System Identification under Constraints and Disturbance: A Bayesian Estimation Approach

2026-02-18

AI Summary

This work addresses the challenge of high-precision joint estimation of robotic states and physical parameters under constraints and disturbances by proposing a Bayesian system identification framework. The approach embeds physically consistent inverse dynamics, contact and closed-loop kinematic constraints, and a comprehensive joint friction model as hard equality constraints within the estimation process. Energy-based regressors are incorporated to enhance parameter observability, while prior constraints on inertial and actuation parameters are explicitly supported. A constrained Riccati recursion algorithm preserving banded matrix structure is devised to achieve linear time complexity for efficient computation. Evaluations in simulation and experiments on the Unitree B1 robot demonstrate that, compared to forward-dynamics and decoupled estimation methods, the proposed framework significantly accelerates convergence, reduces errors in inertial and friction parameter estimates, improves contact consistency, and substantially enhances trajectory tracking performance in complex terrains when integrated into model predictive control (MPC).

Technology Category

• Intelligent Robots: State Estimation
• Planning, Routing, and Scheduling: Activity and Plan Recognition
• Search and Optimization: Sampling/Simulation-based Search

Application Category

• User Modeling, Personalization and Recommendation: User modeling and simulation for interactive and conversational systems
• Systems and Infrastructure for Web, Mobile and WoT: Experiences and lessons learnt from Web-based algorithms and system deployments
• Responsible Web: Machine-in-the-loop, human agency and autonomy

Abstract

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.

Problem

• System Identification
• Bayesian Estimation
• Physical Constraints
• Disturbance Rejection
• Parameter Estimation

Innovation

• Bayesian system identification
• inverse dynamics constraints
• energy-based regressors
• equality-constrained Riccati recursion
• nonlinear friction modeling