A dynamic model of the motion in the sagittal plane of the lower limbs of the exoskeleton, integrated with a human operator, was created with account of its lean on rigid weightless crutches. This model describes a mockup of the exoskeleton, which is a 5-link system incorporating the knee and hip drives, as well as massless hand supports. The dynamic model is based on the Lagrange equations of the second kind, which, alongside with the kinematic parameters, also includes the reaction support forces of the point feet and weightless crutches. When the parameters of the mathematical model were set, the inertial mass of the body characteristics of the resulting statistical processing of the tomography slices of a certain number of subjects were taken into account. In the model, the crutches are considered as an extension of the human hands, so the force application points of the crutches are the shoulders of the operator. Human reaction in the shoulder joint to the torque of the crutches is considered irrelevant. The model also takes into account the dynamics of the DC electrical drives. The synthesis is based on the method of solving the inverse tasks of the dynamics. Synthesis of the control system was carried out on the example of a flat, single support for comfortable walking. Since it is assumed that an operator has a weakened musculoskeletal system, but workable hands, it is considered that the given influences on the control system of the exoskeleton are the required torques in the hip and knee joints, viewed as a time function, while a person is assigned the function of providing power to the crutches. As a result, an analytical law motion control exoskeleton was designed, which provided locomotion to the hip and knee joints in accordance with the selected desired mode. The synthesized algorithms were applied to the constructed mathematical models and a numerical study of them was conducted. The article presents the results of the numerical simulation and of the investigated precision control.