Method for processing the parameters of a spatiotemporal trajectory

Method for processing parameters of a spatiotemporal trajectory (1) of movement of a moving body (2) along at least one axis (X, Y), this trajectory (1) comprising at east one starting point (A) and being made up of at least one segment (AB, BC, CD, . . . ), each segment being defined by parameters which determine at least

• the coordinates of its point of origin (A, B, C, . . . ) relative to a reference point (0) situated on each axis (X, Y), the length, as well as the shape and the geometric tolerance, accepted on the path defined by this segment,
• the value of the curvilinear speed of movement of the moving body (2) which is desired over said segment, this method being characterized in that:
• the data of the trajectory (1), i.e., the parameters of each segment it includes, are collected, and
• the curvilinear abscissa (s) of the trajectory (1) is calculated at least for the point of origin (A, B, C, . . . ) of each segment comprised by this trajectory (1), and
• the result of the calculation of the curvilinear abscissa (s) of each point of origin of a segment is associated with at least one item of information relative to the desired speed (V) of movement of the moving body (2) over the segment in question, this in such a way that it is possible, on the one hand, to establish a graph representing the desired speed (V) in terms of the total path traveled from the starting point (A) of the trajectory (1) and, on the other hand, to detect any instantaneous jump in the desired speed (V) which is situated at least at the level of the point of origin of a segment,
• at least one predetermined law of acceleration (a(t)) is chosen which is so formulated that the application of this law of acceleration (a(t)) to any instantaneous jump in the desired speed (V) results in gradually getting up speed beyond the point of origin of the segment in question, capable of extending over several segments, or even beyond the trajectory,
• said predetermined law of acceleration (a(t)) is applied to every instantaneous positive jump in speed present in the graph of the desired speed (V) in terms of the curvilinear abscissa (s), this in such a way as to associate with each positive jump in the desired speed (V) an expression of the speed in terms of the curvilinear abscissa, then these data are stored,
• the expressions of speed obtained are combined so as to obtain, for the whole trajectory (1), a single expression giving the final speed in terms of the curvilinear abscissa (s),
• successive intervals of time of predetermined value are defined and, for each of the successive intervals of time, the curvilinear path traveled from the starting point (A) of the trajectory is calculated,
• for each of the intervals of time, the position of the moving body (2) along each axis (X, Y) is extracted in terms of the curvilinear path traveled,
• the positions of said moving body (2) along each axis (X, Y) are stored, as a function of the time elapsed from the starting point of the trajectory (1),
• these data are utilized to control the movement of said moving body (2) on a machine comprising this moving body (2).