In this thesis, two different control theoretic topics are studied, nonlinear observer design for orientation estimation and control design under limited communication. The specific problems studied originate from control of mobile robots in difficult terrain, especially walking robots.
In Paper A, the fusion of rate gyro data and inclinometer data with a high-gain observer and a time-varying observer is studied. The Euler angle representation of rigid body motion is used. It is shown that even in the process of rate gyro offsets and slow inclinometer dynamics it is possible to derive exponentially convergent attitude observers with arbitrarily small bounded errors. The high-gain observer is evaluated experimentally.
In Paper B, rate gyro data and accelerometer data are fused in order to obtain attitude estimates. Two exponentially convergent observers are presented. The underlying kinematic model used for the observer design is global and the state evolves on the unit sphere. The observers are evaluated experimentally on a walking robot.
In Paper C, the use of inertial sensors and computer vision is investigated. Orientation estimation is studied and it is shown that orientation can be estimated in the presence of an unknown time-varying position. The problem is phrased as an observer problem for an implicit output system evolving on $SO(3)$. Observability is studied and a generalization of the unobservable subspace, the unobservable subgroup, is derived. A locally convergent exponential observer is presented and the domain of attraction is estimated numerically. It is shown that position estimation can be formulated as a linear implicit output problem.
In Paper D, the problem of control design under limited communication is studied. It is shown how a limited communication channel can be modeled and how the constraint due to this limitation is incorporated into the system model. An algorithm for computing optimal communication schedules and corresponding LQ-controllers is given.
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