scholarly journals Space Debris Collision Detection using Reachability

10.29007/5313 ◽  
2018 ◽  
Author(s):  
Kerianne Hobbs ◽  
Peter Heidlauf ◽  
Alexander Collins ◽  
Stanley Bak
Keyword(s):  
Collision Detection ◽  
Space Debris ◽  
Reachability Analysis ◽  
Problem Structure ◽  
Initial State ◽  
Time Step ◽  
Variable Size ◽  
Abstraction Refinement ◽  
Counter Example ◽  
State Uncertainty

Benchmark Proposal: Space debris tracking and collision prediction is a growing world- wide problem as more and more objects are placed into orbit. While traditional methods simulate particles with Gaussian uncertainty to make collision predictions, we instead ana- lyze the problem from a reachability perspective. The problem appears to require methods capable of quickly analyzing high-dimensional nonlinear systems, but we take advantage multiple kinds of problem structure to show that reachability analysis may be viable for this problem. In particular we present an initial analysis approach that uses numerical simulation for reachability analysis, and interval arithmetic with AABB trees for fast col- lision detection. The analysis uses a variable size time step with a counter-example guided abstraction refinement (CEGAR) method to increase analysis speed without sacrificing accuracy. Our approach can analyze upwards of thousands of orbiting objects faster than real-time, where each object is subject to some initial state uncertainty.

scholarly journals Design and Optimal Control of a Multistable, Cooperative Microactuator

Actuators ◽  
2021 ◽  
Vol 10 (8) ◽  
pp. 183
Author(s):  
Michael Olbrich ◽  
Arwed Schütz ◽  
Tamara Bechtold ◽  
Christoph Ament
Keyword(s):  
Deflection Angle ◽  
Initial State ◽  
New Concepts ◽  
Vertical Displacements ◽  
State Uncertainty ◽  
Stable Equilibria ◽  
Freely Moving ◽  
Time And Energy ◽  
Multiple Stable Equilibria ◽  
Optimal Trajectory Planning

In order to satisfy the demand for the high functionality of future microdevices, research on new concepts for multistable microactuators with enlarged working ranges becomes increasingly important. A challenge for the design of such actuators lies in overcoming the mechanical connections of the moved object, which limit its deflection angle or traveling distance. Although numerous approaches have already been proposed to solve this issue, only a few have considered multiple asymptotically stable resting positions. In order to fill this gap, we present a microactuator that allows large vertical displacements of a freely moving permanent magnet on a millimeter-scale. Multiple stable equilibria are generated at predefined positions by superimposing permanent magnetic fields, thus removing the need for constant energy input. In order to achieve fast object movements with low solenoid currents, we apply a combination of piezoelectric and electromagnetic actuation, which work as cooperative manipulators. Optimal trajectory planning and flatness-based control ensure time- and energy-efficient motion while being able to compensate for disturbances. We demonstrate the advantage of the proposed actuator in terms of its expandability and show the effectiveness of the controller with regard to the initial state uncertainty.

scholarly journals A Note on the Majority Dynamics in Inhomogeneous Random Graphs

2021 ◽  
Vol 76 (3) ◽  
Author(s):  
Yilun Shang
Keyword(s):  
Random Graph ◽  
Initial State ◽  
Time Step ◽  
Dynamic Monopoly ◽  
Inhomogeneous Random Graphs ◽  
Assignment Probability ◽  
Edge Probability ◽  
Consensus Reaching Process ◽  
Consensus Reaching ◽  
Inhomogeneous Random Graph

AbstractIn this note, we study discrete time majority dynamics over an inhomogeneous random graph G obtained by including each edge e in the complete graph $$K_n$$ K n independently with probability $$p_n(e)$$ p n ( e ) . Each vertex is independently assigned an initial state $$+1$$ + 1 (with probability $$p_+$$ p + ) or $$-1$$ - 1 (with probability $$1-p_+$$ 1 - p + ), updated at each time step following the majority of its neighbors’ states. Under some regularity and density conditions of the edge probability sequence, if $$p_+$$ p + is smaller than a threshold, then G will display a unanimous state $$-1$$ - 1 asymptotically almost surely, meaning that the probability of reaching consensus tends to one as $$n\rightarrow \infty $$ n → ∞ . The consensus reaching process has a clear difference in terms of the initial state assignment probability: In a dense random graph $$p_+$$ p + can be near a half, while in a sparse random graph $$p_+$$ p + has to be vanishing. The size of a dynamic monopoly in G is also discussed.

Multi-Scale Virtual Reality of Sintering

2007 ◽  
Vol 534-536 ◽  
pp. 573-576
Author(s):  
Eugene Olevsky
Keyword(s):  
Global Scale ◽  
Initial State ◽  
Model Framework ◽  
Time Step ◽  
Computational Framework ◽  
Multi Scale ◽  
Scale Modeling ◽  
History Of ◽  
On Line ◽  
Damage Criteria

The directions of further developments in the modeling of sintering are pointed out, including multi-scale modeling of sintering, on-line sintering damage criteria, particle agglomeration, sintering with phase transformations. A true multi-scale approach is applied for the development of a new meso-macro methodology for modeling of sintering. The developed macroscopic level computational framework envelopes the mesoscopic simulators. No closed forms of constitutive relationships are assumed for the parameters of the material. When a time-step of the calculations is finished for one macroscopic element, the mesostructures of the next element are restored from the initial state according to the history of loading. The model framework is able to predict the final dimensions of the sintered specimen on a global scale and identify the granular structure in any localized area for prediction of the material properties.

scholarly journals Efficient n-to-n Collision Detection for Space Debris using 4D AABB Trees

10.29007/5pl1 ◽  
2019 ◽  
Author(s):  
Stanley Bak ◽  
Kerianne Hobbs
Keyword(s):  
Collision Detection ◽  
Space Debris ◽  
Dynamics Simulation ◽  
Video Gaming ◽  
Time Dimension ◽  
Detection Algorithms ◽  
Space Objects ◽  
Tree Data ◽  
Tree Data Structure ◽  
Three Space

Collision detection algorithms are used in aerospace, swarm robotics, automotive, video gaming, dynamics simulation and other domains. As many applications of collision detection run online, timing requirements are imposed on the algorithm runtime: algorithms must, at a minimum, keep up with the passage of time. Even offline reachability computation can be slowed down by the process of safety checking when n is large and the specification is n-to-n collision avoidance. In practice, this places a limit on the number of objects, n, that can be concurrently tracked or verified. In this paper, we present an improved method for efficient object tracking and collision detection, based on a modified version of the axis-aligned bounding-box (AABB) tree data structure. We consider 4D AABB Trees, where a time dimension is added to the usual three space dimensions, in order to enable per-object time steps when checking for collisions in space-time. We evaluate the approach on a space debris collision benchmark, demonstrating efficient checking beyond the full catalog of n = 16848 space objects made public by the U.S. Strategic Command on www.space-track.org.

scholarly journals A Driver’s License Test for Driverless Vehicles

2017 ◽  
Vol 139 (12) ◽  
pp. S13-S16 ◽  
Author(s):  
Houssam Abbas ◽  
Matthew E. O’Kelly ◽  
Alena Rodionova ◽  
Rahul Mangharam
Keyword(s):  
Formal Methods ◽  
Theorem Proving ◽  
Autonomous Vehicle ◽  
Reachability Analysis ◽  
Initial State ◽  
Left Turn ◽  
Interactive Technique ◽  
Driver's License

This article elaborates the approaches that can be used to verify an autonomous vehicle (AV) before giving it a driver’s license. Formal methods applied to the problem of AV verification include theorem proving, reachability analysis, synthesis, and maneuver design. Theorem proving is an interactive technique in which the computer is largely responsible for demonstrating that the model satisfies the specification, with occasional help from the user. The latter provides lemmas and axioms that the tool leverages to advance the proof towards its conclusion. Reachability analysis is used to verify the operation of the AV during navigation. This provides an extension of onboard diagnostics to whole-AV operation, where the diagnosis does not concern one component’s requirements, but the safety of the entire AV. Another approach is to design correct-by-construction controllers from preverified maneuvers. The basic idea is that one builds a library of maneuvers, such as Left-Turn and Right-Turn, and verifies that the car can perform these maneuvers from any initial state.

scholarly journals Temporal variability of partially-contaminated sediments in a strongly regulated reservoir of the upper Rhine River

2018 ◽  
Vol 40 ◽  
pp. 04025
Author(s):  
Germain Antoine ◽  
Thomas Pretet ◽  
Matthieu Secher ◽  
Anne Clutier
Keyword(s):  
Suspended Sediment ◽  
Contaminated Sediments ◽  
Measured Data ◽  
Regulated River ◽  
Suspended Sediment Transport ◽  
Rhine River ◽  
Initial State ◽  
Time Step ◽  
Field Campaigns ◽  
Upper Rhine

The upper Rhine River is a highly harnessed and regulated river. EDF (a French electricity company) is in charge of eight dams on the upper Rhine River for producing hydro-electricity. In order to increase the safety and the competitiveness of the installations, but also to reduce their environmental impact, the sediment dynamics in these reservoirs has become a key factor to control and predict. In this study, we focused on the Marckolsheim reservoir, which is located 50 kilometers upstream the city of Strasbourg. Since its construction in 1961, this reservoir has been filled continuously with cohesive sediments, partially contaminated. Two field campaigns were performed in 2015 and 2016 under two different discharge conditions, with the objectives of quantifying the complex velocity fields on this site. The numerical codes TELEMAC-2D and SISYPHE were used to simulate in 2D the hydrodynamic and the suspended sediment transport of the reservoir. A ten kilometers long model was built and calibrated with the measured data of the 2015 and 2016 field campaigns, but also with measurements of sediment parameters that have been done separately. The originality of this model consists in an explicit 3D representation of the dam gates. An algorithm was implemented in TELEMAC in order to adapt the gates position at each time step, in conformity with the real regulation rules followed by the dam operator. By using upstream measured data of discharge and suspended sediment concentration, a four months period was simulated. The comparison of the simulated results with bathymetric surveys shows good agreements if specific properties of sediments related to settling processes are taken into account. Finally, the dynamics of the contaminated sediments was simulated. A 3D spatial distribution of the contaminated sediments in the reservoir was defined at the initial state by using in situ measurements. The fully coupled hydraulic-sediment-pollutant simulation performed over a single flood event gives first interesting highlights on the resuspension conditions of the contaminated sediments.

Space debris: ex facto sequitur lex

1988 ◽  
Vol 1 (1) ◽  
pp. 89-96
Author(s):  
Tanja L. Zwaan
Keyword(s):  
Space Debris ◽  
Outer Space ◽  
Space Missions ◽  
Variable Size ◽  
The Earth

Unfortunately, today's exploration of outer space is exposed to a rapidly expanding collection of what has come to be called space debris. Innumerous objects of variable size ranging from tiny paint chips to entire - defunct - satellites and produced by various causes, such as collisions, explosions, or simply exhaustion of fuel, are rotating around the Earth and create dangers to our space missions.

scholarly journals Implicit Coordination Using FOND Planning

2020 ◽  
Vol 34 (05) ◽  
pp. 7151-7159
Author(s):  
Thorsten Engesser ◽  
Tim Miller
Keyword(s):  
Computational Complexity ◽  
The Other ◽  
Path Finding ◽  
Initial State ◽  
Arbitrary Initial State ◽  
State Uncertainty ◽  
Multi Agent ◽  
Decidable Fragment ◽  
Implicit Coordination

Epistemic planning can be used to achieve implicit coordination in cooperative multi-agent settings where knowledge and capabilities are distributed between the agents. In these scenarios, agents plan and act on their own without having to agree on a common plan or protocol beforehand. However, epistemic planning is undecidable in general. In this paper, we show how implicit coordination can be achieved in a simpler, propositional setting by using nondeterminism as a means to allow the agents to take the other agents' perspectives. We identify a decidable fragment of epistemic planning that allows for arbitrary initial state uncertainty and non-determinism, but where actions can never increase the uncertainty of the agents. We show that in this fragment, planning for implicit coordination can be reduced to a version of fully observable nondeterministic (FOND) planning and that it thus has the same computational complexity as FOND planning. We provide a small case study, modeling the problem of multi-agent path finding with destination uncertainty in FOND, to show that our approach can be successfully applied in practice.

scholarly journals Near real-time adjusted reanalysis forcing data for hydrology

2017 ◽  
Author(s):  
Peter Berg ◽  
Chantal Donnelly ◽  
David Gustafsson
Keyword(s):  
Real Time ◽  
Arctic Region ◽  
Analysis Data ◽  
Global Scale ◽  
Current Data ◽  
The Arctic ◽  
Data Sets ◽  
Initial State ◽  
Time Step ◽  
Data Set

Abstract. Updating climatological forcing data to near current data are compelling for impact modelling, e.g. to update model simulations or to simulate recent extreme events. Hydrological simulations are generally sensitive to bias in the meteorological forcing data, especially relative to the data used for the calibration of the model. The lack of daily resolution data at a global scale has previously been solved by adjusting re-analysis data global gridded observations. However, existing data sets of this type have been produced for a fixed past time period, determined by the main global observational data sets. Long delays between updates of these data sets leaves a data gap between present and the end of the data set. Further, hydrological forecasts require initialisations of the current state of the snow, soil, lake (and sometimes river) storage. This is normally conceived by forcing the model with observed meteorological conditions for an extended spin-up period, typically at a daily time step, to calculate the initial state. Here, we present a method named GFD (Global Forcing Data) to combine different data sets in order to produce near real-time updated hydrological forcing data that are compatible with the products covering the climatological period. GFD resembles the already established WFDEI method (Weedon et al., 2014) closely, but uses updated climatological observations, and for the near real-time it uses interim products that apply similar methods. This allows GFD to produce updated forcing data including the previous calendar month around the 10th of each month. We present the GFD method and different produced data sets, which are evaluated against the WFDEI data set, as well as with hydrological simulations with the HYPE model over Europe and the Arctic region. We show that GFD performs similarly to WFDEI and that the updated period significantly reduces the bias of the reanalysis data, although less well for the last two months of the updating cycle. For real-time updates until the current day, extending GFD with operational meteorological forecasts, a large drift is present in the hydrological simulations due to the bias of the meteorological forecasting model.

Dynamical Simulation of Planar Systems With Changing Contacts Using Configuration Spaces

1998 ◽  
Vol 120 (2) ◽  
pp. 181-187 ◽  
Author(s):  
E. Sacks ◽  
L. Joskowicz
Keyword(s):  
Configuration Space ◽  
Collision Detection ◽  
Contact Analysis ◽  
Configuration Spaces ◽  
Time Step ◽  
Analysis Algorithm ◽  
Time Performance ◽  
Dynamical Simulation ◽  
Planar Systems ◽  
Space Approach

This paper presents a contact analysis algorithm for pairs of rigid, curved, planar parts based on configuration space computation. The algorithm is part of a dynamical simulator for planar systems with changing contact topologies. The configuration space of a pair of parts is a data structure that encodes the contact configurations for all pairs of part features. The configuration spaces of the interacting pairs in the mechanical system are constructed before the simulation. At each time step, the simulator queries the configuration spaces for contact changes instead of performing collision detection. The simulator demonstrates the efficacy of the configuration space approach to contact analysis. It achieves real-time performance on systems with complex contact geometry, curved parts, and changing contacts.

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