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The geometric approach tests identifiability across the infinite space of configurations using only a finite set of conditions and without approximation. It can be applied to general open-chain kinematic trees ranging from industrial manipulators to legged robots, and it is the first solution for this broad set of systems that is provably correct. The high-level operation of the algorithm is based on a key observation: Undetectable changes in inertial parameters can be represented as sequences of inertial transfers across the joints. Drawing on the exponential parameterization of rigid-body kinematics, undetectable inertial transfers are analyzed in terms of observability from linear systems theory. This analysis can be applied recursively, and lends an overall complexity of O( N) to characterize parameter identifiability for a system of N bodies. Matlab source code for the new algorithm is provided. <\/jats:p>","DOI":"10.1177\/02783649241258215","type":"journal-article","created":{"date-parts":[[2024,7,25]],"date-time":"2024-07-25T09:45:36Z","timestamp":1721900736000},"page":"2274-2302","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":2,"title":["A geometric characterization of observability in inertial parameter identification"],"prefix":"10.1177","volume":"43","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-9041-5175","authenticated-orcid":false,"given":"Patrick M.","family":"Wensing","sequence":"first","affiliation":[{"name":"Department of Aerospace and Mechanical Engineering, University of Notre Dame, Notre Dame, IN, USA"}]},{"given":"G\u00fcnter","family":"Niemeyer","sequence":"additional","affiliation":[{"name":"Department of Mechanical and Civil Engineering, Caltech, Pasadena, CA, USA"}]},{"given":"Jean-Jacques E.","family":"Slotine","sequence":"additional","affiliation":[{"name":"Department of Mechanical Engineering, Department of Brain and Cognitive Sciences, Massachusetts Institute of Technology, Cambridge, MA, USA"}]}],"member":"179","published-online":{"date-parts":[[2024,7,25]]},"reference":[{"key":"bibr1-02783649241258215","doi-asserted-by":"publisher","DOI":"10.1177\/027836498600500306"},{"key":"bibr2-02783649241258215","doi-asserted-by":"crossref","unstructured":"Ayusawa K, Venture G, Nakamura Y (2008) Identification of the inertial parameters of a humanoid robot using unactuated dynamics of the base link. 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