Numerical Method for Optimization of Semi-Passively Controlled Dynamical Systems

Paper in proceeding, 2004

Controlled dynamical systems with different type of actuators (e.g. external powered electromotors, magnetostrictive actuators, internal unpowered (passive) spring-damper-like drives, etc.) are considered.  These systems are termed semi-passively controlled. Mathematical statement of optimization problem has proposed that is suitable both for modeling of optimal motion and for optimization of structure of semi-passively controlled dynamical systems with different degree of actuation. Numerical method for solving the proposed optimization problem is described. The method was successfully used for solving optimal control problems for several semi-passively controlled dynamical systems (industrial robots, human locomotor system with intelligent lower limb prosthesis, bipedal locomotion robots, others). The results obtained have confirmed the efficiency of the proposed numerical method for solving optimization problems for semi-passively controlled dynamical systems. Analysis of the results gives insight into the study of the role of inherent dynamics in controlled motion and how much a dynamical system should be governed by external drives and how much by a system’s inherent dynamics. It has been shown that complex goal-directed and cost-efficient controlled motion of underactuated dynamical system can be design using optimal interaction between external powered drives and internal unpowered spring-damper-like drives. This constitutes the powerful ability of semi-passively controlled dynamical systems.