Constrained Attitude Control of the 3D Pendulum

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AbstractThis novel research program investigates the global attitude control of a 3D pendulum with control constraints. The research program is motivated by the scientific and engineering significance of attitude control problems, the lack of prior research on global attitude control with control constraints, and by prior theoretical and experimental research of the principal investigator on attitude dynamics and control. The key feature of the 3D pendulum, as for all attitude control systems, is that the set of all possible attitude configurations is a compact, noncommutative Lie group. The control problems to be investigated fall into two categories: algorithms and computational methods for open loop optimal and near-optimal attitude control maneuvers and Liapunov-based methods for closed loop attitude stabilization using feedback. In each category of attitude control problems, new results will be globally valid without requiring use of local attitude charts or coordinates. A physical implementation of a 3D pendulum, referred to as the triaxial attitude control testbed (TACT), is the basis for the experimental part of the research. The TACT, consisting of a rigid base body supported by a near-frictionless air-bearing pivot, is an excellent laboratory-based research tool for studying the practical aspects of attitude dynamics and control. The research is motivated by important attitude dynamics and control problems that arise in diverse scientific and engineering fields. Important applications of constrained attitude dynamics and control include robotic devices such as gantry cranes and construction equipment for transporting rigid bodies loads; advanced ground-based pointing and tracking systems; and numerous space applications including inertial platforms and spacecraft attitude stabilization and maneuvers. The research also has important connections with full body problems in celestial mechanics, such as the mutual dynamics of binary asteroids and the near Earth passage of asteroids. The research on global attitude control of the 3D pendulum, with control constraints, is motivated by these applications and it will seek to develop spin-off results in several of these areas.