil e excusado, utiliza-se uma tolerância em redor deste, proporcionando a passagem na vizinhança definida por uma esfera com o raio igual a essa mesma tolerância. Neste trabalho é proposto um algoritmo que encontra o ponto tridimensional no interior dessa esfera que minimiza o comprimento do trajecto entre o waypoint anterior e o seguinte. A trajetória por sua vez é definida interpolando as coordenadas dos waypoints através de um polinómio de ordem cinco. Desta forma é possível restringí-la de modo a criar uma trajectória cujos parâmetros de voo cumprem os limites de navegação associados ao veículo. Utilizando dados de um veículo aéreo não tripulado de pequenas dimensões, foi possível criar uma trajetória definida por waypoints 4D com um comportamento regular e bastante suave. O percurso escolhido consiste num loiter em hipódromo definido por seis waypoints cujo tempo foi definido de modo a tentar manter de uma velocidade constante em todo o percurso. A simulação foi realizada com sucesso, sendo os limites impostos respeitados ao longo de todo o domínio de tempo. Desta forma comprova-se a possibiliadde da criação de trajetórias a partir de waypoints 4D específicas para cada veículo aéro não tripulado, gerando assim uma nova área de oportunidades para missões em que o tempo é um factor crítico, ou onde a forma do percurso é crucial

Cooperative Path-Planning for Multi-Vehicle Systems

In this paper, we propose a collision avoidance algorithm for multi-vehicle systems, which is a common problem in many areas, including navigation and robotics. In dynamic environments, vehicles may become involved in potential collisions with each other, particularly when the vehicle density is high and the direction of travel is unrestricted. Cooperatively planning vehicle movement can effectively reduce and fairly distribute the detour inconvenience before subsequently returning vehicles to their intended paths. We present a novel method of cooperative path planning for multi-vehicle systems based on reinforcement learning to address this problem as a decision process. A dynamic system is described as a multi-dimensional space formed by vectors as states to represent all participating vehicles’ position and orientation, whilst considering the kinematic constraints of the vehicles. Actions are defined for the system to transit from one state to another. In order to select appropriate actions whilst satisfying the constraints of path smoothness, constant speed and complying with a minimum distance between vehicles, an approximate value function is iteratively developed to indicate the desirability of every state-action pair from the continuous state space and action space. The proposed scheme comprises two phases. The convergence of the value function takes place in the former learning phase, and it is then used as a path planning guideline in the subsequent action phase. This paper summarizes the concept and methodologies used to implement this online cooperative collision avoidance algorithm and presents results and analysis regarding how this cooperative scheme improves upon two baseline schemes where vehicles make movement decisions independently

Stochastic trajectory generation using particle swarm optimization for quadrotor unmanned aerial vehicles (UAVs)

The aim of this paper is to provide a realistic stochastic trajectory generation method for unmanned aerial vehicles that offers a tool for the emulation of trajectories in typical flight scenarios. Three scenarios are defined in this paper. The trajectories for these scenarios are implemented with quintic B-splines that grant smoothness in the second-order derivatives of Euler angles and accelerations. In order to tune the parameters of the quintic B-spline in the search space, a multi-objective optimization method called particle swarm optimization (PSO) is used. The proposed technique satisfies the constraints imposed by the configuration of the unmanned aerial vehicle (UAV). Further particular constraints can be introduced such as: obstacle avoidance, speed limitation, and actuator torque limitations due to the practical feasibility of the trajectories. Finally, the standard rapidly-exploring random tree (RRT*) algorithm, the standard (A*) algorithm and the genetic algorithm (GA) are simulated to make a comparison with the proposed algorithm in terms of execution time and effectiveness in finding the minimum length trajectory

Control of free-ranging automated guided vehicles in container terminals

Container terminal automation has come to the fore during the last 20 years to improve their efficiency. Whereas a high level of automation has already been achieved in vertical handling operations (stacking cranes), horizontal container transport still has disincentives to the adoption of automated guided vehicles (AGVs) due to a high degree of operational complexity of vehicles. This feature has led to the employment of simple AGV control techniques while hindering the vehicles to utilise their maximum operational capability. In AGV dispatching, vehicles cannot amend ongoing delivery assignments although they have yet to receive the corresponding containers. Therefore, better AGV allocation plans would be discarded that can only be achieved by task reassignment. Also, because of the adoption of predetermined guide paths, AGVs are forced to deploy a highly limited range of their movement abilities while increasing required travel distances for handling container delivery jobs. To handle the two main issues, an AGV dispatching model and a fleet trajectory planning algorithm are proposed. The dispatcher achieves job assignment flexibility by allowing AGVs towards to container origins to abandon their current duty and receive new tasks. The trajectory planner advances Dubins curves to suggest diverse optional paths per origin-destination pair. It also amends vehicular acceleration rates for resolving conflicts between AGVs. In both of the models, the framework of simulated annealing was applied to resolve inherent time complexity. To test and evaluate the sophisticated AGV control models for vehicle dispatching and fleet trajectory planning, a bespoke simulation model is also proposed. A series of simulation tests were performed based on a real container terminal with several performance indicators, and it is identified that the presented dispatcher outperforms conventional vehicle dispatching heuristics in AGV arrival delay time and setup travel time, and the fleet trajectory planner can suggest shorter paths than the corresponding Manhattan distances, especially with fewer AGVs.Open Acces

Diseño de nuevos algoritmos de guiado y navegación con evasión de colisiones para vehículos aéreos no tripulados.

Tesis por compendio[ES] Debido a la creciente popularidad sobre la variedad de los Vehículos No Tripulados tanto en el campo militar como en el comercial, y de sus capacidades para navegar por diversos entornos, ya sean terrestres, aéreos o marinos, se evidencia que la clásica planificación de trayectorias y movimientos bidimensionales 2D podría no ser suficiente en un futuro inmediato. De esta manera, se debe resaltar que el presente trabajo aborda el problema de los Vehículos Aéreos No Tripulados (UAVs) de ala fija. En este sentido, la necesidad de encontrar una trayectoria navegable en el espacio euclídeo 3D se hace cada vez más necesario. En el caso de los UAV, considerar su cinemática para generar trayectorias suaves en tres dimensiones puede tener un interés significativo para la navegación autónoma aérea. Finalmente, los beneficios adicionales que se pueden producir son importantes. La principal dificultad de este problema es que los vehículos aéreos de características no-holonómicas se ven obligados a avanzar sin la posibilidad de detenerse a través de trayectorias 3D con curvaturas limitadas. En este sentido, se ha investigado la manera de proporcionar una completa caracterización de trayectorias óptimas para UAVs con un radio de giro limitado que se mueve en el plano tridimensional a una velocidad constante. Para completar tales tareas, un planificador de trayectorias no sólo debe proporcionar rutas tridimensionales para alcanzar una posición de destino sin colisionar con obstáculos, sino también debe asegurar que tal trayectoria sea adecuada para los UAVs que poseen propiedades cinemáticas específicas. Por lo tanto, el desarrollo del trabajo ha completado la algoritmia que genera una trayectoria discreta tridimensional al definir un conjunto de puntos 3D, resultantes de una división del espacio euclídeo tridimensional de manera dinámica, determinando las mejores opciones de avance, evitando analizar cada espacio del entorno completo. De esta manera, partiendo de los puntos 3D resultantes de la planificación de trayectoria tridimensional, se ha generado una trayectoria en forma de curva suave construida en función de las limitaciones de giro del UAV (resaltando que es difícil asegurar que el camino resultante cumpla con las restricciones cinemáticas en las tres dimensiones simultáneamente). Finalmente, es importante destacar que a menudo las restricciones mencionadas se calculan secuencialmente y de forma bidimensional, sobre un par de dimensiones desacopladas, lo que limita la capacidad de optimización. Para todo ello, se ha desarrollado un algoritmo de suavizado para un planificador de trayectorias que considera las restricciones cinemáticas tridimensionales completas sin desacoplar las dimensiones.[CA] Debut a la creixent popularitat sobre la varietat dels Vehicles No Tripulats tant en el camp militar com en el comercial, i de les seves capacitats per navegar per diversos entorns, ja siguin terrestres, aeris o marins, s'evidencia que la clàssica planificació de trajectòries i moviments bidimensionals 2D podria no ser suficient en un futur immediat. D'aquesta manera, s'ha de ressaltar que el present treball aborda el problema dels Vehicles Aeris No Tripulats (UAV) d'ala fixa. En aquest sentit, la necessitat de trobar una trajectòria navegable en l'espai euclidià 3D es fa cada vegada més necessari. En el cas dels UAV, considerar la seva cinemàtica per generar trajectòries suaus en tres dimensions pot tenir un interès significatiu per a la navegació autònoma aèria. Finalment, els beneficis addicionals que es poden produir són importants. La principal dificultat d'aquest problema és que els vehicles aeris de característiques no-holonómicas es veuen obligats a avançar sense la possibilitat de detenir-se a través de trajectòries 3D amb curvatures limitades. En aquest sentit, s'ha investigat la manera de proporcionar una completa caracterització de trajectòries òptimes per UAVs amb un radi de gir limitat que es mou en el pla tridimensional a una velocitat constant. Per completar aquestes tasques, un planificador de trajectòries no només ha de proporcionar rutes tridimensionals per assolir una posició de destinació sense col·lisionar amb obstacles, sinó també ha d'assegurar que tal trajectòria sigui adequada per als UAVs que posseeixen propietats cinemàtiques específiques. Per tant, el desenvolupament de la feina ha completat la algorísmia que genera una trajectòria discreta tridimensional a l'definir un conjunt de punts 3D, resultants d'una divisió de l'espai euclidià tridimensional de manera dinàmica, determinant les millors opcions d'avanç, evitant analitzar cada espai de l' entorn complet. D'aquesta manera, partint dels punts 3D resultants de la planificació de trajectòria tridimensional, s'ha generat una trajectòria en forma de corba suau construïda en funció de les limitacions de gir de l'UAV (ressaltant que és difícil assegurar que el camí resultant compleixi amb les restriccions cinemàtiques en les tres dimensions simultàniament). Finalment, és important destacar que sovint les restriccions esmentades es calculen seqöencialment i de forma bidimensional, sobre un parell de dimensions desacoblades, el que limita la capacitat d'optimització. Per tot això, s'ha desenvolupat un algoritme de suavitzat per a un planificador de trajectòries que considera les restriccions cinemàtiques tridimensionals completes sense desacoblar les dimensions.[EN] Due to the growing popularity of the variety of Unmanned Vehicles in both the military and commercial fields, and their capabilities to navigate diverse environments, whether land, air or sea, it is evident that the classic two-dimensional 2D trajectory and motion planning may not be enough in the near future. Thus, it should be noted that this paper addresses the problem of fixed-wing Unmanned Aerial Vehicles (UAVs). In this sense, the need to find a navigable path in 3D Euclidean space becomes more and more necessary. In the case of UAVs, considering their kinematics to generate smooth trajectories in three dimensions may be of significant interest for autonomous air navigation. Finally, the additional benefits that can be produced are important. The main difficulty of this problem is that air vehicles with non-holonomic characteristics are forced to advance without the possibility of stopping through 3D trajectories with limited curvatures. In this regard, research has been conducted to provide a complete characterization of optimal trajectories for UAVs with a limited turning radius that move in the 3D plane at a constant speed. To complete such tasks, a path planner must not only provide three-dimensional paths to reach a target position without colliding with obstacles, but must also ensure that such a path is suitable for UAVs that possess specific kinematic properties. Therefore, the development of the work has completed the algorithm that generates a discrete three-dimensional path by defining a set of 3D points, resulting from a division of the three-dimensional Euclidean space in a dynamic way, determining the best forward options, avoiding to analyze each space of the whole environment. In this way, starting from the 3D points resulting from the three-dimensional path planning, a smooth curve path has been generated, built according to the UAV turning constraints (highlighting that it is difficult to ensure that the resulting path meets the kinematic constraints in the three dimensions simultaneously). Finally, it is important to note that often the constraints mentioned are calculated sequentially and in a two-dimensional shape, on a pair of decoupled dimensions, which limits the ability to optimize. For all this, a smoothing algorithm has been developed for a path planner that considers the complete three-dimensional kinematic constraints without decoupling the dimensions.Este trabajo ha sido parcialmente financiado por el Gobierno de España a través del Ministerio de Economía y Competitividad bajo el proyecto de Investigación DP I2015−71443−R, y por la administración local de la Generalitat Valenciana a través de los proyectos GV /2017/029 y AICO/2019/055. El autor ha sido beneficiario de una beca otorgada por el Instituto de Fomento al Talento Humano (IFTH) (2015−AR2Q9209) a través del Gobierno de Ecuador.Samaniego Riera, FE. (2021). Diseño de nuevos algoritmos de guiado y navegación con evasión de colisiones para vehículos aéreos no tripulados [Tesis doctoral]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/161274TESISCompendi

MINVO Basis: Finding Simplexes with Minimum Volume Enclosing Polynomial Curves

This paper studies the problem of finding the smallest $n$-simplex enclosing a given $n^{\text{th}}$-degree polynomial curve. Although the Bernstein and B-Spline polynomial bases provide feasible solutions to this problem, the simplexes obtained by these bases are not the smallest possible, which leads to undesirably conservative results in many applications. We first prove that the polynomial basis that solves this problem (MINVO basis) also solves for the $n^\text{th}$-degree polynomial curve with largest convex hull enclosed in a given $n$-simplex. Then, we present a formulation that is \emph{independent} of the $n$-simplex or $n^{\text{th}}$-degree polynomial curve given. By using Sum-Of-Squares (SOS) programming, branch and bound, and moment relaxations, we obtain high-quality feasible solutions for any $n\in\mathbb{N}$ and prove numerical global optimality for $n=1,2,3$. The results obtained for $n=3$ show that, for any given $3^{\text{rd}}$-degree polynomial curve, the MINVO basis is able to obtain an enclosing simplex whose volume is $2.36$ and $254.9$ times smaller than the ones obtained by the Bernstein and B-Spline bases, respectively. When $n=7$, these ratios increase to $902.7$ and $2.997\cdot10^{21}$, respectively.Comment: 25 pages, 16 figure

Hybrid PSO-cubic spline for autonomous robots optimal trajectory planning

This paper presents a new version of the Particle Swarm Optimization algorithm where the particles are replaced by spline functions. The developed algorithm generates smooth motion trajectories with two times continuously differentiable curvature avoiding obstacles placed in the workspace. It can be used for autonomous robot path planning or transport problems. The spline based trajectory generation gives us continuous, smooth and optimized path trajectories. Simulation and experimental results demonstrate the effectiveness of the proposed method.info:eu-repo/semantics/publishedVersio

Analysis and Comparison of Clothoid and Dubins Algorithms for UAV Trajectory Generation

The differences between two types of pose-based UAV path generation methods clothoid and Dubins are analyzed in this thesis. The Dubins path is a combination of circular arcs and straight line segments; therefore its curvature will exhibit sudden jumps between constant values. The resulting path will have a minimum length if turns are performed at the minimum possible turn radius. The clothoid path consists of a similar combination of arcs and segments but the difference is that the clothoid arcs have a linearly variable curvature and are generated based on Fresnel integrals. Geometrically, the generation of the clothoid arc starts with a large curvature that decreases to zero. The clothoid path results are longer than the Dubins path between the same two poses and for the same minimum turn radius. These two algorithms are the focus of this research because of their geometrical simplicity, flexibility, and low computational requirements.;The comparison between clothoid and Dubins algorithms relies on extensive simulation results collected using an ad-hoc developed automated data acquisition tool within the WVU UAV simulation environment. The model of a small jet engine UAV has been used for this purpose. The experimental design considers several primary factors, such as different trajectory tracking control laws, normal and abnormal flight conditions, relative configuration of poses, and wind and turbulence. A total of five different controllers have been considered, three conventional with fixed parameters and two adaptive. The abnormal flight conditions include locked or damaged actuators (stabilator, aileron, or rudder) and sensor bias affecting roll, pitch, or yaw rate gyros that are used in the feedback control loop. The relative configuration of consecutive poses is considered in terms of heading (required turn angle) and relative location of start and end points (position quadrant). Wind and turbulence effects were analyzed for different wind speed and direction and several levels of turbulence severity. The evaluation and comparison of the two path generation algorithms are performed based on generated and actual path length and tracking performance assessed in terms of tracking errors and control activity.;Although continuous position and velocity are ensured, the Dubins path yields discontinuous changes in path curvature and hence in commanded lateral accelerations at the transition points between the circular arcs and straight segments. The simulation results show that this generally leads to increased trajectory tracking errors, longer actual paths, and more intense control surface activity. The gradual (linear) change in clothoid curvature yields a continuous change in commanded lateral accelerations with general positive effects on the overall UAV performance based on the metrics considered. The simulation results show general similar trends for all factors considered. As a result, it may be concluded that, due to the continuous change in commanded lateral acceleration, the clothoid path generation algorithm provides overall better performance than the Dubins algorithm, at both normal and abnormal flight conditions, if the UAV mission involves significant maneuvers requiring intense lateral acceleration commands