Coordinate-Independent Robot Model Identification

Abstract

Robot model identification is commonly performed by least-squares regression on inverse dynamics, but existing formulations measure residuals directly in coordinate force space and therefore depend on the chosen coordinate chart, units, and scaling. This paper proposes a coordinate-independent identification method that weights inverse-dynamics residuals by the dual metric induced by the system Riemannian metric. Using the force--velocity vector--covector duality, the dual metric provides a physically meaningful normalization of generalized forces, pulling coordinate residuals back into the ambient mechanical space and eliminating coordinate-induced bias. The resulting objective remains convex through an affine-metric and Schur-complement reformulation, and is compatible with physical-consistency constraints and geometric regularization. Experiments on an inertia-dominated Crazyflie--pendulum system and a drag-dominated LandSalp robot show improved identification accuracy, especially on shape coordinates, in both low-data and high-data settings.

Figures (7)

• Figure 1: Two robotic systems studied in this paper for model identification: an inertia-dominated system (left) and a drag-dominated system (right). In both systems, the generalized coordinates have different units and scales, and the magnitude of the inner product of a unit coordinate velocity under the corresponding Riemannian metric depends on the configuration, as illustrated in the bottom-left and bottom-right panels, which plot the inner-product value along the $\dot{\theta}$ direction for the two systems, respectively. Together, these factors illustrate the coordinate dependence in the system identification problem addressed in this paper.
• Figure 2: Metric and dual-metric normalization illustrated by a pan--tilt mechanism. (a) A pan--tilt mechanism with a massless link and a point mass at the end effector; its generalized coordinates parameterize the configuration manifold through a nonlinear chart. (b) The Riemannian metric induced in the ambient Euclidean space by the point-mass motion constrained by the mechanism. The red ellipses denote the unit-$M$-norm set; their intercepts indicate the metric-normalized tangent directions at each configuration. (c) An $M$-orthonormal tangent basis and its dual co-basis, together with the vector--covector duality through power. The covector can be interpreted as a slope measuring how much power is produced by motion in a given direction. (d) The pullback of the metric and dual metric into coordinate space, visualized by the red and blue ellipses corresponding to unit velocity and force norms, respectively.
• Figure 3: Experimental platforms: the inertia-dominated Crazyflie with a pendulum attached through a universal joint (left), and the drag-dominated three-link LandSalp robot (right), together with snapshots of representative execution trajectories.
• Figure 4: Normalized cross-correlation between predicted and measured forward dynamics for the Crazyflie--pendulum system; larger values are better, and error bars indicate the standard deviation over the test set. The proposed method (DM) consistently outperforms the alternatives, especially on the shape coordinates ($\ddot{\alpha}_1$ and $\ddot{\alpha}_2$). Top: low-data case. Bottom: high-data case. Left: comparison with WLS and energy-based least squares. Right: comparison with regularized WLS using Bregman divergence and constant pullback.
• Figure 5: Predicted and measured $\ddot{\alpha}_2$ for the Crazyflie--pendulum system in the high-data case, comparing the proposed method, WLS, energy-based least squares, and the two regularized WLS variants.