This paper presents control and coordination algorithms for groups of vehicles. The focus is on autonomous vehicle networks performing distributed sensing tasks where each vehicle plays the role of a mobile tunable sensor. The paper proposes gradient descent algorithms for a class of utility functions which encode optimal coverage and sensing policies. The resulting closed-loop behavior is adaptive, distributed, asynchronous, and verifiably correct.

Coverage control for mobile sensing networks

This self-contained introduction to the distributed control of robotic networks offers a distinctive blend of computer science and control theory. The book presents a broad set of tools for understanding coordination algorithms, determining their correctness, and assessing their complexity; and it analyzes various cooperative strategies for tasks such as consensus, rendezvous, connectivity maintenance, deployment, and boundary estimation. The unifying theme is a formal model for robotic networks that explicitly incorporates their communication, sensing, control, and processing capabilities--a model that in turn leads to a common formal language to describe and analyze coordination algorithms.Written for first- and second-year graduate students in control and robotics, the book will also be useful to researchers in control theory, robotics, distributed algorithms, and automata theory. The book provides explanations of the basic concepts and main results, as well as numerous examples and exercises.Self-contained exposition of graph-theoretic concepts, distributed algorithms, and complexity measures for processor networks with fixed interconnection topology and for robotic networks with position-dependent interconnection topology Detailed treatment of averaging and consensus algorithms interpreted as linear iterations on synchronous networks Introduction of geometric notions such as partitions, proximity graphs, and multicenter functions Detailed treatment of motion coordination algorithms for deployment, rendezvous, connectivity maintenance, and boundary estimation

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Distributed Control of Robotic Networks: A Mathematical Approach to Motion Coordination Algorithms

(1987). Applied Probability and Queues. Journal of the Operational Research Society: Vol. 38, No. 11, pp. 1095-1096.

https://link.springer.com/content/pdf/10.1057%2Fjors.1987.184.pdf

Applied Probability and Queues

This paper addresses the connectedness issue in multiagent coordination, i.e., the problem of ensuring that a group of mobile agents stays connected while achieving some performance objective. In particular, we study the rendezvous and the formation control problems over dynamic interaction graphs, and by adding appropriate weights to the edges in the graphs, we guarantee that the graphs stay connected.

Distributed Coordination Control of Multiagent Systems While Preserving Connectedness

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http://carmenere.ucsd.edu/pdfs/DCRN-BulloCortesMartinez-bibliography.pdf

Distributed Control of Robotic Networks

In this paper, we study minimum-time motion planning and routing problems for the Dubins vehicle, i.e., a nonholonomic vehicle that is constrained to move along planar paths of bounded curvature, without reversing direction. Motivated by autonomous aerial vehicle applications, we consider the traveling salesperson problem for the Dubins vehicle (DTSP): given n points on a plane, what is the shortest Dubins tour through these points, and what is its length? First, we show that the worst-case length of such a tour grows linearly with n and we propose a novel algorithm with performance within a constant factor of the optimum for the worst-case point sets. In doing this, we also obtain an upper bound on the optimal length in the classical point-to-point problem. Second, we study a stochastic version of the DTSP where the n targets are randomly and independently sampled from a uniform distribution. We show that the expected length of such a tour is of order at least n 2/3 and we propose a novel algorithm yielding a solution with length of order n 2/3 with probability one. Third and finally, we study a dynamic version of the DTSP: given a stochastic process that generates target points, is there a policy that guarantees that the number of unvisited points does not diverge over time? If such stable policies exist, what is the minimum expected time that a newly generated target waits before being visited by the vehicle? We propose a novel stabilizing algorithm such that the expected wait time is provably within a constant factor from the optimum.

Traveling Salesperson Problems for the Dubins Vehicle

Recent years have witnessed great advancements in the science and technology of autonomy, robotics, and networking. This paper surveys recent concepts and algorithms for dynamic vehicle routing (DVR), that is, for the automatic planning of optimal multivehicle routes to perform tasks that are generated over time by an exogenous process. We consider a rich variety of scenarios relevant for robotic applications. We begin by reviewing the basic DVR problem: demands for service arrive at random locations at random times and a vehicle travels to provide on-site service while minimizing the expected wait time of the demands. Next, we treat different multivehicle scenarios based on different models for demands (e.g., demands with different priority levels and impatient demands), vehicles (e.g., motion constraints, communication, and sensing capabilities), and tasks. The performance criterion used in these scenarios is either the expected wait time of the demands or the fraction of demands serviced successfully. In each specific DVR scenario, we adopt a rigorous technical approach that relies upon methods from queueing theory, combinatorial optimization, and stochastic geometry. First, we establish fundamental limits on the achievable performance, including limits on stability and quality of service. Second, we design algorithms, and provide provable guarantees on their performance with respect to the fundamental limits.

/pdf/dynamic-vehicle-routing-for-robotic-systems-1awbux7gva.pdf

Dynamic Vehicle Routing for Robotic Systems

In this paper we study the length of optimal paths for Dubins' vehicle, i.e., a vehicle constrained to move forward along paths of bounded curvature. First, we obtain an upper bound on the optimal length in the point-to-point problem. Next, we consider the corresponding traveling salesperson problem (TSP). We provide an algorithm with worst-case performance within a constant factor approximation of the optimum. We also establish an asymptotic bound on the worst-case length of the Dubins' TSP.

/pdf/on-the-point-to-point-and-traveling-salesperson-problems-for-13f7gi5fit.pdf

On the point-to-point and traveling salesperson problems for Dubins' vehicle

In this paper we consider ad-hoc networks of robotic agents with double integrator dynamics. For such networks, the connectivity maintenance problems are as follows: (i) Do there exist control inputs for each agent to maintain network connectivity, and (ii) given desired controls for each agent, can we compute the closest connectivity-maintaining controls in a distributed fashion? The proposed solution is based on three contributions. First, we define and characterize admissible sets for double integrators to remain inside disks. Second, we establish an existence theorem for the connectivity maintenance problem by introducing a novel state-dependent graph, called the double-integrator disk graph. Specifically, we show that one can always maintain connectivity by maintaining a spanning tree of this new graph, but one will not always maintain connectivity of a particular agent pair that happens to be connected at one instant of time. Finally, we design a distributed “flow-control” algorithm for distributed computation of connectivity-maintaining controls.

/pdf/maintaining-limited-range-connectivity-among-second-order-j5s3kp8xfa.pdf

Maintaining Limited-Range Connectivity Among Second-Order Agents

In this paper we consider ad-hoc networks of robotic agents with double integrator dynamics. For such networks, the connectivity maintenance problems are: (i) do there exist control inputs for each agent to maintain network connectivity, and (ii) given desired controls for each agent, can one compute the closest connectivity-maintaining controls in a distributed fashion. The proposed solution is based on three contributions. First, we define and characterize admissible sets for double integrators to remain inside disks. Second, we establish an existence theorem for the connectivity maintenance problem by introducing a novel state-dependent graph, called the double-integrator disk graph. Finally, we design a distributed "flow-control" algorithm to compute optimal connectivity-maintaining controls.

/pdf/maintaining-limited-range-connectivity-among-second-order-2knykn0b7k.pdf

Ketan Savla

Papers

Traveling Salesperson Problems for the Dubins Vehicle

Dynamic Vehicle Routing for Robotic Systems

On the point-to-point and traveling salesperson problems for Dubins' vehicle

Maintaining Limited-Range Connectivity Among Second-Order Agents

Maintaining limited-range connectivity among second-order agents