The invention relates to an arm exoskeleton comprising a moving system of joints placed in parallel with the joints of the human arm, the exoskeleton comprising a shoulder exoskeleton, an elbow exoskeleton, and a wrist exoskeleton. In all, the exoskeleton has sixteen joints providing sixteen degrees of freedom. A support worn on the torso of a human operator comprises a rigid front plate and a rigid back plate. The shoulder exoskeleton has its proximal end fixed to the front plate, whereby the front plate provides a fixed reference for all movements of the exoskeleton, and the wrist exoskeleton is fixed to a rigid glove worn on the hand of the operator. Active joints are controlled by flexible cable tendons bridging the exoskeleton, said tendons themselves being actuated by control units disposed on the rigid back plate. Inflatable cushions prevent the wrist exoskeleton and the shoulder exoskeleton from moving relative to the arm of the operator. The invention is applicable in particular to remotely controlling a robot in space.