Apparatus for recovering twist in cable shape

An apparatus comprising:

• a cable, said cable comprising a length;
• at least three curvature sensors located at at least three respective curvature sensor positions along the length of said cable and generating respective curvature values at the at least three respective curvature sensor positions;
• at least one position sensor along the length of said cable and generating at least one positional value;
• and
• a processor receiving the respective curvature values from said at least three curvature sensors and receiving the respective measured positional value from said at least one position sensor, said processor recovering at least three respective angles of twist at the at least three respective curvature sensor positions at least based on the respective curvature values and the at least one respective measured positional value,
• wherein said cable comprises a cable shape,
• wherein said processor recovering the at least three angle of twists at the respective curvature sensor positions by:
• generating a naïve estimate of the cable shape based on the respective curvature values and free of the at least one respective measured positional value;
• generating expected positional values based on the naïve estimate of the cable shape;
• correcting the naïve estimate of the cable shape by minimizing an error between the expected positional values based on the naïve estimate of the cable shape and the at least one respective measured positional value.