提出可提前终止的能源安全耦合方法，保障机器人系统并行仿真稳定性。
Early-Terminable Energy-Safe Iterative Coupling for Parallel Simulation of Partitioned Port-Hamiltonian Systems
- 基于波域坐标与Douglas-Rachford分裂，实现能量安全耦合。
- 任意有限迭代次数下均保持离散能量守恒，数值误差低至1e-14。
- 适合需要高稳定性的多体机器人系统并行仿真场景。
机器人系统的并行仿真需将动力学拆分为耦合子系统。跨分区的有限次迭代耦合可能引入虚假能量，即使各子系统本身是无源的。本文提出一种基于波（散射）坐标下Douglas--Rachford分裂的可提前终止、能源安全的端口-哈密顿子系统耦合接口。波域公式将无源性简化为范数不等式，耦合转化为正交性。在此框架下，利用单调算子理论与离散无源性的深层对应关系，构建具有Fejér单调性的内迭代，实现算法耗散。在子系统积分器无源且满足阻抗调谐条件下，该方法对任意有限内迭代预算均保证增广储能的离散无源性，并随预算增加收敛至整体离散化结果。在线性-Duffing耦合振子基准实验中，数值舍入误差下验证了有限迭代能量不等式（双精度1e-14），状态误差随迭代次数提升而降低。
原文摘要 · Abstract (English)
Parallel simulation of robotic systems requires partitioning the dynamics into coupled subsystems. Finite-iteration coupling across the partition boundary can inject spurious energy, even when each subsystem is passive. We propose an early-terminable, energy-safe coupling interface for port-Hamiltonian subsystems based on Douglas--Rachford splitting in wave (scattering) coordinates. The wave-domain formulation reduces passivity to norm inequalities and coupling to orthogonality. Within this setting, the deep correspondence between monotone operator theory and discrete passivity can be exploited to construct a Douglas--Rachford inner iteration whose Fejér monotonicity provides algorithmic dissipation. Under passivity of the subsystem integrators and an impedance-tuning condition, the proposed method guarantees discrete passivity of the augmented storage for any finite inner-iteration budget and converges to the monolithic discretization as the budget increases. Experiments on a linear--Duffing coupled-oscillator benchmark support the finite-iteration energy inequality at numerical roundoff (1e-14 in double precision), with state-error metrics decreasing over the tested inner-iteration budgets.
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