Determining control inputs for drilling a wellbore trajectory in a geologic formation

A system comprising:

• a wellbore trajectory modeling system comprising a wellbore trajectory model associated with a drilling system;
• and
• a device to:
• receive a performance objective for drilling a wellbore in a geologic formation, the wellbore trajectory model, an indication of wellbore length, and a constraint associated with drilling the wellbore;
• determine whether one or more first wellbore trajectories and respective control inputs meets the wellbore trajectory model, the constraint, and the wellbore length;
• if the one or more first wellbore trajectories and respective control inputs meets the wellbore trajectory model, the constraint, and the wellbore length, then identify which wellbore trajectory and respective control input of the one or more first wellbore trajectories and respective control inputs minimizes a cost function associated with the performance objective;
• if the one or more first wellbore trajectories and respective control inputs does not meet the wellbore trajectory model, the constraint, and the wellbore length, then adjust the wellbore length;
• determine whether one or more second wellbore trajectories and respective control inputs meets the wellbore trajectory model, the constraint, and the adjusted wellbore length;
• if the one or more second wellbore trajectories and respective control inputs meets the wellbore trajectory model, the constraint, and the adjusted wellbore length, then identify which wellbore trajectory and respective control input of the one or more second wellbore trajectories and respective control inputs minimizes the cost function associated with the performance objective;
• and
• output the control inputs associated with the wellbore trajectory of the one or more first wellbore trajectories or the one or more second wellbore trajectories that minimizes the cost function.

One or more non-transitory machine-readable media comprising program code executable by a processor to perform the functions of:

• receiving a performance objective for drilling a wellbore in a geologic formation;
• a wellbore trajectory model, an indication of wellbore length, and a constraint associated with drilling the wellbore;
• determining whether one or more first wellbore trajectories and respective control inputs meets the wellbore trajectory model, the constraint, and the wellbore length;
• if the one or more first wellbore trajectories and respective control inputs meets the wellbore trajectory model, the constraint, and the wellbore length, then identifying which wellbore trajectory and respective control input of the one or more first wellbore trajectories and respective control inputs minimizes a cost function associated with the performance objective;
• if the one or more first wellbore trajectories and respective control inputs does not meet the wellbore trajectory model, the constraint, and the wellbore length, then adjusting the wellbore length;
• determining whether one or more second wellbore trajectories and respective control inputs meets the wellbore trajectory model, the constraint, and the adjusted wellbore length;
• if the one or more second wellbore trajectories and respective control inputs meets the wellbore trajectory model, the constraint, and the adjusted wellbore length;
• then identifying which wellbore trajectory and respective control input of the one or more second wellbore trajectories and respective control inputs minimizes the cost function associated with the performance objective;
• and
• outputting the control inputs associated with the wellbore trajectory of the one or more first wellbore trajectories or the one or more second wellbore trajectories that minimizes the cost function.