Maziar Izadi

Nonlinear observer for 3D rigid body motion

Observer design for rigid body translational and rotational motion has important applications to unmanned or manned vehicles operating in air, underwater, or in space. An observer design for pose and velocity estimation for three-dimensional rigid body motion, in the framework of geometric mechanics, is presented here. Resorting to convenient defined Lyapunov function, a nonlinear observer on the Special Euclidean Group (SE(3)) is derived. This observer is based on the exponential coordinates, which are used to represent the group of rigid body motions. Exponential convergence of the estimation errors is shown and boundedness of the estimation error under bounded unmodeled torques and forces is established. Since exponential coordinates can describe uniquely almost the entire group of rigid body motions, the resulting observer design is almost globally exponentially convergent. The observer is then applied to the free dynamics of a rigid vehicle. Numerical simulation results are presented to show the performance of this observer, both in the absence and with unmodeled forces and torques.

Determination of relative motion of a space object from simultaneous measurements of range and range rate

This tutorial paper considers determination of instantaneous relative motion of a space object, from line-of-sight range and range rate measurements made by sensors fixed to a spacecraft in its proximity. Practical applications of this relative motion determination problem include uncooperative rendezvous prior to docking between space vehicles, capture of out-of-control spacecraft, capture of space debris and asteroids, locating and determining the attitude of space objects, and proximity operations near asteroids and comets. It is shown that the relative attitude of the space object with respect to the observing spacecraft can be determined from line-of-sight range measurements to at least three points on the object being observed, which requires three lidar or radar Doppler sensors. Determining the instantaneous relative translational and angular velocities of the space object also requires range and range rate measurements for at least three distinct points on the object, provided that certain conditions on the locations of the corresponding sensors and directions of their lines of sight are met.

A Nonlinear Observer Design for a Rigid Body in the Proximity of a Spherical Asteroid

We consider an observer design for a spacecraft modeled as a rigid body in the proximity of an asteroid. The nonlinear observer is constructed on the nonlinear state space of motion of a rigid body, which is the tangent bundle of the Lie group of rigid body motions in three-dimensional Euclidean space. The framework of geometric mechanics is used for the observer design. States of motion of the spacecraft are estimated based on state measurements. In addition, the observer designed can also estimate the gravity parameter of the asteroid, assuming the asteroid to have a spherically symmetric mass distribution. Almost global convergence of state estimates and gravity parameter estimate to their corresponding true values is demonstrated analytically, and verified numerically.Copyright

Estimation of Dynamics of Space Objects from Visual Feedback during Proximity Operations

Autonomous proximity operations to explore small solar system bodies (asteroids and comets), servicing of aerospace vehicles, and active space debris removal, are likely to increase in the future with NASA’s Asteroid Redirect Mission and Grand Challenge, and planned activities in autonomous rendezvous/proximity operations (ARPO) and active debris removal. Autonomous navigation is essential for these applications. The concept proposed here is to have a single stable estimator for the naturally coupled translational and rotational motion of an observed object from only vision-based, infra-red or lidar measurements, without needing a dynamics model for this object, during proximity operations. This estimator can also be used to improve an existing dynamics model. This avoids the need for measurements from external sources, like GPS, which is anyway not available for proximity operations near asteroids or comets. It also avoids mishaps due to changes in sensors and estimation schemes used during close proximity operations between spacecraft, as witnessed during the DART and Orbital Express missions. Attitude and translational motion of spacecraft, asteroids and comets are dynamically coupled through natural effects like gravity as well as control forces and torques for spacecraft. This coupling can also be used to estimate the mass and gravity parameters of the asteroid/comet.

Robust stabilization of rigid body attitude motion in the presence of a stochastic input torque

This paper investigates robust asymptotic stabilization of rigid body attitude dynamics evolving on the tangent bundle of SO(3) using geometric stochastic feedback control, where the system is subject to a stochastic input torque. To start with, the attitude dynamics is interpreted in the Ito sense. However, due to evolution of the kinematic differential equation of the system on SO(3), analyzing the stochastic system on TSO(3) is non-trivial. To address this challenging problem of robust asymptotic stabilization of attitude dynamics, the back-stepping method along with a suitable Morse-Lyapunov (M-L) function candidate with constant control gain parameters are used to obtain a nonlinear stochastic feedback control law. The control gain matrix and the M-L function control gain can be obtained by solving a feasible LMI, which can guarantee the robust asymptotic stability of the rigid body on TSO(3). Numerical simulations are performed to demonstrate and validate the effectiveness of the proposed controller in the state space of rigid body attitude motion in TSO(3).

An Observer for Rigid Body Motion With Almost Global Finite-Time Convergence

An observer that obtains estimates of the translational and rotational motion states for a rigid body under the influence of known forces and moments is presented. This nonlinear observer exhibits almost global convergence of state estimates in finite time, based on state measurements of the rigid body’s pose and velocities. It assumes a known dynamics model with known resultant force and resultant torque acting on the body, which may include feedback control force and control torque. The observer design based on this model uses the exponential coordinates to describe rigid body pose estimation errors on SE(3), which provides an almost global description of the pose estimate error. Finite-time convergence of state estimates and the observer are shown using a Lyapunov analysis on the nonlinear state space of motion. Numerical simulation results confirm these analytically obtained convergence properties for the case that there is no measurement noise and no uncertainty (noise) in the dynamics. The robustness of this observer to measurement noise in body velocities and additive noise in the force and torque components is also shown through numerical simulation results.Copyright

Nonlinear Observer for 3D Rigid Body Motion Estimation Using Doppler Measurements

This work presents a nonlinear observer that estimates the translational and rotational motion of a rigid body based on measurements of configuration (pose), angular velocity, and radial velocity as well as modeled forces and torques. The radial velocity measurements are provided by a single direction Doppler sensor. Using a conveniently defined Lyapunov function, a nonlinear observer on the Special Euclidean Group (SE(3)) is derived and almost globally stability is guaranteed. The resulting estimation error is almost globally exponentially convergent for sufficiently rich motion. Numerical simulation results are presented that illustrate the performance of the proposed solution.

Stable Estimation of Rigid Body Motion Based on the Lagrange–d’Alembert Principle

Stable estimation of rigid body rotational and translational motion states from noisy measurements, without any knowledge of the dynamics model, is treated using the Lagrange–d’Alembert principle from variational mechanics. With body-fixed sensor measurements, a Lagrangian is obtained as the difference between a kinetic energy-like term that is quadratic in velocity estimation errors and an artificial potential function of configuration (attitude and position) estimation errors. An additional dissipation term that is linear in the velocity estimation errors is introduced, and the Lagrange–d’Alembert principle is applied to the Lagrangian with this dissipation. This estimation scheme is shown to be almost globally asymptotically stable in the state space of rigid body motions. It is discretized for computer implementation using the discrete Lagrange–d’Alembert principle, as a first-order Lie group variational integrator (LGVI). In the presence of bounded measurement noise in the measurements, numerical simulations show that the estimated states converge to a bounded neighborhood of the actual states. CONTENTS 4.