Gait generation on periodically unlevel grounds for the compass-type biped robot via discrete mechanics

This paper addresses a gait generation problem for the compass-type biped robot on periodically unlevel grounds. We first derive the continuous/discrete compass-type biped robots (CCBR/DCBR) via continuous/discrete mechanics, respectively. Next, we formulate a optimal gait generation problem on periodically unlevel grounds for the DCBR as a finite dimensional nonlinear optimization problem, and show that a discrete control input can be obtained by solving the optimization problem with the sequential quadratic programming. Then, we develop a transformation method from a discrete control input into a continuous zero-order hold input based on discrete Lagrange-d'Alembert principle. Finally, we show numerical simulations, and it turns out that our new method can generate a stable gaits on a periodically unlevel ground for the CCBR.