Optimal trajectory control for rotary steerable systems

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.

What is claimed: 
     
         1 . A method for directional drilling, comprising:
 defining a cost function that includes at least one penalty condition associated with a control input;   detecting, via a controller of a drilling tool, a current position of the drilling tool and a reference position of a predetermined wellbore path;   determining, via the controller, an optimal trajectory for a curved path based on the cost function, the optimal trajectory originates from the current position and substantially intersects the reference position; and   instructing, via the controller, the drilling tool to generate a wellbore path based on the optimal trajectory.   
     
     
         2 . The method of  claim 1 , wherein the at least one penalty condition reduces at least one of a trajectory error, a target error, and a control effort. 
     
     
         3 . The method of  claim 1 , wherein determining the optimal trajectory further comprises:
 selecting a value for the at least one penalty condition; and minimizing the cost function based on the at least one penalty condition.   
     
     
         4 . The method of  claim 1 , further comprising:
 updating the optimal trajectory based on a change in at least one of a position or an attitude of the drilling tool.   
     
     
         5 . The method of  claim 1 , wherein the reference position includes a waypoint substantially proximate a predetermined wellbore path. 
     
     
         6 . The method of  claim 1 , further comprising:
 tracking, via the controller, the current position of the directional drilling tool based on an inclination, an azimuth, and a depth.   
     
     
         7 . The method of  claim 1 , wherein instructing the directional drilling tool to generate an updated path further comprises:
 providing an input vector to one of a force controller or a bending controller of the directional drilling tool; and   radially moving one or more pads or changing an eccentricity of a drill shaft based on the input vector.   
     
     
         8 . The method of  claim 1 , wherein the cost function comprises a finite-horizon linear quadratic tracker logic. 
     
     
         9 . A system comprising:
 a directional drilling tool disposed in a wellbore;   at least one processor in communication with the directional drilling tool;   a non-transitory computer-readable storage medium configured to store instructions, the instructions, when executed by the at least one processor, cause the at least one processor to:   define a cost function that includes at least one penalty condition associated with a control input;   detect, via a controller of a drilling tool, a current position of the drilling tool and the reference position of a predetermined wellbore path;
 determine, via the controller, an optimal trajectory based on the cost function for a curved path that originates from the current position and substantially intersects the reference; and 
   instruct, via the controller, the drilling tool to generate a wellbore path based on the optimal trajectory.   
     
     
         10 . The system of  claim 9 , wherein the at least one penalty condition reduces at least one of a trajectory error, a target error, and a control effort. 
     
     
         11 . The system of  claim 9 , wherein the instructions, when executed by the at least one processor to determine the optimal trajectory, further cause the processor to:
 select a value for at least one penalty condition; and   minimize the cost function based on the at least one penalty condition.   
     
     
         12 . The system of  claim 9 , wherein the value of the at least one penalty condition is selected to minimize the cost function. 
     
     
         13 . The system of  claim 9 , wherein the non-transitory computer-readable storage medium stores further instructions, which when executed by the at least one processor, cause the at least one processor to:
 update the optimal trajectory based on a change in at least one of a position or an attitude of the drilling tool.   
     
     
         14 . The system of  claim 9 , wherein the reference position includes a waypoint substantially proximate a predetermined wellbore path. 
     
     
         15 . The system of  claim 9 , wherein the instructions to instruct the drilling tool to generate the wellbore path further cause the drilling tool to move one or more pads or change an eccentricity of a drill shaft based on the optimal trajectory. 
     
     
         16 . The system of  claim 9 , wherein the cost function comprises a finite-horizon linear quadratic tracker logic. 
     
     
         17 . A tangible non-transitory computer-readable storage medium having instructions stored thereon which, when executed by one or more processors, cause the one or more processors to:
 define a cost function that includes at least one penalty condition associated with a control input;   detect, via a controller of a drilling tool, a current position of the drilling tool and a the reference position of a predetermined wellbore path;   determine, via the controller, an optimal trajectory based on the cost function for a curved path that originates from the current position and substantially intersects the reference; and   instruct, via the controller, the drilling tool to generate a wellbore path based on the optimal trajectory.   
     
     
         18 . The tangible non-transitory computer-readable storage medium of  claim 17 , wherein the at least one penalty condition reduces at least one of a trajectory error, a target error, and a control effort. 
     
     
         19 . The tangible non-transitory computer-readable storage medium of  claim 17 , wherein the instructions, when executed by the one or more processors to determine the optimal trajectory, further causes the one or more processors to:
 select a value for the at least one penalty condition; and   minimize the cost function based on the at least one penalty condition.   
     
     
         20 . The tangible non-transitory computer-readable storage medium of  claim 17 , wherein the reference position includes a waypoint substantially proximate a predetermined wellbore path, and wherein the instructions, when executed by the processor to instruct the drilling tool to generate the wellbore path further cause the drilling tool to radially move one or more pads or change an eccentricity of a drill shaft based on the optimal trajectory.