Abstract: Spherical robot is a kind of mobile robot, and then it is inevitable to encounter with the problem of climbing slope. According to the spherical robot designed, each independent variable describing the state of climbing an arbitrary slope is analyzed. The calculation formula to estimate climbing capability is given and simultaneously the concept of critical pendulum angle is proposed. Dynamic equations of the robot climbing slope is derived from using Lagrangian function equation based on energy dissipation. In order to solve the problem of constant terms in the equation, the coordinate transformation method is adopted, and ultimately the system is converted into state-space form. When every state of the robot system can be measured, a corresponding linear quadratic objective function is designed with the consideration of the practical requirements of both steady movement and less energy assumption. At last, the state feedback matrix is designed, which can control the robot to move at an expected velocity on slope, and the simulation results prove the validity of the above control technique.

Key words: Climbing capability, Critical pendulum angle, Lagrange equation, Optimal control, contact pressure, finite element method, fretting friction, fretting wear, relative slip, spline coupling