Local issues in trajectory planning

Abstract

The trajectory planning problem for MIMO linear systems is considered in this work. The problem has received wide interest due to its relevance in aviation, robotics, and biomechanics to name a few. It is naturally formulated in the settingof a constrained ptimization problem where the cost of control is minimized subject to the path constraints related to the time history. The convex nature of the resulting optimization problem enables the use of the method of Lagrange multipliers to solve it. Many authors have considered this problem. However, their work is only with respect to SISO linear systems, where we consider the more general and harder MIMO case. An example is provided to illustrate the results derived.