Trajectory tracking of a knife-edge on a flat surface

The paper discusses trajectory tracking control of a knife-edge on a flat surface. The knife-edge has a single point of contact with the surface and it can slide on the surface without friction. A nonlinear trajectory tracking controller is designed for the knife-edge moving on a flat surface. The tracking control results show that the knife-edge successfully tracks the trajectories that satisfy a persistent excitation condition. A switching control algorithm is proposed to achieve stabilization in case the persistent excitation condition is violated. Simulation results are included to illustrate the effectiveness of the tracking control algorithm developed in the paper.