Abstract
This research paper deals with computation of Feasible command strategies to guide a
four-wheeled autonomous vehicle to move from a specified initial state to an eventual final
state while minimizing a running cost. The problem is solved as follows: The vehicle is
mathematically modeled as a non-linear system of seven ODEs with seven state and four
command variables. The commands represent the controls. A costate system of seven
ODEs is generated. The control’s Feasibility conditions generate four constrained Feasible
command strategies and each of them is defined as a function of states and costates. The
state system and the costate system are rewritten accordingly. Such systems are then joined
to give a nonlinear system of fourteen ODEs and an initial value problem. The results are
the Feasible system response involving the robot path in the horizontal XY plane and the
robot velocity, the costate functions, the command functions. Computational Simulations
are developed and presented to summarize the results and to convince the readers on the
accuracy.