Multi-Contact Inertial Parameters Estimation and Localization in Legged Robots

TL;DR

This paper tackles the problem of estimating inertial parameters and localizing legged robots under multi-contact conditions by introducing a parametric, structure-exploiting optimization framework. The core methods combine a multi-contact DDP (DDP with parametrized dynamics) and new inertial-parameter manifolds—the exponential eigenvalue and log-Cholesky styles—to ensure physical consistency, along with a nullspace approach to handle singularities. It also provides analytical derivatives of the parametrized dynamics and employs multiple shooting rollouts to enhance convergence and robustness, demonstrated on complex maneuvers and experimental trials with the Go1 robot, where payload estimation and localization improve markedly over least-squares baselines and conventional methods. Overall, the work delivers a practical, real-time capable toolkit for simultaneous inertial identification and hybrid-dynamics localization in legged robotics, with open-source implementation planned.

Abstract

Optimal estimation is a promising tool for estimation of payloads' inertial parameters and localization of robots in the presence of multiple contacts. To harness its advantages in robotics, it is crucial to solve these large and challenging optimization problems efficiently. To tackle this, we (i) develop a multiple shooting solver that exploits both temporal and parametric structures through a parametrized Riccati recursion. Additionally, we (ii) propose an inertial manifold that ensures the full physical consistency of inertial parameters and enhances convergence. To handle its manifold singularities, we (iii) introduce a nullspace approach in our optimal estimation solver. Finally, we (iv) develop the analytical derivatives of contact dynamics for both inertial parametrizations. Our framework can successfully solve estimation problems for complex maneuvers such as brachiation in humanoids, achieving higher accuracy than conventional least squares approaches. We demonstrate its numerical capabilities across various robotics tasks and its benefits in experimental trials with the Go1 robot.

Figures (5)

• Figure 1: Talos executing intricate monkey bar maneuvers with an unidentified payload. In the initial stages, our estimator meticulously pinpoints Talos' localization and estimates its payload's properties: mass, barycenter, and rotational inertia. The boxes' sizes, positions, shape, and colors serve as visual indicators, representing estimations of the payload's mass, barycenter, principal components of inertia, and algorithm convergence. To watch the video, click the picture or see \video.
• Figure 2: Snapshots illustrating simulated online multi-contact inertial estimation and localization. (top) ANYmal with a Kinova arm carries an unknown payload while grasping an unknown object. (bottom) Talos performs a backflip while simultaneously estimating its backpack. Unknown payloads are represented in magenta, and upon convergence of the estimator, the estimated payload is depicted in green. The horizon of the estimator is set to the length of the simulation. To watch the video, click the picture or see \video.
• Figure 3: Top: Local convergence for both parametrizations, showing better convergence the exponential eigenvalue (exp-eigval) parametrization in all cases. Bottom: Evolution of the estimation error, computed as the $\ell_1$-norm of difference between the optimized trajectory and the nominal one. Both parametrizations converge to the same local minima.
• Figure 4: Top: Go1 performing four walking gaits while carrying an unknown payload. In the top snapshots, Go1 struggled to maintain its posture due to model mismatch in the . In the bottom snapshots, after correctly estimating the robot's payload, Go1 confidently maintained its nominal posture. Bottom: Foot-swing tracking, the foot position is obtained from the VICON system, ignoring any localization effects. Our encountered difficulties in tracking the reference swing-foot trajectory (dashed line) when the payload was unknown (magenta line). Specifically, the Go1 robot failed to reach the desired step height, an error accumulated over time. In contrast, our improved its foot-swing tracking performance when our estimator identified the payload (blue line).
• Figure 5: Contact estimation of contact and Go1's localization errors when performing a jump. Our optimal estimator (blue lines) exhibits a smaller estimation error compared to Pronto.