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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. 

A discrete time, optimal trajectory planning scheme for position trajectory generation of a vehicle is given here, considering the mission duration as a free variable. The vehicle is actuated in three rotational degrees of freedom and one translational degree of freedom. This model is applicable to vehicles that have a body-fixed thrust vector direction for translational motion control, including fixed-wing and rotorcraft unmanned aerial vehicles (UAVs), unmanned underwater vehicles (UUVs) and spacecraft. The lightweight scheme proposed here generates the trajectory in inertial coordinates, and is intended for real time, on-the-go applications. The unspecified terminal time can be considered as an additional design parameter. This is done by deriving the optimality conditions in a discrete time setting, which results in the discrete transversality condition. The trajectory starts from an initial position and reaches a desired final position in an unspecified final time that ensures the cost on state and control is optimized. The trajectory generated by this scheme can be considered as the desired trajectory for a tracking control scheme. Numerical simulation results validate the performance of this trajectory generation scheme used in conjunction with a nonlinear tracking control scheme. 

A framework for autonomous waypoint planning, trajectory generation through waypoints, and trajectory tracking for multi-rotor unmanned aerial vehicles (UAVs) is proposed in this work. Safe and effective operations of these UAVs is a problem that demands obstacle avoidance strategies and advanced trajectory planning and control schemes for stability and energy efficiency. To address this problem, a two-level optimization strategy is used for trajectory generation, then the trajectory is tracked in a stable manner. The framework given here consists of the following components: (a) a deep reinforcement learning (DRL)-based algorithm for optimal waypoint planning while minimizing control energy and avoiding obstacles in a given environment; (b) an optimal, smooth trajectory generation algorithm through waypoints, that minimizes a combinaton of velocity, acceleration, jerk and snap; and (c) a stable tracking control law that determines a control thrust force for an UAV to track the generated trajectory.