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In order to perform highly dynamic and agile maneuvers, legged robots typically spend time in underactuated domains (e.g. with feet off the ground) where the system has limited command of its acceleration and a constrained amount of time before transitioning to a new domain (e.g. foot touchdown). Meanwhile, these transitions can instantaneously change the system’s state, possibly causing perturbations to be mapped arbitrarily far away from the target trajectory. These properties make it difficult for local feedback controllers to effectively recover from disturbances as the system evolves through underactuated domains and hybrid impact events. To address this, we utilize the fundamental solution matrix that characterizes the evolution of perturbations through a hybrid trajectory and its 2-norm, which represents the worst-case growth of perturbations. In this paper, the worst-case perturbation analysis is used to explicitly reason about the tracking performance of a hybrid trajectory and is incorporated in an iLQR framework to optimize a trajectory while taking into account the closed-loop convergence of the trajectory under an LQR tracking controller. The generated convergent trajectories recover more effectively from perturbations, are more robust to large disturbances, and use less feedback control effort than trajectories generated with traditional methods.
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Change point detection of events in molecular simulations using dupin
Particle tracking is commonly used to study time-dependent behavior in many different types of physical and chemical systems involving constituents that span many length scales, including atoms, molecules, nanoparticles, granular particles, and even larger objects. Behaviors of interest studied using particle tracking information include disorder-order transitions, thermodynamic phase transitions, struc- tural transitions, protein folding, crystallization, gelation, swarming, avalanches and fracture. A common challenge in studies of these systems involves change detection. Change point detection discerns when a temporal signal undergoes a change in distribution. These changes can be local or global, instantaneous or prolonged, obvious or subtle. Moreover, system-wide changes marking an interesting physical or chemical phenomenon (e.g. crystallization of a liquid) are often preceded by events (e.g. pre-nucleation clusters) that are localized and can occur anywhere at anytime in the system. For these reasons, detecting events in particle trajectories generated by molecular simulation is challenging and typically accomplished via ad hoc solutions unique to the behavior and system under study. Consequently, methods for event detec- tion lack generality, and those used in one field are not easily used by scientists in other fields. Here we present a new Python-based tool, dupin, that allows for universal event detection from particle trajectory data irrespective of the system details. dupin works by creating a signal representing the simulation and partitioning the signal based on events (changes within the trajectory). This approach allows for studies where manual annotating of event boundaries would require a prohibitive amount of time. Furthermore, dupin can serve as a tool in automated and reproducible workflows. We demonstrate the application of dupin using two examples and discuss its applicability to a wider class of problems.
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- Award ID(s):
- 2302470
- PAR ID:
- 10550475
- Publisher / Repository:
- Elsevier
- Date Published:
- Journal Name:
- Computer Physics Communications
- Volume:
- 304
- Issue:
- C
- ISSN:
- 0010-4655
- Page Range / eLocation ID:
- 109297
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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