Anoop Jain

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 in the database with respect to Q. In this scenario, it is possible that a majority of the answers may be very similar to one or more of the other answers, 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 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.

Collective behavior with heterogeneous controllers

In this paper, we study the collective motion of individually controlled planar particles when they are coupled through heterogeneous controller gains. Two types of collective formations, synchronization and balancing, are described and analyzed under the influence of these heterogeneous controller gains. These formations are characterized by the motion of the centroid of the group of particles. In synchronized formation, the particles and their centroid move in a common direction, while in balanced formation the movement of particles possess a fixed location of the centroid. We show that, by selecting suitable controller gains, these formations can be controlled significantly to obtain not only a desired direction of motion but also a desired location of the centroid. We present the results for N-particles in synchronized formation, while in balanced formation our analysis is confined to two and three particles.

Stabilization of collective motion in synchronized, balanced and splay phase arrangements on a desired circle

This paper proposes a design methodology to stabilize collective circular motion of a group of N-identical agents moving at unit speed around individual circles of different radii and different centers. The collective circular motion studied in this paper is characterized by the clockwise rotation of all agents around a common circle of desired radius as well as center, which is fixed. Our interest is to achieve those collective circular motions in which the phases of the agents are arranged either in synchronized, in balanced or in splay formation. In synchronized formation, the agents and their centroid move in a common direction while in balanced formation, the movement of the agents ensures a fixed location of the centroid. The splay state is a special case of balanced formation, in which the phases are separated by multiples of 2π/N. We derive the feedback controls and prove the asymptotic stability of the desired collective circular motion by using Lyapunov theory and the LaSalles Invariance principle.

Stabilization of collective formations with speed and controller gain heterogeneity and saturation

This paper studies collective formations of multi-agent systems, modeled with unicycle dynamics, while admitting heterogeneity in both controller gains and speeds of the agents along with saturation on the controller outputs. This addresses a practical scenario where the speeds are usually nonidentical and the controller gains may vary due to imperfect implementation. The paper analyzes the effect of both heterogeneous controller gains and speeds simultaneously on the collective formations obtained by optimizing the average linear momentum of the group of agents. A detailed analysis of the two-agent system is given in the paper and some results on the locus of the collective centroid with varying controller gains are obtained. Effect of saturation is also studied for two cases when the controller gains are bounded and when the control efforts are bounded. Simulation examples are given to illustrate the theoretical findings

Achieving a desired collective centroid by a formation of agents moving in a controllable force field

In this paper, we study the problem of a formation of agents trying to achieve a desired stationary or moving collective centroid. The agents are assumed to be moving in a force field which is controlled externally. The stabilization of the collective centroid to a fixed desired location results in a balanced formation of the agents about that point. Similarly, the centroid of the system of agents may be required to move along a certain given trajectory. For this, the centroid of the formation must converge to the desired trajectory. To solve this problem, we propose an all-to-all coupled planar motion model that explicitly incorporates an additional control pertaining to the external force field. Simulation results are presented to support the theoretical findings.

A heterogeneous control gain approach to achieve a desired collective centroid by a formation of agents

This paper proposes a heterogeneous gains based controller design methodology to stabilize a particular type of collective motion in a multi-agent system where the heading angles of the agents are in balanced formation. Balancing refers to the situation in which the movement of agents causes the position of their centroid to become stationary. Our interest, in this paper, is to achieve balanced formation about a desired location of the centroid while allowing the agents to move either along straight line paths or around individual circular orbits. For this purpose, we derive feedback control laws that operate with heterogeneous control gains, and are more practical compared to the homogeneous gains based controls existing in the literature. We also show that if the heterogeneous control gains are zero for almost half of the agents of the group, it is possible to achieve balanced formation at an additional advantage of reduced computational complexity of the proposed control law. Simulations are given to illustrate the theoretical findings.

Stabilization of Balanced Circular Motion About a Desired Center

Abstract In this paper, we study the collective motion of a group of N(⩾ 2) identical agents trying to achieve a circular formation centered at a desired location, which is fixed. A circular formation is characterized by the motion of all agents around the same circle in the same direction. To solve this problem, we propose a planar motion model that incorporates two control inputs. One of the control inputs is chosen independently and the other control input is decided by using the composite Lyapunov function. We show that the desired location of the center of this circular formation, which is fixed, is obtained by directing the centroid of the group of agents to that desired location. This leads to a collective formation of all the agents, known as balanced circular formation. The theoretical findings are supported by simulations.