Design and Analysis of Feedback Controller for Underactuated 3D Bipedal Robots During the Single Support Phase

Underactuated bipedal robots are quite useful for researching on high-speed and dynamic bipedal walking. In the last five years, many achievements focused on the gait planning and stabile control of planar underactuated bipedal robots, which were validated through experiment on the physical prototype. But underactuated 3D bipedal robots gradually become a hotspot in this field recently. In this paper, design and analysis of feedback controller for underactuated 3D bipedal robots during the single support phase are proposed. The dynamic model during the single support phase is given. A finite-time feedback controller is designed based on the dynamic model during the single support phase and a simple demonstration of its stability in the sense of Lyapunov is also deduced. Then the comparison of convergence rate between the finite-time feedback controller and classical PD feedback controller is carried out by numerical simulation and the finite-time feedback controller converges in less time than the PD one.

I. Introduction

Underactuated bipedal robots are a sort of biped robots that proposed to study the high-speed and dynamic bipedal walking. This kind of biped robot has no feet and forms point contact between stance leg end and ground. The motion control is the difficulty and hotspot in the field of underactuated bipedal robot. Chevallereau C, et al have researched on the walking control of planar underactuated bipedal robot in detail, using the means of partial feedback linearization to design controller, and their theory has validated on the Rabbit successfully, which is a well-known prototype of planar underactuated bipedal robot developed in France[1]. Sabourin. C et al proved the stability of planar underactuated bipedal robot by experiment and proposed a robust control strategy to control the step length and walking velocity successfully in virtue of modifying gait parameters [2] [3]. Tao Geng et al achieved a high-speed and dynamic walking of planar underactuated bipedal robot and they designed a controller combining neuron network and learning strategy and validated on the RunBot successfully, which is experimental platform they developed[4]. Song et al designed a robust controller to track offline trajectory planned in advance based on the theory of Linear Matrix Inequality (LMI) and realize the dynamic walking for 3D underactuated bipedal robots [5]. Recently a lot of achievement about planar underactuated bipedal robot can be seen in the literature[6]. But the research on 3D underactuated bipedal robots is fewer and the performance analysis on the controller of 3D underactuated bipedal robots in detail can be hardly found. So the design and analysis of stable controller for 3D underactuated bipedal robots is worth to discuss.