Identities for Deriving Equations of Motion Using Constrained Attitude Parameterizations

Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/140646/1/1.G000221.pd

Passivity-Based Attitude Control on the Special Orthogonal Group of Rigid-Body Rotations

Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/140654/1/1.G000510.pd

Direction‐cosine‐matrix‐based attitude control subject to actuator saturation

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/166291/1/cth2bf00839.pd

Closed-Loop Koopman Operator Approximation

The Koopman operator allows a nonlinear system to be rewritten as an infinite-dimensional linear system by viewing it in terms of an infinite set of lifting functions instead of a state vector. The main feature of this representation is its linearity, making it compatible with existing linear systems theory. A finite-dimensional approximation of the Koopman operator can be identified from experimental data by choosing a finite subset of lifting functions, applying it to the data, and solving a least squares problem in the lifted space. Existing Koopman operator approximation methods are designed to identify open-loop systems. However, it is impractical or impossible to run experiments on some systems without a feedback controller. Unfortunately, the introduction of feedback control results in correlations between the system's input and output, making some plant dynamics difficult to identify if the controller is neglected. This paper addresses this limitation by introducing a method to identify a Koopman model of the closed-loop system, and then extract a Koopman model of the plant given knowledge of the controller. This is accomplished by leveraging the linearity of the Koopman representation of the system. The proposed approach widens the applicability of Koopman operator identification methods to a broader class of systems. The effectiveness of the proposed closed-loop Koopman operator approximation method is demonstrated experimentally using a Harmonic Drive gearbox exhibiting nonlinear vibrations.Comment: 21 pages, 13 figure

Mind the Gap: Norm-Aware Adaptive Robust Loss for Multivariate Least-Squares Problems

Measurement outliers are unavoidable when solving real-world robot state estimation problems. A large family of robust loss functions (RLFs) exists to mitigate the effects of outliers, including newly developed adaptive methods that do not require parameter tuning. All of these methods assume that residuals follow a zero-mean Gaussian-like distribution. However, in multivariate problems the residual is often defined as a norm, and norms follow a Chi-like distribution with a non-zero mode value. This produces a "mode gap" that impacts the convergence rate and accuracy of existing RLFs. The proposed approach, "Adaptive MB," accounts for this gap by first estimating the mode of the residuals using an adaptive Chi-like distribution. Applying an existing adaptive weighting scheme only to residuals greater than the mode leads to more robust performance and faster convergence times in two fundamental state estimation problems, point cloud alignment and pose averaging.Comment: 8 pages, 4 figures. This paper has been accepted for publication in IEEE Robotics and Automation Letters. V2: Update weighting in (13), (28) and re-run results. Hypothesis, methodology, and general findings remain unchanged. Update Sec. II-A to reference IRLS, and update citation [11] accordingly. Include acknowledgement to Mitchell Cohe

Improving Self-Consistency in Underwater Mapping Through Laser-Based Loop Closure (Extended)

Accurate, self-consistent bathymetric maps are needed to monitor changes in subsea environments and infrastructure. These maps are increasingly collected by underwater vehicles, and mapping requires an accurate vehicle navigation solution. Commercial off-the-shelf (COTS) navigation solutions for underwater vehicles often rely on external acoustic sensors for localization, however survey-grade acoustic sensors are expensive to deploy and limit the range of the vehicle. Techniques from the field of simultaneous localization and mapping, particularly loop closures, can improve the quality of the navigation solution over dead-reckoning, but are difficult to integrate into COTS navigation systems. This work presents a method to improve the self-consistency of bathymetric maps by smoothly integrating loop-closure measurements into the state estimate produced by a commercial subsea navigation system. Integration is done using a white-noise-on-acceleration motion prior, without access to raw sensor measurements or proprietary models. Improvements in map self-consistency are shown for both simulated and experimental datasets, including a 3D scan of an underwater shipwreck in Wiarton, Ontario, Canada.Comment: 26 pages, 18 figures. V2 correct Table III x2 parameter values, Table VIII 'INS' values, and equation A.2