Abstract

Given a topology of local parity-check constraints, a maximally recoverable code (MRC) can correct all erasure patterns that are information-theoretically correctable. In a grid-like topology, there are a local constraints in every column forming a column code, b local constraints in every row forming a row code, and h global constraints in an (m × n) grid of codeword. Recently, Gopalan et al. initiated the study of MRCs under grid-like topology, and derived a necessary and sufficient condition, termed as the regularity condition, for an erasure pattern to be recoverable when a = 1, h = 0. In this paper, we consider MRCs for product topology ( h = 0). First, we construct a certain bipartite graph based on the erasure pattern satisfying the regularity condition for product topology (any a, b, h = 0) and show that there exists a complete matching in this graph. We then present an alternate direct proof of the sufficient condition when a = 1, h = 0. We later extend our technique to study the topology for a = 2, h = 0, and characterize a subset of recoverable erasure patterns in that case. For both a = 1, 2, our method of proof is uniform, i.e., by constructing tensor product G col ⊗ G row of generator matrices of column and row codes such that certain square sub-matrices retain full rank. The full-rank condition is proved by resorting to the matching identified earlier and also another set of matchings in erasure sub-patterns.

Abstract

n Index Coding, the goal is to use a broadcast channel as efficiently as possible to communicate information from a source to multiple receivers which can possess some of the information symbols at the source as side-information. In this work, we present a duality relationship between index coding (IC) and multiple-unicast network coding (NC). It is known that the IC problem can be represented using a side-information graph G (with number of vertices n equal to the number of source symbols). The size of the maximum acyclic induced subgraph, denoted by MAI S is a lower bound on the broadcast rate. For IC problems with MAIS = n - 1 and MAI S = n - 2, prior work has shown that binary (over F 2) linear index codes achieve the MAI S lower bound for the broadcast rate and thus are optimal. In this work, we use the the duality relationship between NC and IC to show that for a class of IC problems with MAIS = n - 3 …

Abstract

Index coding for broadcast channels allows each receiver or client to retrieve its demanded message from its side information and the transmitted codeword. In general, a client may have to observe the entire codeword to decode its demanded message. However, downloading or querying the codeword symbols might involve costs at a client - such as network utilization costs and storage. Traditional index coding does not consider this client perspective, and as a result, for these codes the number of codeword symbols queried by a client per decoded message symbol, which we refer to as locality, could be large. In this paper we study a `client aware' approach to index coding by viewing the problem as a trade-off between the achievable broadcast rate and locality, where the objective is to minimize the rate for a given value of locality and vice versa. We first consider the minimum possible locality 1 and show that the …

Abstract

We present a coded caching framework using line graphs of bipartite graphs. A clique cover of the line graph describes the uncached subfiles at users. A clique cover of the complement of the square of the line graph gives a transmission scheme that satisfies user demands. We then define a specific class of such caching line graphs, for which the subpacketization, rate, and uncached fraction of the coded caching problem can be captured via its graph theoretic parameters. We present a construction of such caching line graphs using projective geometry. The presented scheme has a rate bounded from above by a constant with subpacketization level q O((IogqK)^2) and uncached fraction Θ(1/√K), where K is the number of users and q is a prime power. We also present a subpacketization-dependent lower bound on the rate of coded caching schemes for a given broadcast setup.

Abstract

Most reinforcement learning algorithms are inefficient for learning multiple tasks in complex robotic systems, where different tasks share a set of actions. In such environments a compound policy may be learnt with shared neural network parameters, which performs multiple tasks concurrently. However such compound policy may get biased towards a task or the gradients from different tasks negate each other, making the learning unstable and sometimes less data efficient. In this paper, we propose a new approach for simultaneous training of multiple tasks sharing a set of common actions in continuous action spaces, which we call as DiGrad (Differential Policy Gradient). The proposed framework is based on differential policy gradients and can accommodate multi-task learning in a single actor-critic network. We also propose a simple heuristic in the differential policy gradient update to further improve the learning. The proposed architecture was tested on 8 link planar manipulator and 27 degrees of freedom (DoF) Humanoid for learning multi-goal reachability tasks for 3 and 2 end effectors respectively. We show that our approach supports efficient multi-task learning in complex robotic systems, outperforming related methods in continuous action spaces.

Abstract

With the advent of artificial intelligence and machine learning, humanoid robots are made to learn a variety of skills which humans possess. One of fundamental skills which humans use in day-to-day activities is performing tasks with coordination between both the hands. In case of humanoids, learning such skills require optimal motion planning which includes avoiding collisions with the surroundings. In this paper, we propose a framework to learn coordinated tasks in cluttered environments based on DiGrad - A multi-task reinforcement learning algorithm for continuous action-spaces. Further, we propose an algorithm to smooth the joint space trajectories obtained by the proposed framework in order to reduce the noise instilled during training. The proposed framework was tested on a 27 degrees of freedom (DoF) humanoid with articulated torso for performing coordinated object-reaching task with both the hands in four different environments with varying levels of difficulty. It is observed that the humanoid is able to plan collision free trajectory in real-time. Simulation results also reveal the usefulness of the articulated torso for performing tasks which require coordination between both the arms.

Abstract

General Inverse Kinematic (IK) solvers may not guarantee real-time control of the end-effectors in external coordinates along with maintaining stability. This work addresses this problem by using Reinforcement Learning (RL) for learning an inverse kinematics solver for reachability tasks which ensures stability and self-collision avoidance while solving for end effectors. We propose an actor-critic based algorithm to learn joint space trajectories of stable configuration for solving inverse kinematics that can operate over continuous action spaces. Our approach is based on the idea of exploring the entire workspace and learning the best possible configurations. The proposed strategy was evaluated on the highly articulated upper body of a 27 degrees of freedom (DoF) humanoid for learning multi-goal reachability tasks of both hands along with maintaining stability in double support phase. We show that the trained model was able to solve inverse kinematics for both the hands, where the articulated torso contributed to both the tasks.

Abstract

Performing dual arm coordinated (reachability)tasks in humanoid robots require complex planning strategies and this complexity increases further, in case of humanoids with articulated torso. These complex strategies may not be suitable for online motion planning. This paper proposes a faster way to accomplish dual arm coordinated tasks using methodology based on Reinforcement Learning. The contribution of this paper is twofold. Firstly, we propose DiGrad (Differential Gradients), a new RL framework for multi-task learning in manipulators. Secondly, we show how this framework can be adopted to learn dual arm coordination in a 27 degrees of freedom (DOF)humanoid robot with articulated spine. The proposed framework and methodology are evaluated in various environments and simulation results are presented. A comparative study of DiGrad with its parent algorithm in different settings is also presented

Abstract

The concept of discrete-time higher order sliding mode (DHOSM) has received increased attention. However, because of the dearth of knowledge on bound of the external disturbance in the system, an adaptive control law is desirable. This brief presents a technique to design a DHOSM control with adaptive switching gains where the bound on the disturbance is considered to be unknown.

Abstract

One of the major issues in an interconnected power system is the low damping of inter-area oscillations. A proportional-derivative (PD) compensator is a popular control method which is extensively being used as an active damping control in various domains such as robotics, smart structure, etc. However, existence of noise in wide-area signal makes an ideal PD compensator unrealisable in power systems. In this endeavour, a new methodology christened as time-delayed control is proposed where artificial delay is used to provide derivative action which acts as a damping component of wide-area controller. The delay margin is computed for the closed loop system using Razumikhin approach. It is observed that the proposed controller is able to damp the oscillations adequately with reduced sensitivity to the noise in the signals. Further, the proposed controller is able to provide robustness against uncertainties arising from the system dynamics and inherent delay in communication channel.