Modifications are made by using two-dimensional wheeled mobile robot as the control object for solving
drawbacks existing in higher order sliding mode control algorithms, such as slowness of the convergence rate and
discontinuity of the control action. Firstly, by utilizing virtual item for increasing the relative order of system, a new higher
order sliding mode algorithm is achieved. Compared with original algorithms, faster convergence rate and smooth control
action can be achieved. Then, by using tracking error’s derivative of higher order as the sliding surface, the problem that
super-twisting algorithm only holds true for systems of first relative order is solved and the new algorithm can be applied to
higher relative order systems. Finally, numerical simulations show effectiveness of the algorithms.