arXiv subjects

Anoop Jain

Publications and source records attributed to Anoop Jain.

16 recordsLinked to original sources

arXiv2026

Bearing-based Circumnavigation with Collision Avoidance in Time-varying Graphs under Limited Target Information

In this paper, we study distributed circumnavigation of a stationary target by a heterogeneous team of agents. Each agent is modelled as a disk rather than a point mass to account for its physical dimensions. The target location is assumed to be accessible only to a small subset of agents, called leaders. The rest, called followers, therefore use only local information available from their designated out-neighbour in the interaction graph characterised by the selection of nearest neighbours. By controlling only angular speeds, we develop a distributed guidance law to circumnavigate a stationary target. The proposed guidance law works for both static and time-varying interaction graphs. Inter-agent collision avoidance is enforced through a logarithmic Barrier Lyapunov (BLF) Function, which guarantees forward invariance of the collision-free set. We show that every follower converges to circumnavigation about the same target as the leader at the end of its directed path in the interaction graph, provided the initial conditions are admissible. Numerical simulations illustrate the effectiveness of the proposed method for both static and time-varying topologies.

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arXiv2025

Phase-Coordinated Circular Formation Control of Unicycle Agents Under Non-Concentric Boundary Constraints

This paper addresses the problem of collective circular motion control for unicycle agents, with the objective of achieving phase coordination of their velocity vectors while ensuring that their trajectories remain confined within a prescribed non-concentric circular boundary. To accommodate such nonuniform motion constraints, we build upon our earlier work and extend the use of Mobius transformation to a multi-agent framework. The Mobius transformation maps two nonconcentric circles to concentric ones, thereby converting spatially nonuniform constraints into uniform ones in the transformed plane. Leveraging this property, we introduce the notion of a phase-shifted order parameter, along with the associated concepts of Mobius phase-shift coupled synchronization and balancing, which characterize the phase-coordinated patterns studied in this paper. We establish an equivalence between the unicycle dynamics in the original and transformed planes under the Mobius transformation and its inverse, and show that synchronization is preserved across both planes, whereas balancing is generally not. Distributed control laws are then designed in the transformed plane using barrier Lyapunov functions, under the assumption of an undirected and connected communication topology among agents. These controllers are subsequently mapped back to the original plane to obtain the linear acceleration and turn-rate control inputs applied to the actual agents. Both simulations and experimental results are provided to illustrate the proposed framework.

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arXiv2025

On Event-Triggered Resilient Consensus Using Auxiliary Layer

Due to its design simplicity, auxiliary layer-based resilient control is widely discussed in the literature to mitigate the effects of False Data Injection (FDI) attacks. However, the increased communication burden due to additional communication links for connecting an extra layer is often overlooked in the literature. This paper bridges this gap by considering an event-triggered approach for inter-layer communication between the physical layer (containing actual agents) and the auxiliary layer (containing virtual agents) for the resilient state consensus in a multi-agent system. We provide state-based and dynamic event-triggering mechanisms, the former being the motivation for the latter. The exclusion of Zeno behavior is established by proving positive minimum inter-event time (MIET). Extensive simulation and experimental results are provided to illustrate the proposed methodology.

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arXiv2025

Range-Only Dynamic Output Feedback Controller for Safe and Secure Target Circumnavigation

The safety and security of robotic systems are paramount when navigating around a hostile target. This paper addresses the problem of circumnavigating an unknown target by a unicycle robot while ensuring it maintains a desired safe distance and remains within the sensing region around the target throughout its motion. The proposed control design methodology is based on the construction of a joint Lyapunov function that incorporates: (i) a quadratic potential function characterizing the desired target-circumnavigation objective, and (ii) a barrier Lyapunov function-based potential term to enforce safety and sensing constraints on the robot's motion. A notable feature of the proposed control design is its reliance exclusively on local range measurements between the robot and the target, realized using a dynamic output feedback controller that treats the range as the only observable output for feedback. Using the Lyapunov stability theory, we show that the desired equilibrium of the closed-loop system is asymptotically stable, and the prescribed safety and security constraints are met under the proposed controllers. We also obtain restrictive bounds on the post-design signals and provide both simulation and experimental results to validate the theoretical contributions.

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arXiv2025

Safe Circumnavigation of a Hostile Target Using Range-Based Measurements

Robotic systems are frequently deployed in missions that are dull, dirty, and dangerous, where ensuring their safety is of paramount importance when designing stabilizing controllers to achieve their desired goals. This paper addresses the problem of safe circumnavigation around a hostile target by a nonholonomic robot, with the objective of maintaining a desired safe distance from the target. Our solution approach involves incorporating an auxiliary circle into the problem formulation, which assists in navigating the robot around the target using available range-based measurements. By leveraging the concept of a barrier Lyapunov function, we propose a novel control law that ensures stable circumnavigation around the target while preventing the robot from entering the safety circle. This controller is designed based on a parameter that depends on the radii of three circles, namely the stabilizing circle, the auxiliary circle, and the safety circle. By identifying an appropriate range for this design parameter, we rigorously prove the stability of the desired equilibrium of the closed-loop system. Additionally, we provide an analysis of the robot's motion within the auxiliary circle, which is influenced by a gain parameter in the proposed controller. Simulation and experimental results are presented to illustrate the key theoretical developments.

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arXiv2024

Mobius Transformation-Based Circular Motion Control for Unicycle Robots in Nonconcentric Circular Geofences

Nonuniform motion constraints are ubiquitous in robotic applications. Geofencing control is one such paradigm where the motion of a robot must be constrained within a predefined boundary. This paper addresses the problem of stabilizing a unicycle robot around a desired circular orbit while confining its motion within a nonconcentric external circular boundary. Our solution approach relies on the concept of the so-called Mobius transformation that, under certain practical conditions, maps two nonconcentric circles to a pair of concentric circles, and hence, results in uniform spatial motion constraints. The choice of such a Mobius transformation is governed by the roots of a quadratic equation in the post-design analysis that decides how the regions enclosed by the two circles are mapped onto the two planes. We show that the problem can be formulated either as a trajectory-constraining problem or an obstacle-avoidance problem in the transformed plane, depending on these roots. Exploiting the idea of the barrier Lyapunov function, we propose a unique control law that solves both these contrasting problems in the transformed plane and renders a solution to the original problem in the actual plane. By relating parameters of two planes under Mobius transformation and its inverse map, we further establish a connection between the control laws in two planes and determine the control law to be applied in the actual plane. Simulation and experimental results are provided to illustrate the key theoretical developments.

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arXiv2024

Passivity-based Attack Identification and Mitigation with Event-triggered Observer Feedback and Switching Controller

This paper addresses the problem of output consensus in linear passive multi-agent systems under a False Data Injection (FDI) attack, considering the unavailability of complete state information. Our formulation relies on an event-based cryptographic authentication scheme for sensor integrity and considers FDI attacks at the actuator end, inspired by their practical nature and usages. For secure consensus, we propose (i) a passivity-based approach for detecting FDI attacks on the system and (ii) a Zeno-free event-triggered observer-based switching controller, which switches between the normal and the defense modes following an attack detection. We show that the closed-loop system achieves practical consensus under the controller's action in the defense mode. Simulation examples are provided to support the theoretical findings.

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arXiv2024

Multi-Agent Phase-Balancing around Polar Curves with Bounded Trajectories: An Experimental Study using Crazyflies and MoCap System

In this experimental work, we implement the control design from our earlier work on a swarm of Crazyflie 2.1 quad-copters by deriving the original control in terms of variables that are available to the user in this practical system. A suitable model is developed using the Crazyswarm2 package within ROS2 to facilitate the execution of the control law. We also discuss various components that are part of this experiment and the challenges we encountered during the experimentation. Extensive experimental results, along with the links to the YouTube videos for actual Crazyflie quad-copters, are provided.

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arXiv2023

Auxiliary Network-Enabled Attack Detection and Resilient Control of Islanded AC Microgrid

This paper proposes a cyber-resilient distributed control strategy equipped with attack detection capabilities for islanded AC microgrids in the presence of bounded stealthy cyber attacks affecting both frequency and power information exchanged among neighboring distributed generators (DGs). The proposed control methodology relies on the construction of an auxiliary layer and the establishment of effective inter-layer cooperation between the actual DGs in the control layer and the virtual DGs in the auxiliary layer. This cooperation aims to achieve robust frequency restoration and proportional active power-sharing. It is shown that the in situ presence of a concealed auxiliary layer not only guarantees resilience against stealthy bounded attacks on both frequency and power-sharing but also facilitates a network-enabled attack identification mechanism. The paper provides rigorous proof of the stability of the closed-loop system and derives bounds for frequency and power deviations under attack conditions, offering insights into the impact of the attack signal, control and pinning gains, and network connectivity on the system's convergence properties. The performance of the proposed controllers is illustrated by simulating a networked islanded AC microgrid in a Simulink environment showcasing both attributes of attack resilience and attack detection.

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arXiv2022

A Partially Distributed Fixed-Time Economic Dispatch Algorithm with Kron's Modeled Power Transmission Losses

A partially distributed economic dispatch algorithm, which renders optimal value in fixed time with the objective of supplying the load requirement as well as the power transmission losses, is proposed in this paper. The transmission losses are modeled using Kron's $\mathcal{B}-$loss formula, under a standard assumption on the values of $\mathcal{B}-$coefficients. The total power supplied by the generators is subjected to time-varying equality constraints due to time-varying nature of the transmission losses. Using Lyapunov and optimization theory, we rigorously prove the convergence of the proposed algorithm and show that the optimal value of power is reached within a fixed-time, whose upper bound dependents on the values of $\mathcal{B}-$coefficients, parameters characterizing the convexity of the cost functions associated with each generator and the interaction topology among them. Finally, an example is simulated to illustrate the theoretical results.

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arXiv2021

Synchronization and Balancing around Simple Closed Polar Curves with Bounded Trajectories and Control Saturation

The problem of synchronization and balancing around simple closed polar curves is addressed for unicycle-type multi-agent systems. Leveraging the concept of barrier Lyapunov function in conjunction with bounded Lyapunov-like curve-phase potential functions, we propose distributed feedback control laws and show that the agents asymptotically stabilize to the desired closed curve, their trajectories remain bounded within a compact set, and their turn-rates adhere to the saturation limits. We also characterize the explicit nature of the boundary of this trajectory-constraining set based on the magnitude of the safe distance of the exterior boundary from the desired curve. We further establish a connection between the perimeters and areas of the trajectory-constraining set with that of the desired curve. We obtain bounds on different quantities of interest in the post-design analysis and provide simulation results to illustrate the theoretical findings.

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arXiv2019

A Geometric Method for Passivation and Cooperative Control of Equilibrium-Independent Passivity-Short Systems

Equilibrium-independent passive-short (EIPS) systems are a class of systems that satisfy a passivity-like dissipation inequality with respect to any forced equilibria with non-positive passivity indices. This paper presents a geometric approach for finding a passivizing transformation for such systems, relying on their steady-state input-output relation and the notion of projective quadratic inequalities (PQIs). We show that PQIs arise naturally from passivity-shortage characteristics of an EIPS system, and the set of their solutions can be explicitly expressed. We leverage this connection to build an input-output mapping that transforms the steady-state input-output relation to a monotone relation, and show that the same mapping passivizes the EIPS system. We show that the proposed transformation can be implemented through a combination of feedback, feed-through, post- and pre-multiplication gains. Furthermore, we consider an application of the presented passivation scheme for the analysis of networks comprised of EIPS systems. Numerous examples are provided to illustrate the theoretical findings.

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arXiv2016

Phase Balancing of Two and Three-Agent Heterogeneous Gain Systems With Extensions to Multiple Agents

This paper studies the phase balancing of a two and three-agent system where the agents are coupled through heterogeneous controller gains. Balancing refers to the situation in which the movement of agents causes the position of their centroid to become stationary. We generalize existing results and show that by using heterogeneous controller gains, the velocity directions of the agents in balanced formation can be controlled. The effect of heterogeneous gains on the reachable set of these velocity directions is further analyzed. For the two-agents case, the locus of steady-state location of the centroid is also analyzed against the variations in the heterogeneous controller gains. Simulations are given to illustrate the theoretical findings.

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arXiv2016

Collective Circular Motion of Multi-Agent Systems in Synchronized and Balanced Formations With Second-Order Rotational Dynamics

This paper considers the collective circular motion of multi-agent systems in which all the agents are required to traverse different circles or a common circle at a prescribed angular velocity. It is required to achieve these collective motions with the heading angles of the agents synchronized or balanced. In synchronization, the agents and their centroid have a common velocity direction, while in balancing, the movement of agents causes the location of the centroid to become stationary. The agents considered are initially moving at unit speed around individual circles at different angular velocities. It is assumed that the agents are subjected to limited communication constraints, and exchange relative information according to a time-invariant undirected graph. We present suitable feedback control laws for each of these motion coordination tasks by considering a second-order rotational dynamics of the agent. Simulations are given to illustrate the theoretical findings.

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arXiv2015

Synchronization of Multi-Agent Systems With Heterogeneous Controllers

This paper studies the synchronization of a multi-agent system where the agents are coupled through heterogeneous controller gains. Synchronization refers to the situation where all the agents in a group have a common velocity direction. We generalize existing results and show that by using heterogeneous controller gains, the final velocity direction at which the system of agents synchronize can be controlled. The effect of heterogeneous gains on the reachable set of this final velocity direction is further analyzed. We also show that for realistic systems, a limited control force to stabilize the agents to the synchronized condition can be achieved by confining these heterogeneous controller gains to an upper bound. Simulations are given to support the theoretical findings.

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arXiv2003

Providing Diversity in K-Nearest Neighbor Query Results

Given a point query Q in multi-dimensional space, K-Nearest Neighbor (KNN) queries return the K closest answers according to given distance metric in the database with respect to Q. In this scenario, it is possible that a majority of the answers may be very similar to some other, especially when the data has clusters. For a variety of applications, such homogeneous result sets may not add value to the user. In this paper, we consider the problem of providing diversity in the results of KNN queries, that is, to produce the closest result set such that each answer is sufficiently different from the rest. We first propose a user-tunable definition of diversity, and then present an algorithm, called MOTLEY, for producing a diverse result set as per this definition. Through a detailed experimental evaluation on real and synthetic data, we show that MOTLEY can produce diverse result sets by reading only a small fraction of the tuples in the database. Further, it imposes no additional overhead on the evaluation of traditional KNN queries, thereby providing a seamless interface between diversity and distance.

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