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

Trajectory planning is an imperative aspect in aviation, robotic manipulation, navigation of mobile robots, and unmanned anal 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 multi-input-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.