{"id":"W2331130433","doi":"10.1109/tro.2016.2522442","title":"Inversion Symmetry of the Euclidean Group: Theory and Application to Robot Kinematics","year":2016,"lang":"en","type":"article","venue":"IEEE Transactions on Robotics","topic":"Robotic Mechanisms and Dynamics","field":"Engineering","cited_by":50,"is_retracted":false,"has_abstract":true,"ca_institutions":"","funders":"European Regional Development Fund; Hong Kong University of Science and Technology; National Natural Science Foundation of China; Canadian Institute for Advanced Research","keywords":"Euclidean group; Kinematics; Euclidean space; Euclidean geometry; Inverse kinematics; Group (periodic table); Mathematics; Symmetry (geometry); Inversion (geology); Lie group; Geometry; Pure mathematics; Physics; Classical mechanics; Affine space","routes":{"ca_aff":false,"ca_fund":true,"ca_venue":false,"about_ca":false,"invisible_to_affiliation_only":true},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0003281025,0.0005142885,0.0004331884,0.001008491,0.0004345974,0.0008286629,0.0005303955,0.0005766411,0.002862376],"category_scores_gemma":[0.0006605239,0.0001992912,0.0006799653,0.0005815765,0.001956526,0.001269139,0.0009451826,0.0009428244,0.0006857043],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0003958883,"about_ca_system_score_gemma":0.0003038757,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0007066746,"about_ca_topic_score_gemma":0.0005763285,"domain_scores_codex":[0.9998428,0.00004622517,0.00001289644,0.00003106758,0.0000457863,0.00002124723],"domain_scores_gemma":[0.9998232,0.00005160448,0.00003399054,0.00002914197,0.00003993649,0.00002219155],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","study_design_scores_codex":[0.000008093924,0.00001061661,0.000200383,0.00005992499,0.000007082655,0.00007540688,0.0001125174,0.01064988,0.002272245,0.9663084,0.000771785,0.01952366],"study_design_scores_gemma":[0.000006948204,0.00004929094,0.0002514072,0.00002449839,0.00000400831,0.0001912078,0.00008208834,0.05689914,0.0009875757,0.9308165,0.01066913,0.00001813686],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.05478327,0.003560471,0.8986037,0.0005645248,0.0003744042,0.00006895215,0.000137669,0.0001654494,0.04174158],"genre_scores_gemma":[0.7229197,0.006395634,0.2525244,0.0003106707,0.0007842649,0.0001775922,0.0002979002,0.000135895,0.01645396],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.002862376,"threshold_uncertainty_score":0.009575546,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.005630952032692744,"score_gpt":0.1960028822182127,"score_spread":0.19037193018552,"validation_status":"score_only:v0-immature-baseline","note":"Baseline scores from an immature model (maturity gate not passed). Scores rank; they never assert a category."}}