Shortest Dubins Path to a Circle

The Dubins path problem had enormous applications in path planning for autonomous vehicles. In this paper, we consider a generalization of the Dubins path planning problem, which is to find a shortest Dubins path that starts from a given initial position and heading, and ends on a given target circle with the heading in the tangential direction. This problem has direct applications in Dubins neighborhood traveling salesman problem, obstacle avoidance Dubins path planning problem etc. We characterize the length of the four CSC paths as a function of angular position on the target circle, and derive the conditions which to find the shortest Dubins path to the target circle

The Cost of Bounded Curvature

We study the motion-planning problem for a car-like robot whose turning radius is bounded from below by one and which is allowed to move in the forward direction only (Dubins car). For two robot configurations $\sigma, \sigma'$, let $\ell(\sigma, \sigma')$ be the shortest bounded-curvature path from $\sigma$ to $\sigma'$. For $d \geq 0$, let $\ell(d)$ be the supremum of $\ell(\sigma, \sigma')$, over all pairs $(\sigma, \sigma')$ that are at Euclidean distance $d$. We study the function \dub(d) = \ell(d) - d, which expresses the difference between the bounded-curvature path length and the Euclidean distance of its endpoints. We show that \dub(d) decreases monotonically from \dub(0) = 7\pi/3 to \dub(\ds) = 2\pi, and is constant for d \geq \ds. Here \ds \approx 1.5874. We describe pairs of configurations that exhibit the worst-case of \dub(d) for every distance $d$

Diseño e implementación de un sistema de generación de trayectorias para un robot móvil utilizando control odométrico

La generación de trayectorias es uno de los aspectos básicos del desarrollo de robots móviles. Permite al móvil poder desplazarse de un lugar a otro de manera óptima y segura, a partir de un modelo de obstáculos que lo rodean y a un camino ya calculado. Los estudios en generación de trayectorias son importantes debido a que son la base del desplazamiento de un robot móvil. El movimiento debe de ser seguro, esquivando los obstáculos, y eficiente, que se traslade de un lugar a otro en el menor tiempo posible, o con el menor consumo de potencia. Para esto, en primer lugar, se debe de calcular una trayectoria. Ésta puede ser calculada por distintos métodos dependiendo del algoritmo utilizado. Una vez calculada la trayectoria, debe ser realizada por el robot real, lo que lleva a un problema de incertidumbre en su ejecución. Esto se debe a la inexactitud de la ejecución de las órdenes de velocidad y a la inexactitud en la localización del robot mediante los cálculos odométricos. Esta incertidumbre es acumulativa, es decir, mientras más larga sea la trayectoria, se generan errores mayores. La implementación de un sistema de generación de trayectorias servirá para que luego existan estudios sobre mejoras en la automatización de robots móviles, y que lleve a su vez a un impulso al desarrollo de la robótica en general. La presente investigación aplicada propone un sistema de generación de trayectorias que permitirá a un usuario aplicar parámetros iniciales a un algoritmo generador de trayectorias para luego ser enviado al robot móvil que recorrerá el camino planteado y llegar al lugar de destino. El objetivo es el diseño y construcción de un robot móvil para pruebas de generación de trayectorias óptimas, usando distintos algoritmos para este propósito, con la finalidad de poder realizar estudios posteriores sobre el tema.Tesi

Motion Planning for a Tethered Mobile Robot

Recently there has been surge of research in motion planning for tethered robots. In this problem a planar robot is connected via a cable of limited length to a fixed point in R2. The configuration space in this problem is more complicated than the one of a classic motion planning problem as existence of the cable causes additional constraints on the motion of the robot. In this thesis we are interested in finding a concise representation of the configuration space that results in a straightforward planning algorithm. To achieve such a representation we observe that configuration space manifold has a discrete structure that conveniently can be separated from its continuous aspect when it is represented as an atlas of charts. We provide a method for generating either the complete atlas or a subset of its charts based on special cable events. Generating parts of the configuration space on-the-fly enables the following improvements over the state-of-the-art. a) We decompose the environment into cells as needed rather than an off-line global discretization, obtaining competitive time and space complexity for our planner. b) We are able to exploit topological structure to represent robot-cable configurations concisely leading us towards solutions to the more complex problems of interest. To underscore the potential of this representation, we take further steps to generalize it to two more complicated instances of the tethered robot planning problem that has been widely disregarded in the literature. We will first consider a simplified model of cable-to-cable contacts, giving the robot the option to perform knot-like tying motions. Next, we will address the planning problem for a tethered robot whose cable has a constraint on its curvature. This adds to the realism of the model since most practical cables have some degree of stiffness which limits curvature. In this case we provide a novel technique to relate Dubins' theory of curves with work on planning with topological constraints. Our results show the efficiency of the method and indicate further promise for procedures that represent manifolds via an amalgamation of implicit discrete topological structure and explicit Euclidean cells

Mobile robotic network deployment for intruder detection and tracking

This thesis investigates the problem of intruder detection and tracking using mobile robotic networks. In the first part of the thesis, we consider the problem of seeking an electromagnetic source using a team of robots that measure the local intensity of the emitted signal. We propose a planner for a team of robots based on Particle Swarm Optimization (PSO) which is a population based stochastic optimization technique. An equivalence is established between particles generated in the traditional PSO technique, and the mobile agents in the swarm. Since the positions of the robots are updated using the PSO algorithm, modifications are required to implement the PSO algorithm on real robots to incorporate collision avoidance strategies. The modifications necessary to implement PSO on mobile robots, and strategies to adapt to real environments are presented in this thesis. Our results are also validated on an experimental testbed. In the second part, we present a game theoretic framework for visibility-based target tracking in multi-robot teams. A team of observers (pursuers) and a team of targets (evaders) are present in an environment with obstacles. The objective of the team of observers is to track the team of targets for the maximum possible time. While the objective of the team of targets is to escape (break line-of-sight) in the minimum time. We decompose the problem into two layers. At the upper level, each pursuer is allocated to an evader through a minimum cost allocation strategy based on the risk of each evader, thereby, decomposing the agents into multiple single pursuer-single evader pairs. Two decentralized allocation strategies are proposed and implemented in this thesis. At the lower level, each pursuer computes its strategy based on the results of the single pursuer-single evader target-tracking problem. We initially address this problem in an environment containing a semi-infinite obstacle with one corner. The pursuer\u27s optimal tracking strategy is obtained regardless of the evader\u27s strategy using techniques from optimal control theory and differential games. Next, we extend the result to an environment containing multiple polygonal obstacles. We construct a pursuit field to provide a guiding vector for the pursuer which is a weighted sum of several component vectors. The performance of different combinations of component vectors is investigated. Finally, we extend our work to address the case when the obstacles are not polygonal, and the observers have constraints in motion