This paper presents a nonlinear finite-time stable attitude estimation scheme for a rigid body with unknown dynamics. Attitude is estimated from a minimum of two linearly independent known vectors measured in the body-fixed frame, and the angular velocity vector is assumed to have a constant bias in addition to measurement errors. Estimated attitude evolves directly on the special Euclidean group SO(3), avoiding any ambiguities. The constant bias in angular velocity measurements is also estimated. The estimation scheme is proven to be almost globally finite time stable in the absence of measurement errors using a Lyapunov analysis. For digital implementation, the estimation scheme is discretized as a geometric integrator. Numerical simulations demonstrate the robustness and convergence capabilities of the estimation scheme. 
                        more » 
                        « less   
                    
                            
                            A Finite-Time Stable Observer for Relative Attitude Estimation
                        
                    
    
            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   
        
    
                            - Award ID(s):
- 1739748
- PAR ID:
- 10195625
- Date Published:
- Journal Name:
- 2019 IEEE 58th Conference on Decision and Control (CDC)
- Page Range / eLocation ID:
- 7911 to 7916
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
More Like this
- 
            
- 
            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
- 
            This article presents an extended state observer for a vehicle modeled as a rigid body in three-dimensional translational and rotational motions. The extended state observer is applicable to a multi-rotor aerial vehicle with a fixed plane of rotors, modeled as an under-actuated system on the state-space TSE(3), the tangent bundle of the six-dimensional Lie group SE(3). This state-space representation globally represents rigid body motions without singularities. The extended state observer is designed to estimate the resultant external disturbance force and disturbance torque acting on the vehicle. It guarantees stable convergence of disturbance estimation errors in finite time when the disturbances are constant, and finite time convergence to a bounded neighborhood of zero errors for time-varying disturbances. This extended state observer design is based on a Hölder-continuous fast finite time stable differentiator that is similar to the super-twisting algorithm, to obtain fast convergence. Numerical simulations are conducted to validate the proposed extended state observer. The proposed extended state observer is compared with other existing research to show its advantages. A set of experimental results implementing disturbance rejection control using feedback of disturbance estimates from this extended state observer is also presented.more » « less
- 
            Unlike many current navigation approaches for micro air vehicles, the relative navigation (RN) framework presented in this paper ensures that the filter state remains observable in GPS-denied environments by working with respect to a local reference frame. By subtly restructuring the problem, RN ensures that the filter uncertainty remains bounded, consistent, and normally-distributed, and insulates flight-critical estimation and control processes from large global updates. This paper thoroughly outlines the RN framework and demonstrates its practicality with several long flight tests in unknown GPS-denied and GPS-degraded environments. The relative front end is shown to produce low-drift estimates and smooth, stable control while leveraging off-the-shelf algorithms. The system runs in real time with onboard processing, fuses a variety of vision sensors, and works indoors and outdoors without requiring special tuning for particular sensors or environments. RN is shown to produce globally-consistent, metric, and localized maps by incorporating loop closures and intermittent GPS measurementsmore » « less
- 
            This paper addresses the problem of generating a continuous and differentiable trajectory on the Lie group of rigid body motions, SE(3), for a class of underactuated vehicles modeled as rigid bodies. The three rotational degrees of freedom (DOF) are independently actuated, while only one translational DOF is actuated by a body-fixed thrust vector. This model is applicable to a large set of unmanned vehicles, including fixed-wing and rotorcraft unmanned aerial vehicles (UAVs). The formulation utilizes exponential coordinates to express the underactuation constraint as an intrinsic part of the problem. It provides steps to generate a rest-to-rest trajectory after obtaining conditions that guarantee controllability. An attitude trajectory is selected to satisfy the given initial and final attitude state. The position trajectory generation is subsequently posed as an optimal control problem expressed as a linear quadratic regulator (LQR) in the exponential coordinates corresponding to position. As a result, an optimal position trajectory is obtained which ensures that the trajectory generated is feasible with realistic velocities and with given initial pose and final pose, while satisfying the underactuation constraint. Numerical simulation results are obtained that validate this trajectory generation scheme.more » « less
 An official website of the United States government
An official website of the United States government 
				
			 
					 
					
 
                                    