From motion planning through waypoints to open-loop trajectory tracking algorithm

This paper addresses the trajectory tracking problem which will be regarded as an open-loop planning problem, in contrast to various feedback motion control methods. The trajectory tracking problem is formulated as the constrained motion planning problem, whereas constraints reflect the distance in the task space between the system output and the desired trajectory. The problem consists in defining a control function that drives the system output through selected points in the task space at given time instants, and simultaneously maintains the trajectory tracking constraints. The original constrained motion planning problem is replaced by an unconstrained one addressed in an extended control system representation, and solved with the task priority version of the Lifted Newton method. Solutions of example trajectory tracking problems for the kinematic car type platform illustrate the theoretical concepts.