Nonlinear Pose Filters on the Special Euclidean Group SE(3) With Guaranteed Transient and Steady-State Performance

Abstract

Two novel nonlinear pose (i.e, attitude and position) filters developed directly on the Special Euclidean Group SE (3) able to guarantee prescribed characteristics of transient and steady-state performance are proposed. The position error and normalized Euclidean distance of attitude error are trapped to arbitrarily start within a given large set and converge systematically and asymptotically to the origin from almost any initial condition. The transient error is guaranteed not to exceed a prescribed value while the steady-state error is bounded by a predefined small value. The first pose filter operates based on a set of vectorial measurements coupled with a group of velocity vectors and requires preliminary pose reconstruction. The second filter, on the contrary, is able to perform its function using a set of vectorial measurements and a group of velocity vectors directly. Both proposed filters provide reasonable pose estimates with superior convergence properties while being able to use measurements obtained from low-cost inertial measurement, landmark measurement, and velocity measurement units. Simulation results demonstrate effectiveness and robustness of the proposed filters considering large error in initialization and high level of uncertainties in velocity vectors as well as in the set of vector measurements.

Landmark and IMU Data Fusion: Systematic Convergence Geometric Nonlinear Observer for SLAM and Velocity Bias

“…where P ∈ R 3 refers to position and R ∈ SO (3) refers to orientation, commonly termed attitude, which together constitute a homogeneous transformation matrix [20], [22] T = Z(R, P ) =…”

Nonlinear Stochastic Estimators on the Special Euclidean Group SE(3) Using Uncertain IMU and Vision Measurements

“…In this context, R y refers to uncertain attitude which can be reconstructed, for instance [7,8] and for attitude construction methods visit [6]. From (18) and (19), P y can be reconstructed…”

“…The structure of nonlinear pose estimators developed on SE (3) relies on angular and translational velocity measurements, vector measurements, landmark(s) measurements, and estimates of the uncertain components associated with the velocity measurements (for example [1,4,5,[18][19][20][21]). With the aim of improving the convergence behavior, several nonlinear deterministic pose estimators have been proposed [1,4,[19][20][21][22][23]].…”

“…The work in [19] has been modified to obtain a direct deterministic pose estimator on SE (3) [21] which utilizes the measurements directly, thus obviating the necessity for pose reconstruction. The noteworthy feature of the nonlinear deterministic pose estimators in [1,4,[18][19][20][21][22][23] is the guarantee of the almost global To cite this article: H. A. Hashim, and F. L. Lewis, "Nonlinear Stochastic Estimators on the Special Euclidean Group SE(3) Using Uncertain IMU and Vision Measurements," IEEE Transactions on Systems, Man, and Cybernetics: Systems, vol. PP, no.…”

Guaranteed Performance Nonlinear Observer for Simultaneous Localization and Mapping

“…If pose of a robot or vehicle is known, while the map of its surroundings is unknown, the problem is referred to as a mapping problem [1]. On the contrary, if the map of the environment is known, while the pose is unknown, the problem is described as pose estimation [2][3][4][5]. Simultaneous Localization and Mapping (SLAM) combines mapping and pose estimation problems and requires the autonomous system to simultaneously build a map of the environment and track its own pose (i.e.…”