Parallel cable robot comprising: - a mobile tool (10, 12) intended to be moved along a path, called the target path, in a three-dimensional working environment, - a plurality of cables (21, 22, 23) each having a first end (21a; 22a; 23a) adapted to be able to be connected to the mobile tool (10, 12) and a second end (21b; 22b; 23b) adapted to be able to be connected to an anchor point of a fixed structure arranged in the vicinity of said working environment, and comprising at least one cable, said suspended cable, configured to be able to be arranged so that said second end of the cable is higher than said first end of the cable, and at least one cable, said stay cable (22; 23), configured to be able to be arranged so that said second end of the cable (22b; 23b) is lower than said first end of the cable (22a; 23a), during movement of the mobile tool following at least a portion of said target path, - a plurality of actuators configured to be able to adjust on command the length of the cables (21, 22, 23) extending between the mobile tool (10, 12) and said anchor points, - a control unit configured to be able to provide said actuators with cable length control instructions which allow the movement of the mobile tool (10, 12) in the working environment along said target path, characterized in that said control unit is configured to release any cable, said annoying cable, which intersects with at least one volume of at least one element of the working environment during the movement of the mobile tool (10, 12) along an interval of said target trajectory, said collision interval, by supplying the actuator of this cable with a cable length control instruction greater than the theoretical cable length for this interfering cable during the movement of the mobile tool over this collision interval. - a mobile tool (10, 12) intended to be moved along a path, called the target path, in a three-dimensional working environment, - a plurality of cables (21, 22, 23) each having a first end (21a; 22a; 23a) adapted to be able to be connected to the mobile tool (10, 12) and a second end (21b; 22b; 23b) adapted to be able to be connected to an anchor point of a fixed structure arranged in the vicinity of said working environment, and comprising at least one cable, said suspended cable, configured to be able to be arranged so that said second end of the cable is higher than said first end of the cable, and at least one cable, said stay cable (22; 23), configured to be able to be arranged so that said second end of the cable (22b; 23b) is lower than said first end of the cable (22a; 23a), during movement of the mobile tool following at least a portion of said target path, - a plurality of actuators configured to be able to adjust on command the length of the cables (21, 22, 23) extending between the mobile tool (10, 12) and said anchor points, - a control unit configured to be able to provide said actuators with cable length control instructions which allow the movement of the mobile tool (10, 12) in the working environment along said target path, characterized in that said control unit is configured to release any cable, said annoying cable, which intersects with at least one volume of at least one element of the working environment during the movement of the mobile tool (10, 12) along an interval of said target trajectory, said collision interval, by supplying the actuator of this cable with a cable length control instruction greater than the theoretical cable length for this interfering cable during the movement of the mobile tool over this collision interval.