Biomimetic walking trajectory generation of humanoid robot on an inclined surface using Fourier series

This article describes a novel method to generate a biomimetic walking trajectory for a biped humanoid robot on an inclined surface. We assume that the configuration of the inclined surface is known, and we solve the human-like walking trajectory generation problem by obtaining the solution from the desired zero moment point (ZMP) trajectory to the center of gravity (CoG) trajectory. We present an analytic solution for the walking trajectory generation by using Fourier series. From the given ZMP trajectory biomimetically represented by the Fourier series, we focus on how to find the CoG trajectory in an analytical way. A time-segmentation based approach is adopted for generating the trajectories. The trajectory functions need to be continuous between the segments; thus, the solution is found by calculating the coefficients under these connectivity conditions. We derive a general form of the ZMP equation using a simple inverted pendulum model (SIPM), which includes the ZMP and the CoG trajectories in the horizontal and vertical directions to quantify the walking parameters on the inclined surface. The performance of the proposed approach is verified by conducting walking simulations using a full-body dynamic simulator on three different inclined surfaces and comparing them to the authors' previous approach.