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) piecewise smooth and continuous 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. We further extend these provable properties to practically motivated limited range sensing models

Exact Robot Navigation Using Power Diagrams

We reconsider the problem of reactive navigation in sphere worlds, i.e., the construction of a vector field over a compact, convex Euclidean subset punctured by Euclidean disks, whose flow brings a Euclidean disk robot from all but a zero measure set of initial conditions to a designated point destination, with the guarantee of no collisions along the way. We use power diagrams, generalized Voronoi diagrams with additive weights, to identify the robot’s collision free convex neighborhood, and to generate the value of our proposed candidate solution vector field at any free configuration via evaluation of an associated convex optimization problem. We prove that this scheme generates a continuous flow with the specified properties. We also propose its practical extension to the nonholonomically constrained kinematics of the standard differential drive vehicle.For more information: Kod*la

Adaptive Robot Navigation with Collision Avoidance subject to 2nd-order Uncertain Dynamics

This paper considers the problem of robot motion planning in a workspace with obstacles for systems with uncertain 2nd-order dynamics. In particular, we combine closed form potential-based feedback controllers with adaptive control techniques to guarantee the collision-free robot navigation to a predefined goal while compensating for the dynamic model uncertainties. We base our findings on sphere world-based configuration spaces, but extend our results to arbitrary star-shaped environments by using previous results on configuration space transformations. Moreover, we propose an algorithm for extending the control scheme to decentralized multi-robot systems. Finally, extensive simulation results verify the theoretical findings

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

Navigation of a Quadratic Potential with Ellipsoidal Obstacles

Given a convex quadratic potential of which its minimum is the agent's goal and a space populated with ellipsoidal obstacles, one can construct a Rimon-Koditschek artificial potential to navigate. These potentials are such that they combine the natural attractive potential of which its minimum is the destination of the agent with potentials that repel the agent from the boundary of the obstacles. This is a popular approach to navigation problems since it can be implemented with spatially local information that is acquired during operation time. However, navigation is only successful in situations where the obstacles are not too eccentric (flat). This paper proposes a modification to gradient dynamics that allows successful navigation of an environment with a quadratic cost and ellipsoidal obstacles regardless of their eccentricity. This is accomplished by altering gradient dynamics with the addition of a second order curvature correction that is intended to imitate worlds with spherical obstacles in which Rimon-Koditschek potentials are known to work. Convergence to the goal and obstacle avoidance is established from every initial position in the free space. Results are numerically verified with a discretized version of the proposed flow dynamics

Distributed cooperation of multiple robots under operational constraints via lean communication

Η αυτόνομη λειτουργία των ρομπότ εντός περίπλοκων χώρων εργασίας αποτελεί ένα επίκαιρο θέμα έρευνας και η αυτόνομη πλοήγηση είναι αναμφισβήτητα ένα θεμελιώδες κομμάτι αυτής. Επιπλέον, καθώς οι εργασίες που τα ρομπότ καλούνται να εκπληρώσουν αυξάνονται σε πολυπλοκότητα μέρα με τη μέρα, η χρήση πολύ-ρομποτικών συστημάτων, τα οποία εμφανίζουν γενικά υψηλότερη ευρωστία και ευελιξία, αυξάνεται προοδευτικά. Ως εκ τούτου, τα προβλήματα αυτόνομης πλοήγησης που πρέπει να επιλυθούν γίνονται όλο και πιο απαιτητικά, αυξάνοντας την ανάγκη για πιο αποτελεσματικά και σθεναρά σχήματα σχεδιασμού πορείας και κίνησης

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