System Identification under Constraints and Disturbance: A Bayesian Estimation Approach

TL;DR

This paper presents a Bayesian system identification framework for robots that accurately estimates states and parameters by incorporating physical constraints, energy observations, and efficient algorithms, leading to improved model accuracy and control performance.

Contribution

It introduces a scalable Bayesian estimation method with physically consistent constraints and energy-based regressors for robotic system identification.

Findings

Faster convergence and lower estimation errors compared to baseline methods.

Improved contact consistency and friction modeling in simulations and hardware.

Enhanced tracking performance in model predictive control during locomotion.

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.