Reproducible Dynamic Parameter Identification for a Low-Cost Robot Arm: A Positive-Definiteness Audit for Model Acceptance

Abstract

Dynamic parameter identification of low-cost robot arms is challenging because limited sensing and drivetrain nonidealities can yield models that predict measured torques well but are physically unsuitable for model-based control. This paper presents a reproducible dynamic parameter identification pipeline for CRANE-X7, a low-cost seven-degree-of-freedom arm driven by modular smart actuators. A 39-parameter OpenSYMORO base-parameter model is identified without CAD inertial data using fully specified single-joint and adjacent-pair excitation, ordinary least squares, a conditional semidefinite-programming projection, and closed-loop input error refinement. Model acceptance is decided by a separate positive-definiteness audit of the identified inertia matrix over 221,875 sampled configurations. Experiments cover 40 identification trajectories at four sampling intervals and three held-out validation trajectories. The reduced model improves held-out prediction over the full 65-parameter model on all seven identification trajectories used for the model comparison. Fixed-configuration analyses show the distinct role of the feasibility audit: models with similar torque predictions can produce unstable acceleration-resolved dynamics and reverse the direction of the inertia inversion. For the selected identification trajectory, two executions separated by 26 days yield a 1.25% relative spread in held-out root-mean-square error. The accepted model passes audits with five random seeds, and sensitivity analyses quantify the effects of the sampling interval and of torque-constant uncertainty. The complete trajectory specification and numerical record support independent implementation and comparison. These results establish predictive performance, inertia-matrix feasibility, and repeatability as complementary criteria for evaluatingdynamic models of low-cost arms.

25 pages, 10 figures, 20 tables. v3: retitled; former supplementary material now Appendices B-E; trajectory data as ancillary files. Supersedes v1, v2: four defects corrected, all 160 identification conditions recomputed. This work has been submitted to the IEEE for possible publication. Copyright may be transferred without notice, after which this version may no longer be accessible