Abstract: A method for directional drilling including defining, by a sliding mode controller, a sliding hypersurface for reducing a trajectory error in one or more error dimensions; determining a current trajectory error between a current trajectory of a directional drilling tool and a reference trajectory for a curved path, the current trajectory error corresponding to a current error position in the one or more error dimensions; calculating a sliding mode vector originating from the current error position and substantially conforming to the sliding hypersurface in the one or more error dimensions; determining a feedback control input for the directional drilling tool based on the sliding mode vector; instructing the directional drilling tool to generate a wellbore path according to the feedback control input; and updating the current trajectory error based on either a change in position or a change in attitude of the directional drilling tool.

Abstract: The disclosed embodiments include systems and methods to improve down-hole drilling. In one embodiment, a method to improve downhole drilling includes receiving a well plan, where the well plan is indicative of a well path to form a borehole of a hydrocarbon well is provided. The method also includes receiving measurements indicative of a previously-drilled section of the borehole. The method further includes generating, based on the measurements, a trajectory of the borehole, where the trajectory is a function of a depth. The method further includes providing the trajectory of the borehole to a Model Predictive Controller. The method further includes steering a tool towards the well path based on an output of the Model Predictive Controller.

Abstract: One or more wellbore trajectories and respective control inputs are determined which meet a wellbore trajectory model, a constraint, and a wellbore length. A wellbore trajectory and respective control input from the one or more wellbore trajectories and respective control inputs are then identified which minimize a cost function associated with the performance objective. The control input associated with this wellbore trajectory are output to a drilling system for drilling a wellbore.

Abstract: Techniques for estimating a current inclination and azimuth of a drill bit of a wellbore drilling system are described. The estimates for the current inclination and azimuth are generated using measurements obtained for one or more parameters associated with the drilling process performed by the drill bit and taken over a range of the wellbore falling within a sliding window having a predefined distance D extending along the wellbore.

Abstract: One or more sensors are positioned downhole in a wellbore of a geological formation. One or more survey directional measurements associated with the wellbore are performed and one or more continuous directional measurements associated with the wellbore are performed. A wellbore trajectory model projects a trajectory of the wellbore to respective measured depths where at least one of the one or more survey directional measurements and one or more continuous directional measurements were performed to predict one or more directional measurements of the wellbore at the respective measured depths. One or more errors are determined based on the predicted one or more directional measurements, the one or more survey directional measurements, and the one or more continuous directional measurements. The wellbore trajectory model is calibrated based on the one or more errors.

Abstract: One or more wellbore trajectories and respective control inputs are determined which meet a wellbore trajectory model, a constraint, and a wellbore length. A wellbore trajectory and respective control input from the one or more wellbore trajectories and respective control inputs are then identified which minimize a cost function associated with the performance objective. The control input associated with this wellbore trajectory are output to a drilling system for drilling a wellbore.

Abstract: A method of drilling tendency estimation including receiving, at a processor, one or more directional sensor measurements from a drilling tool disposed on a drill string, processing, at the processor, the one or more directional sensor measurements to determine an actual wellbore trajectory over a defined interval, and identifying, at the processor, a set of directional disturbance parameters by optimization of the actual trajectory of the drilling tool, steering inputs, and/or a set of pre-defined directional disturbance parameters of the drilling tool.

Abstract: A drilling optimization method including perturbing one or more drilling control parameters with a periodic or a stochastic signal during a drilling process, estimating at least one drilling performance measure to optimize the drilling process based on the perturbed one or more drilling control parameters, perturbing the at least one drilling performance measure with a periodic or a stochastic perturbation source through demodulation, determine a next best estimate of the one or more drilling control parameters to optimize the at least one drilling performance measure, perturbing the next best estimate by a periodic or a stochastic perturbation source through modulation, and feeding the perturbation next best estimates of the one or more drilling control parameters back to the drilling process.

Abstract: A method for controlling directional drilling including defining a cost function that includes at least one penalty condition associated with a control input. A controller is provided with a current position of the drilling tool and a reference position of a predetermined wellbore path. The controller determines an optimal trajectory for a curved path based on the cost function and the current position and reference position. The optimal trajectory originates from the current position and substantially intersects the reference position. As a result, the controller instructs the drilling tool to generate a wellbore path based on the optimal trajectory.

Abstract: A method for directional drilling including defining, by a sliding mode controller, a sliding hypersurface for reducing a trajectory error in one or more error dimensions; determining a current trajectory error between a current trajectory of a directional drilling tool and a reference trajectory for a curved path, the current trajectory error corresponding to a current error position in the one or more error dimensions; calculating a sliding mode vector originating from the current error position and substantially conforming to the sliding hypersurface in the one or more error dimensions; determining a feedback control input for the directional drilling tool based on the sliding mode vector; instructing the directional drilling tool to generate a wellbore path according to the feedback control input; and updating the current trajectory error based on either a change in position or a change in attitude of the directional drilling tool.