Safe and Quasi-Optimal Autonomous Navigation in Environments with Convex Obstacles

We propose a continuous feedback control strategy that steers a point-mass vehicle safely to a destination, in a quasi-optimal manner, in sphere worlds. The main idea consists in avoiding each obstacle via the shortest path within the cone enclosing the obstacle and moving straight toward the target when the vehicle has a clear line of sight to the target location. In particular, almost global asymptotic stability of the target location is achieved in two-dimensional (2D) environments under a particular assumption on the obstacles configuration. We also propose a reactive (sensor-based) approach, suitable for real-time implementations in a priori unknown 2D environments with sufficiently curved convex obstacles, guaranteeing almost global asymptotic stability of the target location. Simulation results are presented to illustrate the effectiveness of the proposed approach.Comment: arXiv admin note: substantial text overlap with arXiv:2302.1230

Safety using Analytically Constructed Density Functions

This paper presents a novel approach for safe control synthesis using the dual formulation of the navigation problem. The main contribution of this paper is in the analytical construction of density functions for almost everywhere navigation with safety constraints. In contrast to the existing approaches, where density functions are used for the analysis of navigation problems, we use density functions for the synthesis of safe controllers. We provide convergence proof using the proposed density functions for navigation with safety. Further, we use these density functions to design feedback controllers capable of navigating in cluttered environments and high-dimensional configuration spaces. The proposed analytical construction of density functions overcomes the problem associated with navigation functions, which are known to exist but challenging to construct, and potential functions, which suffer from local minima. Application of the developed framework is demonstrated on simple integrator dynamics and fully actuated robotic systems

Safe Navigation of Quadruped Robots Using Density Functions

Safe navigation of mission-critical systems is of utmost importance in many modern autonomous applications. Over the past decades, the approach to the problem has consisted of using probabilistic methods, such as sample-based planners, to generate feasible, safe solutions to the navigation problem. However, these methods use iterative safety checks to guarantee the safety of the system, which can become quite complex. The navigation problem can also be solved in feedback form using potential field methods. Navigation function, a class of potential field methods, is an analytical control design to give almost everywhere convergence properties, but under certain topological constraints and mapping onto a sphere world. Alternatively, the navigation problem can be formulated in the dual space of density. Recent works have shown the use of linear operator theory on density to convexly approach the navigation problem. Inspired by those works, this work uses the physical-based interpretation of occupation through density to synthesize a safe controller for the navigation problem. Moreso, by using this occupation-based interpretation of density, we design a feedback density-based controller to solve the almost everywhere navigation problem. Furthermore, due to the recent popularity of legged locomotion for the navigation problem, we integrate this analytical feedback density-based controller into the quadruped navigation problem. By devising a density-based navigation architecture, we show in simulation and hardware the results of the density-based navigation

Sensor-Based Reactive Navigation in Unknown Convex Sphere Worlds

We construct a sensor-based feedback law that provably solves the real-time collision-free robot navigation problem in a compact convex Euclidean subset cluttered with unknown but sufficiently separated and strongly convex obstacles. Our algorithm introduces a novel use of separating hyperplanes for identifying the robot’s local obstacle-free convex neighborhood, affording a reactive (online-computed) continuous and piecewise smooth closed-loop vector field whose smooth flow brings almost all configurations in the robot’s free space to a designated goal location, with the guarantee of no collisions along the way. Specialized attention to planar navigable environments yields a necessary and sufficient condition on convex obstacles for almost global navigation towards any goal location in the environment. We further extend these provable properties of the planar setting to practically motivated limited range, isotropic and anisotropic sensing models, and the nonholonomically constrained kinematics of the standard differential drive vehicle. We conclude with numerical and experimental evidence demonstrating the effectiveness of the proposed sensory feedback motion planner

Stochastic Control Foundations Of Autonomous Behavior

The goal of this thesis is to develop a mathematical framework for autonomous behavior. We begin by describing a minimum notion of autonomy, understood as the ability that an agent operating in a complex space has to satisfy in the long run a set of constraints imposed by the environment of which the agent does not have information a priori. In particular, we care about endowing agents with greedy algorithms to solve problems of the form previously described. Although autonomous behavior will require logic reasoning, the goal is to understand what is the most complex autonomous behavior that can be achieved through greedy algorithms. Being able to extend the class of problems that can be solved with these simple algorithms can allow to free the logic of the system and to focus it towards high-level reasoning and planning. The second and third chapters of this thesis focus on the problem of designing gradient controllers that allow an agent to navigate towards the minimum of a convex potential in punctured spaces. Such problem is related to the problem of satisfying constraints since we can interpret each constraint as a separate potential that needs to be minimized. We solve this problem first in the case where the information about the potential and the obstacles is deterministic and complete and later, in Chapter \ref{chap_stochnf}, we consider the case where this information is only available from a stochastic model. In both cases, we derive sufficient conditions in which a Rimon-Koditschek artificial potential can be tuned into a navigation function and hence being able to solve the problem. These conditions relate the geometry of the potential of interest and the geometry of the obstacles. Chapter \ref{chap_feasibility} considers the problem of satisfying a set of constraints when their temporal evolution is arbitrary. We show that an online version of a saddle point controller generates trajectories whose fit and regret are bounded by sublinear functions. These metrics are associated with online operation and they are analogous to feasibility and optimality in classic deterministic optimization. The fact that these quantities are bounded by sublinear functions suggests that the trajectories approach the optimal solution. Saddle points have the advantage of providing an intuition on the relative hardness of satisfying each constraint. The limit values of the multipliers are a measure of such relative difficulty, the larger the multiplier the larger is the cost in which one incurs if we try to tighten the corresponding constraint. In Chapter \ref{chap_counterfactuals} we exploit this property and modify the saddle point controller to deal with situations in which the problems of interest are not feasible. The modification of the algorithm allows us to identify which are the constraints that are harder to satisfy. This information can later be used by a high logic reasoning to modify the problem of interest to make it feasible. Before concluding remarks and future work we devote our attention to the problem of non-myopic agents. In Chapter \ref{chap_rl} we consider the setting of reinforcement learning where the objective is to maximize the expected cumulative rewards that the agent gathers, i.e., the $Q$-function. We model the policy of the agent as a function in a Reproducing Kernel Hilbert Space since this class of functions has the advantage of being quite rich and allows us to compute policy gradients in a simple way. We present an unbiased estimator of the policy gradient that can be constructed in finite time and we establish convergence of the stochastic gradient policy ascent to a function that is a critical point of the $Q$-function

Mobile Robot Navigation for Person Following in Indoor Environments

Service robotics is a rapidly growing area of interest in robotics research. Service robots inhabit human-populated environments and carry out specific tasks. The goal of this dissertation is to develop a service robot capable of following a human leader around populated indoor environments. A classification system for person followers is proposed such that it clearly defines the expected interaction between the leader and the robotic follower. In populated environments, the robot needs to be able to detect and identify its leader and track the leader through occlusions, a common characteristic of populated spaces. An appearance-based person descriptor, which augments the Kinect skeletal tracker, is developed and its performance in detecting and overcoming short and long-term leader occlusions is demonstrated. While following its leader, the robot has to ensure that it does not collide with stationary and moving obstacles, including other humans, in the environment. This requirement necessitates the use of a systematic navigation algorithm. A modified version of navigation function path planning, called the predictive fields path planner, is developed. This path planner models the motion of obstacles, uses a simplified representation of practical workspaces, and generates bounded, stable control inputs which guide the robot to its desired position without collisions with obstacles. The predictive fields path planner is experimentally verified on a non-person follower system and then integrated into the robot navigation module of the person follower system. To navigate the robot, it is necessary to localize it within its environment. A mapping approach based on depth data from the Kinect RGB-D sensor is used in generating a local map of the environment. The map is generated by combining inter-frame rotation and translation estimates based on scan generation and dead reckoning respectively. Thus, a complete mobile robot navigation system for person following in indoor environments is presented

Obstacle Avoidance in Formation Using Navigation-like Functions and Constraint Based Programming

Abstract-In this paper, we combine navigation functionlike potential fields and constraint based programming to achieve obstacle avoidance in formation. Constraint based programming was developed in robotic manipulation as a technique to take several constraints into account when controlling redundant manipulators. The approach has also been generalized, and applied to other control systems such as dual arm manipulators and unmanned aerial vehicles. Navigation functions are an elegant way to design controllers with provable properties for navigation problems. By combining these tools, we take advantage of the redundancy inherent in a multi-agent control problem and are able to concurrently address features such as formation maintenance and goal convergence, even in the presence of moving obstacles. We show how the user can decide a priority ordering of the objectives, as well as a clear way of seeing what objectives are currently addressed and what are postponed. We also analyze the theoretical properties of the proposed controller. Finally, we use a set of simulations to illustrate the approach

Enhanced Virtuality: Increasing the Usability and Productivity of Virtual Environments

Mit stetig steigender Bildschirmauflösung, genauerem Tracking und fallenden Preisen stehen Virtual Reality (VR) Systeme kurz davor sich erfolgreich am Markt zu etablieren. Verschiedene Werkzeuge helfen Entwicklern bei der Erstellung komplexer Interaktionen mit mehreren Benutzern innerhalb adaptiver virtueller Umgebungen. Allerdings entstehen mit der Verbreitung der VR-Systeme auch zusätzliche Herausforderungen: Diverse Eingabegeräte mit ungewohnten Formen und Tastenlayouts verhindern eine intuitive Interaktion. Darüber hinaus zwingt der eingeschränkte Funktionsumfang bestehender Software die Nutzer dazu, auf herkömmliche PC- oder Touch-basierte Systeme zurückzugreifen. Außerdem birgt die Zusammenarbeit mit anderen Anwendern am gleichen Standort Herausforderungen hinsichtlich der Kalibrierung unterschiedlicher Trackingsysteme und der Kollisionsvermeidung. Beim entfernten Zusammenarbeiten wird die Interaktion durch Latenzzeiten und Verbindungsverluste zusätzlich beeinflusst. Schließlich haben die Benutzer unterschiedliche Anforderungen an die Visualisierung von Inhalten, z.B. Größe, Ausrichtung, Farbe oder Kontrast, innerhalb der virtuellen Welten. Eine strikte Nachbildung von realen Umgebungen in VR verschenkt Potential und wird es nicht ermöglichen, die individuellen Bedürfnisse der Benutzer zu berücksichtigen. Um diese Probleme anzugehen, werden in der vorliegenden Arbeit Lösungen in den Bereichen Eingabe, Zusammenarbeit und Erweiterung von virtuellen Welten und Benutzern vorgestellt, die darauf abzielen, die Benutzerfreundlichkeit und Produktivität von VR zu erhöhen. Zunächst werden PC-basierte Hardware und Software in die virtuelle Welt übertragen, um die Vertrautheit und den Funktionsumfang bestehender Anwendungen in VR zu erhalten. Virtuelle Stellvertreter von physischen Geräten, z.B. Tastatur und Tablet, und ein VR-Modus für Anwendungen ermöglichen es dem Benutzer reale Fähigkeiten in die virtuelle Welt zu übertragen. Des Weiteren wird ein Algorithmus vorgestellt, der die Kalibrierung mehrerer ko-lokaler VR-Geräte mit hoher Genauigkeit und geringen Hardwareanforderungen und geringem Aufwand ermöglicht. Da VR-Headsets die reale Umgebung der Benutzer ausblenden, wird die Relevanz einer Ganzkörper-Avatar-Visualisierung für die Kollisionsvermeidung und das entfernte Zusammenarbeiten nachgewiesen. Darüber hinaus werden personalisierte räumliche oder zeitliche Modifikationen vorgestellt, die es erlauben, die Benutzerfreundlichkeit, Arbeitsleistung und soziale Präsenz von Benutzern zu erhöhen. Diskrepanzen zwischen den virtuellen Welten, die durch persönliche Anpassungen entstehen, werden durch Methoden der Avatar-Umlenkung (engl. redirection) kompensiert. Abschließend werden einige der Methoden und Erkenntnisse in eine beispielhafte Anwendung integriert, um deren praktische Anwendbarkeit zu verdeutlichen. Die vorliegende Arbeit zeigt, dass virtuelle Umgebungen auf realen Fähigkeiten und Erfahrungen aufbauen können, um eine vertraute und einfache Interaktion und Zusammenarbeit von Benutzern zu gewährleisten. Darüber hinaus ermöglichen individuelle Erweiterungen des virtuellen Inhalts und der Avatare Einschränkungen der realen Welt zu überwinden und das Erlebnis von VR-Umgebungen zu steigern