16,151 research outputs found
Optimal Event-Driven Multi-Agent Persistent Monitoring of a Finite Set of Targets
We consider the problem of controlling the movement of multiple cooperating
agents so as to minimize an uncertainty metric associated with a finite number
of targets. In a one-dimensional mission space, we adopt an optimal control
framework and show that the solution is reduced to a simpler parametric
optimization problem: determining a sequence of locations where each agent may
dwell for a finite amount of time and then switch direction. This amounts to a
hybrid system which we analyze using Infinitesimal Perturbation Analysis (IPA)
to obtain a complete on-line solution through an event-driven gradient-based
algorithm which is also robust with respect to the uncertainty model used. The
resulting controller depends on observing the events required to excite the
gradient-based algorithm, which cannot be guaranteed. We solve this problem by
proposing a new metric for the objective function which creates a potential
field guaranteeing that gradient values are non-zero. This approach is compared
to an alternative graph-based task scheduling algorithm for determining an
optimal sequence of target visits. Simulation examples are included to
demonstrate the proposed methods.Comment: 12 pages full version, IEEE Conference on Decision and Control, 201
An Optimal Control Approach for the Data Harvesting Problem
We propose a new method for trajectory planning to solve the data harvesting
problem. In a two-dimensional mission space, mobile agents are tasked with
the collection of data generated at stationary sources and delivery to a
base aiming at minimizing expected delays. An optimal control formulation of
this problem provides some initial insights regarding its solution, but it is
computationally intractable, especially in the case where the data generating
processes are stochastic. We propose an agent trajectory parameterization in
terms of general function families which can be subsequently optimized on line
through the use of Infinitesimal Perturbation Analysis (IPA). Explicit results
are provided for the case of elliptical and Fourier series trajectories and
some properties of the solution are identified, including robustness with
respect to the data generation processes and scalability in the size of an
event set characterizing the underlying hybrid dynamic system
Optimal control approaches for persistent monitoring problems.
Thesis (Ph. D.)--Boston UniversityPersistent monitoring tasks arise when agents must monitor a dynamically changing environment which cannot be fully covered by a stationary team of available agents. It differs from traditional coverage tasks due to the perpetual need to cover a changing environment, i.e., all areas of the mission space must be visited infinitely often. This dissertation presents an optimal control framework for persistent monitoring problems where the objective is to control the movement of multiple cooperating agents to minimize an uncertainty metric in a given mission space. In an one-dimensional mission space, it is shown that the optimal solution is for each agent to move at maximal speed from one switching point to the next, possibly waiting some time at each point before reversing its direction. Thus, the solution is reduced to a simpler parametric optimization problem: determining a sequence of switching locations and associated waiting times at these switching points for each agent. This amounts to a hybrid system which is analyzed using Infinitesimal Perturbation Analysis
(IPA) , to obtain a complete on-line solution through a gradient-based algorithm. IPA is a
method used to provide unbiased gradient estimates of performance metrics with respect
to various controllable parameters in Discrete Event Systems (DES) as well as in Hybrid
Systems (HS). It is also shown that the solution is robust with respect to the uncertainty
model used, i.e., IPA provides an unbiased estimate of the gradient without any detailed
knowledge of how uncertainty affects the mission space.
In a two-dimensional mission space, such simple solutions can no longer be derived.
An alternative is to optimally assign each agent a linear trajectory, motivated by the one dimensional analysis. It is proved, however, that elliptical trajectories outperform linear ones. With this motivation, the dissertation formulates a parametric optimization problem to determine such trajectories. It is again shown that the problem can be solved using IPA to obtain performance gradients on line and obtain a complete and scalable solution. Since the solutions obtained are generally locally optimal, a stochastic comparison algorithm is incorporated for deriving globally optimal elliptical trajectories. The dissertation also approaches the problem by representing an agent trajectory in terms of general function families characterized by a set of parameters to be optimized. The approach is applied to the family of Lissajous functions as well as a Fourier series representation of an agent trajectory. Numerical examples indicate that this scalable approach provides solutions that are near optimal relative to those obtained through a computationally intensive two point boundary value problem (TPBVP) solver. In the end, the problem is tackled using centralized and decentralized Receding Horizon Control (RHC) algorithms, which dynamically determine the control for agents by solving a sequence of optimization problems over a planning horizon and executing them over a shorter action horizon
Multi-Agent Coverage Control with Energy Depletion and Repletion
We develop a hybrid system model to describe the behavior of multiple agents
cooperatively solving an optimal coverage problem under energy depletion and
repletion constraints. The model captures the controlled switching of agents
between coverage (when energy is depleted) and battery charging (when energy is
replenished) modes. It guarantees the feasibility of the coverage problem by
defining a guard function on each agent's battery level to prevent it from
dying on its way to a charging station. The charging station plays the role of
a centralized scheduler to solve the contention problem of agents competing for
the only charging resource in the mission space. The optimal coverage problem
is transformed into a parametric optimization problem to determine an optimal
recharging policy. This problem is solved through the use of Infinitesimal
Perturbation Analysis (IPA), with simulation results showing that a full
recharging policy is optimal
Multi-agent persistent monitoring of a finite set of targets
The general problem of multi-agent persistent monitoring finds applications in a variety of domains ranging from meter to kilometer-scale systems, such as surveillance or environmental monitoring, down to nano-scale systems such as tracking biological macromolecules for studying basic biology and disease. The problem can be cast as moving the agents between targets, acquiring information from or in some fashion controlling the states of the targets. Under this formulation, at least two questions need to be addressed. The first is the design of motion trajectories for the agents as they move among the spatially distributed targets and jointly optimize a given cost function that describes some desired application. The second is the design of the controller that an agent will use at a target to steer the target's state as desired.
The first question can be viewed in at least two ways: first, as an optimal control problem with the domain of the targets described as a continuous space, and second as a discrete scheduling task. In this work we focus on the second approach, which formulates the target dynamics as a hybrid automaton, and the geometry of the targets as a graph. We show how to find solutions by translating the scheduling problem into a search for the optimal route. With a route specifying the visiting sequence in place, we derive the optimal time the agent spends at each target analytically.
The second question, namely that of steering the target's state, can be formulated from the perspective of the target, rather than the agent. The mobile nature of the agents leads to intermittencontrol, such that the controller is assumed to be disconnected when no agent is at the target. The design of the visiting schedule of agents to one target can affect the reachability (controllability) of this target's control system and the design of any specific controller. Existing test techniques for reachability are combined with the idea of lifting to provide conditions on systems such that reachability is maintained in the presence of periodic disconnections from the controller. While considering an intermittently connected control with constraints on the control authority and in the presence of a disturbance, the concept of 'degree of controllability' is introduced. The degree is measured by a region of states that can be brought back to the origin in a given finite time. The size of this region is estimated to evaluate the performance of a given sequence
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