Finite difference method to find period-one gait cycles of simple passive walkers

• A simple method is presented to obtain appropriate initial conditions and period of gait cycles of biped robot.
• The method is based on finite difference formula.
• This method is based on solving the nonlinear differential equations of motion on a discrete time.
• Numerical simulations reveal the performance of the presented method in finding two stable and unstable gait patterns.

Passive dynamic walking refers to a class of bipedal robots that can walk down an incline with no actuation or control input. These bipeds are sensitive to initial conditions due to their style of walking. According to small basin of attraction of passive limit cycles, it is important to start with an initial condition in the basin of attraction of stable walking (limit cycle). This paper presents a study of the simplest passive walker with point and curved feet. A new approach is proposed to find proper initial conditions for a pair of stable and unstable period-one gait limit cycles. This methodology is based on finite difference method which can solve the nonlinear differential equations of motion on a discrete time. Also, to investigate the physical configurations of the walkers and the environmental influence such as the slope angle, the parameter analysis is applied. Numerical simulations reveal the performance of the presented method in finding two stable and unstable gait patterns.