cs.ROMar 15, 2026

Coordinate-Independent Robot Model Identification

Authors: Yanhao Yang, Ross L. Hatton

Organizations: Collaborative Robotics and Intelligent Systems (CoRIS) Institute at Oregon State University, Corvallis, OR USA

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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, on both downsampled and full datasets.

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Fig. 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 θ˙\dot{\theta} direction for the two systems, respectively. Together, these factors illustrate the coordinate dependence in the system identification problem addressed in this paper.
Fig. 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 by the point-mass motion constrained by the mechanism and measured in the ambient Euclidean space. Red ellipses denote unit- MM -norm velocity sets; their intercepts indicate metric-normalized tangent directions at each configuration. (c) Generalized velocities are tangent vectors, and generalized forces are covectors; their pairing produces power. A force covector specifies the rate of power production associated with motion in a given velocity direction. Through this vector–covector duality, the velocity metric canonically induces the corresponding dual metric on generalized-force space. (d) Coordinate representations of the velocity metric and its induced dual metric, visualized by red and blue ellipses representing unit velocity and unit force norms, respectively.
Fig. 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.

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