Mohammadreza Doostmohammadian

PhD candidate, Electrical and Computer Engineering

SPaRTN lab, Tufts University

Distributed Estimation of Large-scale Systems: (PhD Thesis)

Networked estimation is where a network of agents is tasked to estimate the state of a dynamical system by sharing  information over a sparse communication network;  

Recently, consensus-based estimation has been proposed as a distributed solution.The agents implement a message-passing algorithm on their measurements between every two successive time-steps of the system dynamics. However, when the network is unable to consensus due to, e.g., resource-constraints or fast system dynamics, distributed solutions with finite information exchanges have been proposed, at the price of sharing state-predictions. In this scenario, one first has to guarantee the existence of a communication network that will result into a bounded estimation error, i.e., networked observability.

As the main contribution we, first, provide a novel construction of the distributed estimator and distributed observability from the first principles. Secondly, we describe a graph-theoretic agent classification that establishes the importance and role of each agent towards estimation. In particular, we classify agents as Type-\alpha as the most crucial agent, Type-\beta as the less crucial agent, and Type-\gamma as the non-crucial agent. Thirdly, to achieve distributed observability, we derive the necessary and sufficient conditions on the agents' communication network based on the aforementioned agent classification. We prove that for distributed observability every Type-\alpha agent has a direct connection to every other agent, and every agent has a directed path to every Type-\beta agent. The combination of these two requirements defines the multi-agent network.

Advances in the current state-of-the-art:

1. Only one information exchange is allowed among the agents.

2. The results are structure-based in contrast to widely used algebraic (rank-based) tests.
social network
sample connectivity requirement for different type of agents

3. When the system matrix is structured-rank deficient, then no agent communication network can guarantee observability with agreement in the state-predictor space alone, and hence, fusion in  the observation space is required.

4. For a system matrix with full structured-rank, a weakly-connected network is sufficient to guarantee observability; the requirements on the underlying network topology are explicitly characterized.

5. The proposed solutions are shown to work with constrained LMI-based iterative gain matrix design.

Distributed Randomized Shortest Path Problem:

This work presents a new distributed and coordination-free algorithm for single source shortest path  problem.  This algorithm is based on information recorded by a travelling token. Every node only knows its immediate neighbors. At each time step active node, i.e. the node holding the token, sends the token to one of its randomly chosen neighbors. The token saves its traveling path through the graph. This travel continues until the token returns to the source node. Now, source node uses the data given by the token to realize the shortest paths to the other nodes, and again sends the token to start a new travel to update the shortest paths. Such algorithm converges in almost surely finite time. However, the stopping time of the algorithm has to be defined; using Monte-Carlo method,  we find the stopping criteria for known random graphs as the time algorithm finds the pre-known shortest path. The sample convergence time data  is best realized by Log-Normal distribution. This is based on the error of its corresponding parameters as compared to the other distributions. The Log-Normal parameters are shown to be related to the graph characterstics, e.g. its diameter. This relation is used to approximate the stopping criteria of the algorithm for a given unknown graph with only those specific characteristics known.

Advances in the current state-of-the-art:

1. The algorithm is distributed in the sense that each node only need to know its immediate neighbors.

2. The graph topology is unknwon but get discovered gradually for the source node. This rises application in Network Tomography.

Network of connected airports

Sample data for convergence time

Finite-time Consensus and Discrete Resource Allocation: (M.Sc. Thesis)

In this research, we explore the required conditions for reaching consensus in finite-time. We derive the necessary condition as having non-Lipschitz consensus function at the origin, e.g. sign function. Since applying such condition is not feasible for real-world actuators, smooth approximations such as tanh() function are proposed to acheive a consensus boundary in finite-time. Lyapunov stability analysis is performed to prove the convergence.  One application of this consensus protocol is in discrete coverage control over a convex polygon, also regarded as discrete source allocation problem.

A group of mobile agents deploying over a convex area to optimally allocate resources: the blue circles represent two centers of resource density distribution. Each agent (shown as black square) is assigned with resources (yellow dots) in its Voronoi cell. In the figure this assignment is represented by a yellow line connecting the resource to the agent.

Kinematic and Dynamic Analysis of Mechanisms:

As part of my M.Sc. and B.Sc. research, I was working on projects in the field of robotics and mechanism design, some of them presented below:

Parallel robots: Parallel mechanisms are known for high precision, fast tracking and high load to weight ratio. In this course project a 3pod Delta robot is cinematically analyzed (inverse kinematics) for fast machining process. Specifically, the tradeoff between speed and geometric workspace is examined and compared to the industrial series manipulators.

Steering Mechanism (B.Sc. Thesis): When a car is turning over a curve, the inner wheel turns sharper than the outer one. This is because the entire car must turn around a common center point. The purpose of the steering mechanism is to point the wheels to follow such directions. In this project, 4-Linkage steering mechanism is considered. The error for different rotation angles is obtained for different size of linkages and the result shows a consistency with Ackermann steering geometry.