Online trajectory planning and filtering for robotic applications via B-spline smoothing filters

In this paper, a novel technique for online generating trajectories in the 3-D space is presented. The trajectory planner is based on cubic B-splines. However, while the definition of B-splines requires the solution of a global problem that involves the entire set of via-points to be interpolated/approximated, and therefore it is not suitable for online implementation, the proposed generator is able to approximate spline functions with the prescribed precision on the basis of local computations, which only need the knowledge of a very limited number of via-points. FIR filters are the foundation of this result. As a matter of fact the planner is composed by a first FIR filter for the computation of the control points from the sequence of desired via-points, followed by a chain of moving average filters. Therefore, the generator combines the characteristics of B-spline trajectories (smoothness and minimum curvature) and those of FIR filters (simple structure and computational efficiency). Moreover, besides standard cubic curves, the so-called smoothing B-splines have been considered for online trajectory generation. This allows to find a tradeoff between the possibility of exactly crossing the given via-points and the smoothness of the resulting trajectory. A simple teleoperation task with a Puma 560 industrial manipulator has been arranged for experimentally validating the proposed method.