Abstract
In this brief, a novel filter for online trajectory generation is presented. The filter can be categorized as an input smoother since it acts on the input signal by increasing its continuity level. When fed with simple signals, as, e.g., a step input, it behaves like a trajectory generator that produces harmonic motions. Moreover, it can be combined with other filters, and in particular, with smoothers having a rectangular impulse response, in order to generate (online) more complex trajectories compliant with several kinematic constraints. On the other hand, being a filter, it possesses the capability of shaping the frequency spectrum of the output signal. This possibility can be profitably exploited to suppress residual vibration by imposing that the zeros of the filter cancel the oscillatory dynamics of the plant. For this purpose, the standard harmonic filter has been generalized in order to consider not only the natural frequency but also the damping coefficient of the plant. In this manner, the so-called “damped harmonic filter” and the related “damped harmonic trajectory” have been defined. By means of theoretical considerations, supported by experimental tests, the novel approach has been compared with the existing methods, and the advantages of its use have been proved.
Highlights
T HE growing interest for planning trajectories online has led to the development of a number of filters able to produce motion profiles with the desired degree of smoothness starting from basic reference signals to set the desired final position, such as step functions
We start from the results presented in the conference papers [15], [16], concerning the generation of trajectories by means of dynamic filters with trigonometric velocity, acceleration, or jerk profiles
The damped harmonic smoother Sσ,1(s) and the cascade of two exponential smoothers Mσ,1(s)Mσ,2(s) lead to similar performances, with a slight superiority of Sσ,1(s), which is characterized by a lower velocity and a smaller tracking error (q MAX = 6.0902 mm). The aim of this brief is to prove advantages and disadvantages of trajectories based on the trigonometric functions, starting from the initial consideration that this kind of motion profiles can be obtained by a cascade of smoothers with the rectangular and sinusoidal impulse response
Summary
T HE growing interest for planning trajectories online has led to the development of a number of filters able to produce motion profiles with the desired degree of smoothness starting from basic reference signals to set the desired final position, such as step functions For this purpose, many strategies have been proposed, including filtering and smoothing techniques by means of various kind of filters, ranging from finite impulse response filters [1]–[3] to inverse dynamics of the plant, or feedback control of a chain of integrators with bounds on velocity, acceleration, jerk, and so on, as, e.g., in [4]–[7]. For this reason, a deep analysis of the performance achievable in vibrations suppression with this type of filter has been carried out, along with a comparison with some well-settled techniques available in the literature that involve the same motion duration.
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