Curvature-based feedback control techniques for directional drilling

Abstract

Systems, methods, and computer-readable media for directional drilling based on curvature-based feedback. In some examples, a drilling tool tracks a current position and a current attitude, determines a curvature value for a curved path that intersects the current position, tangent to the current attitude, and a curvilinear position on or substantially proximate a target wellbore path, tangent to a target attitude, generates a wellbore path based on the curvature value, and updates the current position or the current attitude based on at least one of a change in the current position or a change in the current attitude.

What is claimed is: 
     
         1 . A method for directional drilling, comprising:
 tracking a current position and a current attitude for a steerable drilling tool;   determining a curvature value for a curved path that intersects the current position, tangent to the current attitude, and a curvilinear position on or substantially proximate to a target wellbore path, tangent to a target attitude;   instructing the steerable drilling tool to generate a wellbore path based on the curvature value; and   updating the current position or the current attitude based on at least one of a change in the current position or a change in the current attitude.   
     
     
         2 . The method of  claim 1 , further comprising:
 defining a plurality of target waypoints to form the target wellbore path, wherein the curvilinear position corresponds to one of the plurality of target waypoints.   
     
     
         3 . The method of  claim 1 , wherein determining the curvature value for the curved path further comprises:
 determining a second curvature value for the curved path that intersects one or more derivative positions of the current position, tangent to one or more derivative angles of the current attitude.   
     
     
         4 . The method of  claim 1 , further comprising:
 updating the curvilinear position on or substantially proximate to the target wellbore path based on the change in the current position or the change in the current attitude.   
     
     
         5 . The method of  claim 1 , wherein determining the curvature value for the curved path further comprises:
 determining the curvature value for the curved path based on an Euler-Berrnoulli beam equation.   
     
     
         6 . The method of  claim 1 , wherein tracking the current position and the current attitude further comprises:
 receiving the current position and the current attitude from one or more sensors of the steerable drilling tool.   
     
     
         7 . The method of  claim 1 , further comprising:
 generating the curved path to intersect the current position, tangent to the current attitude, and intersect the curvilinear position on or substantially proximate to the target wellbore path, tangent to the target attitude.   
     
     
         8 . A directional drilling system comprising:
 one or more sensors that detect a position and an attitude for a steerable drilling tool;   a processor in communication with the one or more sensors and adapted to execute one or more processes; and   a memory configured to store a process executable by the processor, the process, when executed, is operable to:
 track a current position and a current attitude for the steerable drilling tool; 
 determine a curvature value for a curved path that intersects the current position, tangent to the current attitude, and a curvilinear position on or substantially proximate to a target wellbore path, tangent to a target attitude; 
 instruct the steerable drilling tool to generate a wellbore path based on the curvature value; and 
 update the current position or the current attitude based on at least one of a change in the current position or a change in the current attitude. 
   
     
     
         9 . The directional drilling system of  claim 8 , wherein the process, when executed by the processor, is further operable to:
 define a plurality of target waypoints to form the target wellbore path, wherein the curvilinear position corresponds to one of the plurality of target waypoints.   
     
     
         10 . The directional drilling system of  claim 8 , wherein the process to determine the curvature value for the curved path, when executed by the processor, is further operable to:
 determine a second curvature value for the curved path that intersects one or more derivative positions of the current position, tangent to one or more derivative angles of the current attitude.   
     
     
         11 . The directional drilling system of  claim 8 , wherein the process, when executed by the processor, is further operable to:
 update the curvilinear position on or substantially proximate to the target wellbore path based on the change in the current position or the change in the current attitude.   
     
     
         12 . The directional drilling system of  claim 8 , wherein the process, when executed by the processor, is further operable to:
 determine the curvature value for the curved path based on an Euler-Berrnoulli beam equation.   
     
     
         13 . The directional drilling system of  claim 8 , wherein the process to track the current position and the current attitude, when executed by the processor, is further operable to:
 receive the current position and the current attitude from one or more sensors of the steerable drilling tool.   
     
     
         14 . The directional drilling system of  claim 8 , wherein the process, when executed by the processor, is further operable to:
 generate the curved path to intersect the current position, tangent to the current attitude, and the curvilinear position on or substantially proximate to the target wellbore path, tangent to the target attitude.   
     
     
         15 . The directional drilling system of  claim 8 , wherein the wellbore path substantially conforms to the curved path. 
     
     
         16 . A tangible, non-transitory, computer-readable media having instructions encoded thereon, the instructions, when executed by a processor, operable to:
 track a current position and a current attitude for a steerable drilling tool;   determine a curvature value for a curved path that intersects the current position, tangent to the current attitude, and a curvilinear position on or substantially proximate to a target wellbore path, tangent to a target attitude;   instruct the steerable drilling tool to generate a wellbore path based on the curvature value; and   update the current position or the current attitude based on at least one of a change in the current position or a change in the current attitude.   
     
     
         17 . The tangible, non-transitory, computer-readable media of  claim 16 , wherein, the instructions, when executed by a processor, is further operable to:
 define a plurality of target waypoints to form the target wellbore path, wherein the curvilinear position corresponds to one of the plurality of target waypoints.   
     
     
         18 . The tangible, non-transitory, computer-readable media of  claim 16 , wherein, the instructions to determine the curvature value for the curved path, when executed by the processor, is further operable to:
 determine a second curvature value for the curved path that intersects one or more derivative positions of the current position, tangent to one or more derivative angles of the current attitude.   
     
     
         19 . The tangible, non-transitory, computer-readable media of  claim 16 , wherein, the instructions, when executed by a processor, is further operable to:
 update the curvilinear position on or substantially proximate to the target wellbore path based on the change in the current position or the change in the current attitude.   
     
     
         20 . The tangible, non-transitory, computer-readable media of  claim 16 , wherein, the instructions, when executed by a processor, is further operable to:
 determine the curvature value for the curved path based on an Euler-Berrnoulli beam equation.