State estimation based on kinematic model and relay feedback stability arising in controlled mechanical systems

This thesis considers two particular issues arising in the controlled mechanical systems: state estimation based on kinematic models using more sensors and the unified approach to understand the nonlinear dynamics coming from the Coulomb friction.;The recent advances in sensor technologies raise basic questions on how to synthesize the information from different sensors synergistically and how to implement new sensors in a reliable and cost-effective manner. The first part of this thesis deals with these issues from the state estimation point of view by exploiting the sensor-based estimation method called the kinematic Kalman filter (KKF). The KKF refers to the Kalman filter applied to a kinematic model. Being independent of physical parameters, the KKF is immune to modeling uncertainties and parameter variations. In its simplest form, the KKF combines an encoder with an accelerometer to provide a robust and accurate velocity estimation. Detailed error analysis of the KKF shows its superiority to the model-based scheme in its tolerance to the resolution of the encoder. We then extend the basic idea of the KKF to a general rigid body motion leading to the formulation of the multi-dimensional KKF (MD-KKF). The MD-KKF combines the measurements from the vision sensor, accelerometers and gyroscopes to remedy the inherent limitations of the vision sensor, i.e., the slow sampling rate and the latency. The main ideas are verified on two experimental testbeds: the instrumented indirect drive (IID) setup and the NSK two-link planar robot.;In control of mechanical systems with drive trains, the Coulomb friction is an important nonlinearity not only as the source of tracking error but also as the cause of instability generating limit cycles. The second part of this thesis focuses on the latter. First, we show that a series of drive trains with multiple Coulomb friction sources can be formulated as a class of relay feedback systems characterized by the zero DC gain property and the positivity of the first Markov parameter. Then, employing the piecewise quadratic Lyapunov (PWQL) function and the integral quadratic constraint (IQC), new sufficient conditions are developed to guarantee the pointwise global stability. The theoretical results are verified by simulation and experimental results with a single link flexible joint mechanism. The results are useful to design mechanical systems free from the limit cycle.