Trajectory planning for multi-input-multi-output linear systems subject to nonlinear inequality constraints on the output

Abstract

Trajectory planning is an imperative aspect in
aviation, robotic manipulation, navigation of mobile robots,
and unmanned arial and underwater vehicles. A popular
approach to trajectory planning is to formulate it in the setting
of a constrained optimization problem. In this approach the cost
of control is minimized subject to path constraints specified
by nonlinear inequality constraints on the output trajectory at
predefined time instances. This problem was first solved for the
case of single-input-multi-output linear systems. In the present
study the results have been extended to the more general multiinput-multi-output linear systems. The convex nature of the
resulting optimization problem ensures a unique solution. A
methodology based on the Lagrange multiplier technique is used
for the computation of the unique solution. An explicit solution
for the optimal output trajectory as well as the controller that
will ensure the real time generation of the solution are derived
in terms of the solution to the nonlinear equations. An example
ubiquitous in the field of nonholonomic mobile robots is used
to illustrate the results derived.