Avoiding Feedback-Linearization Singularity Using a Quotient Method -- The Field-Controlled DC Motor Case

Feedback linearization requires a unique feedback law and a unique diffeomorphism to bring a system to Brunovsk´y normal form. Unfortunately, singularities might arise both in the feedback law and in the diffeomorphism. This paper demonstrates the ability of a quotient method to avoid or mitigate the singularities that typically arise with feedback linearization. The quotient method does it by relaxing the conditions on diffeomorphism, which can be achieved since there is an additional degree of freedom at each step of the iterative procedure. This freedom in choosing quotients and the resulting advantage are demonstrated for a field-controlled DC motor. Using a Lyapunov function, the domain of attraction of the control law obtained with the quotient method is proved to be larger than the domain of attraction of a control law obtained using feedback linearization

Posture Dependent Vibration Resistance of Serial Robot Manipulators to Applied Oscillating Loads

There are several advantages to replacing CNC machinery with robotic machine tools and as such robotic machining is emerging into the manufacturing and metal cutting industry. There remain several disadvantages to using robots over CNC stations primarily due to flexibility in robotic manipulators, which severely reduces accuracy when operating under high machining forces. This flexibility is dependent on configuration and thus the configuration can be optimised through posture selection to minimise deflection. In previous work little has been done to account for operating frequency and the additional complications that can arise from frequency dependent responses of robotic machine tools. A Fanuc S-360 manipulator was used to experimentally investigate the benefits of including frequency compensation in posture selection. The robot dynamics first had to be identified and experimental modal analysis was selected due the inherent dependency on frequency characteristics. Specifically, a circle fit operation identified modal parameters and a least squares optimisation generated dynamic parameters for a spatial model. A rigid-link flexible-joint model was selected and a pseudo-joint was used to create an additional DOF to accommodate link flexibility. Posture optimisation was performed using a gradient-descent algorithm that used several starting points to identify a global minimum. The results showed that a subset of modal data that excluded the mode shape vectors could be used to create a model to predict the manipulator vibration response. It was also found that the receptance variation of the manipulator with configuration was insufficient to verify the optimisation throughout the entire selected workspace; however the model was shown to be useful in regions containing multiple peaks where the modelled dynamics were dominant over the highly volatile measured data. Simulations were performed on a redundant planar manipulator to overcome the lack of receptance variation found in the Fanuc manipulator. These simulations showed that there were two mechanisms driving the optimisation; overall amplitude reduction and frequency specific amplitude reduction. Using a stiffness posture measure for comparison, the results of the frequency specific reduction could be separated and were found to be particularly beneficial when operating close to resonant frequencies

Modular Hopping and Running via Parallel Composition

Though multi-functional robot hardware has been created, the complexity in its functionality has been constrained by a lack of algorithms that appropriately manage flexible and autonomous reconfiguration of interconnections to physical and behavioral components. Raibert pioneered a paradigm for the synthesis of planar hopping using a composition of ``parts\u27\u27: controlled vertical hopping, controlled forward speed, and controlled body attitude. Such reduced degree-of-freedom compositions also seem to appear in running animals across several orders of magnitude of scale. Dynamical systems theory can offer a formal representation of such reductions in terms of ``anchored templates,\u27\u27 respecting which Raibert\u27s empirical synthesis (and the animals\u27 empirical performance) can be posed as a parallel composition. However, the orthodox notion (attracting invariant submanifold with restriction dynamics conjugate to a template system) has only been formally synthesized in a few isolated instances in engineering (juggling, brachiating, hexapedal running robots, etc.) and formally observed in biology only in similarly limited contexts. In order to bring Raibert\u27s 1980\u27s work into the 21st century and out of the laboratory, we design a new family of one-, two-, and four-legged robots with high power density, transparency, and control bandwidth. On these platforms, we demonstrate a growing collection of $\{$body, behavior$\}$ pairs that successfully embody dynamical running / hopping ``gaits\u27\u27 specified using compositions of a few templates, with few parameters and a great deal of empirical robustness. We aim for and report substantial advances toward a formal notion of parallel composition---embodied behaviors that are correct by design even in the presence of nefarious coupling and perturbation---using a new analytical tool (hybrid dynamical averaging). With ideas of verifiable behavioral modularity and a firm understanding of the hardware tools required to implement them, we are closer to identifying the components required to flexibly program the exchange of work between machines and their environment. Knowing how to combine and sequence stable basins to solve arbitrarily complex tasks will result in improved foundations for robotics as it goes from ad-hoc practice to science (with predictive theories) in the next few decades

Nonlinear Dynamics Analysis and Control of Space Vehicles with Flexible Structures

Space vehicles that implement hardware such as antennas, solar panels, and other extended appendages necessary for their respective missions must consider the nonlinear rotational and vibrational dynamics of these flexible structures. Formulation and analysis of these flexible structures must account for the rigid-flexible coupling present in the system dynamics for stability analysis and control design. The system model is represented by a flexible appendage attached to a central rigid body, where the flexible appendage is modeled as a cantilevered Euler-Bernoulli beam. Discretization techniques, such as the assumed modes method and the finite element method, are used to model the coupled dynamics by transforming the partial differential equations of motion into a finite set of differential equations. State feedback control laws are designed to achieve stability and desired motion in the presence of rigid-flexible coupling. An optimal control law in the form of a linear quadratic regulator is presented and compared with a Lyapunov-based control law that guarantees asymptotic stability. Conventional and adaptive sliding mode control laws are also presented to account for any uncertainties in the linearized system model. Full-order and reduced-order observers are included in the control system to account for lack of velocity state measurements that are generally unavailable in real world applications

Control Engineering

Control means a speci?c action to reach the desired behavior of a system. In the control of industrial processes generally technological processes, are considered, but control is highly required to keep any physical, chemical, biological, communication, economic, or social process functioning in a desired manner

Proceedings of the NASA Conference on Space Telerobotics, volume 2

These proceedings contain papers presented at the NASA Conference on Space Telerobotics held in Pasadena, January 31 to February 2, 1989. The theme of the Conference was man-machine collaboration in space. The Conference provided a forum for researchers and engineers to exchange ideas on the research and development required for application of telerobotics technology to the space systems planned for the 1990s and beyond. The Conference: (1) provided a view of current NASA telerobotic research and development; (2) stimulated technical exchange on man-machine systems, manipulator control, machine sensing, machine intelligence, concurrent computation, and system architectures; and (3) identified important unsolved problems of current interest which can be dealt with by future research

Systems and control : 21th Benelux meeting, 2002, March 19-21, Veldhoven, The Netherlands

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