Emergent dynamics of the Kuramoto ensemble under the effect of inertia

We study the emergent collective behaviors for an ensemble of identical Kuramoto oscillators under the effect of inertia. In the absence of inertial effects, it is well known that the generic initial Kuramoto ensemble relaxes to the phase-locked states asymptotically (emergence of complete synchronization) in a large coupling regime. Similarly, even for the presence of inertial effects, similar collective behaviors are observed numerically for generic initial configurations in a large coupling strength regime. However, this phenomenon has not been verified analytically in full generality yet, although there are several partial results in some restricted set of initial configurations. In this paper, we present several improved complete synchronization estimates for the Kuramoto ensemble with inertia in two frameworks for a finite system. Our improved frameworks describe the emergence of phase-locked states and its structure. Additionally, we show that as the number of oscillators tends to infinity, the Kuramoto ensemble with infinite size can be approximated by the corresponding kinetic mean-field model uniformly in time. Moreover, we also establish the global existence of measure-valued solutions for the Kuramoto equation and its large-time asymptotics

Topology-Guided Path Integral Approach for Stochastic Optimal Control in Cluttered Environment

This paper addresses planning and control of robot motion under uncertainty that is formulated as a continuous-time, continuous-space stochastic optimal control problem, by developing a topology-guided path integral control method. The path integral control framework, which forms the backbone of the proposed method, re-writes the Hamilton-Jacobi-Bellman equation as a statistical inference problem; the resulting inference problem is solved by a sampling procedure that computes the distribution of controlled trajectories around the trajectory by the passive dynamics. For motion control of robots in a highly cluttered environment, however, this sampling can easily be trapped in a local minimum unless the sample size is very large, since the global optimality of local minima depends on the degree of uncertainty. Thus, a homology-embedded sampling-based planner that identifies many (potentially) local-minimum trajectories in different homology classes is developed to aid the sampling process. In combination with a receding-horizon fashion of the optimal control the proposed method produces a dynamically feasible and collision-free motion plans without being trapped in a local minimum. Numerical examples on a synthetic toy problem and on quadrotor control in a complex obstacle field demonstrate the validity of the proposed method.Comment: arXiv admin note: text overlap with arXiv:1510.0534

Text2Action: Generative Adversarial Synthesis from Language to Action

In this paper, we propose a generative model which learns the relationship between language and human action in order to generate a human action sequence given a sentence describing human behavior. The proposed generative model is a generative adversarial network (GAN), which is based on the sequence to sequence (SEQ2SEQ) model. Using the proposed generative network, we can synthesize various actions for a robot or a virtual agent using a text encoder recurrent neural network (RNN) and an action decoder RNN. The proposed generative network is trained from 29,770 pairs of actions and sentence annotations extracted from MSR-Video-to-Text (MSR-VTT), a large-scale video dataset. We demonstrate that the network can generate human-like actions which can be transferred to a Baxter robot, such that the robot performs an action based on a provided sentence. Results show that the proposed generative network correctly models the relationship between language and action and can generate a diverse set of actions from the same sentence.Comment: 8 pages, 10 figure