Parallel simulation and control of large-scale robotic systems often rely on partitioned time stepping, yet finite-iteration coupling can inject spurious energy by violating power consistency--even when each subsystem is passive. This letter proposes a novel energy-safe, early-terminable iterative coupling for port-Hamiltonian subsystems by embedding a Douglas--Rachford (DR) splitting scheme in scattering (wave) coordinates. The lossless interconnection is enforced as an orthogonal constraint in the wave domain, while each subsystem contributes a discrete-time scattering port map induced by its one-step integrator. Under a discrete passivity condition on the subsystem time steps and a mild impedance-tuning condition, we prove an augmented-storage inequality certifying discrete passivity of the coupled macro-step for any finite inner-iteration budget, with the remaining mismatch captured by an explicit residual. As the inner budget increases, the partitioned update converges to the monolithic discrete-time update induced by the same integrators, yielding a principled, adaptive accuracy--compute trade-off, supporting energy-consistent real-time parallel simulation under varying computational budgets. Experiments on a coupled-oscillator benchmark validate the passivity certificates at numerical roundoff (on the order of 10e-14 in double precision) and show that the reported RMS state error decays monotonically with increasing inner-iteration budgets, consistent with the hard-coupling limit.

翻译：大规模机器人系统的并行仿真与控制常依赖于分区时间步进方法，然而有限次数的迭代耦合可能因违反功率一致性而引入虚假能量——即使每个子系统本身是被动的。本文提出一种新颖的能量安全、可提前终止的迭代耦合方法，用于端口哈密顿子系统，其通过在散射（波）坐标中嵌入Douglas-Rachford（DR）分裂格式实现。无损互连在波域中被强制为正交约束，而每个子系统则提供由其一步积分器导出的离散时间散射端口映射。在子系统时间步长满足离散无源性条件及温和的阻抗调谐条件下，我们证明了一个增强存储不等式，该不等式确保了耦合宏步长对于任意有限内迭代预算均具有离散无源性，剩余失配则由显式残差捕获。随着内迭代预算的增加，分区更新收敛于由相同积分器导出的整体离散时间更新，从而形成一种原则性的自适应精度-计算权衡机制，支持在变化计算预算下实现能量一致的实时并行仿真。在耦合振荡器基准测试上的实验验证了数值舍入误差级别（双精度下约为10e-14量级）的无源性证书，并表明所报告的RMS状态误差随内迭代预算增加而单调衰减，这与硬耦合极限的理论预期一致。