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.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.