Further Analysis of the Passive Dynamics of the Compass Biped Walker and Control of Chaos via Two Trajectory Tracking Approaches

Essia Added,Safya Belghith,Hassène Gritli,Leo Y Zhang

doi:10.1155/2021/5533451

Abstract

This work consists in analyzing and controlling the walk of the compass-type bipedal walker in order to stabilize its passive dynamic gait. The dynamic walking of the compass-gait walker is modeled by an impulsive hybrid nonlinear system. This impulsive hybrid nature is considered very complex as it can generate unwanted phenomena such as chaos and bifurcations. We show first by means of bifurcation diagrams and by varying the slope angle of the walking surface and also the length of the lower leg segment that the passive dynamic walking exhibits successive period-doubling bifurcations leading to chaos. Furthermore, in order to control chaos and hence obtain one-periodic walking behavior, we propose two control approaches based on tracking a desired trajectory. The first method consists in tracking the one-periodic passive dynamic walking generated by the compass model itself. The second control method lies in following a planned trajectory using the 4th-order Spline function. An optimization method is also achieved to design the parameters of the desired trajectory. Some features of the period-1 passive gait are used in the design of such Spline trajectory. Finally, we show some simulation results revealing the efficiency of the two proposed control methods in the control of the chaotic passive gait of the compass-gait walker. Moreover, we demonstrate the stabilization of the bipedal locomotion of the compass biped walker on different slopes: descending and ascending inclined planes and walking on a level ground. A comparison with the OGY-based control method is also performed to further show the superiority of these two control approaches.

Highlights

IntroductionResearch in bipedal robotics has continued to evolve increasingly in these recent years
In order to control the passive gaits of the compass-gait biped robot into a period-1 gait for all values of the lower leg segment length a and of the slope angle of the walking surface φ, we will apply two approaches. e first control approach is mainly based on the passive dynamic walking
We show the validity of proposed FF + PD control law (23) or, as discussed previously, PD control law (31), in the first control approach based on the passive dynamic walking

Summary

Introduction

Research in bipedal robotics has continued to evolve increasingly in these recent years. Many prototypes of biped robots were built worldwide, and tasks performed by different researchers in the robotic community have become more complex and a challenging issue [1,2,3]. Concerning bipedal robotic walking, the latest studies have focused on the control of two-legged bipedal robots and on the minimization of energy consumption. One goal that emerges from all these studies is to try to reproduce as much as possible the human walking. E major challenge is to construct a biped robot capable of walking on different types of ground. E researchers tried to reproduce as closely as possible the human and his locomotion by means of a biped robot via control One goal that emerges from all these studies is to try to reproduce as much as possible the human walking. e major challenge is to construct a biped robot capable of walking on different types of ground. e researchers tried to reproduce as closely as possible the human and his locomotion by means of a biped robot via control

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