This paper aims at computing feasible control strategies and the corresponding feasible state trajectories to drive an autonomous rear-axle bicycle robot from a given initial state to a final state such that the total running cost is minimized. Pontryagin’s Minimum Principle is applied and derives the optimality conditions from which the feasible control functions, expressed as functions of state and costate variables, are substituted into the combined state-costate system to obtain a new free-control state-costate nonlinear system of ordinary differential equations. A computer program was written in Scilab to solve the combined state-costate system and obtain the feasible state functions, the feasible costate functions and the feasible control functions. Associated Computational Simulations were provided to show the effectiveness and the reliability of the approach.

This paper aims at computing feasible control strategies and the corresponding feasible state trajectories to drive an autonomous rear-axle bicycle robot from a given initial state to a final state such that the total running cost is minimized. Pontryagin’s Minimum Principle is applied and derives the optimality conditions from which the feasible control functions, expressed as functions of state and costate variables, are substituted into the combined state-costate system to obtain a new free-control state-costate nonlinear system of ordinary differential equations. A computer program was written in Scilab to solve the combined state-costate system and obtain the feasible state functions, the feasible costate functions and the feasible control functions. Associated Computational Simulations were provided to show the effectiveness and the reliability of the approach.

This paper develops a methodology to control the navigation of an autonomous ship robot from an initial state to a final. To solve the problem the following approach is used: The ship robot system is modelled as a control system of six ordinary differential equations involving six state variables and three control variables. After having computed the system Hamiltonian, the feasible controls for optimality are derived from the normal equations of optimality as functions of the state and costate variables. Such controls are substituted into the state and the costate equations and give a combined control-free state-costate system of ordinary differential equations which is solved numerically by using a developed Matlab computer program. Associated computational simulations are designed and provided to show the reliability of the approach.

This paper develops feasible control strategies and associated system responses to bring an autonomous front-axle bicycle robot from specified initial conditions to final conditions such that a specific performance index is minimized. To solve the problem, the following approach is used: The feasible controls derived from the normal equations of optimality are substituted into the state and the costate systems and form a combined control-free state-costate system which is vectorized to enable and ease the application of a numerical method. A computer program written in Matlab computer programming language, codes a fourth-order Runge-Kutta numerical method and then solve the combined state-costate system of ordinary differential equations. The obtained results are the feasible bicycle robot trajectory, the feasible state functions, the feasible costate functions and the feasible control functions. Associated Computational Simulations are designed and provided to persuade on the effectiveness and the reliability of the approach.