Multi-Robot Persistent Coverage in Complex Environments

Los recientes avances en robótica móvil y un creciente desarrollo de robots móviles asequibles han impulsado numerosas investigaciones en sistemas multi-robot. La complejidad de estos sistemas reside en el diseño de estrategias de comunicación, coordinación y controlpara llevar a cabo tareas complejas que un único robot no puede realizar. Una tarea particularmente interesante es la cobertura persistente, que pretende mantener cubierto en el tiempo un entorno con un equipo de robots moviles. Este problema tiene muchas aplicaciones como aspiración o limpieza de lugares en los que la suciedad se acumula constantemente, corte de césped o monitorización ambiental. Además, la aparición de vehículos aéreos no tripulados amplía estas aplicaciones con otras como la vigilancia o el rescate.Esta tesis se centra en el problema de cubrir persistentemente entornos progresivamente mas complejos. En primer lugar, proponemos una solución óptima para un entorno convexo con un sistema centralizado, utilizando programación dinámica en un horizonte temporalnito. Posteriormente nos centramos en soluciones distribuidas, que son más robustas, escalables y eficientes. Para solventar la falta de información global, presentamos un algoritmo de estimación distribuido con comunicaciones reducidas. Éste permite a los robots teneruna estimación precisa de la cobertura incluso cuando no intercambian información con todos los miembros del equipo. Usando esta estimación, proponemos dos soluciones diferentes basadas en objetivos de cobertura, que son los puntos del entorno en los que más se puedemejorar dicha cobertura. El primer método es un controlador del movimiento que combina un término de gradiente con un término que dirige a los robots hacia sus objetivos. Este método funciona bien en entornos convexos. Para entornos con algunos obstáculos, el segundométodo planifica trayectorias abiertas hasta los objetivos, que son óptimas en términos de cobertura. Finalmente, para entornos complejos no convexos, presentamos un algoritmo capaz de encontrar particiones equitativas para los robots. En dichas regiones, cada robotplanifica trayectorias de longitud finita a través de un grafo de caminos de tipo barrido.La parte final de la tesis se centra en entornos discretos, en los que únicamente un conjunto finito de puntos debe que ser cubierto. Proponemos una estrategia que reduce la complejidad del problema separándolo en tres subproblemas: planificación de trayectoriascerradas, cálculo de tiempos y acciones de cobertura y generación de un plan de equipo sin colisiones. Estos subproblemas más pequeños se resuelven de manera óptima. Esta solución se utiliza en último lugar para una novedosa aplicación como es el calentamiento por inducción doméstico con inductores móviles. En concreto, la adaptamos a las particularidades de una cocina de inducción y mostramos su buen funcionamiento en un prototipo real.Recent advances in mobile robotics and an increasing development of aordable autonomous mobile robots have motivated an extensive research in multi-robot systems. The complexity of these systems resides in the design of communication, coordination and control strategies to perform complex tasks that a single robot can not. A particularly interesting task is that of persistent coverage, that aims to maintain covered over time a given environment with a team of robotic agents. This problem is of interest in many applications such as vacuuming, cleaning a place where dust is continuously settling, lawn mowing or environmental monitoring. More recently, the apparition of useful unmanned aerial vehicles (UAVs) has encouraged the application of the coverage problem to surveillance and monitoring. This thesis focuses on the problem of persistently covering a continuous environment in increasingly more dicult settings. At rst, we propose a receding-horizon optimal solution for a centralized system in a convex environment using dynamic programming. Then we look for distributed solutions, which are more robust, scalable and ecient. To deal with the lack of global information, we present a communication-eective distributed estimation algorithm that allows the robots to have an accurate estimate of the coverage of the environment even when they can not exchange information with all the members of the team. Using this estimation, we propose two dierent solutions based on coverage goals, which are the points of the environment in which the coverage can be improved the most. The rst method is a motion controller, that combines a gradient term with a term that drives the robots to the goals, and which performs well in convex environments. For environments with some obstacles, the second method plans open paths to the goals that are optimal in terms of coverage. Finally, for complex, non-convex environments we propose a distributed algorithm to nd equitable partitions for the robots, i.e., with an amount of work proportional to their capabilities. To cover this region, each robot plans optimal, nite-horizon paths through a graph of sweep-like paths. The nal part of the thesis is devoted to discrete environment, in which only a nite set of points has to be covered. We propose a divide-and-conquer strategy to separate the problem to reduce its complexity into three smaller subproblem, which can be optimally solved. We rst plan closed paths through the points, then calculate the optimal coverage times and actions to periodically satisfy the coverage required by the points, and nally join together the individual plans of the robots into a collision-free team plan that minimizes simultaneous motions. This solution is eventually used for a novel application that is domestic induction heating with mobile inductors. We adapt it to the particular setting of a domestic hob and demonstrate that it performs really well in a real prototype.<br /

Exploiting structures of trajectory optimization for efficient optimal motion planning

Trajectory optimization is an important tool for optimal motion planning due to its flexibility in cost design, capability to handle complex constraints, and optimality certification. It has been widely used in robotic applications such as autonomous vehicles, unmanned aerial vehicles, humanoid robots, and highly agile robots. However, practical robotic applications often possess nonlinear dynamics and non-convex constraints and cost functions, which makes the trajectory optimization problem usually difficult to be efficiently solved to global optimum. The long computation time, possibility of non-convergence, and existence of local optima impose significant challenges to applying trajectory optimization in reactive tasks with requirements of real-time replanning. In this thesis, two structures of optimization problems are exploited to significantly improve the efficiency, i.e. computation time, reliability, i.e. success rate, and optimality, i.e. quality of the solution. The first structure is the existence of a convex sub-problem, i.e. the problem becomes convex if a subset of optimization variables is fixed and removed from the optimization. This structure exists in a wide variety of problems, especially where decomposition of spatial and temporal variables may result in convex sub-problem. A bilevel optimization framework is proposed that optimizes the subset and its complement hierarchically where the upper level optimizes the subset with convex constraints and the lower level uses convex optimization to solve its complement. The key is to use the solution of the lower level problem to compute analytic gradients for the upper-level problem. The bilevel framework is reliable due to its convex lower problem, efficient due to its simple upper problem, and yields better solutions than alternatives, although the existing requirement of convex sub-problem is generally too strict for many applications. The second structure is the local continuity of the argmin function for parametric optimization problems which map from problem parameters to the corresponding optimal solutions. The argmin function can be approximated from data which is collected offline by sampling the problem parameters and solving them to optima. Three approaches are proposed to learn the argmin from data each suited best for distinct applications. The nearest-neighbor optimal control searches problems with similar parameters and uses their solution to initialize nonlinear optimization. For problems with globally continuous argmin, neural networks can be used to learn from data and a few steps of convex optimization can further improve their predictions. As for problems with discontinuous argmin, mixture of experts (MoE) models are used. The MoE contains several experts and a classifier and is trained by splitting the data first according to discontinuity of argmin and then training each expert independently. Both empirical $k$-Means and theoretical topological data analysis approaches are explored for discontinuity identification and finding suitable data splits. Both methods result in data splits that help train MoE models that outperform the discontinuity-agnostic learning pipeline using standard neural networks. The trajectory learning approach is efficient since it only requires model evaluation to compute a trajectory, reliable since the MoE model is accurate after correctly handling discontinuity, and optimal since the data are collected offline and solved to optimal. Moreover, this local continuity structure is less restrictive and exists for a wide range of non-degenerate problems. The exploitation of these two structures helps build an efficient optimal motion planner with high reliability