Scalable Approach to Uncertainty Quantification and Robust Design of Interconnected Dynamical Systems

Development of robust dynamical systems and networks such as autonomous aircraft systems capable of accomplishing complex missions faces challenges due to the dynamically evolving uncertainties coming from model uncertainties, necessity to operate in a hostile cluttered urban environment, and the distributed and dynamic nature of the communication and computation resources. Model-based robust design is difficult because of the complexity of the hybrid dynamic models including continuous vehicle dynamics, the discrete models of computations and communications, and the size of the problem. We will overview recent advances in methodology and tools to model, analyze, and design robust autonomous aerospace systems operating in uncertain environment, with stress on efficient uncertainty quantification and robust design using the case studies of the mission including model-based target tracking and search, and trajectory planning in uncertain urban environment. To show that the methodology is generally applicable to uncertain dynamical systems, we will also show examples of application of the new methods to efficient uncertainty quantification of energy usage in buildings, and stability assessment of interconnected power networks

Ergodic Exploration using Tensor Train: Applications in Insertion Tasks

By generating control policies that create natural search behaviors in autonomous systems, ergodic control provides a principled solution to address tasks that require exploration. A large class of ergodic control algorithms relies on spectral analysis, which suffers from the curse of dimensionality, both in storage and computation. This drawback has prohibited the application of ergodic control in robot manipulation since it often requires exploration in state space with more than 2 dimensions. Indeed, the original ergodic control formulation will typically not allow exploratory behaviors to be generated for a complete 6D end-effector pose. In this paper, we propose a solution for ergodic exploration based on the spectral analysis in multidimensional spaces using low-rank tensor approximation techniques. We rely on tensor train decomposition, a recent approach from multilinear algebra for low-rank approximation and efficient computation of multidimensional arrays. The proposed solution is efficient both computationally and storage-wise, hence making it suitable for its online implementation in robotic systems. The approach is applied to a peg-in-hole insertion task using a 7-axis Franka Emika Panda robot, where ergodic exploration allows the task to be achieved without requiring the use of force/torque sensors