arXiv subjects

Hai Lin

Publications and source records attributed to Hai Lin.

At least 127 records · Page 7Linked to original sources

arXiv2020

Approximate Simulation for Template-Based Whole-Body Control

Reduced-order template models are widely used to control high degree-of-freedom legged robots, but existing methods for template-based whole-body control rely heavily on heuristics and often suffer from robustness issues. In this letter, we propose a template-based whole-body control method grounded in the formal framework of approximate simulation. Our central contribution is to demonstrate how the Hamiltonian structure of rigid-body dynamics can be exploited to establish approximate simulation for a high-dimensional nonlinear system. The resulting controller is passive, more robust to push disturbances, uneven terrain, and modeling errors than standard QP-based methods, and naturally enables high center of mass walking. Our theoretical results are supported by simulation experiments with a 30 degree-of-freedom Valkyrie humanoid model.

cs.RO↗

arXiv2020

Coherent state superpositions, entanglement and gauge/gravity correspondence

We focus on two types of coherent states, the coherent states of multi graviton states and the coherent states of giant graviton states, in the context of gauge/gravity correspondence. We conveniently use a phase shift operator and its actions on the superpositions of these coherent states. We find $N$-state Schrodinger cat states which approach the one-row Young tableau states, with fidelity between them asymptotically reaches 1 at large $N$. The quantum Fisher information of these states is proportional to the variance of the excitation energy of the underlying states, and characterizes the localizability of the states in the angular direction in the phase space. We analyze the correlation and entanglement between gravitational degrees of freedom using different regions of the phase space plane in bubbling AdS. The correlation between two entangled rings in the phase space plane is related to the area of the annulus between the two rings. We also analyze two types of noisy coherent states, which can be viewed as interpolated states that interpolate between a pure coherent state in the noiseless limit and a maximally mixed state in the large noise limit.

hep-th↗

arXiv2020

Trajectory Optimization for High-Dimensional Nonlinear Systems under STL Specifications

Signal Temporal Logic (STL) has gained popularity in recent years as a specification language for cyber-physical systems, especially in robotics. Beyond being expressive and easy to understand, STL is appealing because the synthesis problem---generating a trajectory that satisfies a given specification---can be formulated as a trajectory optimization problem. Unfortunately, the associated cost function is nonsmooth and non-convex. As a result, existing synthesis methods scale poorly to high-dimensional nonlinear systems. In this letter, we present a new trajectory optimization approach for STL synthesis based on Differential Dynamic Programming (DDP). It is well known that DDP scales well to extremely high-dimensional nonlinear systems like robotic quadrupeds and humanoids: we show that these advantages can be harnessed for STL synthesis. We prove the soundness of our proposed approach, demonstrate order-of-magnitude speed improvements over the state-of-the-art on several benchmark problems, and demonstrate the scalability of our approach to the full nonlinear dynamics of a 7 degree-of-freedom robot arm.

cs.RO↗

arXiv2020

Boundary contributions to three loop superstring amplitudes

In type II superstring theory, the vacuum amplitude at a given loop order $g$ can receive contributions from the boundary of the compactified, genus $g$ supermoduli space of curves $\overline{\mathfrak M}_g$. These contributions capture the long distance or infrared behaviour of the amplitude. The boundary parametrises degenerations of genus $g$ super Riemann surfaces. A holomorphic projection of the supermoduli space onto its reduced space would then provide a way to integrate the holomorphic, superstring measure and thereby give the superstring vacuum amplitude at $g$-loop order. However, such a projection does not generally exist over the bulk of the supermoduli spaces in higher genera. Nevertheless, certain boundary divisors in $\partial\overline{\mathfrak M}_g$ may holomorphically map onto a bosonic space upon composition with universal morphisms, thereby enabling an integration of the holomorphic, superstring measure here. Making use of ansatz factorisations of the superstring measure near the boundary, our analysis shows that the boundary contributions to the three loop vacuum amplitude will vanish in closed oriented type II superstring theory with unbroken spacetime supersymmetry.

hep-th↗

arXiv2020

Automatic Trajectory Synthesis for Real-Time Temporal Logic

Many safety-critical systems must achieve high-level task specifications with guaranteed safety and correctness. Much recent progress towards this goal has been made through controller synthesis from temporal logic specifications. Existing approaches, however, have been limited to relatively short and simple specifications. Furthermore, existing methods either consider some prior discretization of the state-space, deal only with a convex fragment of temporal logic, or are not provably complete. We propose a scalable, provably complete algorithm that synthesizes continuous trajectories to satisfy non-convex \gls*{rtl} specifications. We separate discrete task planning and continuous motion planning on-the-fly and harness highly efficient boolean satisfiability (SAT) and \gls*{lp} solvers to find dynamically feasible trajectories that satisfy non-convex \gls*{rtl} specifications for high dimensional systems. The proposed design algorithms are proven sound and complete, and simulation results demonstrate our approach's scalability.

eess.SY↗

arXiv2020

Specification mining and automated task planning for autonomous robots based on a graph-based spatial temporal logic

We aim to enable an autonomous robot to learn new skills from demo videos and use these newly learned skills to accomplish non-trivial high-level tasks. The goal of developing such autonomous robot involves knowledge representation, specification mining, and automated task planning. For knowledge representation, we use a graph-based spatial temporal logic (GSTL) to capture spatial and temporal information of related skills demonstrated by demo videos. We design a specification mining algorithm to generate a set of parametric GSTL formulas from demo videos by inductively constructing spatial terms and temporal formulas. The resulting parametric GSTL formulas from specification mining serve as a domain theory, which is used in automated task planning for autonomous robots. We propose an automatic task planning based on GSTL where a proposer is used to generate ordered actions, and a verifier is used to generate executable task plans. A table setting example is used throughout the paper to illustrate the main ideas.

cs.AI↗

arXiv2020

Deep Reinforcement Learning for Joint Beamwidth and Power Optimization in mmWave Systems

This paper studies the joint beamwidth and transmit power optimization problem in millimeter wave communication systems. A deep reinforcement learning based approach is proposed. Specifically, a customized deep Q network is trained offline, which is able to make real-time decisions when deployed online. Simulation results show that the proposed approach significantly outperforms conventional approaches in terms of both performance and complexity. Besides, strong generalization ability to different system parameters is also demonstrated, which further enhances the practicality of the proposed approach.

cs.IT↗

arXiv2020

PDE-based Dynamic Density Estimation for Large-scale Agent Systems

Large-scale agent systems have foreseeable applications in the near future. Estimating their macroscopic density is critical for many density-based optimization and control tasks, such as sensor deployment and city traffic scheduling. In this paper, we study the problem of estimating their dynamically varying probability density, given the agents' individual dynamics (which can be nonlinear and time-varying) and their states observed in real-time. The density evolution is shown to satisfy a linear partial differential equation uniquely determined by the agents' dynamics. We present a density filter which takes advantage of the system dynamics to gradually improve its estimation and is scalable to the agents' population. Specifically, we use kernel density estimators (KDE) to construct a noisy measurement and show that, when the agents' population is large, the measurement noise is approximately ``Gaussian''. With this important property, infinite-dimensional Kalman filters are used to design density filters. It turns out that the covariance of measurement noise depends on the true density. This state-dependence makes it necessary to approximate the covariance in the associated operator Riccati equation, rendering the density filter suboptimal. The notion of input-to-state stability is used to prove that the performance of the suboptimal density filter remains close to the optimal one. Simulation results suggest that the proposed density filter is able to quickly recognize the underlying modes of the unknown density and automatically ignore outliers, and is robust to different choices of kernel bandwidth of KDE.

eess.SY↗

arXiv2020

A Smooth Robustness Measure of Signal Temporal Logic for Symbolic Control

Recent years have seen an increasing use of Signal Temporal Logic (STL) as a formal specification language for symbolic control, due to its expressiveness and closeness to natural language. Furthermore, STL specifications can be encoded as cost functions using STL's robust semantics, transforming the synthesis problem into an optimization problem. Unfortunately, these cost functions are non-smooth and non-convex, and exact solutions using mixed-integer programming do not scale well. Recent work has focused on using smooth approximations of robustness, which enable faster gradient-based methods to find local maxima, at the expense of soundness and/or completeness. We propose a novel robustness approximation that is smooth everywhere, sound, and asymptotically complete. Our approach combines the benefits of existing approximations, while enabling an explicit tradeoff between conservativeness and completeness.

eess.SY↗

arXiv2020

Calabi-Yau generalized complete intersections and aspects of cohomology of sheaves

We consider generalized complete intersection manifolds in the product space of projective spaces, and work out useful aspects pertaining to the cohomology of sheaves over them. First, we present and prove a vanishing theorem on the cohomology groups of sheaves for subvarieties of the ambient product space of projective spaces. We then prove an equivalence between configuration matrices of complete intersection Calabi-Yau manifolds. We also present a formula of the genus of curves in generalized complete intersection manifolds. Some of these curves arise as the fixed point locus of certain symmetry group action on the generalized complete intersection Calabi-Yau manifolds. We also make a blowing-up along the curves, by which one can generate new Calabi-Yau manifolds. Moreover, an approach on spectral sequences is used to compute Hodge numbers of generalized complete intersection Calabi-Yau manifolds and the genus of curves therein.

hep-th↗

arXiv2020

A graph-based spatial temporal logic for knowledge representation and automated reasoning in cognitive robots

We propose a new graph-based spatial temporal logic for knowledge representation and automated reasoning in this paper. The proposed logic achieves a balance between expressiveness and tractability in applications such as cognitive robots. The satisfiability of the proposed logic is decidable. We apply a Hilbert style axiomatization for the proposed graph-based spatial temporal logic, in which Modus ponens and IRR are the inference rules. We show that the corresponding deduction system is sound and complete and can be implemented through SAT.

cs.LO↗

arXiv2020

Robust Approximate Simulation for Hierarchical Control of Linear Systems under Disturbances

Approximate simulation, an extension of simulation relations from formal methods to continuous systems, is a powerful tool for hierarchical control of complex systems. Finding an approximate simulation relation between the full "concrete" system and a simplified "abstract" system establishes a bound on the output error between the two systems, allowing one to design a controller for the abstract system while formally certifying performance on the concrete system. However, many real-world control systems are subject to external disturbances, which are not accounted for in the standard approximate simulation framework. We present a notion of robust approximate simulation, which considers external disturbances to the concrete system. We derive output error bounds for the case of linear systems subject to two types of additive disturbances: bounded disturbances and a sequence of (unbounded) impulse disturbances. We demonstrate the need for robust approximate simulation and the effectiveness of our proposed approach with a simulated robot motion planning example.

eess.SY↗

arXiv2020

Ensuring Privacy in Location-Based Services: A Model-based Approach

In recent years, the widespread of mobile devices equipped with GPS and communication chips has led to the growing use of location-based services (LBS) in which a user receives a service based on his current location. The disclosure of user's location, however, can raise serious concerns about user privacy in general, and location privacy in particular which led to the development of various location privacy-preserving mechanisms aiming to enhance the location privacy while using LBS applications. In this paper, we propose to model the user mobility pattern and utility of the LBS as a Markov decision process (MDP), and inspired by probabilistic current state opacity notation, we introduce a new location privacy metric, namely $ε-$privacy, that quantifies the adversary belief over the user's current location. We exploit this dynamic model to design a LPPM that while it ensures the utility of service is being fully utilized, independent of the adversary prior knowledge about the user, it can guarantee a user-specified privacy level can be achieved for an infinite time horizon. The overall privacy-preserving framework, including the construction of the user mobility model as a MDP, and design of the proposed LPPM, are demonstrated and validated with real-world experimental data.

cs.CR↗

arXiv2020

Unsupervised Learning for Passive Beamforming

Reconfigurable intelligent surface (RIS) has recently emerged as a promising candidate to improve the energy and spectral efficiency of wireless communication systems. However, the unit modulus constraint on the phase shift of reflecting elements makes the design of optimal passive beamforming solution a challenging issue. The conventional approach is to find a suboptimal solution using the semi-definite relaxation (SDR) technique, yet the resultant suboptimal iterative algorithm usually incurs high complexity, hence is not amenable for real-time implementation. Motivated by this, we propose a deep learning approach for passive beamforming design in RIS-assisted systems. In particular, a customized deep neural network is trained offline using the unsupervised learning mechanism, which is able to make real-time prediction when deployed online. Simulation results show that the proposed approach maintains most of the performance while significantly reduces computation complexity when compared with SDR-based approach.

cs.IT↗

arXiv2019

AdS backgrounds and induced gravity

In this paper we look for AdS solutions to generalised gravity theories in the bulk in various spacetime dimensions. The bulk gravity action includes the action of a non-minimally coupled scalar field with gravity, and a higher-derivative action of gravity. The usual Einstein-Hilbert gravity is induced when the scalar acquires a non-zero vacuum expectation value. The equation of motion in the bulk shows scenarios where AdS geometry emerges on-shell. We further obtain the action of the fluctuation fields on the background at quadratic and cubic orders.

hep-th↗

arXiv2019

Kalman Filtering with Gaussian Processes Measurement Noise

Real-world measurement noise in applications like robotics is often correlated in time, but we typically assume i.i.d. Gaussian noise for filtering. We propose general Gaussian Processes as a non-parametric model for correlated measurement noise that is flexible enough to accurately reflect correlation in time, yet simple enough to enable efficient computation. We show that this model accurately reflects the measurement noise resulting from vision-based Simultaneous Localization and Mapping (SLAM), and argue that it provides a flexible means of modeling measurement noise for a wide variety of sensor systems and perception algorithms. We then extend existing results for Kalman filtering with autoregressive processes to more general Gaussian Processes, and demonstrate the improved performance of our approach.

stat.ML↗

arXiv2019

Formal Connections between Template and Anchor Models via Approximate Simulation

Reduced-order template models like the Linear Inverted Pendulum (LIP) and Spring-Loaded Inverted Pendulum (SLIP) are widely used tools for controlling high-dimensional humanoid robots. However, connections between templates and whole-body models have lacked formal underpinnings, preventing formal guarantees when it comes to integrated controller design. We take a small step towards addressing this gap by considering the notion of approximate simulation. Derived from simulation relations for discrete transition systems in formal methods, approximate similarity means that the outputs of two systems can remain $ε$-close. In this paper, we consider the case of controlling a balancer via planning with the LIP model. We show that the balancer approximately simulates the LIP and derive linear constraints that are sufficient conditions for maintaining ground contact. This allows for rapid planning and replanning with the template model by solving a quadratic program that enforces contact constraints in the full model. We demonstrate the efficacy of this planning and control paradigm in a simulated push recovery scenario for a planar 4-link balancer.

cs.RO↗

arXiv2019

Reactive Supervisory Control of Open Discrete-event Systems

The conventional Wonham-Ramadge supervisory control framework of discrete event systems enforces a closed discrete event system to generate correct behaviors under certain environments, which can be captured by an appropriate plant model. Nevertheless, such control methods cannot be directly applied for many practical engineering systems nowadays since they are open systems and their operation heavily depends on nontrivial interactions between the systems and the external environments. These open systems should be controlled in such a way that accomplishment of the control objective can be guaranteed for any possible environment, which may be dynamic, uncertain and sometimes unpredictable. In this paper, we aim at extending the conventional supervisory control theory to open discrete event systems in a reactive manner. Starting from a novel input-output automaton model of an open system, we consider control objectives that characterize the desired input-output behaviors of the system, based on which a game-theoretic approach is carried out to compute a reactive supervisor that steers the system to fulfill the specifications regardless of the environment behaviors. We present a necessary and sufficient conditions for the existence of such a reactive supervisor. Furthermore, illustrative examples are given throughout this paper to demonstrate the key definitions and the effectiveness of the proposed reactive supervisor synthesis framework.

eess.SP↗