Ehsan Samiei

Comparison of an attitude estimator based on the Lagrange-d'Alembert principle with some state-of-the-art filters

Discrete-time estimation of rigid body attitude and angular velocity without any knowledge of the attitude dynamics model, is treated using the discrete Lagrange-dAlembert principle. Using body-fixed sensor measurements of direction vectors and angular velocity, a Lagrangian is obtained as the difference between a kinetic energy-like term that is quadratic in the angular velocity estimation error, and an artificial potential obtained from Wahbas function. An additional dissipation term that depends linearly on the angular velocity estimation error is introduced, and the discrete Lagrange-dAlembert principle is applied to the Lagrangian with this dissipation. An implicit and an explicit first-order version of this discrete-time estimation scheme is presented. A comparison of this estimator is made with certain state-of-the-art attitude estimators in the absence of bias in sensor readings. Numerical simulations show that this estimator is robust and unlike extended Kalman filter-based schemes, its convergence does not depend on the gain values. In addition, the variational estimator is found to be more computationally efficient than these other estimators.

Discrete-time rigid body attitude state estimation based on the discrete Lagrange-d'Alembert principle

Discrete-time estimation of rigid body attitude and angular velocity without any knowledge of the attitude dynamics model, is treated using the discrete Lagrange-dAlembert principle. Using body-fixed sensor measurements of direction vectors and angular velocity, a Lagrangian is obtained as the difference between a kinetic energy-like term that is quadratic in the angular velocity estimation error and an artificial potential obtained from Wahbas function. An additional dissipation term that depends on the angular velocity estimation error is introduced, and the discrete Lagrange-dAlembert principle is applied to the Lagrangian with this dissipation. An explicit first order and a symmetric second-order version of this discrete-time filtering scheme are also presented, with a discussion of their advantages. A numerical simulation comparing the performances of the second-order estimator and the first-order estimator is carried out.

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).

Observer-based delayed feedback attitude control for single- and multi-actuator maneuvers

Observer-based attitude controllers for single- and multi-actuator maneuvers are developed from the delayed state feedback control laws obtained by the Lyapunov-Krasovskii functional and inverse dynamics approaches, respectively. The TRIAD algorithm is employed to process the observations. The observer gain is selected based on the extended Kalman-Bucy (EKB) filter, and a novel delay estimation approach is used to provide the estimates of the delay. The observer-based delayed feedback control laws are shown to be capable of accurate control of spacecraft attitude from noise-corrupted attitude measurements.

Integrated Guidance and Feedback Control of Underactuated Robotics System in SE(3)

An integrated guidance and feedback control scheme for steering an underactuated vehicle through desired waypoints in three-dimensional space, is developed here. The underactuated vehicle is modeled as a rigid body with four control inputs. These control inputs actuate the three degrees of freedom of rotational motion and one degree of freedom of translational motion in a vehicle body-fixed coordinate frame. This actuation model is appropriate for a wide range of underactuated vehicles including spacecraft with internal attitude actuators, vertical take-off and landing (VTOL) aircraft, fixed-wing multirotor unmanned aerial vehicles (UAVs), maneuverable robotic vehicles, etc. The guidance problem is developed on the special Euclidean group of rigid body motions, SE(3), in the framework ofgeometric mechanics, which represents the vehicle dynamics globally on this configuration manifold. The integrated guidance and control algorithm selects the desired trajectory for the translational motion that passes through the given waypoints, and the desired trajectory for the attitude based on the desired thrust direction to achieve the translational motion trajectory. A feedback control law is then obtained to steer the underactuated vehicle towards the desired trajectories in translation and rotation. This integrated guidance and control scheme takes into account known bounds on control inputs and generates a trajectory that is continuous and at least twice differentiable, which can be implemented with continuous and bounded control inputs. The integrated guidance and feedback control scheme is applied to an underactuated quadcopter UAV to autonomously generate a trajectory through a series of given waypoints in SE(3) and track the desired trajectory in finite time. The overall stability analysis of the feedback system is addressed. Discrete time models for the dynamics and control schemes of the UAV are obtained in the form of Lie group variational integrators using the discrete Lagrange-d’Alembert principle. Almost global asymptotic stability of the feedback system over its state space is shown analytically and verified through numerical simulations.

Almost Global Stochastic Stabilization of Attitude Motion with Unknown Multiplicative Diffusion Coefficient

In this paper, we design a geometric stochastic feedback controller to almost globally asymptotically stabilize the rigid body attitude in probability. The attitude motion is represented on the tangent bundle of SO(3) and is subject to an stochastic input torque with an unknown multiplicative diffusion coefficient. In addition, we assume that the variance parameter of the stochastic input torque is unknown. We, first, interpret the attitude dynamics in the Ito sense and the Frobenius norm of the unknown diffusion coefficient is approximated by an unknown bounded scalar parameter. An adaptive backstepping method and a suitable Morse-Lyapunov (M-L) function candidate is then employed to obtain a nonlinear continuous stochastic feedback control law. The almost global asymptotic stability of system is guaranteed in probability and the control gain matrix is obtained through solving LMI feasibility problem. A simulation example is performed to demonstrate the effectiveness of the proposed control scheme on TSO(3).