The rigid body attitude estimation problem is treated using the discrete-time Lagrange-d'Alembert principle. Three different possibilities are considered for the multi-rate relation between angular velocity measurements and direction vector measurements for attitude: 1) integer relation between sampling rates, 2) time-varying sampling rates, 3) non-integer relation between sampling rates. In all cases, it is assumed that angular velocity measurements are sampled at a higher rate compared to the inertial vectors. The attitude determination problem from two or more vector measurements in the body-fixed frame is formulated as Wahba's problem. At instants when direction vector measurements are absent, a discrete-time model for attitude kinematics is used to propagate past measurements. A discrete-time Lagrangian is constructed as the difference between a kinetic energy-like term that is quadratic in the angular velocity estimation error and an artificial potential energy-like term obtained from Wahba's cost function. An additional dissipation term is introduced and the discrete-time Lagrange-d'Alembert principle is applied to the Lagrangian with this dissipation to obtain an optimal filtering scheme. A discrete-time Lyapunov analysis is carried out to show that the optimal filtering scheme is asymptotically stable in the absence of measurement noise and the domain of convergence is almost global. For a realistic evaluation of the scheme, numerical experiments are conducted with inputs corrupted by bounded measurement noise. These numerical simulations exhibit convergence of the estimated states to a bounded neighborhood of the actual states.
- Award ID(s):
- 1739748
- PAR ID:
- 10119510
- Date Published:
- Journal Name:
- 2019 18th European Control Conference (ECC)
- Page Range / eLocation ID:
- 4047 to 4052
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
More Like this
-
more » « less
-
Relative motion estimation of one rigid body with respect to another is a problem that has immediate applications to formations and maneuvers involving multiple unmanned vehicles or collision avoidance between vehicles. A finite-time stable observer for relative attitude estimation of a rigid object using onboard sensors on an unmanned vehicle, is developed and presented here. This observer assumes sensor inputs from onboard vision and inertial sensors, with the vision sensors measuring at least three points on the object whose relative locations with respect to a body-fixed frame on the object are also assumed to be known. In the absence of any measurement noise, the estimated relative attitude is shown to converge to the actual relative pose in a finite-time stable manner. Numerical simulations indicate that this relative attitude observer is robust to persistent measurement errors and converges to a bounded neighborhood of the true attitude.more » « less
-
This paper presents a finite-time stable (FTS) attitude tracking control scheme in discrete time for an unmanned vehicle. The attitude tracking control scheme guarantees discrete-time stability of the feedback system in finite time. This scheme is developed in discrete time as it is more convenient for onboard computer implementation and guarantees stability irrespective of sampling period. Finite-time stability analysis of the discrete-time tracking control is carried out using discrete Lyapunov analysis. This tracking control scheme ensures stable convergence of attitude tracking errors to the desired trajectory in finite time. The advantages of finite-time stabilization in discrete time over finite-time stabilization of a sampled continuous time tracking control system is addressed in this paper through a numerical comparison. This comparison is performed using numerical simulations on continuous and discrete FTS tracking control schemes applied to an unmanned vehicle model.more » « less
-
In this paper, an anti-windup compensation scheme is proposed for the manual mode of a rigid body attitude control system to make the angular velocity dynamics globally asymptotically stable despite actuator saturation. The addressed anti-windup design problem is challenging since the nominal control law includes a nonlinear dynamic inversion element to cancel the nonlinearity in the angular velocity dynamics. The stability of the compensated closed-loop system is proved via the Lyapunov stability criterion appropriately. Moreover, the superiority of the compensated system versus the uncompensated one is demonstrated by simulation.more » « less
-
more » « less
This article reports an adaptive sensor bias observer and attitude observer operating directly on [Formula: see text] for true-north gyrocompass systems that utilize six-degree-of-freedom inertial measurement units (IMUs) with three-axis accelerometers and three-axis angular rate gyroscopes (without magnetometers). Most present-day low-cost robotic vehicles employ attitude estimation systems that employ microelectromechanical system (MEMS) magnetometers, angular rate gyros, and accelerometers to estimate magnetic attitude (roll, pitch, and magnetic heading) with limited heading accuracy. Present-day MEMS gyros are not sensitive enough to dynamically detect the Earth’s rotation, and thus cannot be used to estimate true-north geodetic heading. Relying on magnetic compasses can be problematic for vehicles that operate in environments with magnetic anomalies and those requiring high-accuracy navigation as the limited accuracy ([Formula: see text] error) of magnetic compasses is typically the largest error source in underwater vehicle navigation systems. Moreover, magnetic compasses need to undergo time-consuming recalibration for hard-iron and soft-iron errors every time a vehicle is reconfigured with a new instrument or other payload, as very frequently occurs on oceanographic marine vehicles. In contrast, the gyrocompass system reported herein utilizes fiber optic gyroscope (FOG) IMU angular rate gyro and MEMS accelerometer measurements (without magnetometers) to dynamically estimate the instrument’s time-varying true-north attitude (roll, pitch, and geodetic heading) in real-time while the instrument is subject to a priori unknown rotations. This gyrocompass system is immune to magnetic anomalies and does not require recalibration every time a new payload is added to or removed from the vehicle. Stability proofs for the reported bias and attitude observers, preliminary simulations, and a full-scale vehicle trial are reported that suggest the viability of the true-north gyrocompass system to provide dynamic real-time true-north heading, pitch, and roll utilizing a comparatively low-cost FOG IMU.
- Free Publicly Accessible Full Text
-
Accepted Manuscript1.0
- Conference Paper:
- https://doi.org/10.23919/ECC.2019.8796262
