An application-based characterization of dynamical distance geometry problems

Antonio Mucherino 1 Jérémy Omer 2, 3 Ludovic Hoyet 1 Paolo Robuffo Giordano 4 Franck Multon 1
1 MIMETIC - Analysis-Synthesis Approach for Virtual Human Simulation
UR2 - Université de Rennes 2, Inria Rennes – Bretagne Atlantique , IRISA-D6 - MEDIA ET INTERACTIONS
4 RAINBOW - Sensor-based and interactive robotics
Inria Rennes – Bretagne Atlantique , IRISA-D5 - SIGNAUX ET IMAGES NUMÉRIQUES, ROBOTIQUE
Abstract : The dynamical Distance Geometry Problem (dynDGP) is the problem of finding a realization in a Euclidean space of a weighted undirected graph G representing an animation by relative distances, so that the distances between realized vertices are as close as possible to the edge weights. In the dynDGP, the vertex set of the graph G is the set product of V , representing certain objects, and T , representing time as a sequence of discrete steps. We suppose moreover that distance information is given together with the priority of every distance value. The dynDGP is a special class of the DGP where the dynamics of the problem comes to play an important role. In this work, we propose an application-based characterization of dynDGP instances, where the main criteria are the presence or absence of a skeletal structure, and the rigidity of such a skeletal structure. Examples of considered applications include: multi-robot coordination, crowd simulations, and human motion retargeting.
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Antonio Mucherino, Jérémy Omer, Ludovic Hoyet, Paolo Robuffo Giordano, Franck Multon. An application-based characterization of dynamical distance geometry problems. Optimization Letters, Springer Verlag, 2018, pp.1-15. ⟨10.1007/s11590-018-1302-6⟩. ⟨hal-01846265⟩

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