Optimization method for dynamics of non-holonomic system based on Gauss’ principle

Abstract

The real-time control of the non-holonomic wheel robot has put forward higher requirements for the accuracy and speed of dynamical simulation, so it is necessary to study the new dynamic modeling and calculation methods adapting to modern information processing technology. Different from the traditional method solving differential–algebraic equation, the objective is to establish optimization model and effective calculating scheme for dynamics of non-holonomic system based on basic dynamical principle. The optimization model cannot be obtained directly from the traditional Gauss’ principle. By using Gauss’ principle of variational form, this paper deduces the minimum principle in the form of generalized coordinates and quasi-coordinates, respectively, thus allowing dynamical problems of non-holonomic systems to be incorporated into the framework of solving constrained or unconstrained optimization problems. Furthermore, we study a numerical calculation scheme that uses an optimization algorithm for the second form of the above optimization models. As an example, the dynamical problem of a differential-driven wheeled mobile-robot system is discussed. The optimization dynamic model of a non-holonomic robot system and the calculation model of the optimization algorithm are established. Comparing the results of the optimization calculation with the differential–algebraic equations commonly used in dynamical problem for non-holonomic system reveals that the method in this paper is superior in terms of calculation speed and can more effectively handle constraint violations without extra constraint revision needed.