The control task of tracking a reference pointing direction (the attitude about the pointing direction is irrelevant) while obtaining a desired angular velocity (PDAV) around the pointing direction using geometric techniques is addressed here. Existing geometric controllers developed on the two-sphere only address the tracking of a reference pointing direction while driving the angular velocity about the pointing direction to zero. In this paper a tracking controller on the two-sphere, able to address the PDAV control task, is developed globally in a geometric frame work, to avoid problems related to other attitude representations such as unwinding (quaternions) or singularities (Euler angles). An attitude error function is constructed resulting in a control system with desired tracking performance for rotational maneuvers with large initial attitude/angular velocity errors and the ability to negotiate bounded modeling inaccuracies. The tracking ability of the developed control system is evaluated by comparing its performance with an existing geometric controller on the two-sphere and by numerical simulations, showing improved performance for large initial attitude errors, smooth transitions between desired angular velocities and the ability to negotiate bounded modeling inaccuracies.
The quadrotor task of negotiating aggressive attitude maneuvers while adhering to motor constraints is addressed here. The majority of high level quadrotor Nonlinear Control System (NCS) solutions ignore motor control authority limitations, especially important during aggressive attitude maneuvers, generating unrealizable thrusts and negating the validity of the accompanying stability proofs. Here, an attitude control framework is developed, comprised by a thrust allocation strategy and a specially designed geometric attitude tracking controller, allowing the quadrotor to achieve aggressive attitude maneuvers, while complying to actuator constraints and simultaneously staying "close" to a desired position command in a computationally inexpensive way. This is a novel contribution resulting in thrusts realizable by available quadrotors during aggressive attitude maneuvers, and enhanced performance guaranteed by valid stability proofs. Also, it is shown that the developed controller can be combined with a collective thrust expression in producing a position/yaw tracking controller. Through rigorous stability proofs, both the position and attitude frameworks are shown to have desirable closed loop properties that are almost global. This establishes a quadrotor control solution allowing the vehicle to negotiate aggressive maneuvers position/attitude on SE(3). Simulations illustrate and validate the effectiveness and capabilities of the developed solution.
Tracking a desired Pointing Direction and simultaneously obtaining a reference Angular Velocity (PDAV) around the pointing direction constitutes a very involved and complicated motion encountered in a variaty of robotic, industrial and military applications. In this paper through the utilization of global analysis and simulation techniques, the smooth closed-loop vector fields induced by the geometric PDAV controller from [1], are visualized to gain a deeper understanding of its global stabilization properties. First through the calculation of a coordinate-free form of the closed-loop linearized dynamics, the local stability of each equilibrium of the system is analyzed. The results acquired by means of eigenstructure analysis, are used in predicting the frequency of complex precession/nutation oscillations that arise during PDAV trajectory tracking; an important tool in actuator selection. Finally, by utilizing variational integration schemes, the flow converging to the desired equilibrium and the flow "close" to the stable manifold of the saddle equilibrium of the closedloop system is visualized and analyzed. Results offer intimate knowledge of the closed-loop vector fields bestowing to the control engineer the ability to anticipate and/or have a rough estimate of the evolution of the solutions.
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