Guaranteed Performance of Nonlinear Pose Filter on SE(3)

Abstract

This paper presents a novel nonlinear pose filter evolved directly on the Special Euclidean Group SE(3) with guaranteed characteristics of transient and steady-state performance. The above-mention characteristics can be achieved by trapping the position error and the error of the normalized Euclidean distance of the attitude in a given large set and guiding them to converge systematically to a small given set. The error vector is proven to approach the origin asymptotically from almost any initial condition. The proposed filter is able to provide a reliable pose estimate with remarkable convergence properties such that it can be fitted with measurements obtained from low-cost measurement units. Simulation results demonstrate high convergence capabilities and robustness considering large error in initialization and high level of uncertainties in measurements. Keywords: Pose, estimator, observer, attitude, position, estimate, special orthogonal group, special Euclidean group, prescribed performance, steady-state, transient response, homogeneous transformation matrix, complimentary filter, mapping, Parameterization, Representation, Robust, stability, uncertain, Gaussian, noise, vectorial measurement, vector measurement, translational velocity, angular velocity, singular value decomposition, rotational matrix, identity, deterministic, comparison, inertial frame, rigid body, three dimensional, 3D, space, Lie group, projection, landmark, feature, gyroscope, micro electromechanical systems, Inertial measurement units, sensor, IMUs, Fixed, moving, orientation, Roll, Pitch, Yaw, SVD, UAVs, QUAV, unmanned, underwater vehicle, robot, robotic System, spacecraft, quadrotor, quadcopter, overview, autonomous, xyz, axis, SO(3), SE(3).