A gait generation method for the compass-type biped robot on slopes via discrete mechanics

In this paper, we develop a discrete mechanics approach to gait generation on slopes for the compass-type biped robot. We formulate a optimal gait generation problem for the discrete compass-type robot and show a solving method of it by the sequential quadratic programming to calculate a discrete control input. Then, we propose a transformation method from a discrete control input into a continuous zero-order hold input based on discrete Lagrange-d´Alembert principle. As a result of numerical simulations, it is confirmed that stable gaits on both downward and upward slopes can be generated for the continuous compass-type robot by the proposed method.