Parametric optimization for optimal synthesis of robotic systems motions

This paper presents how a problem of optimal trajectory planning, that is an optimal control problem, can be transformed into a parametric optimization problem and in consequence be tackled using efficient deterministic or stochastic parametric optimization techniques. The transformation is done thanks to discretizing some or all continuous system’s variables and forming their time-histories by interpolation. We will discuss three different methods where, in addition to transfer time T, considered optimization parameters are: 1) independent state and control parameters, 2) control parameters and 3) independent position parameters. The simplicity and the efficiency of the third mode allow us to use it to solve the problem of optimal trajectory planning in complex situations, in particular for holonomic and nonholonomic systems.