[2M4-OS-11b] OS-11

[2M4-OS-11b-01] Modeling Methods for Multi-body Collisions in a Hybrid Constraint Solver HyLaGI

〇Hidenori Shida¹, Hotaka Tominaga¹, Kazunori Ueda¹ (1. Waseda University)

Keywords:hybrid systems, constraint satisfaction problem, overconstraint, multi-body collision, modeling

Hybrid systems are dynamical systems exhibiting both discrete and continuous changes. HydLa, a hybrid system modeling language, features constraints and constraint hierarchies. HyLaGI, the implementation of HydLa, symbolically solves constraint satisfaction problems. We address multi-body simultaneous collision in one dimension to investigate the unclarified aspects of constraint-based modeling and the solvability of HyLaGI. Strict multi-body simultaneous collision on rigid bodies is an over-constrained problem. We could introduce an infinitesimal parameter into the rigid model to circumvent the problem, but this approach does not properly handle the simultaneity. In order to solve this issue, we try using non-rigid bodies. In general, when an object compresses by δ, it exerts a force of the form −Kδⁿ. We investigate the sensitivity of the initial conditions of K and n using interval arithmetic (kv library) as an alternative tool which can guarantee precision.