Abstract

As a well-explored template that captures the essential dynamical behaviors of legged locomotion on sagittal plane, the spring-loaded inverted pendulum (SLIP) model has been extensively employed in both biomechanical study and robotics research. Aiming at fully leveraging the merits of the SLIP model to generate the adaptive trajectories of the center of mass (CoM) with maneuverability, this study presents a novel two-layered sagittal SLIP-anchored (SSA) task space control for a monopode robot to deal with terrain irregularity. This work begins with an analytical investigation of sagittal SLIP dynamics by deriving an approximate solution with satisfactory apex prediction accuracy, and a two-layered SSA task space controller is subsequently developed for the monopode robot. The higher layer employs an analytical approximate representation of the sagittal SLIP model to form a deadbeat controller, which generates an adaptive reference trajectory for the CoM. The lower layer enforces the monopode robot to reproduce a generated CoM movement by using a task space controller to transfer the reference CoM commands into joint torques of the multi-degree of freedom monopode robot. Consequently, an adaptive hopping behavior is exhibited by the robot when traversing irregular terrain. Simulation results have demonstrated the effectiveness of the proposed method.

Highlights

  • Diverse in terms of morphology and gait patterns [1], Received May 20, 2019; accepted August 19, 2019✉ Haitao YU ( ), Haibo GAO, Liang DING, Zongquan DENGHopping, as the most ordinary movement observed in kangaroo and galago, is the fundamental gait pattern from which other complex gaits, such as bipedal running, quadrupedal trotting, bounding, and galloping, can be further evolved [6]

  • Aiming at fully leveraging the aforementioned benefits of the sagittal spring-loaded inverted pendulum (SLIP) model, this study presents a SLIPanchored task space control for a monopode robot to deal with terrain perturbations

  • Scheduled by the finite state machine (FSM) that switches the flight/stance phase according to the contact detection triggered by monopode-ground interaction, the bottom layer transfers the target center of mass (CoM) trajectory into individual joint commands via the task space controller, enforcing the whole body of the actuated robot to bounce in accordance with the SLIP dynamics generated by the high layer

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Summary

Introduction

Diverse in terms of morphology and gait patterns [1], Received May 20, 2019; accepted August 19, 2019. Our previous work [13] presented a perturbation-based analytical approximation for the sagittal SLIP dynamics in stance phase and is valid for both the symmetric and asymmetric trajectories of CoM, and it can preserve mathematical tractability and high apex prediction accuracy. Garofalo and Albu-Schäffer [20] developed a controller based on the dual-SLIP model to stabilize a five-link fully actuated bipedal walking robot, in which the reference CoM trajectory is generated by numerically computing the SLIP dynamics. Aside from the sagittal SLIP model used to control legged robots, the 3D-SLIP model can be applied to generate the reference CoM trajectory for humanoids [21], in which high-speed stabilized running as fast as 6.5 m/s is achieved. Aiming at fully leveraging the aforementioned benefits of the sagittal SLIP model, this study presents a SLIPanchored task space control for a monopode robot to deal with terrain perturbations.

Control objective
Sagittal SLIP-anchored double-layered control architecture
Sagittal SLIP model and the analytical approximate solution
Deadbeat controller
Extension to an irregular terrain case
Dynamics of the monopode robot
Finite state machine
Task space controller
Simulation setups
Periodic hopping on flat surface
Target apex tracking on flat surface
Traversing irregular terrains
General feature synthesis
Discussions
Findings
Conclusions
Full Text
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