Method and system for computing reference signals for machines with redundant positioning

A method for computing a reference trajectory to position a machine that includes a slow positioning subsystem and a fast positioning subsytem, comprising the steps of:

• generating a reference trajectory according to an ordered list of points;
• producing a slow subsystem reference trajectory by either filtering the reference trajectory or chosing a value of the reference trajectory;
• determining whether the reference trajectory violates feasibility constraints by checking a recursive feasibility condition and a persistent tracking condition to determine whether the reference trajectory and the reference trajectory for the slow subsystem violate the feasibility constraints, wherein the checking for the recursive feasibility condition is performed by a forward reachability test;
• and if true;
• slowing down the reference trajectory and repeating the generating and determining steps;
• and otherwise
• sending the slow subsystem reference trajectory to the slow positioning subsystem;
• and
• sending a combination of the slow subsystem reference trajectory and the reference trajectory to the fast substem, wherein the steps are performed in a processor.