This paper proposes a decentralized approach for solving the problem of moving a swarm of agents into a desired formation. We propose a decentralized assignment algorithm which prescribes goals to each agent using only local information. The assignment results are then used to generate energy-optimal trajectories for each agent which have guaranteed collision avoidance through safety constraints. We present the conditions for optimality and discuss the robustness of the solution. The efficacy of the proposed approach is validated through a numerical case study to characterize the framework's performance on a set of dynamic goals.
The problem of generating a desired formation was approached with a scheduling model by @cite_5 , where an initial assignment is achieved using a scheduling-based heuristic run on a central computer with global information. A large subset of approaches, such as those taken by Wang and Xin @cite_6 , Sun and Cassandras @cite_12 , Xu and Carrillo @cite_28 , and Rajasree and Jisha @cite_8 also use optimization techniques in their solutions. However, these methods use optimal control to position each agent in a virtual potential field and do not consider the energy consumed by each agent.
@cite_8 @cite_28 @cite_6 @cite_5 @cite_12
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Two major decisions are made when scheduling the operations of a fossil-fuel power-generating system over a short time horizon. The “unit commitment” decision indicates what generating units are to be in use at each point in time. The “economic dispatch” decision is the allocation of system demand among the generating units in operation at any point in time. Both these decisions must be considered to achieve a least-cost schedule over the short time horizon. In this paper we present a mixed integer programming model for the short time horizon power-scheduling problem. The objective of the model is to minimize the sum of the unit commitment and economic dispatch costs subject to demand, reserve, and generator capacity and generator schedule constraints. A branch-and-bound algorithm is proposed using a Lagrangian method to decompose the problem into single generator problems. A sub gradient method is used to select the Lagrange multipliers that maximize the lower bound produced by the relaxation. We present... Chen (1994) develops an attractive variant of the classical problem of preemptively scheduling independent jobs with release dates and due dates. Chen suggests that in practice one can often pay to reduce the processing requirement of a job. This leads to two parametric max flow problems. Serafini (1996) considers scheduling independent jobs with due dates on multiple machines, where jobs can be split among machines so that pieces of a single job can execute in parallel. Minimizing the maximum tardiness again gives a parametric max flow problem. A third problem of this type is deciding how many more games a baseball team can lose part way through a season without being eliminated from finishing first (assuming a best possible distribution of wins and losses by other teams). A fourth such problem is an extended selection problem of (1995a), where we want to discount the costs of "tree-structured" tools as little as possible to be able to process all jobs at a profit. It is tempting to try to solve these problems with the parametric push-relabel max flow methods of (GGT) (1989). However, all these applications appear to violate the conditions necessary to apply GGT. We extend GGT in three ways that allow it to be applied to all four of the above applications. We also consider some other applications where these ideas apply. Our extensions to GGT yield faster algorithms for all these applications. This paper presents a two-level hierarchical approach that combines an expert system (ES) with an elite particle swarm optimization (EPSO) to solve the unit commitment (UC) problem. Existing UC solution methods have the problems of stopping at a local optimum and slow convergence when applied to large-scale, heavily constrained UC applications. In this work, an ES is developed to handle all constraints. The ES is initially used as a pre-dispatch tool to create a robust swarm. Then, the ES and EPSO are combined to seek the optimal solution. All constraints are incorporated and satisfied during the pre-dispatch and the evolution process. Hence, infeasible positions in the solution space will not be visited. The execution time of the proposed approach grows approximately linearly, rather than geometrically, with problem size. This feature is attractive in large-scale systems. The proposed approach is successfully applied to a popular test system of up to 100 units and the real Taipower 40-unit 168-h system. Both solution cost and execution time are superior to those of published methods. Total fuel costs of the proposed approach are several millions of dollars less than those of existing methods in the Taipower case. In this semi-tutorial paper, we first review the information-theoretic approach to account for the computational costs incurred during the search for optimal actions in a sequential decision-making problem. The traditional (MDP) framework ignores computational limitations while searching for optimal policies, essentially assuming that the acting agent is perfectly rational and aims for exact optimality. Using the free-energy, a variational principle is introduced that accounts not only for the value of a policy alone, but also considers the cost of finding this optimal policy. The solution of the variational equations arising from this formulation can be obtained using familiar Bellman-like value iterations from dynamic programming (DP) and the Blahut-Arimoto (BA) algorithm from rate distortion theory. Finally, we demonstrate the utility of the approach for generating hierarchies of state abstractions that can be used to best exploit the available computational resources. A numerical example showcases these concepts for a path-planning problem in a grid world environment.