On modeling and control of a holonomic vectoring tricopter

Global closed-loop equilibrium properties of a geometric PDAV controller via a coordinate-free linearization

“…In aerial or underwater robotics, propulsion is obtained frequently by pointing a rotating high-speed propeller in 3D space (vectored actuation) [1], [2]. As the motors of a platform get pointed, they operate in extreme spinning velocities to produce the needed thrust for the platform locomotion, i.e., the motors track a reference Pointing Direction and simultaneously a reference Angular Velocity (PDAV) about the pointing direction.…”

“…Tiltrotor aircrafts and surveillance apparatus like radar or sonar sensors are a few examples, [3]. In UAVs, this occurs in aerial platforms driven by out-runner motors [1].…”

“…A singularity-free controller was developed, demonstrating improved performance for large initial attitude errors and the ability to negotiate bounded parametric uncertainties. The modeling and control of an aerial platform (a vectoring tricopter UAV actuated by three outrunner motors that are pointed in 3D space) was studied, with rampmich@mail.ntua.gr 2 E. Papadopoulos is with the Department of Mechanical Engineering, NTUA, 15780 Athens (tel: +30-210-772-1440; fax: +30-210-772-1455) egpapado@central.ntua.gr the UAV utilizing the PDAV controller from [4], along with core modifications to cope with the platforms high precision vectoring requirements [1].…”

“…The analysis demonstrated the nontrivial influences of those manifolds on the solutions. This work is motivated by the need to gain a deeper understanding of the global stabilization properties of the PDAV controller developed in, [1], since we intend to employ this controller on an experimental implementation of the aerial platform described in [1]. Resultantly the analysis techniques and computational tools described in [8], are employed in visualizing the smooth closed-loop vector fields of the PDAV controller, in an attempt to obtain an understanding of its global closed-loop properties.…”

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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.

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