Simple Wriggling is Hard unless You Are a Fat Hippo

We prove that it is NP-hard to decide whether two points in a polygonal domain with holes can be connected by a wire. This implies that finding any approximation to the shortest path for a long snake amidst polygonal obstacles is NP-hard. On the positive side, we show that snake's problem is "length-tractable": if the snake is "fat", i.e., its length/width ratio is small, the shortest path can be computed in polynomial time.Comment: A shorter version is to be presented at FUN 201

Emotion-based Parameter Modulation for a Mobile Robot Planning and Control System

The hypothesis that artificial emotion-like mechanisms can improve the adaptive performance of robots and intelligent systems has gained considerable support in recent years. While artificial emotions are typically employed to facilitate human-machine interaction, this thesis instead focuses on modelling emotions and affect in a non-social context. In particular, affective mechanisms are applied to the problem of mobile robot navigation. A three-layered reactive/deliberative controller is developed and implemented, resulting in several contributions to the field of mobile robot control. Rather than employing a reactive layer, a deliberative layer and an interface between them, the control problem is decomposed into three different conceptual spaces - position space, direction space and velocity space - with a distinct control layer applied to each. Existing directional and velocity space approaches such as the vector field histogram (VFH) and dynamic window methods employ different underlying mechanisms and terminology. This thesis unifies these approaches in order to compare and combine them. The weighted sum objective functions employed by some existing approaches that inspired the presented directional and velocity control layers are replaced by weighted products. This enables some hard constraints to be relaxed in favour of weighted contributions, potentially improving a system's flexibility without sacrificing safety (but coming at a cost to efficiency). An affect model is developed that conceptualises emotions and other affective interactions as modulations of cognitive processes. Unlike other models of affect-modulated cognition (e.g. Dorner and Hille, 1995), this model is designed specifically to address problems relating to mobile robot navigation. The role of affect in this model is to continuously adapt a controller's behaviour patterns in response to different environments and momentary conditions encountered by the robot. Affective constructs such as moods and emotions are represented as intensity values that arise from hard-coded interpretations of local stimuli, as well as from learned associations stored in global maps. They are expressed as modulations of control parameters and location-specific biases to path-planning. Extensive simulation experiments are conducted in procedurally-generated environments to assess the performance contributions of this model and its individual components

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 $d$

Speed profile variation as a surrogate measure of road safety based on GPS-equipped vehicle data

The identification of roadway sections with a higher than expected number of crashes is usually based on long term crash frequency data. In situations where historical crash data are limited or not available, surrogate safety measures, based on characteristics such as road geometries, traffic volume, and speed variation are often considered. Most of existing crash prediction models relate safety to speed variation at a specific point on the roadway. However, such point-specific explanatory variables do not capture the effect of speed consistency along the roadway. This study developed several measures based on the speed profiles along road segments to estimate the crash frequency on urban streets. To collect speed profile data, second-by-second speed data were obtained from more than 460 GPS-equipped vehicles participating in the Commute Atlanta Study over the 2004 calendar year. A series of speed data filters have been developed to identify likely free-flow speed data. The quantified relationships between surrogate measures and crash frequency are developed using regression tree and generalized linear modeling (GLM) approaches. The results indicate that safety characteristics of roadways are likely a function of the roadway classification. Two crash prediction models with different set of explanatory variables were developed for higher and lower classification roadways. The findings support the potential use of the profile-based measures to evaluate the safety of road network as the deployment of GPS-equipped vehicles become more prevalent.Ph.D.Committee Chair: Hunter, Michael; Committee Member: Dixon, Karen; Committee Member: Guensler, Randall; Committee Member: Rodgers, Michael; Committee Member: Tsui, Kwok-Leun

Generating timed trajectories foran autonomous robot

Tese de Doutoramento Programa Doutoral em Engenharia Electrónica e ComputadoresThe inclusion of timed movements in control architectures for mobile navigation has received an increasing attention over the last years. Timed movements allow modulat- ing the behavior of the mobile robot according to the elapsed time, such that the robot reaches a goal location within a specified time constraint. If the robot takes longer than expected to reach the goal location, its linear velocity is increased for compen- sating the delay. Timed movements are also relevant when sequences of missions are considered. The robot should follow the predefined time schedule, so that the next mission is initiated without delay. The performance of the architecture that controls the robot can be validated through simulations and field experiments. However, ex- perimental tests do not cover all the possible solutions. These should be guided by a stability analysis, which might provide directions to improve the architecture design in cases of inadequate performance of the architecture. This thesis aims at developing a navigation architecture and its stability analysis based on the Contraction Theory. The architecture is based on nonlinear dynamical systems and must guide a mobile robot, such that it reaches a goal location within a time constraint while avoiding unexpected obstacles in a cluttered and dynamic real environment. The stability analysis based on the Contraction Theory might provide conditions to the dynamical systems parameters, such that the dynamical systems are designed as contracting, ensuring the global exponential stability of the architecture. Furthermore, Contraction Theory provides solutions to analyze the success of the mis- sion as a stability problem. This provides formal results that evaluate the performance of the architecture, allowing the comparison to other navigation architectures. To verify the ability of the architecture to guide the mobile robot, several experi- mental tests were conducted. The obtained results show that the proposed architecture is able to drive mobile robots with timed movements in indoor environments for large distances without human intervention. Furthermore, the results show that the Con- traction Theory is an important tool to design stable control architectures and to analyze the success of the robotic missions as a stability problem.A inclusão de movimentos temporizados em arquitecturas de controlo para navegação móvel tem aumentado ao longo dos últimos anos. Movimentos temporizados permitem modular o comportamento do robô de tal forma que ele chegue ao seu destino dentro de um tempo especificado. Se o robô se atrasar, a sua velocidade linear deve ser aumen- tada para compensar o atraso. Estes movimentos são também importantes quando se consideram sequências de missões. O robô deve seguir o escalonamento da sequência, de tal forma que a próxima missão seja iniciada sem atraso. O desempenho da arqui- tectura pode ser validado através de simulações e experiências reais. Contudo, testes experimentais não cobrem todas as possíveis soluções. Estes devem ser conduzidos por uma análise de estabilidade, que pode fornecer direcções para melhorar o desempenho da arquitectura. O objectivo desta tese é desenvolver uma arquitectura de navegação e analisar a sua estabilidade através da teoria da Contracção. A arquitectura é baseada em sistemas dinâmicos não lineares e deve controlar o robô móvel num ambiente real, desordenado e dinâmico, de tal modo que ele chegue à posição alvo dentro de uma restrição de tempo especificada. A análise de estabilidade baseada na teoria da Contracção pode fornecer condições aos parâmetros dos sistemas dinâmicos de modo a desenha-los como contracções, e assim garantir a estabilidade exponencial global da arquitectura. Esta teoria fornece ainda soluções interessantes para analisar o sucesso da missão como um problema de estabilidade. Isto providencia resultados formais que avaliam o desem- penho da arquitectura e permitem a comparação com outras arquitecturas. Para verificar a habilidade da arquitectura em controlar o robô móvel, foram con- duzidos vários testes experimentais. Os resultados obtidos mostram que a arquitectura proposta é capaz de controlar robôs móveis com movimentos temporizados em ambi- entes interiores durante grandes distâncias e sem intervenção humana. Além disso, os resultados mostram que a teoria da Contracção é uma ferramenta importante para desenhar arquitecturas de controlo estáveis e para analisar o sucesso das missões efec- tuadas pelo robô como um problema de estabilidade.Portuguese Science and Technology Foundation (FCT) SFRH/BD/68805/2010

Lidar-level localization with radar? The CFEAR approach to accurate, fast and robust large-scale radar odometry in diverse environments

This paper presents an accurate, highly efficient, and learning-free method for large-scale odometry estimation using spinning radar, empirically found to generalize well across very diverse environments -- outdoors, from urban to woodland, and indoors in warehouses and mines - without changing parameters. Our method integrates motion compensation within a sweep with one-to-many scan registration that minimizes distances between nearby oriented surface points and mitigates outliers with a robust loss function. Extending our previous approach CFEAR, we present an in-depth investigation on a wider range of data sets, quantifying the importance of filtering, resolution, registration cost and loss functions, keyframe history, and motion compensation. We present a new solving strategy and configuration that overcomes previous issues with sparsity and bias, and improves our state-of-the-art by 38%, thus, surprisingly, outperforming radar SLAM and approaching lidar SLAM. The most accurate configuration achieves 1.09% error at 5Hz on the Oxford benchmark, and the fastest achieves 1.79% error at 160Hz.Comment: Accepted for publication in Transactions on Robotics. Edited 2022-11-07: Updated affiliation and citatio

Bounded-Curvature Shortest Paths through a Sequence of Points

We consider the problem of computing shortest paths having curvature at most one almost everywhere and visiting a sequence of $n$ points in the plane in a given order. This problem arises naturally in path planning for point car-like robots in the presence of polygonal obstacles, and is also a sub-problem of the Dubins Traveling Salesman Problem. This problem reduces to minimizing the function $F:\R^n\rightarrow\R$ that maps $(\theta_1,\ldots,\theta_n)$ to the length of a shortest curvature-constrained path that visits the points $p_1, \ldots, p_n$ in order and whose tangent in $p_i$ makes an angle $\theta_i$ with the $x$-axis. We show that when consecutive points are distance at least $4$ apart, all minima of $F$ are realized over at most $2^k$ disjoint convex polyhedra over which $F$ is strictly convex; each polyhedron is defined by $4n-1$ linear inequalities and $k$ denotes, informally, the number of $p_i$ such that the angle $\angle(p_{i-1},p_i,p_{i+1})$ is small. A curvature-constrained shortest path visiting a sequence points can therefore be approximated by standard convex optimization methods, which presents an interesting alternative to the known polynomial-time algorithms that can only compute a multiplicative constant factor approximation. Our technique also opens new perspectives for bounded-curvature path planning among polygonal obstacles. In particular, we show that, under certain conditions, if the sequence of points where a shortest path touches the obstacles is known then ``connecting the dots'' reduces to a family of convex optimization problems

Identifying the Links Between Mental Frameworks, Context Features, and Driver Attention in Complete Streets Environments

Complete street systems integrate a wide range of users in the same space, with unequal risks and responsibilities. This makes driver attention a critical factor in assuring the safety of vulnerable users. The Conditioned Anticipation of People psychological model of driver attention proposes that drivers reflexively reengage their metacognitive processes when they anticipate visually interacting with the human face or form due to the neurological priority that the brain places on human recognition. To test this model, an eye-tracking tabulation was generated from the SHRP2 Naturalistic Driving Study that measured midsegment percent of time on-task and multitasking behavior for 200 sites in Tampa, Florida and Seattle, Washington. This attention data was statistically analyzed for the impacts of a wide range of context variables using single variable ANOVA and various multivariate models such as ordered probit fractional split and ordered probit models. Context features with a strong correlation to vulnerable user presence that support driver\u27s visual recognition of that presence were also strongly correlated with driver attention. Features like corridor width, block length, doorway density, and sense of enclosure had the largest impact. Features that did not have an impact on the potential visual connection with street users, like lane width, right of way width, onstreet parking, functional classification, or Walkscore had no impact on driver attention or weak effect sizes, despite strong correlations with vulnerable user presence. Crash history was evaluated in conjunction with the variables most sensitive to driver attention with mixed results. Many of the features that increase the potential for drivers to see and interact with people also contribute to increases in vehicle to vehicle conflicts. A decrease in crash rate with increasing sidewalk width implies that the CAP effect can have some impact on crashes. Implications for complete streets and community design are discussed

Fast Marching Methods in path and motion planning: improvements and high-level applications

Mención Internacional en el título de doctorPath planning is defined as the process to establish the sequence of states a system must go through in order to reach a desired state. Additionally, motion planning (or trajectory planning) aims to compute the sequence of motions (or actions) to take the system from one state to another. In robotics path planning can refer for instance to the waypoints a robot should follow through a maze or the sequence of points a robotic arm has to follow in order to grasp an object. Motion planning is considered a more general problem, since it includes kinodynamic constraints. As motion planning is a more complex problem, it is often solved in a two-level approach: path planning in the first level and then a control layer tries to drive the system along the specified path. However, it is hard to guarantee that the final trajectory will keep the initial characteristics. The objective of this work is to solve different path and motion planning problems under a common framework in order to facilitate the integration of the different algorithms that can be required during the nominal operation of a mobile robot. Also, other related areas such as motion learning are explored using this framework. In order to achieve this, a simple but powerful algorithm called Fast Marching will be used. Originally, it was proposed to solve optimal control problems. However, it has became very useful to other related problems such as path and motion planning. Since Fast Marching was initially proposed, many different alternative approaches have been proposed. Therefore, the first step is to formulate all these methods within a common framework and carry out an exhaustive comparison in order to give a final answer to: which algorithm is the best under which situations? This Thesis shows that the different versions of Fast Marching Methods become useful when applied to motion and path planning problems. Usually, high-level problems as motion learning or robot formation planning are solved with completely different algorithms, as the problem formulation are mixed. Under a common framework, task integration becomes much easier bringing robots closer to everyday applications. The Fast Marching Method has also inspired modern probabilistic methodologies, where computational cost is enormously improved at the cost of bounded, stochastic variations on the resulting paths and trajectories. This Thesis also explores these novel algorithms and their performance.Programa Oficial de Doctorado en Ingeniería Eléctrica, Electrónica y AutomáticaPresidente: Carlos Balaguer Bernaldo de Quirós.- Secretario: Antonio Giménez Fernández.- Vocal: Isabel Lobato de Faria Ribeir

Multi Vehicle Trajectory Planning On Road Networks

When multiple autonomous vehicles work in a shared space, such as in a surface mine or warehouse, they often travel along specified paths through a static road network. Although these vehicles’ actions and performance are coupled, their motion is often planned myopically or omits cooperation beyond avoiding collisions reactively. More desirable solutions could be achieved by coordinating and planning actions ahead of time. To make multi-vehicle systems more productive and efficient, the thesis introduces planning methods that can optimise for travel time, energy consumption, and trajectory smoothness. Vehicle motion is coordinated by using motion models that combine all trajectories, and avoid collisions. Mathematical programming is then used to find optimised solutions. The proposed methods are shown to significantly reduce solution costs compared to an approach based on common driving practices. As the number of vehicles and interactions between them increases, the number of solutions grows exponentially, making finding a solution computationally challenging. A major aim here was to find high quality solutions within practical computation times. To achieve this, techniques were developed that exploit the structure of the problems. This includes a heuristic algorithm that scales better with problem size, and is combined with the mathematical programming techniques to reduce their complexity. These were found to significantly reduce computation times, trading off marginal solution quality