Trajectory Toolbox

A Matlab/Simulink Tool for the Automatic Design of Time-Optimal Trajectory Generators under Kinematic and Frequency Constraints

The toolbox is composed by a Simulink model library containing the (two) basic elements for the design of FIR (Finite Impulse Response) filters based trajectory generators in both the continuous- and the discrete-time domain and a Matlab function which automatically builds the block-scheme of the generator providing the minimum-time polynomial multi-segment trajectory compliant with the given kinematic constraints (max velocity, acceleration, jerk, etc.) and the angular frequencies to be cancelled for complete vibration suppression in resonant plants.

A cascade of FIR (Finite Impulse Response) filters can be used for planning minimum-
time multi-segment polynomial trajectories, i.e. trajectories composed of several polynomial segments,
under constraints of velocity, acceleration, etc. The same filters can be used for shaping the frequency
content of the trajectory with the purpose of suppressing residual vibrations at specific frequencies. To
this end, it is necessary to select the (minimum) number of filters of the chain which are necessary to
impose the desired specifications and compute the characteristic parameter of each filter according to the algorithms reported in Biagiotti, Luigi, and Claudio Melchiorri. “Trajectory Generation via {FIR} Filters: A Procedure for Time-Optimization under Kinematic and Frequency Constraints.” Control Engineering Practice, vol. 87, Elsevier {BV}, June 2019, pp. 43–58. The function BuildTrajectoryGenerator(KinematicConstraints,AngularFrequencies,SamplingPeriod) contained in the toolbox performs this operation on the basis of the given kinematic constraints and of the angular frequencies of the trajectory spectrum to be cancelled. Then, the function builds the Simulink model of the trajectory planner that, along the position trajectory, provides its derivatives up to the order n (being n the order of the trajectory) If the sampling period is specified the trajectory planner is built as a discrete-time filter. Otherwise, a continuous-time model is provided.
See the help of the function it BuildTrajectoryGenerator for additional information about its usage and
some examples.