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˙ 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- M -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.
This paper presents a reproducible and physically feasible dynamic parameter identification framework for CRANE-X7, a low-cost robot arm driven by modular smart actuators. To improve practical identifiability, products of inertia are removed according to approximate link symmetry, reducing the rigid-body model from 65 to 39 base parameters. Identification motions are hand-designed from structured single-joint and adjacent-joint primitives under practical joint-range limits. The proposed pipeline combines preprocessing, inverse-dynamics-regressor-based ordinary least squares (OLS), conditional semidefinite-programming (SDP) projection for feasibility recovery, and closed-loop input error (CLIE) refinement. Candidate solutions from 40 structured trajectories are analyzed in a common principal component analysis (PCA) space to select a statistically central representative model. Because statistical centrality alone does not ensure physical acceptability, the selected model is finally screened by an all-pose positive-definiteness audit of the inertia matrix and, when necessary, corrected by a localized post-CLIE SDP rescue step. Experiments show that the parameter cloud becomes progressively more concentrated from OLS to SDP and CLIE, while the final accepted model preserves high predictive accuracy on held-out validation motions. These results demonstrate a practical route to statistically coherent and physically feasible dynamic models for low-cost robot platforms.
Junji Oaki, Koki Yamane, Koki Inami +1
Institute of Systems and Information Engineering, University of Tsukuba, 1-1-1 Tennodai, Tsukuba, Ibaraki 305-8573, Japan
Accurate physical parameter identification of manipulated objects is fundamental to advanced robotic manipulation and the construction of faithful digital twins. However, acquiring physically consistent inertial and frictional properties from real-world interactions remains challenging due to sensing noise, modeling errors, and limited prior knowledge. This paper presents RigPI, a systematic framework for identifying dynamic parameters of both unconstrained rigid bodies and multi-link rigid bodies during robot-object interaction. RigPI integrates vision-based semantic priors, force-torque measurements, and motion observations within a differentiable simulation pipeline. A vision-language model (VLM) provides informed initialization and a constrained search space, while gradient information from a differentiable physics simulator enables efficient and stable parameter refinement. The proposed two-stage optimization strategy alleviates sensitivity to noise and avoids physically implausible solutions. Extensive real-world experiments on objects with revolute and prismatic joints demonstrate that RigPI achieves accurate and stable parameter estimates, and successfully reproduces manipulation trajectories on a real robot with parameter-aware predictive validity. These results highlight the effectiveness and robustness of RigPI for real-world robotic system identification tasks.
This paper examines three approaches for modeling the dynamics of a flexible-link 2-DoF robotic arm to address unmodeled dynamics not captured by rigid-body models. Two physics informed models combine rigid-body dynamics (RBD) formulations with a Gaussian Mixture Model (GMM) to capture residual model errors and linkage flexibility. A kinematics-based regression model serves as a purely data-driven baseline. Using an open-source dataset, torque predictions are first estimated using Ridge regression on kinematic features, while the physicsbased baseline is constructed from published specifications, and ordinary least-squares regression is subsequently used to estimate the same parameter set directly from data. Results show that the physics-based parameters yield the poorest accuracy, while regularized and least-squares estimators align more closely with measured torques. Residual analysis and error metrics highlight the limitations of purely parametric models for flexible-link systems and underscore the value of regularization and data-driven identification, supporting developments of semi-parametric residual learning methods.
Maciek Popik, Daniel Yang, Mahdis Bisheban
Dept. of Mechanical and Manufacturing Eng at the Schulich School of Engineering, University of Calgary, Alberta, Canada · Intelligent Dynamics and Control Lab, University of Calgary, Alberta, Canada