Robust Design and Effective Control of Mechanical Systems

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The research program I am proposing is a natural extension of the work I have conducted in previous Discovery Grants. The program is now more focused, stressing robustness in design and effectiveness in control. We define robust design (RD) in following G. Taguchi's concept (1980s), in terms of the signal-to-noise ratio. The difficulty in implementing this concept lies in the plausible identification of noise and of signal. At the conceptual level we introduced the concept of complexity, and illustrated it for the case of mechanism design ("complexity" is strongly dependent on the context),  with special emphasis on the six lower kinematic pairs (revolute, prismatic, screw, cylindrical, planar and spherical). At the embodiment and the detailed-design levels, at which a mathematical model of elements or assemblies is available, the signal is identified as the parameters defining the design environment, for example, the frequency and voltage of the electric power coming from the supplier's line, over which the designer has no influence. Noise is defined as the unpredictable variations in the supplier's parameters. These we model as stochastic Gaussian processes with available values of mean and standard deviation.  We plan to use our RD paradigm in the context of robotics. Specifically, we target 2 kinds of robots: 1) Those for fast pick-and-place operations, which are present in a broad range of industrial processes, from the fabrication of hand-held consumer goods designed with a flat geometry (e.g., cell phones) to the packaging of food. These are four-degree-of-freedom (four-dof) robots; and 2) six-dof parallel robots for shaking operations, defined by high frequency (> 10 Hz) (HF) and small amplitude (SA) ("small" w.r.t. the dimensions of the testing machine). Applications thereof are also broad, from simple fluid-mixing to inertia-parameter identification (IPI), a major issue in the attitude control of telecommunications satellites, in which Canada has been a leader since the eighties. Our proposal includes the development of a novel methodology for IPI, using, again, Taguchi's robustness paradigm: maximize the signal-to-noise ratio. Not only this. We also plan to develop simpler, low-cost machines of IPI, by subjecting the test specimen to HF, SA planar displacements. Upon presenting the specimen to the testing machine, a planar 3-dof robot, with different poses, it will be possible, so we claim, to identify all 10 inertia parameters of the rigid object: mass, three coordinates of the centre of mass, and six independent components of the inertia tensor. On the effective control of the mechanical systems we design and prototype, the work is more applied than theoretical. We plan to continue developing control strategies and their algorithms for fast operations, of 10 Hz and beyond, under "small" displacements. The challenges are enormous, because of the risk of exciting the lower natural modes of the moving parts of the machine.