Abstract
This article proposes a new optimization algorithm that assures the minimum possible duration of generalized S-curve trajectories compliant with kinematic limitations and capable of suppressing residual vibrations when tracked by a resonant plant. Thanks to the possibility of generating such kind of trajectories with a chain of filters, called smoothers, each one characterized by a single parameter, i.e., the duration <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$T_i$</tex-math></inline-formula> of its impulse response, the optimization process aims at minimizing the order of the trajectory, and accordingly the number of smoothers in the chain, and leads to rest-to-rest trajectories that, under the given specifications, cannot be made shorter in time. Therefore, the structure of the trajectory is not predetermined but is the outcome of the proposed algorithm together with the optimal parameters defining it. The effectiveness of the proposed approach is proven by applying the designed trajectories to an experimental setup based on a flexible link.
Highlights
The development of motion control systems able to plan fast and accurate trajectories for electromechanical systems, including automatic machines and robots, is a key factor for increasing productivity in many industrial fields
An interesting attempt to mix the compliance with bounds on velocity and acceleration and an explicit frequency constraint aiming at suppressing a residual vibration can be found in [15], [16], where the tuning of the S-curve parameters in the Laplace domain is proposed, while the usual approach for vibration suppression is based on filtering techniques of a reference trajectory already compliant with bounds on velocity, acceleration, etc
In [23], an algorithm that minimizes the duration of the trajectory under kinematic constraints is given, but the integration with the frequency constraints does not lead to the global optimum since the degrees of freedom, that characterize the problem, have been not fully exploited
Summary
The development of motion control systems able to plan fast and accurate trajectories for electromechanical systems, including automatic machines and robots, is a key factor for increasing productivity in many industrial fields. Interesting enough, with this work a new trajectory design and optimization paradigm is proposed: while the most of planners available in the literature have a fixed structure, e.g. based on a parametric expression of the trajectory, and the free parameters are chosen using a nonlinear optimization procedure to comply with the given constraints [25], [26], according to a philosophy that can be defined top-down, in our approach the perspective can be defined bottom-up since each specification is translated in an element of the trajectory planner and all these basic bricks are combined together in an optimal manner The result of this design method is the shortest S-shaped trajectory compliant with all the specifications.
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