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Although proprioceptive sensors such as inertial measurement units (IMU) are compact and widely used on robotic platforms, direct integration of noisy inertial measurements causes small sensor errors to propagate into large pose estimation errors, limiting their use as independent dead reckoning sensors. In this work, we address drift in encoder-free dead reckoning by combining body-frame acceleration profiles from a compact multi-IMU array with commanded motion parameters in a convolutional neural network (CNN) bias estimator. The estimator predicts the difference between commanded and realized platform displacement, without using joint encoders or explicit terrain labels. In outdoor local search experiments with an encoder-free hexapod robot, the proposed approach reduces mean dead reckoning drift by approximately 41% on grass and 59% on sand relative to an idealized commanded-kinematics baseline. These results indicate that a platform-specific dataset collected in controlled indoor terrains improves outdoor dead reckoning performance, even when the deployment terrain is not fully represented in the training dataset. This method provides a low-cost, compact proprioceptive drift reduction method for minimally instrumented legged robots when exteroceptive localization is unavailable due to cost or environmental conditions. We expect this approach to be helpful in developing future low-cost robots for scrambling across extraterrestrial, underwater, or underground granular media where leg slip is both common and hard to predict.<\/jats:p>","DOI":"10.3389\/frobt.2026.1920986","type":"journal-article","created":{"date-parts":[[2026,8,26]],"date-time":"2026-08-26T04:51:38Z","timestamp":1787719898000},"update-policy":"https:\/\/doi.org\/10.3389\/crossmark-policy","source":"Crossref","is-referenced-by-count":0,"title":["Encoder-free hexapod dead reckoning on sand using learned inertial correction"],"prefix":"10.3389","volume":"13","author":[{"given":"Mingyu","family":"Pan","sequence":"first","affiliation":[{"name":"Department of Mechanical and Aerospace Engineering, Case Western Reserve University","place":["Cleveland, OH, United States"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Maxwell A.","family":"Rollins","sequence":"additional","affiliation":[{"name":"Department of Mechanical and Aerospace Engineering, Case Western Reserve University","place":["Cleveland, OH, United States"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Samuel H.","family":"Yang","sequence":"additional","affiliation":[{"name":"Department of Mechanical and Aerospace Engineering, Case Western Reserve University","place":["Cleveland, OH, United States"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Kathryn A.","family":"Daltorio","sequence":"additional","affiliation":[{"name":"Department of Mechanical and Aerospace Engineering, Case Western Reserve University","place":["Cleveland, OH, United States"]}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1965","published-online":{"date-parts":[[2026,8,26]]},"reference":[{"key":"B1","first-page":"929","article-title":"PyTorch 2: faster machine learning through dynamic python bytecode transformation and graph compilation","author":"Ansel","year":"2024"},{"key":"B2","doi-asserted-by":"publisher","first-page":"659","DOI":"10.1007\/s10846-020-01162-8","article-title":"Blind hexapod locomotion in complex terrain with gait adaptation using deep reinforcement learning and classification","volume":"99","author":"Azayev","year":"2020","journal-title":"J. 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