# Identification of Fully Physical Consistent Inertial Parameters using Optimization on Manifolds

arXiv: https://arxiv.org/abs/1610.08703 · HTML: https://mlsanity.com/paper/1610.08703/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 27 Oct 2016.

## Built on by (most cited first, 8 of 8)

- [Differentiable Physics Models for Real-world Offline Model-based Reinforcement Learning](https://mlsanity.com/paper/2011.01734/) (2020)
- [Combining Physics and Deep Learning to learn Continuous-Time Dynamics Models](https://mlsanity.com/paper/2110.01894/) (2021)
- [Morphological Symmetries in Robotics](https://mlsanity.com/paper/2402.15552/) (2024)
- [End-to-End Learning of Hybrid Inverse Dynamics Models for Precise and Compliant Impedance Control](https://mlsanity.com/paper/2205.13804/) (2022)
- [The Sum of Its Parts: Visual Part Segmentation for Inertial Parameter Identification of Manipulated Objects](https://mlsanity.com/paper/2302.06685/) (2023)
- [A Structured Prediction Approach for Robot Imitation Learning](https://mlsanity.com/paper/2309.14829/) (2023)
- [Newtonian and Lagrangian Neural Networks: A Comparison Towards Efficient Inverse Dynamics Identification](https://mlsanity.com/paper/2506.17994/) (2025)
- [Diff-MSM: Differentiable MusculoSkeletal Model for Simultaneous Identification of Human Muscle and Bone Parameters](https://mlsanity.com/paper/2508.13303/) (2025)

## Abstract (arXiv)

This paper presents a new condition, the fully physical consistency for a set of inertial parameters to determine if they can be generated by a physical rigid body. The proposed condition ensure both the positive definiteness and the triangular inequality of 3D inertia matrices as opposed to existing techniques in which the triangular inequality constraint is ignored. This paper presents also a new parametrization that naturally ensures that the inertial parameters are fully physical consistency. The proposed parametrization is exploited to reformulate the inertial identification problem as a manifold optimization problem, that ensures that the identified parameters can always be generated by a physical body. The proposed optimization problem has been validated with a set of experiments on the iCub humanoid robot.