We consider a kinematic model of a spherical robot on an inhomogeneous surface. We study a problem of the optimal motion of the robot from a given initial configuration to a given final one. The problem is formulated as the problem of optimal rolling of a sphere on a plane with a given external cost. The external cost describes the landscape and encodes the inhomogeneity of the surface. We apply a necessary optimality condition — Pontryagin maximum principle, and characterize the extremals. Finally, we present an example of the rolling along the extremal trajectory, obtained via an interface developed in Wolfram Mathematica.
The Second International Conference «Nonlinearity, Information and Robotics»,