A dynamic estimator on SE(3) using range-only measurements

This paper addresses the problem of estimating the attitude and position of a rigid body when the available measurements consist only of the relative distances between a set of body fixed beacons and a set of Earth fixed landmarks. The proposed solution is given in terms of a dynamical system evolving on the Special Euclidean group SE(3), the trajectories of which are shown to locally converge to the actual attitude and position of the rigid body. Local asymptotic stability of the dynamical system is proven by using a suitable Lyapunov function, under the assumption that there is a set of noncoplanar landmarks and beacons. Simulation results are shown to illustrate the behaviour of the proposed estimator.

[1]  G. Wahba.  A Least Squares Estimate of Satellite Attitude , 1965 .

[2]  R. Brockett.  Dynamical systems that sort lists, diagonalize matrices, and solve linear programming problems , 1991 .

[3]  Jean-Pierre Merlet,et al.  Direct kinematics of parallel manipulators , 1993, IEEE Trans. Robotics Autom..

[4]  Richard M. Murray,et al.  A Mathematical Introduction to Robotic Manipulation , 1994 .

[5]  F. Park.  Distance Metrics on the Rigid-Body Motions with Applications to Mechanism Design , 1995 .

[6]  U. Helmke,et al.  Optimization and Dynamical Systems , 1994, Proceedings of the IEEE.

[7]  John L. Crassidis,et al.  NEW ALGORITHM FOR ATTITUDE DETERMINATION USING GLOBAL POSITIONING SYSTEM SIGNALS , 1997 .

[8]  I. Bar-Itzhack,et al.  On algorithms for attitude estimation using GPS , 2000, Proceedings of the 39th IEEE Conference on Decision and Control (Cat. No.00CH37187).

[9]  J. Junkins,et al.  Optimal Attitude and Position Determination from Line-of-Sight Measurements , 2000 .

[10]  David Angeli.  Almost global stabilization of the inverted pendulum via continuous state feedback , 2001, Autom..

[11]  John M. Lee.  Introduction to Smooth Manifolds , 2002 .

[12]  Eduardo Sontag,et al.  Global Stabilization for Systems Evolving on Manifolds , 2004 .

[13]  A. D. Lewis,et al.  Geometric Control of Mechanical Systems , 2004, IEEE Transactions on Automatic Control.

[14]  João M. F. Xavier,et al.  Intrinsic variance lower bound (IVLB): an extension of the Cramer-Rao bound to Riemannian manifolds , 2005, Proceedings. (ICASSP '05). IEEE International Conference on Acoustics, Speech, and Signal Processing, 2005..

[15]  Rita Cunha,et al.  Output-feedback control for stabilization on SE(3) , 2006, Proceedings of the 45th IEEE Conference on Decision and Control.

[16]  João M. F. Xavier,et al.  Estimation of Attitude and Position from Range-Only Measurements using Geometric Descent Optimization on the Special Euclidean Group , 2006, 2006 9th International Conference on Information Fusion.

[17]  Louis L. Whitcomb,et al.  Adaptive Identification on the Group of Rigid-Body Rotations and its Application to Underwater Vehicle Navigation , 2005, IEEE Transactions on Robotics.

[18]  Suguru Arimoto.  Control of mechanical systems , 2009, Scholarpedia.