Trajectory optimization of humanoid robots swinging leg

Increased walking stability and energy efficiency are both important factors for enhancement of the performance of a biped robot. However, it is difficult to derive the optimal control law that is required using optimal control theory because of the strong nonlinearity and the strong coupling of the robot dynamics equation. Use of numerical methods is one effective way to design an optimal control law. This paper presents a method for optimization of the trajectory of a biped robot's swinging leg that is based on a Gaussian pseudospectral method. We first establish a Lagrange optimization function to optimize both the torque and speed during the walking process. By giving different weights to the torque and the speed, optimization of the different targets can be realized, and as a result, a reduction in the velocity can also change the amplitude of the joint motion fluctuations. The effectiveness of the proposed method is demonstrated via simulations and Experiments.