Vertical Jumping for Legged Robot Based on Quadratic Programming.

Dingkui Tian,Yizhou Lu,Chuzhao Liu,Xuanyang Shi,Junyao Gao

doi:10.3390/s21113679

Abstract

The highly dynamic legged jumping motion is a challenging research topic because of the lack of established control schemes that handle over-constrained control objectives well in the stance phase, which are coupled and affect each other, and control robot’s posture in the flight phase, in which the robot is underactuated owing to the foot leaving the ground. This paper introduces an approach of realizing the cyclic vertical jumping motion of a planar simplified legged robot that formulates the jump problem within a quadratic-programming (QP)-based framework. Unlike prior works, which have added different weights in front of control tasks to express the relative hierarchy of tasks, in our framework, the hierarchical quadratic programming (HQP) control strategy is used to guarantee the strict prioritization of the center of mass (CoM) in the stance phase while split dynamic equations are incorporated into the unified quadratic-programming framework to restrict the robot’s posture to be near a desired constant value in the flight phase. The controller is tested in two simulation environments with and without the flight phase controller, the results validate the flight phase controller, with the HQP controller having a maximum error of the CoM in the x direction and y direction of 0.47 and 0.82 cm and thus enabling the strict prioritization of the CoM.

Highlights

Due to the constraints of underactuation, high dimensionality, and the ground reaction force in legged robots, it is remarkably challenging to control a highly dynamic legged robot’s jumping motion
The most common solution for jumping is to reduce the full dynamics to a canonical spring-loaded inverted pendulum (SLIP), which renders the control for legged robots computationally tractable and predicts the energy wave and ground reaction force during the jumping motion in the stance phase [1]
The proposed controller was implemented on MATLAB/Simulink with a fixed sample cycle (4 ms) to achieve repeatable vertical jumping cycles for a planar three-link robot

Summary

Introduction

Due to the constraints of underactuation, high dimensionality, and the ground reaction force in legged robots, it is remarkably challenging to control a highly dynamic legged robot’s jumping motion. The most common solution for jumping is to reduce the full dynamics to a canonical spring-loaded inverted pendulum (SLIP), which renders the control for legged robots computationally tractable and predicts the energy wave and ground reaction force during the jumping motion in the stance phase [1]. A nonlinear controller is employed to synchronize the biped dynamics and SLIP [2,3,4,5,6], which is an effective solution, but makes it difficult to introduce constraints, such as the stability of the robot and acceleration of the joints, into the controller or to guarantee strict prioritization in the overconstrained objective. The majority of previous approaches focus on reducing the angular momentum in the center of mass (CoM) at the launch phase [7], and few studies have paid close attention to how to adjust the position and attitude of the robot during the flight phase

Methods

Results

Discussion

Conclusion