Creating custom motion profiles using 7th order Polynomials
Sysmac Library for advanced motion profile generation
Written by Toby Kilroy
Updated at March 24th, 2023
Introduction
In order to generate continuous position, velocity, acceleration and jerk profile motion movements, polynomials are a very handy mathematical function. Solving the constants for the terminal conditions (start and end position, start and end velocity, acceleration etc) allows the use of the polynomial to calculate intermediate command positions.
The motion instruction MC_SyncMoveAbsolute allows any calculated position to be synchronously sent to the servo drive, and is an extremely flexible way of controlling motion. This allows an axis to be controlled directly from the output of a mathematical function, such as a 5th or 7th order polynomial. Using this Function Block, in Sysmac we can create any motion profile we like using mathematical relationships and use this functionality to control kinematically linked axes such as robots.
In order to simplify this, a library has been created that allows the user to easily set the terminal conditions in order to solve the polynomial for the specific motion profile, and then cyclically execute in order to feed to the MC_SyncMoveAbsolute function block. Examples of advanced feeding applications are included in the manual.
Poly7TrajectoryLibrary is a library consisting of 1 Function Block and 1 Function that supports in the calculation and generation of 7th degree polynomial trajectories.
This library has been designed to implement smooth 7th order polynomial profiles that, later can be commanded to an Axis.
When a 7th degree polynomial is applied as position command we guarantee continuity in position, Velocity (that corresponds to the first derivative of the polynomial), Acceleration (that corresponds to the second derivative of the polynomial) and Jerk (that corresponds to the third derivative of the polynomial)
Info
This library was created by OMRON Europe and is supplied as is. Please ensure that you fully evaluate its performance and behavior before relying on it in your application.
A 7th degree polynomial curve has 8 degrees of freedom so, it can be defined by its:
- Initial position
- Final position
- Initial Velocity
- Final Velocity
- Initial Acceleration
- Final Acceleration
- Initial Jerk
- Final Jerk
And the TimeInitial and TimeFinal
This library is available for customers to use. Please refer to our Precautions and Terms and Conditions before using this library.
7th Order Polynomial Library.zip