On Synchronous Robotic Networks—Part II: Time Complexity of Rendezvous and Deployment Algorithms

This paper analyzes a number of basic coordination algorithms running on synchronous robotic networks. We provide upper and lower bounds on the time complexity of the move-toward-average and circumcenter laws, both achieving rendezvous, and of the centroid law, achieving deployment over a region of interest. The results are derived via novel analysis methods, including a set of results on the convergence rates of linear dynamical systems defined by tridiagonal Toeplitz and circulant matrices.     

A Stochastic and Dynamic Vehicle Routing Problem with Time Windows and Customer Impatience

In this paper, we study the problem of designing motion strategies for a team of mobile agents, required to fulfill request for on-site service in a given planar region. In our model, each service request is generated by a spatio-temporal stochastic process; once a service request has been generated, it remains active for a certain deterministic amount of time, and then expires. An active service request is fulfilled when one of the mobile agents visits the location of the request. Specific problems we investigate are the following: what is the minimum number of mobile agents needed to ensure that a certain fraction of service requests is fulfilled before expiration? What strategy should they use to ensure that this objective is attained? This problem can be viewed as the stochastic and dynamic version of the well-known vehicle routing problem with time windows. We also extend our analysis to the case in which the time service requests remain active is itself a random variable, describing customer impatience. The customers’ impatience is only known to the mobile agents via prior statistics. In this case, it is desired to minimize the fraction of service requests missed because of impatience. Finally, we show how the routing strategies presented in the paper can be executed in a distributed fashion.     

Sharing the load

Modern technological advances make the deployment of large groups of autonomous mobile agents with onboard computing and communication capabilities increasingly feasible and attractive. In the near future, large groups of such autonomous agents will be used to perform complex tasks in dynamic environments, including transportation and distribution, logistics, surveillance, search and rescue operations, humanitarian demining, environmental monitoring, and planetary exploration     

Efficient Routing Algorithms for Multiple Vehicles With no Explicit Communications

In this paper, we consider a class of dynamic vehicle routing problems, in which a number of mobile agents in the plane must visit target points generated over time by a stochastic process. It is desired to design motion coordination strategies in order to minimize the expected time between the appearance of a target point and the time it is visited by one of the agents. We propose control strategies that, while making minimal or no assumptions on communications between agents, provide the same level of steady-state performance achieved by the best known decentralized strategies. In other words, we demonstrate that inter-agent communication does not improve the efficiency of such systems, but merely affects the rate of convergence to the steady state. Furthermore, the proposed strategies do not rely on the knowledge of the details of the underlying stochastic process. Finally, we show that our proposed strategies yield an efficient, pure Nash equilibrium in a game theoretic formulation of the problem, in which each agent's objective is to maximize the expected value of the ldquotime spent alonerdquo at the next target location. Simulation results are presented and discussed.     

Traveling Salesperson Problems for a Double Integrator

This technical note studies the following version of the Traveling Salesperson Problem (TSP) for a double integrator with bounded velocity and bounded control inputs: given a set of points in Ropf^d, find the fastest tour over the point set. 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 a double integrator in Ropf² and Ropf³, where we propose novel algorithms that asymptotically perform within a constant factor of the optimal strategy with probability one. Lastly, we study a dynamic TSP in Ropf² and Ropf³ , where we propose novel stabilizing algorithms whose performances are within a constant factor from the optimum.     

Symbolic planning and control of robot motion [Grand Challenges of Robotics]

In this paper, different research trends that use symbolic techniques for robot motion planning and control are illustrated. As it often happens in new research areas, contributions to this topic started at about the same time by different groups with different emphasis, approaches, and notation. This article tries to describe a framework in which many of the current methods and ideas can be placed and to provide a coherent picture of what the authors want to do, what have they got so far, and what the main missing pieces are. Generally speaking, the aim of symbolic control as is envisioned in this article is to enable the usage of methods of formal logic, languages, and automata theory for solving effectively complex planning problems for robots and teams of robots. The results presented in this article can be divided in two groups: top-down approaches, whereby formal logic tools are employed on rather abstract models of robots; and bottom up approaches, whose aim is to provide means by which such abstractions are possible and effective. The two ends do not quite tie as yet, and much work remains to be done in both directions to obtain generally applicable methods. However, the prospects of symbolic control of robots are definitely promising, and the challenging nature of problems to be solved warrants for the interest of a wide community of researchers     

Decentralized Cooperative Policy for Conflict Resolution in Multivehicle Systems

In this paper, we propose a novel policy for steering multiple vehicles between assigned start and goal configurations, ensuring collision avoidance. The policy rests on the assumption that all agents are cooperating by implementing the same traffic rules. However, the policy is completely decentralized, as each agent decides its own motion by applying those rules only on the locally available information, and scalable, in the sense that the amount of information processed by each agent and the computational complexity of the algorithms do not increase with the number of agents in the scenario. The proposed policy applies to systems in which new vehicles may enter the scene and start interacting with existing ones at any time, while others may leave. Under mild conditions on the initial configurations, the policy is shown to be safe, i.e., it guarantees collision avoidance throughout the system evolution. In the paper, conditions are discussed on the desired configurations of agents, under which the ultimate convergence of all vehicles to their goals can also be guaranteed. To show that such conditions are actually necessary and sufficient, which turns out to be a challenging liveness-verification problem for a complex hybrid automaton, we employ a probabilistic verification method. The paper finally presents and discusses simulations for systems of several tens of vehicles, and reports on some experimental implementation showing the practicality of the approach.     

On Synchronous Robotic Networks—Part I: Models, Tasks, and Complexity

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 illustrate our model and compute the proposed complexity measures in the example of a network of locally connected agents on a circle that agree upon a direction of motion and pursue their immediate neighbors.     

Maneuver-based motion planning for nonlinear systems with symmetries

In this paper, we introduce an approach for the efficient solution of motion-planning problems for time-invariant dynamical control systems with symmetries, such as mobile robots and autonomous vehicles, under a variety of differential and algebraic constraints on the state and on the control inputs. Motion plans are described as the concatenation of a number of well-defined motion primitives, selected from a finite library. Rules for the concatenation of primitives are given in the form of a regular language, defined through a finite-state machine called a Maneuver Automaton. We analyze the reachability properties of the language, and present algorithms for the solution of a class of motion-planning problems. In particular, it is shown that the solution of steering problems for nonlinear dynamical systems with symmetries and invariant constraints can be reduced to the solution of a sequence of kinematic inversion problems. A detailed example of the application of the proposed approach to motion planning for a small aerobatic helicopter is presented.