A Dai–Yuan conjugate gradient algorithm of linear equation constrained optimization approach for optimal robust controller of bipedal robots

M Wang,Zb Sun,Dw Jiang,Bc Zhang,Zx Pang

doi:10.1177/1729881419890178

Abstract

In this article, combined rapidly exponential control Lyapunov function with hybrid zero dynamics, a sufficiently descent projected Dai–Yuan approach is proposed, investigated, and analyzed for online solving optimal robust control problems with linear equation constraints of bipedal robots. Moreover, a new approach is developed for designing optimal robust controller. To demonstrate the effectiveness and feasibility of the proposed method, we will conduct numerical simulations on the model of three-link robot with nonlinear, impulsive, and under-actuated dynamics. Numerical results show that the bipedal robot can walk effectively and stability on the ground though the optimal robust controller when the parameters of the hybrid system model are disturbed three times. Furthermore, under the random noise condition, the bipedal robot can walk stably and effectively through online computing the nonlinear optimization problem for optimal robust controller. In addition, some classical control methods are compared with the developed approach in this article, numerical results are reported and analyzed to substantiate the feasibility and superiority of the proposed method for linear equation constrained optimization problem. Last, this article develops a systematic approach on exploiting optimal robust control technique to design hybrid system models for robustly and accurately via online solving linear equation constrained optimization problems.

Highlights

At present, with the enhancement of human’s ability to detect deep sea and space, more and more robots are utilized to accomplish the impossible tasks
In the process of controller design, it was necessary to adjust the parameters of the controller, if the parameters were not selected at real time, the bipedal robot could not produce stable walking gait or even fall down
Taking the energy consumption as the performance functional, the optimal robust controller is solved via a nonlinear optimization method, and the dynamic walking of bipedal robot is realized and analyzed, the details are similar to the literature.[20]

Summary

Introduction

With the enhancement of human’s ability to detect deep sea and space, more and more robots are utilized to accomplish the impossible tasks. A novel nonlinear optimization algorithm with rapidly convergent property is designed to solve the optimal robust controller to realize the dynamic and stable walking of bipedal robots.

Results

Conclusion