Gradient-like observer design on the Special Euclidean group SE(3) with system outputs on the real projective space

A nonlinear observer on the Special Euclidean group $\mathrm{SE(3)}$ for full pose estimation, that takes the system outputs on the real projective space directly as inputs, is proposed. The observer derivation is based on a recent advanced theory on nonlinear observer design. A key advantage with respect to existing pose observers on $\mathrm{SE(3)}$ is that we can now incorporate in a unique observer different types of measurements such as vectorial measurements of known inertial vectors and position measurements of known feature points. The proposed observer is extended allowing for the compensation of unknown constant bias present in the velocity measurements. Rigorous stability analyses are equally provided. Excellent performance of the proposed observers are shown by means of simulations

Output Regulation for Systems on Matrix Lie-group

This paper deals with the problem of output regulation for systems defined on matrix Lie-Groups. Reference trajectories to be tracked are supposed to be generated by an exosystem, defined on the same Lie-Group of the controlled system, and only partial relative error measurements are supposed to be available. These measurements are assumed to be invariant and associated to a group action on a homogeneous space of the state space. In the spirit of the internal model principle the proposed control structure embeds a copy of the exosystem kinematic. This control problem is motivated by many real applications fields in aerospace, robotics, projective geometry, to name a few, in which systems are defined on matrix Lie-groups and references in the associated homogenous spaces

Guaranteed Performance of Nonlinear Pose Filter on SE(3)

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).Comment: 2019 American Control Conference (ACC

Guaranteed Performance of Nonlinear Pose Filter on SE(3)

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).Comment: 2019 American Control Conference (ACC