Multibody dynamical algorithms, numerical optimal control, with detailed studies in the control of jet engine compressors and biped walking

摘要

Various new methods for the modeling and control of complex mechanical systems are developed, and new techniques are presented to combat the “curse of dimensionality” one often encounters with high dimensional systems. This is done first in the context of developing efficient calculational tools for multibody dynamics and second for nonlinear H2 and H∞ optimal control problems. Their uses and effectiveness are then explored through some important, practical applications. The first focus is on articulated, multibody systems which may collide and have contact with its surrounding environment. Different lines of research into recursive, multibody dynamics are brought together along with new, concise derivations. The development has a great deal of generality allowing for multiple degrees of freedom joints, complex tree-structured systems, contact and collision dynamics, and problems requiring derivatives of the dynamics. The second main focus is on numerical optimal control where the ability to solve nonlinear H2 and H∞ control problems is explored. An extensive listing of proven numerical procedures to solve these problems is presented. One particular proposed approach is discussed at greater length and its strengths and weaknesses are explored through some illustrations. Numerical experiments are performed which provide valuable insight to the potential user of these methods as to the capabilities and limitations of the proposed numerical procedures. An important case study is then presented which describes the optimal control of jet engine compressors. The two research avenues converge in the final case study on walking biped robots. With the use of the recursive, symbolic modeling techniques and numerical optimal control procedures, it is possible to solve the problem of minimum energy gait generation of biped robots with a complete dynamical model. This problem is complicated by contact, collision, and other algebraic forms of constraints which require special attention. Various forms of minimum energy walking are investigated and analyzed.