arXiv subjects

Francesco Bullo

Publications and source records attributed to Francesco Bullo.

173 records · Page 10Linked to original sources

arXiv2006

Multirobot rendezvous with visibility sensors in nonconvex environments

This paper presents a coordination algorithm for mobile autonomous robots. Relying upon distributed sensing the robots achieve rendezvous, that is, they move to a common location. Each robot is a point mass moving in a nonconvex environment according to an omnidirectional kinematic model. Each robot is equipped with line-of-sight limited-range sensors, i.e., a robot can measure the relative position of any object (robots or environment boundary) if and only if the object is within a given distance and there are no obstacles in-between. The algorithm is designed using the notions of robust visibility, connectivity-preserving constraint sets, and proximity graphs. Simulations illustrate the theoretical results on the correctness of the proposed algorithm, and its performance in asynchronous setups and with sensor measurement and control errors.

cs.RO↗

arXiv2006

Traveing Salesperson Problems for a double integrator

In this paper we propose some novel path planning strategies for a double integrator with bounded velocity and bounded control inputs. First, we study the following version of the Traveling Salesperson Problem (TSP): given a set of points in $\real^d$, find the fastest tour over the point set for a double integrator. We first give asymptotic bounds on the time taken to complete such a tour in the worst-case. Then, we study a stochastic version of the TSP for double integrator where the points are randomly sampled from a uniform distribution in a compact environment in $\real^2$ and $\real^3$. We propose novel algorithms that perform within a constant factor of the optimal strategy with high probability. Lastly, we study a dynamic TSP: given a stochastic process that generates targets, is there a policy which guarantees that the number of unvisited targets does not diverge over time? If such stable policies exist, what is the minimum wait for a target? We propose novel stabilizing receding-horizon algorithms whose performances are within a constant factor from the optimum with high probability, in $\real^2$ as well as $\real^3$. We also argue that these algorithms give identical performances for a particular nonholonomic vehicle, Dubins vehicle.

cs.RO↗

arXiv2006

Distributed consensus on enclosing shapes and minimum time rendezvous

In this paper we introduce the notion of optimization under control and communication constraint in a robotic network. Starting from a general setup, we focus our attention on the problem of achieving rendezvous in minimum time for a network of first order agents with bounded inputs and limited range communication. We propose two dynamic control and communication laws. These laws are based on consensus algorithms for distributed computation of the minimal enclosing ball and orthotope of a set of points. We prove that these control laws converge to the optimal solution of the centralized problem (i.e., when no communication constrains are enforced) as the bound on the control input goes to zero. Moreover, we give a bound for the time complexity of one of the two laws.

math.OC↗

arXiv2006

Asymptotic constant-factor approximation algorithm for the Traveling Salesperson Problem for Dubins' vehicle

This article proposes the first known algorithm that achieves a constant-factor approximation of the minimum length tour for a Dubins' vehicle through $n$ points on the plane. By Dubins' vehicle, we mean a vehicle constrained to move at constant speed along paths with bounded curvature without reversing direction. For this version of the classic Traveling Salesperson Problem, our algorithm closes the gap between previously established lower and upper bounds; the achievable performance is of order $n^{2/3}$.

cs.RO↗

arXiv2005

Synchronous robotic networks and complexity of control and communication laws

This paper proposes a formal model for a network of robotic agents that move and communicate. Building on concepts from distributed computation, robotics and control theory, we define notions of robotic network, control and communication law, coordination task, and time and communication complexity. We then analyze a number of basic motion coordination algorithms such as pursuit, rendezvous and deployment.

math.OC↗

arXiv2004

Spatially-distributed coverage optimization and control with limited-range interactions

This paper presents coordination algorithms for groups of mobile agents performing deployment and coverage tasks. As an important modeling constraint, we assume that each mobile agent has a limited sensing/communication radius. Based on the geometry of Voronoi partitions and proximity graphs, we analyze a class of aggregate objective functions and propose coverage algorithms in continuous and discrete time. These algorithms have convergence guarantees and are spatially distributed with respect to appropriate proximity graphs. Numerical simulations illustrate the results.

math.OC↗

arXiv2003

Coordination and geometric optimization via distributed dynamical systems

This paper discusses dynamical systems for disk-covering and sphere-packing problems. We present facility location functions from geometric optimization and characterize their differentiable properties. We design and analyze a collection of distributed control laws that are related to nonsmooth gradient systems. The resulting dynamical systems promise to be of use in coordination problems for networked robots; in this setting the distributed control laws correspond to local interactions between the robots. The technical approach relies on concepts from computational geometry, nonsmooth analysis, and the dynamical system approach to algorithms.

math.OC↗

arXiv2003

A catalog of inverse-kinematics planners for underactuated systems on matrix groups

This paper presents motion planning algorithms for underactuated systems evolving on rigid rotation and displacement groups. Motion planning is transcribed into (low-dimensional) combinatorial selection and inverse-kinematics problems. We present a catalog of solutions for all underactuated systems on $\SE{2}$, $\SO{3}$ and $\SE{2}\times\real$ classified according to their controllability properties.

math.OC↗

arXiv2002

Quantized control via locational optimization

This paper studies state quantization schemes for feedback stabilization of control systems with limited information. The focus is on designing the least destabilizing quantizer subject to a given information constraint. We explore several ways of measuring the destabilizing effect of a quantizer on the closed-loop system, including (but not limited to) the worst-case quantization error. In each case, we show how quantizer design can be naturally reduced to a version of the so-called multicenter problem from locational optimization. Algorithms for solving such problems are discussed. In particular, an iterative solver is developed for a novel weighted multicenter problem which most accurately represents the least destabilizing quantizer design.

math.OC↗

arXiv2002

Motion planning and control problems for underactuated robots

Motion planning and control are key problems in a collection of robotic applications including the design of autonomous agile vehicles and of minimalist manipulators. These problems can be accurately formalized within the language of affine connections and of geometric control theory. In this paper we overview recent results on kinematic controllability and on oscillatory controls. Furthermore, we discuss theoretical and practical open problems as well as we suggest control theoretical approaches to them.

math.OC↗

arXiv2002

Computational problems for vector-valued quadratic forms

Given two real vector spaces $U$ and $V$, and a symmetric bilinear map $B: U\times U\to V$, let $Q_B$ be its associated quadratic map $Q_B$. The problems we consider are as follows: (i) are there necessary and sufficient conditions, checkable in polynomial-time, for determining when $Q_B$ is surjective?; (ii) if $Q_B$ is surjective, given $v\in V$ is there a polynomial-time algorithm for finding a point $u\in Q_B^{-1}(v)$?; (iii) are there necessary and sufficient conditions, checkable in polynomial-time, for determining when $B$ is indefinite? We present an alternative formulation of the problem of determining the image of a vector-valued quadratic form in terms of the unprojectivised Veronese surface. The relation of these questions with several interesting problems in Control Theory is illustrated.

math.AG↗