A Splines–Based Control Method for Robot Manipulators

Abstract

SUMMARYIn this paper, a new splines–based control method for robot manipulators is presented and discussed. The above method can be effectively used for path planning and control of rigid and flexible robots. The computational simplicity of the proposed algorithm, together with its flexibility and its high–level intelligence built in, can be considered as promising tools for achieving the goals of modem robot manipulator design.

Robust Residual Vibration Suppression for Linear Time Invariant Systems by Digital Filtering of the Guidance Function

“…Several methods are available for the design of FIR "lters [18], such as the windowing method, the least-squares method, the Parks}McClellan method (equiripple "lters) and the constrained least-squares method. Since IIR "lters can allow also the presence of non-zero coe$cients (a L , n"1, 2 ,M) in the denominator in equation (9), past terms of the conditioned guidance function u(t) can also appear in equation (6), in contrast to the classical &impulse conditioning' method [13}15], which allows only the presence of past terms of the original guidance function g(t).…”

“…Approaches generalising the method proposed by Smith, include the introduction of multi-switch Bang}Bang inputs [10], or the convolution of the desired guidance function with a series of impulses [11]. Other methods approximate the guidance function by a series of typical mathematical functions such as splines [4,6], sinusoids [12], ramped sinusoids [7], or polynomials [8]. Closed form solutions are also available, using linear quadratic optimal (LQ) techniques [8].…”

“…The splines method proposed in [6], is further extended in [4] with satisfactory results, covering also several possible &alternative dynamic models' of the system, which result from variations of its nominal parameters. However, the application of this method is limited only to systems where the desired guidance function can be approximated by splines, while the choice of the &alternative models' to be used in the design is signi"cantly based on heuristic criteria.…”

Guidance Preconditioning by an Impulse Sequence for Robust Residual Vibration Suppression

“…Residual vibration suppression is quite important in a broad range of mechanical engineering applications: space structures [5], cranes, textile machines, hydraulic machine tools [7], robot manipulators [1,6,8], computer disk heads [4], etc. The traditional approaches to minimize the effect of residual vibrations are focused either to a significant increase of the structure stiffness -resulting thus to bulky structures -or to the application of complex closed loop control methods, which in turn result to complex and failure liable motion systems.…”

“…Approaches generalizing the method proposed by Smith, include the introduction of multi-switch Bang-Bang inputs [12], or the convolution of the desired guidance function with a series of impulses [13][14][15][16]. Other methods approximate the guidance function by a series of typical mathematical functions -such as splines [1,7,8], sinusoids [2], ramped sinusoids [10], or polynomials [4]. Closed form solutions are also available, using linear quadratic (LQ) optimal techniques [4].…”