Stabilization manipulator for cooperation in manipulating and moving drilling elements in a drilling rig; said stabilization manipulator comprising: • a linear guide adapted to be fixed to a drill floor comprised in the drilling rig; • a carriage, comprising a base and sliding blocks, adapted to slide along said linear guide to move at least between a position close to a well (M, H) and a position distant from said well (M, H); • a first arm, a first end of which is constrained to said base of the carriage, so that it can rotate about a horizontal axis; • a second arm, a first end of which is constrained to said base of the carriage, so that it can rotate about a horizontal axis; said second arm is separate from and independent of said first arm; a roller being constrained to the second end of said first arm, which is adapted to rotate about an axis substantially perpendicular to the extension of said first arm, changing position relative to said first arm; a roller being constrained to the second end of said second arm, which is adapted to rotate about an axis substantially perpendicular to the extension of said second arm, changing position relative to said second arm; said carriage comprising a rotation system adapted to cause said base to rotate about a vertical axis; said first arm has a greater longitudinal extension than said second arm; said stabilization manipulator being characterized in that said roller associated with said first arm and the roller associated with the second arm being substantially equal. said stabilization manipulator comprising: • a linear guide adapted to be fixed to a drill floor comprised in the drilling rig; • a carriage, comprising a base and sliding blocks, adapted to slide along said linear guide to move at least between a position close to a well (M, H) and a position distant from said well (M, H); • a first arm, a first end of which is constrained to said base of the carriage, so that it can rotate about a horizontal axis; • a second arm, a first end of which is constrained to said base of the carriage, so that it can rotate about a horizontal axis; • a linear guide adapted to be fixed to a drill floor comprised in the drilling rig; • a carriage, comprising a base and sliding blocks, adapted to slide along said linear guide to move at least between a position close to a well (M, H) and a position distant from said well (M, H); • a first arm, a first end of which is constrained to said base of the carriage, so that it can rotate about a horizontal axis; • a second arm, a first end of which is constrained to said base of the carriage, so that it can rotate about a horizontal axis; said second arm is separate from and independent of said first arm; a roller being constrained to the second end of said first arm, which is adapted to rotate about an axis substantially perpendicular to the extension of said first arm, changing position relative to said first arm; a roller being constrained to the second end of said second arm, which is adapted to rotate about an axis substantially perpendicular to the extension of said second arm, changing position relative to said second arm; said carriage comprising a rotation system adapted to cause said base to rotate about a vertical axis; said first arm has a greater longitudinal extension than said second arm; said stabilization manipulator being characterized in that said roller associated with said first arm and the roller associated with the second arm being substantially equal.