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This article proposes a novel integral geometric control attitude tracking scheme, utilizing a coordinate-free representation of attitude on the Lie group of rigid body rotations, SO(3). This scheme exhibits almost global asymptotic stability in tracking a reference attitude profile. The stability and robustness properties of this integral tracking control scheme are shown using Lyapunov stability analysis. A numerical simulation study, utilizing a Lie Group Variational Integrator (LGVI), verifies the stability of this tracking control scheme, as well as its robustness to a disturbance torque. In addition, a numerical comparison study shows the effectiveness of the proposed geometric integral term, when compared to other state-of-the-art attitude controllers. In addition, software-in-the-loop (SITL) simulations show the advantages of utilizing the proposed attitude controller in PX4 autopilot compared to using PX4’s original attitude controller.

 

This paper presents a novel approach for pointing direction control of a rigid body with a body-fixed sensor, in the presence of control constraints and pointing direction constraints. This scheme relies on the use of artificial potentials where an attractive artificial potential is placed at the desired pointing direction and a repulsive artificial potential is used to avoid an undesirable pointing direction. The proposed control law ensures almost global asymptotic convergence of the rigid body to its desired pointing direction, while satisfying the control input constraints and avoiding the undesirable pointing direction. These theoretical results are followed by numerical simulation results that provide an illustration of the scheme for a realistic spacecraft pointing control scenario. 

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. 

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. 

This paper presents a finite-time stable (FTS) position tracking control scheme in discrete time for an unmanned vehicle. The 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 position 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 tracking control system is addressed in this paper by a numerical comparison. This comparison is performed using numerical simulations on continuous and discrete FTS tracking control schemes applied to an unmanned vehicle model. 

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. 

This paper addresses the problem of generating a position trajectory with pointing direction constraints at given waypoints for underactuated unmanned vehicles. The problem is initially posed on the configuration space ℝ 3 × ℝ 2 and thereafter, upon suitable modifications, is re-posed as a problem on the Lie group SE(3). This is done by determining a vector orthogonal to the pointing direction and using it as the vehicle's thrust direction. This translates to converting reduced attitude constraints to full attitude constraints at the waypoints. For the position trajectory, in addition to position constraints, this modification adds acceleration constraints at the waypoints. For real-time implementation with low computational expenses, a linear-quadratic regulator (LQR) approach is adopted to determine the position trajectory with smoothness upto the fourth time derivative of position (snap). For the attitude trajectory, the thrust direction extracted from the position trajectory is used to first propagate the attitude to the subsequent waypoint and then correct it over time to achieve the desired attitude at this waypoint. Finally, numerical simulation results are presented to validate the trajectory generation scheme. 

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.