Numerically controlled method

A method for controlling the movement of an object along a predetermined locus in space by controlling respective machine control axes, the method comprising:

• approximating said locus by defining a spatial polynomial in a work space, said spatial polynomial having a coefficient λ;
• obtaining said parameter λ as a function of time t by assuming that a length ΔLi of one of the line elements of a curved line defined by said spatial polynomial is equal to a movement distance of said object over a time Δti on the basis of a predetermined speed function F(t), which is a function of time t, by dividing said parameter λ by sequences of numbers O=λ0<λ1<λ2<λ3< . . . <λi< . . . <λn=1;
• converting the spatial polynomial into a time parameter polynomial by substituting λ=α(t) into said spatial polynomial and converting said parameter λ into said function of time parameter t;
• producing a position command, a velocity command and an acceleration command from said time parameter polynomial;
• converting and delivering said produced position command, said velocity command and said acceleration command to said respective control axes in said joint space;
• producing control commands for said respective control axes from said position command, said velocity command, and said acceleration command on the basis of said time parameter polynomial;
• and
• moving said object to be controlled along said locus, while controlling said respective control axes in said space on the basis of said control commands.

A method for controlling the movement of an object in space, the method comprising:

• defining a predetermined locus in space for movement of the object;
• approximating said locus by defining a spatial polynomial in a work space, said spatial polynomial having a coefficient λ;
• relating the coefficient λ to time by assuming that a length ΔLi of one of the line elements of a curved line defined by said spatial polynomial is equal to a movement distance of said object over a time Δti, on the basis of a predetermined speed function F(t) which is a function of time t, by dividing said parameter λ by sequences of numbers O=λ0<λ1<λ2<λ3< . . . <λi< . . . <λn=1;
• converting the spatial polynomial into a time parameter polynomial by substituting λ=α(t) into said spatial polynomial and substituting said parameter λ into said function of time parameter t;
• providing a control command from said spatial polynomial, comprising a position command, a velocity command and an acceleration command to said respective control axes in said joint space;
• moving said object to be controlled along said locus on the basis of said control command.