Stabilization manipulator for cooperation in manipulating and moving drilling elements (P) 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. <EOS>