Resilient and Decentralized Control of Multi-level Cooperative Mobile Networks to Maintain Connectivity under Adversarial Environment

Network connectivity plays an important role in the information exchange between different agents in the multi-level networks. In this paper, we establish a game-theoretic framework to capture the uncoordinated nature of the decision-making at different layers of the multi-level networks. Specifically, we design a decentralized algorithm that aims to maximize the algebraic connectivity of the global network iteratively. In addition, we show that the designed algorithm converges to a Nash equilibrium asymptotically and yields an equilibrium network. To study the network resiliency, we introduce three adversarial attack models and characterize their worst-case impacts on the network performance. Case studies based on a two-layer mobile robotic network are used to corroborate the effectiveness and resiliency of the proposed algorithm and show the interdependency between different layers of the network during the recovery processes.Comment: 9 pages, 6 figure

Combining Homotopy Methods and Numerical Optimal Control to Solve Motion Planning Problems

This paper presents a systematic approach for computing local solutions to motion planning problems in non-convex environments using numerical optimal control techniques. It extends the range of use of state-of-the-art numerical optimal control tools to problem classes where these tools have previously not been applicable. Today these problems are typically solved using motion planners based on randomized or graph search. The general principle is to define a homotopy that perturbs, or preferably relaxes, the original problem to an easily solved problem. By combining a Sequential Quadratic Programming (SQP) method with a homotopy approach that gradually transforms the problem from a relaxed one to the original one, practically relevant locally optimal solutions to the motion planning problem can be computed. The approach is demonstrated in motion planning problems in challenging 2D and 3D environments, where the presented method significantly outperforms a state-of-the-art open-source optimizing sampled-based planner commonly used as benchmark

Pose-graph SLAM sparsification using factor descent

Since state of the art simultaneous localization and mapping (SLAM) algorithms are not constant time, it is often necessary to reduce the problem size while keeping as much of the original graph’s information content. In graph SLAM, the problem is reduced by removing nodes and rearranging factors. This is normally faced locally: after selecting a node to be removed, its Markov blanket sub-graph is isolated, the node is marginalized and its dense result is sparsified. The aim of sparsification is to compute an approximation of the dense and non-relinearizable result of node marginalization with a new set of factors. Sparsification consists on two processes: building the topology of new factors, and finding the optimal parameters that best approximate the original dense distribution. This best approximation can be obtained through minimization of the Kullback-Liebler divergence between the two distributions. Using simple topologies such as Chow-Liu trees, there is a closed form for the optimal solution. However, a tree is oftentimes too sparse and produces bad distribution approximations. On the contrary, more populated topologies require nonlinear iterative optimization. In the present paper, the particularities of pose-graph SLAM are exploited for designing new informative topologies and for applying the novel factor descent iterative optimization method for sparsification. Several experiments are provided comparing the proposed topology methods and factor descent optimization with state-of-the-art methods in synthetic and real datasets with regards to approximation accuracy and computational cost.Peer ReviewedPostprint (author's final draft