Physically-Consistent Parameter Identification of Robots in Contact

TL;DR

This work addresses the problem of identifying inertial parameters for floating-base legged robots under intermittent contact without end-effector force sensing. It projects the whole-body dynamics into the null space of contact constraints, producing a linear-in-parameters form that can be solved as a convex Linear Matrix Inequality (LMI) while enforcing physical feasibility through CoM ellipsoidal constraints and a pseudo-inertia-based second-moment formulation. Compared to black-box neural models and unconstrained baselines, the proposed method achieves better sample efficiency and generalization to unseen motions, demonstrated in simulation on Solo12 and real-world experiments on the Spot quadruped. The approach enables accurate torque prediction and reliable parameter identification using only joint-torque measurements, with practical impact for model-based control and planning in situations where direct contact-force sensing is unavailable.

Abstract

Accurate inertial parameter identification is crucial for the simulation and control of robots encountering intermittent contact with the environment. Classically, robots' inertial parameters are obtained from CAD models that are not precise (and sometimes not available, e.g., Spot from Boston Dynamics), hence requiring identification. To do that, existing methods require access to contact force measurement, a modality not present in modern quadruped and humanoid robots. This paper presents an alternative technique that utilizes joint current/torque measurements -- a standard sensing modality in modern robots -- to identify inertial parameters without requiring direct contact force measurements. By projecting the whole-body dynamics into the null space of contact constraints, we eliminate the dependency on contact forces and reformulate the identification problem as a linear matrix inequality that can handle physical and geometrical constraints. We compare our proposed method against a common black-box identification method using a deep neural network and show that incorporating physical consistency significantly improves the sample efficiency and generalizability of the model. Finally, we validate our method on the Spot quadruped robot across various locomotion tasks, showcasing its accuracy and generalizability in real-world scenarios over different gaits.

Figures (5)

• Figure 1: Whole-body inertial parameter identification —mass, center of mass and moment of inertia matrix— of floating-base robots using constraint-consistent dynamics with joint torque measurements and constrained convex optimization.
• Figure 2: Average RMSE comparison of torque predictions for the LMI (ours), SVD, and MLP models trained on different dataset sizes for Solo12 trot motion. Our LMI model consistently outperforms the MLP on smaller datasets, making it well-suited for real-world applications with limited number of samples.
• Figure 3: Comparison of predicted and measured torques for the front left leg of Solo12 across three joint actuations. Our LMI model consistently delivers accurate torque predictions, even for the challenging jump motion. In contrast, while the Multi Layer Perceptron (MLP) model performs adequately on the validation dataset, it struggles to capture the complex dynamics of the jump, underscoring its limitations in generalizing to out-of-distribution tasks. For clarity, only $t=1$ s of the motion is displayed.
• Figure 4: Data collected from Spot across various locomotion tasks. Top: base motion with all feet in contact. Bottom: forward-backward walking.
• Figure 5: Comparison of predicted and measured torques for the front left leg of Spot across three joint actuations. Our LMI model demonstrates accurate torque predictions for both validation and out-of-distribution tasks, while the MLP model struggles to generalize to new tasks. All torques are projected into the null space of the contact points.