Hossein Rastgoftar

Distributed formation control for collaborative tracking of manifolds in flows

We address the development of a distributed control strategy for tracking Lagrangian coherent structures (LCS) in a geophysical fluid environment like the ocean. LCS are time-dependent structures that divide the flow into dynamically distinct regions and are important because they enable the estimation of the underlying geophysical fluid dynamics. In this work, we present a distributed formation control strategy designed to track stable and unstable manifolds. We build on our existing work and present an N-robot leader-follower tracking strategy that relies solely on local sensing, prediction, and correction. Our approach treats the N-robot team as a deformable body where distributed formation control for tracking coherent structures and manifolds is achieved using a sequence of homogeneous maps. We discuss the theoretical guarantees of the proposed strategy and validate it in simulation on static flows as well as the time-dependent model of a wind-driven double-gyre often seen in the ocean.

Preserving Stability Under Communication Delays in Multi Agent Systems

The effect of time delays on the stability of a recently proposed continuum approach for controlling a multi agent system (MAS) evolving in n-D under a special local inter-agent communication protocol is considered. There a homogenous map determined by n+1 leaders is learned by the follower agents each communicating with n+1 adjacent agents. In this work both position and velocity information of adjacent agents are used for local control of follower agents whereas in previous work [1, 2] only position information of adjacent agents was used. Stability of the proposed method under a time delay h is studied using the cluster treatment of characteristic roots (CTCR) [3]. It is shown that the stability of MAS evolution can be preserved when (i) the velocity of any follower agent is updated using both position and velocity of its adjacent agents at time (t-h); and (ii) the communication matrix has real eigenvalues. In addition, it is shown that when there is no communication delay, deviations from a selected homogenous map during transients may be minimized by updating only the position of a follower using both position and velocity of its adjacent agents.Copyright

Multi-Agent Deployment Based on Homogenous Maps and a Special Inter-Agent Communication Protocol

Abstract This paper proposes a novel analytical model for flexure-based proportion compliant mechanisms. The displacement and stiffness calculations of such flexure-based compliant mechanisms are formulated based on the principle of virtual work and pseudo rigid body model(PRBM). According to the theory and method, a set of closed-form equations are deduced in this paper, which incorporate the stiffness characteristics of each flexure hinge, together with the other geometric and material properties of the compliant mechanism. Displacement proportion, input stiffness, and output stiffness calculations can simply be performed for any serial compliant mechanism. Corner-filleted and circular flexure hinges that are utilized as connectors in proportion compliant mechanisms in this paper. Two types of flexure-based compliant proportion mechanisms based on the novel analytical model are designed and optimized based on these proposed equations. Finite element analysis results show that these design equations are reliable and easier to be used in the design of such proportion compliant mechanisms. This proposed novel analytical model gives a new viewpoint on the design of flexure-based proportion compliant mechanisms. Multi-Agent Deployment based on Homogenous Maps and a Special Inter-Agent Communication Protocol

Specification and evaluation of geofence boundary violation detection algorithms

This paper studies two methods of geofence boundary violation detection. The first method is Ray Casting, which iterates over each geofence boundary edge to determine if a given position of interest is inside the geofence. The second method, called Triangle Weight Characterization (TWC), subdivides the geofence domain into a finite number of triangles, then iterates over each triangle to determine if the given position of interest is inside the geofence. We apply the TWC and Ray Casting methods to case studies that include both keep-in and keep-out geofence boundaries.

An Alignment Strategy for Evolution of Multi-Agent Systems

Formation control of MAS has numerous applications such as air traffic control, formation flight, gaming, transportation engineering, surveillance, terrain mapping, and data mining [1]. Common tools for formation control include leader follower [2‐4], virtual structures [5‐7], artificial potential functions [8,9], behavioral based methods [10,11], and partial differential equation based [12‐15] methods. More recently the authors proposed continuum based techniques [16‐24], for evolution of MAS. In Refs. [16‐19], an approach using homogenous transformation of an MAS under no communication was given. It was extended in Refs. [17‐24 ]t o include homogenous transformation of an MAS under local interagent communication where leaders move independently, with the followers updating their positions based on the positions of several nearby agents. Homogenous transformation of an MAS under local interagent communication has the unique feature that both bulk motion of the MAS and interagent distances can be simultaneously controlled. Most available approaches to formation control that rely on peer-to-peer communication usually require the followers to know the exact absolute or relative positions of adjacent agents. Consequently, sensors with high accuracy may be necessary for obtaining the exact positions of the agents. Moreover, even when accurate measurements are possible there could be communication delays in receiving such position information. If properly designed feedback control strategies are not employed it is likely that robustness against such position uncertainty and communication delays will be lacking. In this paper, we develop an alignment framework for MAS evolution, where every follower agent updates its position based only on its perception of the positions of some local agents, and not their exact positions, thus avoiding having to deal with communication delays and inaccurate measurements. We start by letting the leaders be located at the end points of some finite number of segments, called leading segments, with end points lying on the boundary of a convex domain. The followers are taken to be initially located at the points of intersection of the leading segments. The MAS then evolves from this initial configuration with every follower agent aligning itself with a few chosen adjacent agents to reach the point of intersection of the leading segments, passing through the adjacent agents. We note that the follower agents do not need the exact positions of their adjacent agents to be aligned with them. Although in developing the necessary theory for the alignment technique exact positions of the agents are used, alignment only requires the direction information and not the exact locations. The key idea for this paradigm comes from the hypothesis that natural biological swarms do not perform peer-to-peer communication to sustain their group behavior as a collective. The group evolution is more likely based on what each individual agent perceives of its nearby agents behavior to control its own motion. The paper is organized into six sections: Sec. 1 is the introduction. Section 2 formally presents the initial distribution of the agents followed by the basic alignment strategy in Sec. 3. Section 4 incorporates simple kinematics for agents to develop convergence criteria. Simulations to illustrate the efficacy of the strategy are in Sec. 5 followed by conclusions and future work in Sec. 6.

Swarm Motion as Particles of a Continuum With Communication Delays

In this paper, we give an upper bound for the communication delay in a multi-agent system (MAS) that evolves under a recently developed continuum paradigm for formation control. The MAS is treated as particles of a continuum that transforms under special homeomorphic mapping, called a homogeneous map. Evolution of an MAS in ℝn is achieved under a special communication topology proposed by Rastgoftar and Jayasuriya (2014, “Evolution of Multi Agent Systems as Continua,” ASME J. Dyn. Syst. Meas. Control, 136(4), p. 041014) and (2014, “An Alignment Strategy for Evolution of Multi Agent Systems,” ASME J. Dyn. Syst. Meas. Control, 137(2), p. 021009), employing a homogeneous map specified by the trajectories of n+1 leader agents at the vertices of a polytope in ℝn, called the leading polytope. The followers that are positioned in the convex hull of the leading polytope learn the prescribed homogeneous mapping through local communication with neighboring agents using a set of communication weights prescribed by the initial positions of the agents. However, due to inevitable time-delay in getting positions and velocities of the adjacent agents through local communication, the position of each follower may not converge to the desired state given by the homogeneous map leaving the possibility that MAS evolution may get destabilized. Therefore, ascertaining the stability under time-delay is important. Stability analysis of an MAS consisting of a large number of agents, leading to higher-order dynamics, using conventional methods such as cluster treatment of characteristic roots (CTCR) or Lyapunov–Krasovskii are difficult. Instead we estimate the maximum allowable communication delay for the followers using one of the eigenvalues of the communication matrix that places MAS evolution at the margin of instability. The proposed method is advantageous because the transcendental delay terms are directly used and the characteristic equation of MAS evolution is not approximated by a finite-order polynomial. Finally, the developed framework is used to validate the effect of time-delays in our previous work.

A continuum based approach for multi agent systems under local inter-agent communication

In this paper we develop an approach for the control of evolution of a multi agent system (MAS) based on a new local inter-agent communication protocol. The agents of the MAS occupy a compact region, have n-D dynamics, and are guided by n+ 1 special leader agents that can move independently. The rest of the agents, called followers, have the ability to update their positions via local communication with some adjacent agents. The special communication protocol is brought about by certain distance ratios that must be satisfied by points of a set that transforms as a homogeneous map. It is assumed that the leaders can and will determine on-line, in real time the desired intermediate configurations of the MAS. It is further assumed that the leaders cannot directly communicate such information to the follower agents in the MAS. The followers are expected to acquire that information through communication with n+ 1 local agents. The followers by moving in such a way to preserve, at all times, certain pre-computed distance ratios corresponding to the initial configuration of the MAS will learn the desired homogeneous maps. The proposed technique allows the MAS to (i) deform like a flexible body and/or (ii) undergo rigid body translations by satisfying certain key properties of homogeneous maps guaranteed by the special local inter-agent communication protocol.

Evolution of Multi Agent Systems Under a New Communication Topology

In this paper, a multi agent system (MAS) is considered as particles of a continuum deforming under a specific class of homeomorphic mappings, called a homogenous transformation. We have recently showed how a desired homogenous mapping of the MAS in a n–D space can be prescribed by transient positions of n + 1 leaders placed at the vertices of a n–D polytope, called leading polytope [1–9]. In this article, we first minimize the acceleration norm with (i) initial and final positions of the leaders known and (ii) leaders (located at the vertices of the leading polytope) are constrained to move in such a way that the initial volume of the leading polytope is preserved during evolution. The followers learn the leader-determined homogenous map through local communication with each follower modeled as a double integrator. Proposed is a communication topology that requires every follower agent to update its position based on communication with n + 1 local agents. The weights of communication are uniquely specified by the initial positions of the agents. Simulation of a MAS moving in a plane validates the proposed communication topology.Copyright

Continuum evolution of multi agent systems under a polyhedral communication topology

In this paper, evolution of a multi agent system (MAS) in n-D space where n+1 or more leader agents located on the boundary guide the MAS is studied. We consider the MAS as a deformable body whose motion can be prescribed by a homogeneous map determined by the initial and current positions of the leaders. Each follower agent learns this leader prescribed motion plan by local communication with adjacent agents. In previous work we assumed that each follower communicates with n+1 adjacent agent [1-7]. Here we relax that constraint to include more than 3 adjacent agents by choosing a polyhedral communication topology where the vertices are local agents that are adjacent to a follower agent i. The polytope encloses the follower agent i and is the union of mi sub-polyhedra, with one of the n+1 vertices occupied by agent i. mi volume weights are defined based on the initial position of follower i and the set of adjacent agents to. The motion proceeds by updating the position of every follower agent such that volume weights in intermediate configurations of the MAS are close to the initial volume weights. This update strategy maneuvers the MAS to its final desired formation as a homogenous map of its initial configuration.

Unmanned vehicle mission planning given limited sensory information

This paper proposes an approach to optimal planning under uncertainty with limited sensory information for an autonomous unmanned vehicle (UXV). We consider a surveillance application in which identification of environmental targets is impacted by controllable features commanded by the UXV as well as ambient features with dynamics that are uncontrollable. To manage computational complexity, mission states are defined by abstract or discretized features that are maximally influential based on Shannon information content. A receding horizon optimization method is applied to find optimal actions given uncertain and potentially erroneous sensor readings. Ambient feature transition probabilities are learned from empirical data then integrated with controllable features that evolve as a function of UXV actions.