Suhada Jayasuriya

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

A Uniform Control for Tracking and Point Stabilization of Differential Drive Robots Subject to Hard Input Constraints

This paper develops a unified framework for point stabilization and tracking control of differential drive robots under hard input constraints. The proposed control strategy is based on the recently introduced Pointwise Angle Minimization method and addresses the steering problem by studying a robot’s achievable directions of motion considering the constraints imposed on it. To illustrate the strength of the proposed framework, a new control problem which combines the posture stabilization and tracking control is studied. The problem of interest is steering a constrained-input mobile robot from an initial point towards a final point on a desired trajectory while regulating the robot’s heading such that the control convergence is guaranteed within the admissible input space. Inspired by the geometry of sliding mode control, this paper proposes a new control strategy for this problem. The stability of the closed loop system under the proposed steering scheme is proved by Lyapunov analysis for the shortest path trajectory and generalization to the case of arbitrarily chosen desired trajectory has been proposed. Finally, effectiveness of the discussed control strategies are illustrated by several simulation results.Copyright

Hierarchical control of cooperative nonlinear dynamical systems

Cooperative control methods that are scalable with low computational cost are crucial for networked dynamical systems to respond quickly in unknown or cluttered environments. In an attempt to make the problem tractable, many existing cooperative controls are designed with oversimplified assumptions and/or without the capabilities of rapidly handling different environmental and dynamical constraints. In this article, proposed is a two-level hierarchical, cooperative control framework using a divide-and-conquer strategy so that challenges can be separately handled at different levels. It is scalable and has low computational cost. Based on a simplified homogeneous double-integrator dynamic model, the top-level planner first computes cooperative trajectories satisfying obstacle avoidance requirements. Then at the lower level, state and control constraints, nonlinear dynamics and self-collision/obstacle avoidance as related to the real system are addressed through a bio-inspired fast trajectory planning algorithm. The stability of the overall hierarchical structure is proven. Two examples, a differential-drive ground vehicle formation control and an unmanned aerial vehicle formation flight, are used to illustrate the advantages of the proposed hierarchical framework.

Pointwise Angle Minimization: A Method for Guiding Wheeled Robots Based on Constrained Directions

In this paper we consider the point-to-point steering of a two wheeled differential drive mobile robot subject to constrained control inputs where the robot is expected to follow a given path between initial and final points. Formulation of this steering task as a constrained optimal control problem leads to nonlinear two-point boundary value problems. To avoid dealing with boundary value problems while alleviating the complications in analysis of systems with holonomic/non-holonomic constraints, we tackle the problem from a different perspective. This paper proposes a general framework for guiding wheeled robots using constrained direction method. The proposed scheme is equipped with pointwise angle minimization, a search algorithm useful in devising control strategies for steering problems. In addition to computational efficiency, one of the main advantages of the proposed scheme is that it does not impose any restrictive assumptions on the robot’s model. In this paper, kinematics of the robot under the assumption of rolling without slipping has been used as the model of the system and the efficiency of the proposed navigation scheme is illustrated through simulation results. However, the proposed scheme can be applied to more complicated models representing the two wheeled differential robots such as dynamics under slip occurrence.Copyright

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.

Constrained directions as a path planning algorithm for mobile robots under slip and actuator limitations

In this paper a dynamic model is proposed for a wheeled mobile robot (WMR) that incorporates a novel slip characterization and is used to study navigation under hard control constraints. Many available dynamic models of WMR assume that either the wheels roll without slipping or has longitudinal slip only. As a result they do not necessarily capture the true dynamics of WMRs. The model proposed in this paper considers a two wheeled differential drive mobile robot moving on a flat surface with possibly non-zero lateral and longitudinal slipping. A novel slip characterizing model is introduced and defining parameters are estimated via a set of experiments. Compared with several existing models in the literature simulation results show that trajectories predicted by the proposed model agree better with experimental data. The introduced dynamics and the corresponding slip model coupled with a novel direction search scheme were then used to ascertain the reachable states under constrained control. The scheme involves a finite dimensional search procedure which eliminates having to deal with two point boundary value problems resulting from classic optimal control formulations. The results of the paper can be easily applied to the design of control schemes for WMRs under realistic surface topography and control input constraints.

Experimental Study of a Disturbance Rejection Controller for DFIG Based Wind Energy Conversion Systems

We consider a Double Fed Induction Generator (DFIG) based wind energy conversion system with highly nonlinear dynamics and abrupt changes as a test bed for optimally extracting wind energy. Dynamic backstepping is utilized to implement a sliding mode control that combines high order sliding mode control and Multi-Input/Multi-Output (MIMO) backstepping. A novel adaptive estimator is utilized to obtain the maximum active and reactive output power in the presence of stochastic wind velocity profiles which are fed as the reference signals to the algorithm. The controller developed is tuned and evaluated on a simulator of the DFIG based wind power conversion system; which is subsequently implemented on an experimental setup. Experimental results show that the proposed adaptive method outperforms the traditional control methods in terms of robustness and performance.© 2014 ASME

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.