This paper formulates the attitude filtering problem as a nonlinear stochastic filter problem evolved directly on the Special Orthogonal Group SO (3). One of the traditional potential functions for nonlinear deterministic complimentary filters is studied and examined against angular velocity measurements corrupted with noise. This work demonstrates that the careful selection of the attitude potential function allows to attenuate the noise associated with the angular velocity measurements and results into superior convergence properties of estimator and correction factor. The problem is formulated as a stochastic problem through mapping SO (3) to Rodriguez vector parameterization. Two nonlinear stochastic complimentary filters are developed on SO (3). The first stochastic filter is driven in the sense of Ito and the second one considers Stratonovich. The two proposed filters guarantee that errors in the Rodriguez vector and estimates are semi-globally uniformly ultimately bounded in mean square, and they converge to a small neighborhood of the origin. Simulation results are presented to illustrate the effectiveness of the proposed filters considering high level of uncertainties in angular velocity as well as body-frame vector measurements.
This paper addresses the optimal control and selection of gaits in a class of dynamic locomotion systems that exhibit group symmetries. The authors study near-optimal gaits for an underwater eel-like robot, although the tools and analysis can be applied more broadly to a large family of nonlinear control systems with drift. The approximate solutions to the optimal control problem are found using a truncated basis of cyclic input functions. This generates feasible paths that approach the optimal one as the number of basis functions is increased. The authors describe an algorithm to obtain numerical solutions to this problem and present simulation results that demonstrate the types of solutions that can be achieved. Comparisons are made with experimental data using the REEL II robot platform.
This paper proposes two novel nonlinear attitude filters evolved directly on the Special Orthogonal Group SO (3) able to ensure prescribed measures of transient and steadystate performance. The tracking performance of the normalized Euclidean distance of attitude error is trapped to initially start within a large set and converge systematically and asymptotically to the origin from almost any initial condition. The convergence rate is guaranteed to be less than the prescribed value and the steady-state error does not exceed a predefined small value. The first filter uses a set of vectorial measurements with the need for attitude reconstruction. The second filter does not require attitude reconstruction and instead uses only a rate gyroscope measurement and two or more vectorial measurements. These filters provide good attitude estimates with superior convergence properties and can be applied to measurements obtained from low cost inertial measurement units (IMUs). Simulation results illustrate the robustness and effectiveness of the proposed attitude filters with guaranteed performance considering high level of uncertainty in angular velocity along with body-frame vector measurements.
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