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 processingtechnology.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 theresults 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.
The discontinuous dynamical problem of multi-point contact and collision in multi-body system has always been a hot and difficult issue in this field.Based on the Gauss’principle of least constraint,a unified optimization model for multibody system dynamics with multi-point contact and collision is established.The paper presents the study of the numerical solution scheme,in which particle swarm optimization method is used to deal with the corresponding optimization model.The article also presents the comparison of the Gauss optimization method(GOM)and the hybrid linear complementarity method(i.e.combining differential algebraic equations(DAEs)and linear complementarity problems(LCP)),commonly used to solve the dynamic contact problem of multibody systems with bilateral constraints.The results illustrate that,the GOM has the same advantage of dynamical modelling with LCP and when the redundant constraint exists,the GOM always has a unique solution and so no additional processing is needed,whereas the corresponding DAE-LCP method may have singular cases with multiple solutions or no solutions.Using numerical examples,the GOM is verified to effectively solve the dynamics of multibody systems with redundant unilateral and bilateral constraints without additional redundancy processing.The GOM can also be applied to the optimal control of systems in the future and combined with the parameter optimization of systems to handle dynamic problems.The work given provides the dynamics and control of the complex system with a new train of thought and method.
