Motion Planning of Uncertain Ordinary Differential Equation Systems

This work presents a novel motion planning framework, rooted in nonlinear programming theory, that treats uncertain fully and under-actuated dynamical systems described by ordinary differential equations. Uncertainty in multibody dynamical systems comes from various sources, such as: system parameters, initial conditions, sensor and actuator noise, and external forcing. Treatment of uncertainty in design is of paramount practical importance because all real-life systems are affected by it, and poor robustness and suboptimal performance result if it’s not accounted for in a given design. In this work uncertainties are modeled using Generalized Polynomial Chaos and are solved quantitatively using a least-square collocation method. The computational efficiency of this approach enables the inclusion of uncertainty statistics in the nonlinear programming optimization process. As such, the proposed framework allows the user to pose, and answer, new design questions related to uncertain dynamical systems. Specifically, the new framework is explained in the context of forward, inverse, and hybrid dynamics formulations. The forward dynamics formulation, applicable to both fully and under-actuated systems, prescribes deterministic actuator inputs which yield uncertain state trajectories. The inverse dynamics formulation is the dual to the forward dynamic, and is only applicable to fully-actuated systems; deterministic state trajectories are prescribed and yield uncertain actuator inputs. The inverse dynamics formulation is more computationally efficient as it requires only algebraic evaluations and completely avoids numerical integration. Finally, the hybrid dynamics formulation is applicable to under-actuated systems where it leverages the benefits of inverse dynamics for actuated joints and forward dynamics for unactuated joints; it prescribes actuated state and unactuated input trajectories which yield uncertain unactuated states and actuated inputs. The benefits of the ability to quantify uncertainty when planning the motion of multibody dynamic systems are illustrated through several case-studies. The resulting designs determine optimal motion plans—subject to deterministic and statistical constraints—for all possible systems within the probability space

An LFT/SDP approach to the uncertainty analysis for state

A state estimator is an algorithm that computes the current state of a time-varying system from on-line measurements. Physical quantities such as measurements and parameters are characterised by uncertainty. Understanding how uncertainty affects the accuracy of state estimates is therefore a pre-requisite to the application of such techniques to real systems. In this paper we develop a method of uncertainty analysis based on linear fractional transformations (LFT) and obtain ellipsoid-of-confidence bounds by recasting the LFT problem into a semidefinite programming problem (SDP). The ideas are illustrated by applying them to a simple water distribution network

WiLiTV: A Low-Cost Wireless Framework for Live TV Services

With the evolution of HDTV and Ultra HDTV, the bandwidth requirement for IP-based TV content is rapidly increasing. Consumers demand uninterrupted service with a high Quality of Experience (QoE). Service providers are constantly trying to differentiate themselves by innovating new ways of distributing content more efficiently with lower cost and higher penetration. In this work, we propose a cost-efficient wireless framework (WiLiTV) for delivering live TV services, consisting of a mix of wireless access technologies (e.g. Satellite, WiFi and LTE overlay links). In the proposed architecture, live TV content is injected into the network at a few residential locations using satellite dishes. The content is then further distributed to other homes using a house-to-house WiFi network or via an overlay LTE network. Our problem is to construct an optimal TV distribution network with the minimum number of satellite injection points, while preserving the highest QoE, for different neighborhood densities. We evaluate the framework using realistic time-varying demand patterns and a diverse set of home location data. Our study demonstrates that the architecture requires 75 - 90% fewer satellite injection points, compared to traditional architectures. Furthermore, we show that most cost savings can be obtained using simple and practical relay routing solutions