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Since a nonholonomic system such as a robot with two independent driving wheels includes complicated nonlinear terms generally, it is hard to realize a stable and tractable controller design. However, about a dynamic control method for the motion planning, it is guaranteed that a nonholonomic-controlled object can always be converged to an arbitrary point using a control method based on an invariant manifold. Based on it, the method called “kinodynamic motion planning” was proposed to converge the states of the two-wheeled mobile robot to the arbitrary target position while avoiding obstacles by combining the control based on the invariant manifold and the HPF. In this chapter, how to combine the invariant manifold control and the concept of the HPF is explained in detail, and the usefulness of the proposed approach is verified through some simulations.

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