Variational analysis approach and its applications to robotics

This paper presents a methodology for variational analysis for the control systems emphasize on Robotics. This is achieved by Lagrangian Mechanics and Variational Collision Integrators. Variational techniques are used to analyze the problem of rigid-body dynamics with impacts. Principles of nonsmooth mechanics for rigid bodies are used in both continuous and discrete time, and provide impact models for a variety of collision behaviors. The discrete Euler-Lagrange (E-L) equations that follow from the discrete time analyses yield variational integration schemes for the different impact models. These discrete E-L equations play a vital role in the method of discrete mechanics and optimal control, which generates locally optimal control policies as the solution to equality constrained nonlinear optimization problems.