We introduce a Bayesian system identification (SysID) framework for jointly estimating robot's state trajectories and physical parameters with high accuracy. It embeds physically consistent inverse dynamics, contact and loop-closure constraints, and fully featured joint friction models as hard, stage-wise equality constraints. It relies on energy-based regressors to enhance parameter observability, supports both equality and inequality priors on inertial and actuation parameters, enforces dynamically consistent disturbance projections, and augments proprioceptive measurements with energy observations to disambiguate nonlinear friction effects. To ensure scalability, we derive a parameterized equality-constrained Riccati recursion that preserves the banded structure of the problem, achieving linear complexity in the time horizon, and develop computationally efficient derivatives. Simulation studies on representative robotic systems, together with hardware experiments on a Unitree B1 equipped with a Z1 arm, demonstrate faster convergence, lower inertial and friction estimation errors, and improved contact consistency compared to forward-dynamics and decoupled identification baselines. When deployed within model predictive control frameworks, the resulting models yield measurable improvements in tracking performance during locomotion over challenging environments.

翻译：本文提出一种贝叶斯系统辨识框架，用于高精度联合估计机器人的状态轨迹与物理参数。该框架将物理一致的反向动力学、接触与闭环约束以及完整关节摩擦模型嵌入为严格的阶段式等式约束。其基于能量回归器增强参数可观测性，支持对惯性参数与驱动参数的等式与不等式先验，强制执行动态一致的扰动投影，并通过能量观测增强本体感知测量以消除非线性摩擦效应的歧义。为保障可扩展性，我们推导了参数化等式约束Riccati递归算法，该算法保持问题的带状结构，实现时间维度上的线性复杂度，并开发了计算高效的导数。在典型机器人系统上的仿真研究，以及在配备Z1机械臂的Unitree B1平台上进行的硬件实验表明，相较于正向动力学与解耦辨识基线方法，本框架具有更快的收敛速度、更低的惯性及摩擦估计误差以及更优的接触一致性。将所得模型部署于模型预测控制框架时，在复杂环境下的运动任务中能显著提升轨迹跟踪性能。