Continuous-Time Estimation in the Flat Output Space Using B-Splines

Jacob C. Johnson, Joshua G. Mangelson, and Randal W. Beard

Peer Reviewed

Abstract:	Continuous-time trajectory estimation techniques generally model the state of the dynamic system on its configuration manifold (e.g. SE(2), SE(3)). The resulting trajectories do not account for nonholonomic constraints that may be present, and thus are often redundant or do not represent the motion of the system in a way that is natural to its dynamics. Our previous work showed that it is possible to perform estimation on a differentially flat system’s flat output space rather than its configuration manifold. However, this generally requires precise knowledge of the system’s sensor-to-dynamics parameters which we did not previously consider. In this paper, we show how these parameters can be calibrated and used to enable trajectory estimation in the flat output space. Using simulation results for a differential-drive robot, we show that after these sensor-to-dynamics parameters have been calibrated, flat output-based estimation outperforms trajectory estimation on the configuration manifold in terms of accuracy and computation time. Index Terms—Sensor fusion, calibration and identification, localization, autonomous vehicle navigation.
Published in:	2025 IEEE/ION Position, Location and Navigation Symposium (PLANS) April 28 - 1, 2025 Salt Lake Marriott Downtown at City Creek Salt Lake City, UT
Pages:	1439 - 1446
Cite this article:	Johnson, Jacob C., Mangelson, Joshua G., Beard, Randal W., "Continuous-Time Estimation in the Flat Output Space Using B-Splines," 2025 IEEE/ION Position, Location and Navigation Symposium (PLANS), Salt Lake City, UT, April 2025, pp. 1439-1446.
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