Stability of rigid body motion through an extended intermediate axis theorem: application to rockfall simulation

Leine, Remco I.; Capobianco, Giuseppe; Bartelt, Perry; Christen, Marc; Caviezel, Andrin

doi:10.1007/s11044-021-09792-y

Cited by 19 publications

(10 citation statements)

References 21 publications

(30 reference statements)

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“…In [3] paper we show that the present scheme, which is fully explicit during flight phases of the rock, does not respect the intermediate axis theorem. Furthermore, an implicit scheme is presented which correctly describes the stability properties of a freely rotating body.…”

Section: Introductionmentioning

confidence: 85%

An extended version of the Intermediate Axis Theorem for a freely rotating rigid body

Leine

Capobianco

2021

Proc Appl Math & Mech

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Current numerical schemes for 3D rockfall simulation are not able to correctly represent the stability properties of a freely rotating body. Here, we give a proof using Lyapunov functions of an extended intermediate axis theorem, which not only involves the angular momentum equations but also the orientation of the body. Inspired by the stability proof, we present a novel scheme which respects the stability properties of a freely rotating body and which can be incorporated in numerical schemes for the simulation of rigid bodies with frictional unilateral constraints.

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Section: Introductionmentioning

confidence: 85%

An extended version of the Intermediate Axis Theorem for a freely rotating rigid body

Leine

Capobianco

2021

Proc Appl Math & Mech

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“…These capture the evolution of target body frame relative to Hill frame calculated through a frame transformation applied to (5). The difference between dynamic modes is a direct result of the intermediate axis theorem [27,28] applied to various configurations of initial velocity in (4). Within Hill frame, ECI static represents a slow counterclockwise rotation; Hill static represents no rotation; Single-Axis represents a clockwise rotation and the tumbling modes represent multi-axis rotations about stable and unstable body-frame axes respectively.…”

Section: Clohessy-wiltshire Hill Dynamicsmentioning

confidence: 99%

Exposure-Based Multi-Agent Inspection of a Tumbling Target Using Deep Reinforcement Learning

Aurand¹,

Cutlip²,

Lei³

et al. 2023

Preprint

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As space becomes more congested, on orbit inspection is an increasingly relevant activity whether to observe a defunct satellite for planning repairs or to de-orbit it. However, the task of on orbit inspection itself is challenging, typically requiring the careful coordination of multiple observer satellites. This is complicated by a highly nonlinear environment where the target may be unknown or moving unpredictably without time for continuous command and control from the ground. There is a need for autonomous, robust, decentralized solutions to the inspection task. To achieve this, we consider a hierarchical, learned approach for the decentralized planning of multi-agent inspection of a tumbling target. Our solution consists of two components: a viewpoint or high-level planner trained using deep reinforcement learning and a navigation planner handling point-to-point navigation between pre-specified viewpoints. We present a novel problem formulation and methodology that is suitable not only to reinforcement learning-derived robust policies, but extendable to unknown target geometries and higher fidelity information theoretic objectives received directly from sensor inputs. Operating under limited information, our trained multi-agent high-level policies successfully contextualize information within the global hierarchical environment and are correspondingly able to inspect over 90% of non-convex tumbling targets, even in the absence of additional agent attitude control.

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“…Rockfall simulations were performed with RAMMS::ROCKFALL, a three-dimensional rockfall model based on a rigid-body approach (Leine et al, 2014(Leine et al, , 2021. Compactible soils were integrated according to Lu et al (2019) and Caviezel et al (2019a).…”

Section: Ramms::rockfall Simulationsmentioning

confidence: 99%

“…One mass class of 400 kg or 0.15 m 3 and two shape classes, platy and compact according to the Sneed and Folk (1958) classification, made up of perfectly symmetrical EOTA rock shapes (European Organisation for Technical Assessment, according to ETAG 027, 2013, as used in Caviezel et al, 2019bCaviezel et al, , 2021 were used for the simulations. Each rock was released with 10 different orientations, which led to a total of 7560 trajectories in W1 and 5560 trajectories in W2 for each azimuth scenario.…”

Section: Ramms::rockfall Simulationsmentioning

confidence: 99%

Modeling deadwood for rockfall mitigation assessments in windthrow areas

et al. 2022

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Abstract. Studying how deadwood mitigates the rockfall hazard in mountain forests is key to understanding the influence of climate-induced disturbances on the protective capacity of mountain forests. Both experimental quantification and numerical process modeling are needed to address this question. Modeling provides detailed insights into the rock–deadwood interaction and can therefore be used to develop effective forest management strategies. Here, we introduce an automatic deadwood generator (ADG) for assessing the impact of fresh woody storm debris on the protective capacity of a forest stand against rockfall. The creation of various deadwood scenarios allows us to directly quantify the mitigation potential of deadwood. To demonstrate the functionality of the proposed ADG method, we compare deadwood log patterns, deadwood effective height, and mesoscale surface ruggedness observed in field surveys in a natural windthrow area with their simulated counterparts. Specifically, we consider two sites near Lake Klöntal, Switzerland, where a major windthrow event occurred in 2019. We perform rockfall simulations for the time (a) before, (b) directly after, and (c) 10 years after the windthrow event. We further compare the results with (d) a simulation with complete clearing of the thrown wood: in other words, a scenario with no standing forest remaining. We showcase an integration of deadwood into rockfall simulations with realistic deadwood configurations alongside a diameter at breast height (DBH)- and rot-fungi-dependent maximum deadwood breaking energy. Our results confirm the mitigation effect of deadwood, which significantly reduces the jump heights and velocities of 400 kg rocks. Our modeling results suggest that, even a decade after the windthrow event, deadwood has a stronger protective effect against rockfall than that provided by standing trees. We conclude that an ADG can contribute to the decision-making involved in forest and deadwood management after disturbances.

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Stability of rigid body motion through an extended intermediate axis theorem: application to rockfall simulation

Cited by 19 publications

References 21 publications

An extended version of the Intermediate Axis Theorem for a freely rotating rigid body

An extended version of the Intermediate Axis Theorem for a freely rotating rigid body

Exposure-Based Multi-Agent Inspection of a Tumbling Target Using Deep Reinforcement Learning

Modeling deadwood for rockfall mitigation assessments in windthrow areas

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