This thesis is concerned with the factors that affect robot performance in positioning control. Specifically, we focus on the problem of fine end-point motion control of the robot end-effector about a nominal point where the linearized dynamics can be used. Performance is measured in the context of linear quadratic (LQ) theory. / An LQ based task-space performance index for robots is proposed. Several existing robots are examined for various transient tasks using this index and for each an optimum operating location is found. A cheap control (i.e. large actuator energies) analysis is done. The limits to performance are determined (i.e. singular optimal control). An explicit solution to performance was determined and an examination of the computed-torque control law is done. / An LQ based piecewise linear control (PLC) law is derived that increases the LQ gain in a piecewise-constant manner as the system trajectory converges towards the origin. This law uses a succession of invariant sets of decreasing size and for each an associated LQ gain. The formulation gives rise to an iteration function whose solution is a fixed point. The development of the PLC law led to the unveiling of a number of key properties, namely that the solution to the algebraic Riccati equation is concave with respect to both the actuator weighting and the state weighting matrices. A time-varying extension of the PLC law and an overshoot control scheme are also derived. / Issues regarding state estimation problem are studied. Noise is introduced to account for model uncertainty. A transient and steady state Kalman filter analysis is done. Sensor issues are examined for robots. The Kalman filter is used to fuse joint sensor data, Cartesian position sensor data, and tachometer data to provide a single best estimate of the state and to eliminate position offsets due to model error. / Finally, the effects of unmodeled dynamics, model error, and non-linearities on performance are examined. A Kalman filter is used to eliminate bias positioning errors at the robot's end-effector. Performance-uncertainty curves are generated using a numerical convex optimization method when the system is subject to parametric uncertainty. Describing functions are used to examine the backlash non-linearity.
| Identifer | oai:union.ndltd.org:LACETR/oai:collectionscanada.gc.ca:QMM.41788 |
| Date | January 1994 |
| Creators | Wredenhagen, G. Finn (Gordon Finn) |
| Contributors | Belanger, Pierre R. (advisor) |
| Publisher | McGill University |
| Source Sets | Library and Archives Canada ETDs Repository / Centre d'archives des thèses électroniques de Bibliothèque et Archives Canada |
| Language | English |
| Detected Language | English |
| Type | Electronic Thesis or Dissertation |
| Format | application/pdf |
| Coverage | Doctor of Philosophy (Department of Electrical Engineering.) |
| Rights | All items in eScholarship@McGill are protected by copyright with all rights reserved unless otherwise indicated. |
| Relation | alephsysno: 001393471, proquestno: NN94723, Theses scanned by UMI/ProQuest. |
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