Person:

Egerstedt, Magnus B.

Permanent Link

https://hdl.handle.net/1853/72204

Associated Organization(s)

Organizational Unit

School of Electrical and Computer Engineering

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Publication Search Results

Now showing 1 - 10 of 68

Low-Dimensional Learning for Complex Robots

(Georgia Institute of Technology, 2015-01) O’Flaherty, Rowland ; Egerstedt, Magnus B.

This paper presents an algorithm for learning the switching policy and the boundaries conditions between primitive controllers that maximize the translational movements of a complex locomoting system. The algorithm learns an optimal action for each boundary condition instead of one for each discretized state-action pair of the system, as is typically done in machine learning. The system is model as a hybrid system because it contains both discrete and continuous dynamics. With this hybridification of the system and with this abstraction of learning boundary-action pairs, the “curse of dimensionality” is mitigated. The effectiveness of this learning algorithm is demonstrated on both a simulated system and on a physical robotic system. In both cases, the algorithm is able to learn the hybrid control strategy that maximizes the forward translational movement of the system without the need for human involvement.
Optimal Control of Switched Dynamical Systems Under Dwell Time Constraints

(Georgia Institute of Technology, 2014-12) Ali, Usman ; Egerstedt, Magnus B.

This paper addresses the problem of optimally scheduling the mode sequence and mode duration for switched dynamical systems under dwell time constraints that describe how long a system has to stay in a mode before they can switch to another mode. The schedule should minimize a given cost functional defined on the state trajectory. The topology of the optimization space for switched dynamical systems with and without dwell time constraints is investigated and it is shown that the notion of local optimality must be replaced by stationarity with regards to a suitably chosen optimality function when dwell time constraints are present. Hence, an optimality function is proposed to characterize the solution to the dwell time problem as points that satisfy optimality condition defined in terms of optimality function. A conceptual algorithm is presented to solve the mode scheduling problem and its convergence to stationary points is proved. A numerical example is given to highlight the algorithm.
Decentralized Formation of Random Regular Graphs or Robust Multi-Agent Networks

(Georgia Institute of Technology, 2014-12) Yazıcıoğlu, A. Yasin ; Egerstedt, Magnus B. ; Shamma, Jeff

Multi-agent networks are often modeled via interaction graphs, where the nodes represent the agents and the edges denote direct interactions between the corresponding agents. Interaction graphs have significant impact on the robustness of networked systems. One family of robust graphs is the random regular graphs. In this paper, we present a locally applicable reconfiguration scheme to build random regular graphs through self-organization. For any connected initial graph, the proposed scheme maintains connectivity and the average degree while minimizing the degree differences and randomizing the links. As such, if the average degree of the initial graph is an integer, then connected regular graphs are realized uniformly at random as time goes to infinity.
The Degree of Nonholonomy in Distributed Computations

(Georgia Institute of Technology, 2014-12) Costello, Zak ; Egerstedt, Magnus B.

A network of locally interacting agents can be thought of as performing a distributed computation. But not all computations can be faithfully distributed. This paper discusses which global linear transformations can be computed in finite time using local weighting rules, i.e., rules which rely solely on information from adjacent nodes in a network. Additionally, it is shown that the degree of nonholonomy of the computation can be related to the underlying information exchange graph. The main result states that the degree of nonholonomy of the system dynamics is equal to D – 1 where D is the diameter of the information exchange graph. An optimal control problem is solved for finding the local interaction rules, and a simulation is performed to elucidate how optimal solutions can be obtained.
Cloud-Based Optimization: A Quasi-Decentralized Approach to Multi-Agent Coordination

(Georgia Institute of Technology, 2014-12) Hale, M.T. ; Egerstedt, Magnus B.

New architectures and algorithms are needed to reflect the mixture of local and global information that is available as multi-agent systems connect over the cloud. We present a novel architecture for multi-agent coordination where the cloud is assumed to be able to gather information from all agents, perform centralized computations, and disseminate the results in an intermittent manner. The cloud model accounts for delays in communications both when sending data to and receiving data from the agents. This architecture is used to solve a multi-agent optimization problem in which each agent has a local objective function unknown to the other agents and in which the agents are collectively subject to global constraints. Leveraging the cloud, a dual problem is formulated and solved by finding a saddle point of the associated Lagrangian.
Heterogeneous Multi-Robot Routing

(Georgia Institute of Technology, 2014-06) Chopra, Smriti ; Egerstedt, Magnus B.

We consider the problem of routing multiple robots to service spatially distributed requests at specified time instants, where each robot, as well as each request, is associated with one or more skills (or functions). A request can be serviced by a robot as long as the robot has at least one skill in common with the skill set of that request. We characterize the feasibility aspects of such a heterogeneous routing problem, and provide algorithms for finding the minimum number of robots required to service the requests, and for constructing the corresponding paths of the robots
Minimizing Mobility and Communication Energy in Robotic Networks: an Optimal Control Approach

(Georgia Institute of Technology, 2014-06) Jaleel, Hassan ; Wardi, Yorai Y. ; Egerstedt, Magnus B.

This paper concerns the problem of minimizing the sum of motion energy and communication energy in a network of mobile robots. The robotic network is charged with the task of transmitting sensor information from a given object to a remote station, and it has to arrange itself in a serial (tandem) configuration for point-to-point transmission, where each robot acts as a relay node. The problem is formulated in a dynamic setting where the robots move and communicate at the same time, and it is cast in the framework of optimal control. The paper proposes an effective algorithm for solving this problem and demonstrates its efficacy on a simulation example. In order to highlight the salient features of the algorithm the network is assumed to be one-dimensional, and the case of planar movement with obstacles is deferred to future research.
Set-Valued Protocols for Almost Consensus of Multiagent Systems with Uncertain Interagent Communication

(Georgia Institute of Technology, 2014-06) Sadikhov, Teymur ; Haddad, Wassim M. ; Goebel, Rafal ; Egerstedt, Magnus B.

One of the main challenges in robotics applications is dealing with inaccurate sensor data. Specifically, for a group of mobile robots the measurement of the exact location of the other robots relative to a particular robot is often inaccurate due to sensor uncertainty or detrimental environmental conditions. In this paper, we address the consensus problem for a group of agent robots with uncertain interagent communication. Measurement uncertainty is characterized by balls of radius r centered at the neighboring agents exact locations. We show that the agents reach an almost consensus state and converge to a time-varying ball of radius r and include an analysis approach to the problem based on set-valued analysis. Finally, several illustrative numerical examples are provided to demonstrate the efficacy of the proposed set-valued consensus protocol framework.
Flipping the Controls Classroom Around a MOOC

(Georgia Institute of Technology, 2014-06) Egerstedt, Magnus B. ; de la Croix, Jean-Pierre

Bridging the theory-practice gap in controls education is a well-known challenge. In this paper, we discuss how one can bridge this gap using a flipped classroom. Based on the recent MOOC (Massive Open Online Course), Control of Mobile Robots, we flipped the classroom in a senior robotics and controls class at the Georgia Institute of Technology. The students participated in the MOOC and came to class prepared to solve controls problems on robots. Key to this experience was not only the delivery of theoretical concepts via the MOOC, but also a hardware/software platform that provided a learning environment where exploratory, practical tinkering was grounded in solid theory. This paper reports on the findings of the flipped classroom experiment, as well as discusses why this classroom format is ideal for controls courses.
Proportional Integral Distributed Optimization for Dynamic Network Topologies

(Georgia Institute of Technology, 2014-06) Droge, Greg ; Egerstedt, Magnus B.

This paper investigates proportional-integral distributed optimization when the underlying information exchange network is dynamic. Proportional-integral distributed optimization is a technique which combines consensus-based methods and dual-decomposition methods to form a method which has the convergence guarantees of dual-decomposition and the damped response of the consensus methods. This paper extends PI distributed optimization to allow for dynamic communication networks, permitting agents to change who they can communicate with, without sacrificing convergence to the collective optimum.