Demydyuk M. Mathematical modeling and parametric optimization in problems of dynamics of manipulation and anthropomorphic locomotion systems

In the thesis the numerical-analytical method of parametric optimization is developed for solving of problems of joint optimization of control laws and design parameters of nonlinear manipulation systems with active and passive (spring-damper) drives, nonstationary restrictions on the generalized coordinates and control. The method is based on parameterization of the generalized coordinates of the system in the form of the sum of a cubic polynomial and a finite series of given orthogonal functions, which reduces the initial optimal control problem (with parameters) to a nonlinear programming problem. For a number of manipulators (one-, two-, and four-link), which perform cyclic transport operations under the action of active and passive (spring-damper) drives, the algorithms for joint optimization of control and parameters of passive drives are developed. The algorithms of joint optimization of control and kinematic structure (boundary configurations of links and position of the manipulator in the working zone) are developed for the two-link manipulator. For a four-link manipulator of closed kinematic structure, the conditions for angles at which control in the corresponding pair of joints can be activated are obtained. The algorithms for control optimization with simultaneous selection of a pair of actively controlled joints, joint optimization of control and link sizes are developed. Mathematical models have been developed to calculate the dynamic and energetic characteristics of human gait with orthopedic devices: below-knee prosthesis, ankle joint orthosis, exoskeleton.