Algorithms for Robot Coverage Under Movement and Sensing Constraints

This thesis explores the problem of generating coverage paths—that is, paths that pass within some sensor footprint of every point in an environment—for mobile robots. It both considers models for which navigation is a solved problem but motions are constrained, as well for models in which navigation must be considered along with coverage planning because of the robot’s unreliable sensing and movements. The motion constraint we adopt for the former is a common constraint, that of a Dubins vehicle. We extend previous work that solves this coverage problem as a traveling salesman problem (TSP) by introducing a practical heuristic algorithm to reduce runtime while maintaining near-optimal path length. Furthermore, we show that generating an optimal coverage path is NP-hard by reducing from the Exact Cover problem, which provides justification for our algorithm’s conversion of Dubins coverage instances to TSP instances. Extensive experiments demonstrate that the algorithm does indeed produce path lengths comparable to optimal in significantly less time. In the second model, we consider the problem of coverage planning for a particular type of very simple mobile robot. The robot must be able to translate in a commanded direction (specified in a global reference frame), with bounded error on the motion direction, until reaching the environment boundary. The objective, for a given environment map, is to generate a sequence of motions that is guaranteed to cover as large a portion of that environment as possible, in spite of the severe limits on the robot’s sensing and actuation abilities. We show how to model the knowledge available to this kind of robot about its own position within the environment, show how to compute the region whose coverage can be guaranteed for a given plan, and characterize regions whose coverage cannot be guaranteed by any plan. We also describe an algorithm that generates coverage plans for this robot, based on a search across a specially-constructed graph. Simulation results demonstrate the effectiveness of the approach

Contributions to mobile robot navigation based embedded systems and grid mapping

Tesis doctoral inédita leída en la Universidad Autónoma de Madrid, Escuela Politécnica Superior, Departamento de Tecnología Electrónica y de las Comunicaciones. Fecha de lectura: 13-07-2015Path planning is a problem as old as humankind. The necessity of optimizing the resources to reach a location has been a concern since prehistory. Technology has allowed approaching this problematic using new resources. However, it has also introduced new requirements. This thesis is focused on path planning from the perspective of an embedded system using grid maps. For battery-dependent robots, path length is very relevant because it is directly related to motor consumption and the autonomy of the system. Nevertheless, a second aspect to be considered when using embedded systems is the HW requirements. These requirements comprise floating point units or storage capacity. When computer-based path planning algorithms are directly ported to these embedded systems, their HW requirements become a limitation. This thesis presents two novel path planning algorithms which take into account both the search of the shortest path and the optimization of HW resources. These algorithms are HCTNav and NafisNav. The HCTNav algorithm was developed using the intuitive approach as trying to reach the goal in a straight trajectory until an obstacle is found. When an obstacle is found, it must be surrounded until the straight path to the goal can be continued, reaching this goal or another obstacle. Considering HCTNav as a path planning algorithm, both possible surrounding trajectories can be explored and then choose the best solution. Therefore, for each obstacle the algorithm finds, there is a branch in the search of the solution. Finally, the algorithm includes an optimization procedure which reduces the length of the obtained paths if it is possible to go between nonconsecutive waypoints in straight line. The NafisNav algorithm evolves from a depth-first search. For each iteration of the algorithm, the straight trajectory to the goal position is verified. If this trajectory is not available, the algorithm selects from the unexplored neighbor cells the closest one to the target. If two neighbors were at the same distance, the algorithm would branch evaluating both alternatives. This algorithm includes a backtracking procedure just in case it finds a dead end. Finally, from every possible solution, the algorithm proposes the one that, after optimization, provides the shortest path. The new algorithms have been evaluated and compared with the most extended algorithms of the state of the art: Dijkstra and A*. The two chosen evaluation metrics have been final path length and required dynamic memory. HCTNav provides an average penalization in the path length of 2.1% and NafisNav has this penalization increased to 4.5%. However, these algorithms present a decrease of the memory requirements of a 19% for HCTNav and of a 49% for the NafisNav algorithmLa planificación de una ruta es un problema casi tan antiguo como la humanidad. La necesidad de optimizar esfuerzos para alcanzar un objetivo ha sido una gran preocupación desde la prehistoria. La tecnología ha permitido abordar la solución de esta problemática con nuevos medios, pero también ha planteado otros requisitos distintos. Esta tesis aborda el problema de navegación desde la perspectiva de los sistemas empotrados en entornos de mapas de rejilla. En todo robot dependiente de batería, la longitud final es un factor relevante porque se traduce directamente en el consumo de los motores y repercute en la autonomía del sistema. No obstante, un segundo factor que aparece al utilizar sistemas empotrados es el uso de recursos HW, ya sean unidades de coma flotante o capacidad de almacenamiento. Cuando se intenta adaptar los algoritmos diseñados para ser ejecutados en un ordenador nos enfrentamos a una gran demanda de estos recursos. La tesis plantea dos algoritmos novedosos que tienen en cuenta tanto la búsqueda de un camino lo más corto posible como la optimización de recursos HW: HCTNav y NafisNav. El algoritmo HCTNav se desarrolló siguiendo el movimiento intuitivo de quien trata de ir en línea recta hasta que encuentra un obstáculo y lo rodea hasta que puede continuar en línea recta hasta el destino, o en caso contrario hasta otro obstáculo. Dado que se trata un algoritmo de planificación, se puede plantear rodear el obstáculo por ambos lados y elegir cuál es la mejor opción. Por lo tanto, cada obstáculo genera una bifurcación en la búsqueda de solución. Este algoritmo incluye un proceso de optimización por el que se reduce el recorrido final si se pueden saltar puntos intermedios viajando en línea recta. El algoritmo NafisNav plantea una búsqueda en profundidad modificada. En cada iteración se intenta alcanzar el destino verificando si se puede alcanzar en línea recta. En caso de no poder alcanzarlo, se avanza al vecino, de entre los contiguos no explorados, aplicando un criterio de mínima distancia al objetivo. Si hubiera dos candidatos posibles, la búsqueda se bifurca, evaluando ambas opciones. Por último, se incluye un proceso de retroceso para el caso en el que se llegara a un punto sin salida. De entre las soluciones posibles se presenta aquella que, tras la optimización, obtiene el mínimo recorrido. Los nuevos algoritmos han sido evaluados y comparados con los algoritmos más extendidos en el estado del arte: Dijkstra y A*. Los dos criterios utilizados han sido la longitud final del camino y el espacio de memoria que se necesita. HCTNav tiene una penalización promedio del 2,1 % en la longitud de la solución, mientras que NafisNav aplica una penalización promedio del 4,5 %. HCTNav obtiene una reducción del consumo de memoria del 19 % comparado con la mejor solución entre Dijkstra y A*. NafisNav mejora estos resultados con una reducción del 49